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Magnet

A magnet is a material or object that produces a magnetic field. This magnetic field is invisible but is responsible for the most notable property of a magnet: a force that pulls on other ferromagnetic materials, such as iron, steel, nickel, cobalt, etc. and attracts or repels other magnets.

A permanent magnet is an object made from a material that is magnetized and creates its own persistent magnetic field. An everyday example is a refrigerator magnet used to hold notes on a refrigerator door. Materials that can be magnetized, which are also the ones that are strongly attracted to a magnet, are called ferromagnetic (or ferrimagnetic). These include the elements iron, nickel and cobalt and their alloys, some alloys of rare-earth metals, and some naturally occurring minerals such as lodestone. Although ferromagnetic (and ferrimagnetic) materials are the only ones attracted to a magnet strongly enough to be commonly considered magnetic, all other substances respond weakly to a magnetic field, by one of several other types of magnetism.

Ferromagnetic materials can be divided into magnetically "soft" materials like annealed iron, which can be magnetized but do not tend to stay magnetized, and magnetically "hard" materials, which do. Permanent magnets are made from "hard" ferromagnetic materials such as alnico and ferrite that are subjected to special processing in a strong magnetic field during manufacture to align their internal microcrystalline structure, making them very hard to demagnetize. To demagnetize a saturated magnet, a certain magnetic field must be applied, and this threshold depends on coercivity of the respective material. "Hard" materials have high coercivity, whereas "soft" materials have low coercivity. The overall strength of a magnet is measured by its magnetic moment or, alternatively, the total magnetic flux it produces. The local strength of magnetism in a material is measured by its magnetization.

An electromagnet is made from a coil of wire that acts as a magnet when an electric current passes through it but stops being a magnet when the current stops. Often, the coil is wrapped around a core of "soft" ferromagnetic material such as mild steel, which greatly enhances the magnetic field produced by the coil.

Discovery and development
Ancient people learned about magnetism from lodestones (or magnetite) which are naturally magnetized pieces of iron ore. The word magnet was adopted in Middle English from Latin magnetum "lodestone", ultimately from Greek μαγνῆτις [λίθος] (magnētis [lithos]) meaning "[stone] from Magnesia", a place in Anatolia where lodestones were found (today Manisa in modern-day Turkey). Lodestones, suspended so they could turn, were the first magnetic compasses. The earliest known surviving descriptions of magnets and their properties are from Anatolia, India, and China around 2,500 years ago. The properties of lodestones and their affinity for iron were written of by Pliny the Elder in his encyclopedia Naturalis Historia in the 1st century AD.

In 11th century China, it was discovered that quenching red hot iron in the Earth's magnetic field would leave the iron permanently magnetized. This led to the development of the navigational compass, as described in Dream Pool Essays in 1088. By the 12th to 13th centuries AD, magnetic compasses were used in navigation in China, Europe, the Arabian Peninsula and elsewhere.

A straight iron magnet tends to demagnetize itself by its own magnetic field. To overcome this, the horseshoe magnet was invented by Daniel Bernoulli in 1743. A horseshoe magnet avoids demagnetization by returning the magnetic field lines to the opposite pole.

In 1820, Hans Christian Ørsted discovered that a compass needle is deflected by a nearby electric current. In the same year André-Marie Ampère showed that iron can be magnetized by inserting it in an electrically fed solenoid. This led William Sturgeon to develop an iron-cored electromagnet in 1824. Joseph Henry further developed the electromagnet into a commercial product in 1830–1831, giving people access to strong magnetic fields for the first time. In 1831 he built an ore separator with an electromagnet capable of lifting 750 lb.

Magnetic field

The magnetic flux density (also called magnetic B field or just magnetic field, usually denoted B) is a vector field. The magnetic B field vector at a given point in space is specified by two properties:

 * 1) Its direction, which is along the orientation of a compass needle.
 * 2) Its magnitude (also called strength), which is proportional to how strongly the compass needle orients along that direction.

In SI units, the strength of the magnetic B field is given in teslas.

Magnetic moment
A magnet's magnetic moment (also called magnetic dipole moment and usually denoted μ) is a vector that characterizes the magnet's overall magnetic properties. For a bar magnet, the direction of the magnetic moment points from the magnet's south pole to its north pole, and the magnitude relates to how strong and how far apart these poles are. In SI units, the magnetic moment is specified in terms of A·m2 (amperes times meters squared).

A magnet both produces its own magnetic field and responds to magnetic fields. The strength of the magnetic field it produces is at any given point proportional to the magnitude of its magnetic moment. In addition, when the magnet is put into an external magnetic field, produced by a different source, it is subject to a torque tending to orient the magnetic moment parallel to the field. The amount of this torque is proportional both to the magnetic moment and the external field. A magnet may also be subject to a force driving it in one direction or another, according to the positions and orientations of the magnet and source. If the field is uniform in space, the magnet is subject to no net force, although it is subject to a torque.

A wire in the shape of a circle with area A and carrying current I has a magnetic moment of magnitude equal to IA.

Magnetization
The magnetization of a magnetized material is the local value of its magnetic moment per unit volume, usually denoted M, with units A/m. It is a vector field, rather than just a vector (like the magnetic moment), because different areas in a magnet can be magnetized with different directions and strengths (for example, because of domains, see below). A good bar magnet may have a magnetic moment of magnitude 0.1 A·m2 and a volume of 1 cm3, or 1×10−6 m3, and therefore an average magnetization magnitude is 100,000 A/m. Iron can have a magnetization of around a million amperes per meter. Such a large value explains why iron magnets are so effective at producing magnetic fields.

Modelling magnets

Two different models exist for magnets: magnetic poles and atomic currents.

Although for many purposes it is convenient to think of a magnet as having distinct north and south magnetic poles, the concept of poles should not be taken literally: it is merely a way of referring to the two different ends of a magnet. The magnet does not have distinct north or south particles on opposing sides. If a bar magnet is broken into two pieces, in an attempt to separate the north and south poles, the result will be two bar magnets, each of which has both a north and south pole. However, a version of the magnetic-pole approach is used by professional magneticians to design permanent magnets.

In this approach, the divergence of the magnetization ∇·M inside a magnet is treated as a distribution of magnetic monopoles. This is a mathematical convenience and does not imply that there are actually monopoles in the magnet. If the magnetic-pole distribution is known, then the pole model gives the magnetic field H. Outside the magnet, the field B is proportional to H, while inside the magnetization must be added to H. An extension of this method that allows for internal magnetic charges is used in theories of ferromagnetism.

Another model is the Ampère model, where all magnetization is due to the effect of microscopic, or atomic, circular bound currents, also called Ampèrian currents, throughout the material. For a uniformly magnetized cylindrical bar magnet, the net effect of the microscopic bound currents is to make the magnet behave as if there is a macroscopic sheet of electric current flowing around the surface, with local flow direction normal to the cylinder axis. Microscopic currents in atoms inside the material are generally canceled by currents in neighboring atoms, so only the surface makes a net contribution; shaving off the outer layer of a magnet will not destroy its magnetic field, but will leave a new surface of uncancelled currents from the circular currents throughout the material. The right-hand rule tells which direction positively-charged current flows. However, current due to negatively-charged electricity is far more prevalent in practice.

Polarity
The north pole of a magnet is defined as the pole that, when the magnet is freely suspended, points towards the Earth's North Magnetic Pole in the Arctic (the magnetic and geographic poles do not coincide, see magnetic declination). Since opposite poles (north and south) attract, the North Magnetic Pole is actually the south pole of the Earth's magnetic field. As a practical matter, to tell which pole of a magnet is north and which is south, it is not necessary to use the Earth's magnetic field at all. For example, one method would be to compare it to an electromagnet, whose poles can be identified by the right-hand rule. The magnetic field lines of a magnet are considered by convention to emerge from the magnet's north pole and reenter at the south pole.

Magnetic materials
The term magnet is typically reserved for objects that produce their own persistent magnetic field even in the absence of an applied magnetic field. Only certain classes of materials can do this. Most materials, however, produce a magnetic field in response to an applied magnetic field – a phenomenon known as magnetism. There are several types of magnetism, and all materials exhibit at least one of them.

The overall magnetic behavior of a material can vary widely, depending on the structure of the material, particularly on its electron configuration. Several forms of magnetic behavior have been observed in different materials, including:
 * Ferromagnetic and ferrimagnetic materials are the ones normally thought of as magnetic; they are attracted to a magnet strongly enough that the attraction can be felt. These materials are the only ones that can retain magnetization and become magnets; a common example is a traditional refrigerator magnet. Ferrimagnetic materials, which include ferrites and the longest used and naturally occurring magnetic materials magnetite and lodestone, are similar to but weaker than ferromagnetics. The difference between ferro- and ferrimagnetic materials is related to their microscopic structure, as explained in Magnetism.
 * Paramagnetic substances, such as platinum, aluminum, and oxygen, are weakly attracted to either pole of a magnet. This attraction is hundreds of thousands of times weaker than that of ferromagnetic materials, so it can only be detected by using sensitive instruments or using extremely strong magnets. Magnetic ferrofluids, although they are made of tiny ferromagnetic particles suspended in liquid, are sometimes considered paramagnetic since they cannot be magnetized.
 * Diamagnetic means repelled by both poles. Compared to paramagnetic and ferromagnetic substances, diamagnetic substances, such as carbon, copper, water, and plastic, are even more weakly repelled by a magnet. The permeability of diamagnetic materials is less than the permeability of a vacuum. All substances not possessing one of the other types of magnetism are diamagnetic; this includes most substances. Although force on a diamagnetic object from an ordinary magnet is far too weak to be felt, using extremely strong superconducting magnets, diamagnetic objects such as pieces of lead and even mice can be levitated, so they float in mid-air. Superconductors repel magnetic fields from their interior and are strongly diamagnetic.

There are various other types of magnetism, such as spin glass, superparamagnetism, superdiamagnetism, and metamagnetism.

Common uses

 * Magnetic recording media: VHS tapes contain a reel of magnetic tape. The information that makes up the video and sound is encoded on the magnetic coating on the tape. Common audio cassettes also rely on magnetic tape. Similarly, in computers, floppy disks and hard disks record data on a thin magnetic coating.
 * Credit, debit, and automatic teller machine cards: All of these cards have a magnetic strip on one side. This strip encodes the information to contact an individual's financial institution and connect with their account(s).
 * Older types of televisions (non flat screen) and older large computer monitors: TV and computer screens containing a cathode ray tube employ an electromagnet to guide electrons to the screen.
 * Speakers and microphones: Most speakers employ a permanent magnet and a current-carrying coil to convert electric energy (the signal) into mechanical energy (movement that creates the sound). The coil is wrapped around a bobbin attached to the speaker cone and carries the signal as changing current that interacts with the field of the permanent magnet. The voice coil feels a magnetic force and in response, moves the cone and pressurizes the neighboring air, thus generating sound. Dynamic microphones employ the same concept, but in reverse. A microphone has a diaphragm or membrane attached to a coil of wire. The coil rests inside a specially shaped magnet. When sound vibrates the membrane, the coil is vibrated as well. As the coil moves through the magnetic field, a voltage is induced across the coil. This voltage drives a current in the wire that is characteristic of the original sound.
 * Electric guitars use magnetic pickups to transduce the vibration of guitar strings into electric current that can then be amplified. This is different from the principle behind the speaker and dynamic microphone because the vibrations are sensed directly by the magnet, and a diaphragm is not employed. The Hammond organ used a similar principle, with rotating tonewheels instead of strings.
 * Electric motors and generators: Some electric motors rely upon a combination of an electromagnet and a permanent magnet, and, much like loudspeakers, they convert electric energy into mechanical energy. A generator is the reverse: it converts mechanical energy into electric energy by moving a conductor through a magnetic field.
 * Medicine: Hospitals use magnetic resonance imaging to spot problems in a patient's organs without invasive surgery.
 * Chemistry: Chemists use nuclear magnetic resonance to characterize synthesized compounds.
 * Chucks are used in the metalworking field to hold objects. Magnets are also used in other types of fastening devices, such as the magnetic base, the magnetic clamp and the refrigerator magnet.
 * Compasses: A compass (or mariner's compass) is a magnetized pointer free to align itself with a magnetic field, most commonly Earth's magnetic field.
 * Art: Vinyl magnet sheets may be attached to paintings, photographs, and other ornamental articles, allowing them to be attached to refrigerators and other metal surfaces. Objects and paint can be applied directly to the magnet surface to create collage pieces of art. Metal magnetic boards, strips, doors, microwave ovens, dishwashers, cars, metal I beams, and any metal surface can be used magnetic vinyl art.
 * Science projects: Many topic questions are based on magnets, including the repulsion of current-carrying wires, the effect of temperature, and motors involving magnets.
 * Toys: Given their ability to counteract the force of gravity at close range, magnets are often employed in children's toys, such as the Magnet Space Wheel and Levitron, to amusing effect.
 * Refrigerator magnets are used to adorn kitchens, as a souvenir, or simply to hold a note or photo to the refrigerator door.
 * Magnets can be used to make jewelry. Necklaces and bracelets can have a magnetic clasp, or may be constructed entirely from a linked series of magnets and ferrous beads.
 * Magnets can pick up magnetic items (iron nails, staples, tacks, paper clips) that are either too small, too hard to reach, or too thin for fingers to hold. Some screwdrivers are magnetized for this purpose.
 * Magnets can be used in scrap and salvage operations to separate magnetic metals (iron, cobalt, and nickel) from non-magnetic metals (aluminum, non-ferrous alloys, etc.). The same idea can be used in the so-called "magnet test", in which a car chassis is inspected with a magnet to detect areas repaired using fiberglass or plastic putty.
 * Magnets are found in process industries, food manufacturing especially, in order to remove metal foreign bodies from materials entering the process (raw materials) or to detect a possible contamination at the end of the process and prior to packaging. They constitute an important layer of protection for the process equipment and for the final consumer.
 * Magnetic levitation transport, or maglev, is a form of transportation that suspends, guides and propels vehicles (especially trains) through electromagnetic force. Eliminating rolling resistance increases efficiency. The maximum recorded speed of a maglev train is 581 km/h.
 * Magnets may be used to serve as a fail-safe device for some cable connections. For example, the power cords of some laptops are magnetic to prevent accidental damage to the port when tripped over. The MagSafe power connection to the Apple MacBook is one such example.

Medical issues and safety
Because human tissues have a very low level of susceptibility to static magnetic fields, there is little mainstream scientific evidence showing a health effect associated with exposure to static fields. Dynamic magnetic fields may be a different issue, however; correlations between electromagnetic radiation and cancer rates have been postulated due to demographic correlations (see Electromagnetic radiation and health).

If a ferromagnetic foreign body is present in human tissue, an external magnetic field interacting with it can pose a serious safety risk.

A different type of indirect magnetic health risk exists involving pacemakers. If a pacemaker has been embedded in a patient's chest (usually for the purpose of monitoring and regulating the heart for steady electrically induced beats), care should be taken to keep it away from magnetic fields. It is for this reason that a patient with the device installed cannot be tested with the use of a magnetic resonance imaging device.

Children sometimes swallow small magnets from toys, and this can be hazardous if two or more magnets are swallowed, as the magnets can pinch or puncture internal tissues.

Magnetic imaging devices (e.g. MRIs) generate enormous magnetic fields, and therefore rooms intended to hold them exclude ferrous metals. Bringing objects made of ferrous metals (such as oxygen canisters) into such a room creates a severe safety risk, as those objects may be powerfully thrown about by the intense magnetic fields.

Magnetizing ferromagnets
Ferromagnetic materials can be magnetized in the following ways:
 * Heating the object higher than its Curie temperature, allowing it to cool in a magnetic field and hammering it as it cools. This is the most effective method and is similar to the industrial processes used to create permanent magnets.
 * Placing the item in an external magnetic field will result in the item retaining some of the magnetism on removal. Vibration has been shown to increase the effect. Ferrous materials aligned with the Earth's magnetic field that are subject to vibration (e.g., frame of a conveyor) have been shown to acquire significant residual magnetism. Likewise, striking a steel nail held by fingers in a N-S direction with a hammer will temporarily magnetize the nail.
 * Stroking: An existing magnet is moved from one end of the item to the other repeatedly in the same direction (single touch method) or two magnets are moved outwards from the center of a third (double touch method).
 * Electric Current: The magnetic field produced by passing an electric current through a coil can get domains to line up. Once all of the domains are lined up, increasing the current will not increase the magnetization.

Demagnetizing ferromagnets
Magnetized ferromagnetic materials can be demagnetized (or degaussed) in the following ways:
 * Heating a magnet past its Curie temperature; the molecular motion destroys the alignment of the magnetic domains. This always removes all magnetization.
 * Placing the magnet in an alternating magnetic field with intensity above the material's coercivity and then either slowly drawing the magnet out or slowly decreasing the magnetic field to zero. This is the principle used in commercial demagnetizers to demagnetize tools, erase credit cards, hard disks, and degaussing coils used to demagnetize CRTs.
 * Some demagnetization or reverse magnetization will occur if any part of the magnet is subjected to a reverse field above the magnetic material's coercivity.
 * Demagnetization progressively occurs if the magnet is subjected to cyclic fields sufficient to move the magnet away from the linear part on the second quadrant of the B–H curve of the magnetic material (the demagnetization curve).
 * Hammering or jarring: mechanical disturbance tends to randomize the magnetic domains and reduce magnetization of an object, but may cause unacceptable damage.

Magnetic metallic elements
Many materials have unpaired electron spins, and the majority of these materials are paramagnetic. When the spins interact with each other in such a way that the spins align spontaneously, the materials are called ferromagnetic (what is often loosely termed as magnetic). Because of the way their regular crystalline atomic structure causes their spins to interact, some metals are ferromagnetic when found in their natural states, as ores. These include iron ore (magnetite or lodestone), cobalt and nickel, as well as the rare earth metals gadolinium and dysprosium (when at a very low temperature). Such naturally occurring ferromagnets were used in the first experiments with magnetism. Technology has since expanded the availability of magnetic materials to include various man-made products, all based, however, on naturally magnetic elements.

Composites

Ceramic, or ferrite, magnets are made of a sintered composite of powdered iron oxide and barium/strontium carbonate ceramic. Given the low cost of the materials and manufacturing methods, inexpensive magnets (or non-magnetized ferromagnetic cores, for use in electronic components such as portable AM radio antennas) of various shapes can be easily mass-produced. The resulting magnets are non-corroding but brittle and must be treated like other ceramics.

Alnico magnets are made by casting or sintering a combination of aluminium, nickel and cobalt with iron and small amounts of other elements added to enhance the properties of the magnet. Sintering offers superior mechanical characteristics, whereas casting delivers higher magnetic fields and allows for the design of intricate shapes. Alnico magnets resist corrosion and have physical properties more forgiving than ferrite, but not quite as desirable as a metal. Trade names for alloys in this family include: Alni, Alcomax, Hycomax, Columax, and Ticonal.

Injection-molded magnets are a composite of various types of resin and magnetic powders, allowing parts of complex shapes to be manufactured by injection molding. The physical and magnetic properties of the product depend on the raw materials, but are generally lower in magnetic strength and resemble plastics in their physical properties.

Flexible magnet
Flexible magnets are composed of a high-coercivity ferromagnetic compound (usually ferric oxide) mixed with a resinous polymer binder. This is extruded as a sheet and passed over a line of powerful cylindrical permanent magnets. These magnets are arranged in a stack with alternating magnetic poles facing up (N, S, N, S...) on a rotating shaft. This impresses the plastic sheet with the magnetic poles in an alternating line format. No electromagnetism is used to generate the magnets. The pole-to-pole distance is on the order of 5 mm, but varies with manufacturer. These magnets are lower in magnetic strength but can be very flexible, depending on the binder used.

For magnetic compounds (e.g. Nd2Fe14B) that are vulnerable to a grain boundary corrosion problem it gives additional protection.

Rare-earth magnets

Rare earth (lanthanoid) elements have a partially occupied f electron shell (which can accommodate up to 14 electrons). The spin of these electrons can be aligned, resulting in very strong magnetic fields, and therefore, these elements are used in compact high-strength magnets where their higher price is not a concern. The most common types of rare-earth magnets are samarium–cobalt and neodymium–iron–boron (NIB) magnets.

Single-molecule magnets (SMMs) and single-chain magnets (SCMs)
In the 1990s, it was discovered that certain molecules containing paramagnetic metal ions are capable of storing a magnetic moment at very low temperatures. These are very different from conventional magnets that store information at a magnetic domain level and theoretically could provide a far denser storage medium than conventional magnets. In this direction, research on monolayers of SMMs is currently under way. Very briefly, the two main attributes of an SMM are:

 * 1) a large ground state spin value (S), which is provided by ferromagnetic or ferrimagnetic coupling between the paramagnetic metal centres
 * 2) a negative value of the anisotropy of the zero field splitting (D)

Most SMMs contain manganese but can also be found with vanadium, iron, nickel and cobalt clusters. More recently, it has been found that some chain systems can also display a magnetization that persists for long times at higher temperatures. These systems have been called single-chain magnets.

Nano-structured magnets
Some nano-structured materials exhibit energy waves, called magnons, that coalesce into a common ground state in the manner of a Bose–Einstein condensate.

Rare-earth-free permanent magnets
The United States Department of Energy has identified a need to find substitutes for rare-earth metals in permanent-magnet technology, and has begun funding such research. The Advanced Research Projects Agency-Energy (ARPA-E) has sponsored a Rare Earth Alternatives in Critical Technologies (REACT) program to develop alternative materials. In 2011, ARPA-E awarded 31.6 million dollars to fund Rare-Earth Substitute projects. Iron nitrides are promising materials for rare-earth free magnets.

Costs
The cheapest permanent magnets, allowing for field strengths, are flexible and ceramic magnets, but these are also among the weakest types. The ferrite magnets are mainly low-cost magnets since they are made from cheap raw materials: iron oxide and Ba- or Sr-carbonate. However, a new low cost magnet, Mn–Al alloy, has been developed and is now dominating the low-cost magnets field. It has a higher saturation magnetization than the ferrite magnets. It also has more favorable temperature coefficients, although it can be thermally unstable. Neodymium–iron–boron (NIB) magnets are among the strongest. These cost more per kilogram than most other magnetic materials but, owing to their intense field, are smaller and cheaper in many applications.

Temperature
Temperature sensitivity varies, but when a magnet is heated to a temperature known as the Curie point, it loses all of its magnetism, even after cooling below that temperature. The magnets can often be remagnetized, however.

Additionally, some magnets are brittle and can fracture at high temperatures.

The maximum usable temperature is highest for alnico magnets at over 540 C, around 300 C for ferrite and SmCo, about 140 C for NIB and lower for flexible ceramics, but the exact numbers depend on the grade of material.

Electromagnets
An electromagnet, in its simplest form, is a wire that has been coiled into one or more loops, known as a solenoid. When electric current flows through the wire, a magnetic field is generated. It is concentrated near (and especially inside) the coil, and its field lines are very similar to those of a magnet. The orientation of this effective magnet is determined by the right hand rule. The magnetic moment and the magnetic field of the electromagnet are proportional to the number of loops of wire, to the cross-section of each loop, and to the current passing through the wire.

If the coil of wire is wrapped around a material with no special magnetic properties (e.g., cardboard), it will tend to generate a very weak field. However, if it is wrapped around a soft ferromagnetic material, such as an iron nail, then the net field produced can result in a several hundred- to thousandfold increase of field strength.

Uses for electromagnets include particle accelerators, electric motors, junkyard cranes, and magnetic resonance imaging machines. Some applications involve configurations more than a simple magnetic dipole; for example, quadrupole and sextupole magnets are used to focus particle beams.

Units and calculations
For most engineering applications, MKS (rationalized) or SI (Système International) units are commonly used. Two other sets of units, Gaussian and CGS-EMU, are the same for magnetic properties and are commonly used in physics.

In all units, it is convenient to employ two types of magnetic field, B and H, as well as the magnetization M, defined as the magnetic moment per unit volume.

 * 1) The magnetic induction field B is given in SI units of teslas (T). B is the magnetic field whose time variation produces, by Faraday's Law, circulating electric fields (which the power companies sell). B also produces a deflection force on moving charged particles (as in TV tubes). The tesla is equivalent to the magnetic flux (in webers) per unit area (in meters squared), thus giving B the unit of a flux density. In CGS, the unit of B is the gauss (G). One tesla equals 104 G.
 * 2) The magnetic field H is given in SI units of ampere-turns per meter (A-turn/m). The turns appear because when H is produced by a current-carrying wire, its value is proportional to the number of turns of that wire. In CGS, the unit of H is the oersted (Oe). One A-turn/m equals 4π×10−3 Oe.
 * 3) The magnetization M is given in SI units of amperes per meter (A/m). In CGS, the unit of M is the oersted (Oe). One A/m equals 10−3 emu/cm3. A good permanent magnet can have a magnetization as large as a million amperes per meter.
 * 4) In SI units, the relation B = μ0(H + M) holds, where μ0 is the permeability of space, which equals 4π×10−7 T•m/A. In CGS, it is written as B = H + 4πM. (The pole approach gives μ0H in SI units. A μ0M term in SI must then supplement this μ0H to give the correct field within B, the magnet. It will agree with the field B calculated using Ampèrian currents).

Materials that are not permanent magnets usually satisfy the relation M = χH in SI, where χ is the (dimensionless) magnetic susceptibility. Most non-magnetic materials have a relatively small χ (on the order of a millionth), but soft magnets can have χ on the order of hundreds or thousands. For materials satisfying M = χH, we can also write B = μ0(1 + χ)H = μ0μrH = μH, where μr = 1 + χ is the (dimensionless) relative permeability and μ =μ0μr is the magnetic permeability. Both hard and soft magnets have a more complex, history-dependent, behavior described by what are called hysteresis loops, which give either B vs. H or M vs. H. In CGS, M = χH, but χSI = 4πχCGS, and μ = μr.

Caution: in part because there are not enough Roman and Greek symbols, there is no commonly agreed-upon symbol for magnetic pole strength and magnetic moment. The symbol m has been used for both pole strength (unit A•m, where here the upright m is for meter) and for magnetic moment (unit A•m2). The symbol μ has been used in some texts for magnetic permeability and in other texts for magnetic moment. We will use μ for magnetic permeability and m for magnetic moment. For pole strength, we will employ qm. For a bar magnet of cross-section A with uniform magnetization M along its axis, the pole strength is given by qm = MA, so that M can be thought of as a pole strength per unit area.

Fields of a magnet
Far away from a magnet, the magnetic field created by that magnet is almost always described (to a good approximation) by a dipole field characterized by its total magnetic moment. This is true regardless of the shape of the magnet, so long as the magnetic moment is non-zero. One characteristic of a dipole field is that the strength of the field falls off inversely with the cube of the distance from the magnet's center.

Closer to the magnet, the magnetic field becomes more complicated and more dependent on the detailed shape and magnetization of the magnet. Formally, the field can be expressed as a multipole expansion: A dipole field, plus a quadrupole field, plus an octupole field, etc.

At close range, many different fields are possible. For example, for a long, skinny bar magnet with its north pole at one end and south pole at the other, the magnetic field near either end falls off inversely with the square of the distance from that pole.

Pull force of a single magnet
The strength of a given magnet is sometimes given in terms of its pull force — its ability to pull ferromagnetic objects. The pull force exerted by either an electromagnet or a permanent magnet with no air gap (i.e., the ferromagnetic object is in direct contact with the pole of the magnet ) is given by the Maxwell equation:
 * $$F={{B^2 A}\over{2 \mu_{0}}}$$,

where
 * F is force (SI unit: newton)
 * A is the cross section of the area of the pole in square meters
 * B is the magnetic induction exerted by the magnet

This result can be easily derived using Gilbert model, which assumes that the pole of magnet is charged with magnetic monopoles that induces the same in the ferromagnetic object.

If a magnet is acting vertically, it can lift a mass m in kilograms given by the simple equation:

 * $$m={{B^2 A}\over{2 \mu_{0} g}},$$

where g is the gravitational acceleration.

Force between two magnetic poles
Classically, the force between two magnetic poles is given by:

 * $$F={{\mu q_{m1} q_{m2}}\over{4\pi r^2}}$$

where
 * F is force (SI unit: newton)
 * qm1 and qm2 are the magnitudes of magnetic poles (SI unit: ampere-meter)
 * μ is the permeability of the intervening medium (SI unit: tesla meter per ampere, henry per meter or newton per ampere squared)
 * r is the separation (SI unit: meter).

The pole description is useful to the engineers designing real-world magnets, but real magnets have a pole distribution more complex than a single north and south. Therefore, implementation of the pole idea is not simple. In some cases, one of the more complex formulae given below will be more useful.

Force between two nearby magnetized surfaces of area A
The mechanical force between two nearby magnetized surfaces can be calculated with the following equation. The equation is valid only for cases in which the effect of fringing is negligible and the volume of the air gap is much smaller than that of the magnetized material:
 * $$F=\frac{\mu_0 H^2 A}{2} = \frac{B^2 A}{2 \mu_0}$$

where:
 * A is the area of each surface, in m2
 * H is their magnetizing field, in A/m
 * μ0 is the permeability of space, which equals 4π×10−7 T•m/A
 * B is the flux density, in T.

Force between two bar magnets
The force between two identical cylindrical bar magnets placed end to end at large distance $$z\gg R$$ is approximately:,
 * $$F \simeq \left[\frac {B_0^2 A^2 \left( L^2+R^2 \right)} {\pi\mu_0L^2}\right] \left[{\frac 1 {z^2}} + {\frac 1 {(z+2L)^2}} - {\frac 2 {(z+L)^2}} \right]$$

where:

 * B0 is the magnetic flux density very close to each pole, in T,
 * A is the area of each pole, in m2,
 * L is the length of each magnet, in m,
 * R is the radius of each magnet, in m, and
 * z is the separation between the two magnets, in m.

 * $$B_0 \,=\, \frac{\mu_0}{2}M$$ relates the flux density at the pole to the magnetization of the magnet.

Note that all these formulations are based on Gilbert's model, which is usable in relatively great distances. In other models (e.g., Ampère's model), a more complicated formulation is used that sometimes cannot be solved analytically. In these cases, numerical methods must be used.

Force between two cylindrical magnets
For two cylindrical magnets with radius $$ R $$ and length $$L$$, with their magnetic dipole aligned, the force can be asymptotically approximated at large distance $$z\gg R$$ by,

F(z) \simeq \frac{\pi\mu_0}{4} M^2 R^4 \left[\frac{1}{z^2} + \frac{1}{(z+2L)^2} - \frac{2}{(z + L)^2}\right] $$

where $$M$$ is the magnetization of the magnets and $$z$$ is the gap between the magnets. A measurement of the magnetic flux density very close to the magnet $$ B_0 $$ is related to $$M$$ approximately by the formula

B_0 = \frac{\mu_0}{2} M $$

The effective magnetic dipole can be written as

m = M V $$

Where $$V$$ is the volume of the magnet. For a cylinder, this is $$V = \pi R^2 L$$.

When $$z\gg L$$, the point dipole approximation is obtained,

F(x) = \frac{3\pi\mu_0}{2} M^2 R^4 L^2\frac{1}{z^4} = \frac{3\mu_0}{2\pi} M^2 V^2\frac{1}{z^4} = \frac{3\mu_0}{2\pi} m_1 m_2\frac{1}{z^4} $$

which matches the expression of the force between two magnetic dipoles.

title: Magnet


text:
Richmond

Richmond most often refers to:
 * Richmond, Virginia, the capital of Virginia, United States
 * Richmond, London, a part of London
 * Richmond, North Yorkshire, a town in England
 * Richmond, British Columbia, a city in Canada
 * Richmond, California, a city in California, United States

Richmond may also refer to:

People

 * Richmond (surname)
 * Earl of Richmond
 * Duke of Richmond
 * Richmond C. Beatty (1905–1961), American academic, biographer and critic
 * Richmond Avenal, character in British sitcom The IT Crowd

Australia

 * Richmond, New South Wales
 * RAAF Base Richmond
 * Richmond Woodlands Important Bird Area
 * Richmond River, New South Wales
 * Division of Richmond
 * Electoral district of Richmond (New South Wales)
 * Richmond, Queensland
 * Richmond, South Australia
 * Richmond, Tasmania
 * Richmond, Victoria
 * Electoral district of Richmond (Victoria)
 * City of Richmond
 * Richmond railway station, Melbourne

Canada

 * Richmond, British Columbia, a city in Metro Vancouver
 * Richmond (British Columbia provincial electoral district)
 * Richmond, Calgary, Alberta, a neighbourhood
 * Richmond Parish, New Brunswick
 * Richmond, Nova Scotia
 * Richmond (Nova Scotia federal electoral district)
 * Richmond (Nova Scotia provincial electoral district)
 * Richmond, Ontario, a community part of the city of Ottawa
 * Richmond, Prince Edward Island
 * Richmond, Quebec
 * Richmond (Quebec provincial electoral district)

Germany

 * Schloss Richmond, a castle in Brunswick

Ireland

 * Richmond, County Tipperary, a townland in north County Tipperary
 * Richmond Park (football ground), Dublin

Jamaica

 * Richmond, Jamaica

New Zealand

 * Richmond, New Zealand, a town in the Tasman district in South Island
 * Richmond, Canterbury, a small suburb in Christchurch, South Island
 * Richmond, Invercargill, a minor suburb, South Island

South Africa

 * Richmond, Northern Cape
 * Richmond, KwaZulu-Natal

United Kingdom

 * Richmond, London, previously known as Shene, a town formerly in Surrey and now in the London Borough of Richmond upon Thames
 * The London Borough of Richmond upon Thames, colloquially known as Richmond borough
 * Richmond station
 * Richmond Hill, London
 * Museum of Richmond in Richmond, London
 * Richmond Palace, previously known as Shene Palace
 * Richmond Park in the London Borough of Richmond upon Thames
 * Richmond, The American International University in London
 * Municipal Borough of Richmond (Surrey) (1890 to 1965)
 * Richmond (Surrey) (UK Parliament constituency), 1918–1983
 * Richmond, North Yorkshire, a market town and the administrative centre of the district of Richmondshire
 * Richmond Castle in Richmond, North Yorkshire
 * Honour of Richmond, an English feudal barony in north-west Yorkshire
 * Richmond (Yorks) (UK Parliament constituency), 1885–present
 * Richmonds in the Wood, Thaxted, Essex
 * Richmond, Sheffield, an area of Sheffield, South Yorkshire

United States

 * Richmond, Alabama, an unincorporated community
 * Richmond, Arkansas, an unincorporated community
 * Richmond, California
 * Richmond station (California)
 * Richmond District, San Francisco, California
 * Richmond County, Georgia, a county
 * Richmond, Illinois, a town
 * Richmond, Indiana, a city
 * Richmond, Kansas
 * Richmond, Kentucky
 * Richmond, Louisiana, a village
 * Richmond, Maine, a New England town
 * Richmond (CDP), Maine, village within the town
 * Richmond, Massachusetts, a New England town
 * Richmond, Michigan, in Macomb County
 * New Richmond, Michigan, in Allegan County
 * Richmond, Minnesota
 * Richmond, Missouri
 * Richmond, New Hampshire, a New England town
 * Richmond, New York, a town
 * Richmond County, North Carolina, a county
 * Richmond, Ohio
 * Richmond, Oregon, an unincorporated community
 * Richmond, Portland, Oregon, a neighborhood
 * Richmond, Rhode Island, a New England town
 * Richmond, Texas
 * Richmond, Utah
 * Richmond, Vermont, a New England town
 * Richmond (CDP), Vermont, village within the town
 * Richmond, Virginia, the state's capital city
 * Richmond Raceway
 * University of Richmond
 * Richmond, Shawano County, Wisconsin, a town
 * Richmond, St. Croix County, Wisconsin, a town
 * Richmond, Walworth County, Wisconsin, a town
 * Richmond (community), Wisconsin, an unincorporated community

Bodies of water

 * Richmond Creek (disambiguation)
 * Richmond River, New South Wales, Australia
 * Richmond River (St. Vincent)

Ships

 * Richmond (1811 ship), wrecked in 1822 in the Sea of Java
 * HMS Richmond, several ships in the British Navy
 * USS Richmond, several ships in the United States Navy

Sports clubs

 * Richmond Football Club, Australia
 * Richmond F.C., England

Other uses

 * Confitería Richmond, a former tea room and literary café in Buenos Aires, Argentina
 * Richmond (automobile), cars built in Richmond, Indiana, United States
 * Richmond (cigarette)
 * Richmond Herald, in England, an officer of arms
 * Richmond (Natchez, Mississippi), a historic mansion built in 1810

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Richmond


text:
Mikael Agricola

Mikael Agricola (c. 1510 – 9 April 1557) was a Finnish Lutheran clergyman who became the de facto founder of literary Finnish and a prominent proponent of the Protestant Reformation in Sweden, including Finland, which was a Swedish territory at the time. He is often called the "father of literary Finnish".

Agricola was consecrated as the bishop of Turku (Åbo) in 1554, without papal approval. He continued the reform of the Finnish church (then a part of the Church of Sweden) along Lutheran lines. He translated the New Testament into Finnish and also produced the prayer book and hymns used in Finland's new Lutheran Church. This work set the rules of orthography that are the basis of modern Finnish spelling. His thorough work is particularly remarkable in that he accomplished it in only three years.

He died of sudden illness while returning from a trip during which he assisted in negotiating the Treaty of Novgorod with the Tsardom of Moscovy.

Early life
Michael Olaui or Mikael Olofsson (Finnish Mikael Olavinpoika) was born in c. 1510 in the village of Torsby in Pernå (Pernaja), Nyland (Uusimaa), in what now is part of Finland but then was part of Sweden. He was named after the patron saint of Pernå's church. The exact date of his birth, like most details of his life, is unknown. His family was a quite wealthy gentry family according to the local bailiff's accounting. He had three sisters, but their names are not known. His teachers apparently recognized his aptitude for languages and his rector Bartholomeus sent him to Viborg (Fi. Viipuri; now Vyborg, Russia) for Latin school and some priestly training, where he attended the school of Erasmus. It is not known whether his first language was Finnish or Swedish; Pernå was mostly a Swedish-speaking district, but the language he used in his works indicates that he was a native speaker of Finnish. However, he mastered both languages like a native speaker and was possibly a bilingual child.

Studies
When Michael studied in Viborg (Viipuri) he assumed the surname Agricola ("farmer" gv. "agriculture"); surnames based on one's father's status and occupation were common for first-generation scholars at the time. It was probably in Viipuri where he first came in touch with the Reformation and Humanism. The Viipuri castle was ruled by a German count, Johann, who had served the king of Sweden, Gustav Vasa. The count was a supporter of the Reformation, and they already held Lutheran services.

In 1528 Agricola followed his teacher to Turku (Åbo), then the center of the Finnish side of the Swedish realm and the capital of the bishopric. There Agricola became a scribe in bishop Martinus Skytte's office. While in Turku Agricola met Martin Luther's first Finnish student Petrus Särkilahti, who eagerly spread the idea of the Reformation. Särkilahti died in 1529, and it was up to Agricola to continue Särkilahti's work. Agricola was ordained for priesthood sometime in the early 1530s.

In 1536 the bishop of Turku sent Agricola to study in Wittenberg in Germany. He concentrated on the lectures of Philipp Melanchthon, who was an expert in Greek, the original language of the New Testament. In Wittenberg Agricola studied under Luther. Agricola got recommendations to Swedish King Gustav Vasa from both of the reformers. He sent two letters to Gustav, asking for a confirmation for a stipend. When the confirmation came, Agricola bought books (for example, the complete works of Aristotle). In 1537 he started translating the New Testament into Finnish.

Rector and ordinarius
In 1539 Agricola returned to Turku and ended up as the rector of Turku (Cathedral) School. He did not like his job, calling his students "untamed animals". At the time Gustav Vasa had confiscated the property of the church when he was consolidating his power but he also drove the Reformation. In 1544 Agricola received an order from the crown to send several talented young men to Stockholm's taxing offices. For some reason, Agricola did not obey until the order was sent again the next year, with a more menacing tone. This episode probably affected their relations negatively.

In 1546 Agricola lost his home and school in the Fire of Turku. On 22 February 1548, Gustav Vasa ordered Agricola to retire from his position as a rector. At this time Agricola was already married, but history knows his wife only by her name: Pirjo Olavintytär (Bridget, "daughter of Olavi"; Birgitta Olafsdotter, Brigida Olaui). His only son, Christian Agricola (Christianus Michaelis Agricola), was born 11 December 1550, and became the bishop of Tallinn in 1584.

When an old bishop died in 1554, Gustav Vasa had Agricola consecrated as the ordinarius of Turku parish – for all practical purposes Bishop of Turku and by extension the first Lutheran bishop for all Finland. Agricola was not a particularly strict or dedicated reformer, although he did remove the Canon of the Mass.

Death
In 1557, Agricola headed a delegation going to Russia on a diplomatic mission, and was in Moscow from 21 February to 24 March negotiating a peace treaty, the Treaty of Novgorod (1557). On 9 April he fell ill and died on Kyrönniemi peninsula near the Uusikirkko (now Polyane) village on the Karelian Isthmus. This day is also Elias Lönnrot's birthday and it is celebrated in Finland as the day of the Finnish language. Agricola was probably buried inside Viipuri's church, but the exact location of the grave is not known.

Abckiria
Agricola had thought about translating the New Testament in his early years of study. At the time, however, there was no standard written form of Finnish, so he started developing it. His first book, Abckiria, which is nowadays known as the "ABC-kirja" or ABC book, was a primer for reading and a catechism. It was first printed in 1543. The catechism was included because only very few people could afford the whole Bible at the time. The first printing contained 16 pages.

A second printing was released in 1551 with 24 pages.

In 1966 Åke Åbergin, a librarian, discovered parts, while repairing book bindings, from an as yet unknown (likely the third) edition of the "ABC-kirja" that included the name of the printer, Amund Lauritsanpoika, and fortuitously the publishing date of 1559 (two years after the author's death) of the final as yet undiscovered 8 pages. The pages were likely the result of an imposing error and relegated to padding paper.

Rucouskiria
Agricola's Rucouskiria Bibliasta (contemporary Finnish spelling: Rukouskirja; literally, "Prayer Book from the Bible") was printed in March 1544. At the beginning of the book, Agricola wrote about many topics concerning all-round education and the Reformation's effects in Finland. The book includes four prefaces and about 700 prayers on many topics; it even has twelve structurally different kinds of prayers, instead of the usual two or three. It is the most independent work by Agricola and contains approximately 900 pages. His sources include the works of Luther, Melanchthon, and Erasmus.

New Testament translation
Agricola's most prominent book is the first Finnish-language translation of the New Testament. The manuscript was completed in 1548. It contains 718 pages and many illustrations.

Liturgical books
While Agricola was in Wittenberg, he translated three smaller liturgical books into Finnish. These books were printed in 1549.

Käsikirja Castesta ia muista Christikunnan Menoista includes forms for christening, marriage and burial, as well as speeches for the sick, mourning and dying. It is translated from Olaus Petri's corresponding work except for the christening and marriage portions, which are from Luther. It also contains minor elements translated from works of Caspar Huberinus.

Messu eli Herran echtolinen includes the form for a service. It is also based on Olaus Petri's work and a few Finnish manuscripts. In this book Agricola revealed his next mission: the translation of the Old Testament.

Se meiden Herran Jesusen Christusen Pina, ylesnousemus ia tauiaisen Astumus, niste Neliest Euangelisterist coghottuon tells about Jesus Christ's suffering. It is collected from all four gospels. This book was influenced heavily by Johannes Bugenhagen, a teacher in Wittenberg. It was mainly translated from the German version, but some parts are influenced by the Swedish version and Agricola's own translation of the New Testament.

Commemorations
The Evangelical Lutheran Church in America remembers Bishop Agricola annually on 10 April.

Mikael Agricola Church in Helsinki is named after Agricola. As well the Agricola Lutheran Church memorializes his namesake in Toronto Canada. An asteroid 3212 Agricola is named after Agricola.

In 2007, 450 years after his death, Agricola was selected as the main motif for a commemorative coin, the €10 Mikael Agricola and Finnish language commemorative coin. This collector coin was issued to honor Agricola's life work as a contributor to the Protestant reformation in Finland and as the father of the Finnish written language. The reverse side depicts a quill to reference the writer, while the coin's obverse side contains an artistic interpretation of a human figure.

title: Mikael Agricola


text:
Unconventional superconductor

Unconventional superconductors are materials that display superconductivity which does not conform to conventional BCS theory or its extensions.

History
The superconducting properties of CeCu2Si2, a type of heavy fermion material, were reported in 1979 by Frank Steglich. For a long time it was believed that CeCu2Si2 was a singlet d-wave superconductor, but since the mid-2010s, this notion has been strongly contested. In the early eighties, many more unconventional, heavy fermion superconductors were discovered, including UBe13, UPt3 and URu2Si2. In each of these materials, the anisotropic nature of the pairing was implicated by the power-law dependence of the nuclear magnetic resonance (NMR) relaxation rate and specific heat capacity on temperature. The presence of nodes in the superconducting gap of UPt3 was confirmed in 1986 from the polarization dependence of the ultrasound attenuation.

The first unconventional triplet superconductor, organic material (TMTSF)2PF6, was discovered by Denis Jerome, Klaus Bechgaard and coworkers in 1980. Experimental works by Paul Chaikin's and Michael Naughton's groups as well as theoretical analysis of their data by Andrei Lebed have firmly confirmed unconventional nature of superconducting pairing in (TMTSF)2X (X=PF6, ClO4, etc.) organic materials.

High-temperature singlet d-wave superconductivity was discovered by J.G. Bednorz and K.A. Müller in 1986, who also discovered that the lanthanum-based cuprate perovskite material LaBaCuO4 develops superconductivity  at a critical temperature (Tc) of approximately 35 K (-238 degrees Celsius). This was well above the highest critical temperature known at the time (Tc = 23 K), and thus the new family of materials was called high-temperature superconductors. Bednorz and Müller received the Nobel prize in Physics for this discovery in 1987. Since then, many other high-temperature superconductors have been synthesized.

LSCO (La2−xSrxCuO4) was discovered the same year (1986). Soon after, in January 1987, yttrium barium copper oxide (YBCO) was discovered to have a Tc of 90 K, the first material to achieve superconductivity above the boiling point of liquid nitrogen (77 K). This was highly significant from the point of view of the technological applications of superconductivity because liquid nitrogen is far less expensive than liquid helium, which is required to cool conventional superconductors down to their critical temperature. In 1988 bismuth strontium calcium copper oxide (BSCCO) with Tc up to 107 K, and thallium barium calcium copper oxide (TBCCO) (T=thallium) with Tc of 125 K were discovered. The current record critical temperature is about Tc = 133 K (−140 °C) at standard pressure, and somewhat higher critical temperatures can be achieved at high pressure. Nevertheless, at present it is considered unlikely that cuprate perovskite materials will achieve room-temperature superconductivity.

On the other hand, other unconventional superconductors have been discovered. These include some that do not superconduct at high temperatures, such as strontium ruthenate Sr2RuO4, but that, like high-temperature superconductors, are unconventional in other ways. (For example, the origin of the attractive force leading to the formation of Cooper pairs may be different from the one postulated in BCS theory.) In addition to this, superconductors that have unusually high values of Tc but that are not cuprate perovskites have been discovered. Some of them may be extreme examples of conventional superconductors (this is suspected of magnesium diboride, MgB2, with Tc = 39 K). Others could display more unconventional features.

In 2008 a new class that does not include copper (layered oxypnictide superconductors), for example LaOFeAs, was discovered. An oxypnictide of samarium seemed to have a Tc of about 43 K, which was higher than predicted by BCS theory. Tests at up to 45 T suggested the upper critical field of LaFeAsO0.89F0.11 to be around 64 T. Some other iron-based superconductors do not contain oxygen.

, the highest-temperature superconductor (at ambient pressure) is mercury barium calcium copper oxide (HgBa2Ca2Cu3Ox), at 138 K and is held by a cuprate-perovskite material, possibly 164 K under high pressure.

Other unconventional superconductors not based on cuprate structure have too been found. Some have unusually high values of the critical temperature, Tc, and hence they are sometimes also called high-temperature superconductors.

Graphene
In 2017, scanning tunneling microscopy and spectroscopy experiments on graphene proximitized to the electron-doped (non-chiral) d-wave superconductor Pr2−xCexCuO4 (PCCO) revealed evidence for an unconventional superconducting density of states induced in graphene. Publications in March 2018 provided evidence for unconventional superconducting properties of a graphene bilayer where one layer was offset by a "magic angle" of 1.1° relative to the other.

Ongoing research
After more than twenty years of intensive research, the origin of high-temperature superconductivity is still not clear, being one of the major unsolved problems of theoretical condensed matter physics. But it seems that instead of electron-phonon attraction mechanisms, as in conventional superconductivity, genuine electronic mechanisms (e.g. by antiferromagnetic correlations) are occurring. In addition, instead of s-wave pairing, d-waves are substantial.

One goal of much research is room-temperature superconductivity.

Despite intensive research and many promising leads, an explanation has so far eluded scientists. One reason for this is that the materials in question are generally very complex, multi-layered crystals (for example, BSCCO), making theoretical modeling difficult.

Possible mechanisms
The most controversial topic in condensed matter physics has been the mechanism for high-Tc superconductivity (HTS). There have been two representative theories on the HTS : (See also Resonating valence bond theory )

Weak-coupling theory
Firstly, it has been suggested that the HTS emerges by antiferromagnetic spin fluctuation in a doped system. According to this weak-coupling theory, the pairing wave function of the HTS should have a dx2−y2 symmetry. Thus, whether the symmetry of the pairing wave function is the d symmetry or not is essential to demonstrate on the mechanism of the HTS in respect of the spin fluctuation. That is, if the HTS order parameter (pairing wave function) does not have d symmetry, then a pairing mechanism related to spin fluctuation can be ruled out. The tunnel experiment (see below) seems to detect d symmetry in some HTS.

Interlayer coupling model
Secondly, there is the interlayer coupling model, according to which a layered structure consisting of BCS-type (s symmetry) superconductor can enhance the superconductivity by itself. By introducing an additional tunneling interaction between each layer, this model successfully explained the anisotropic symmetry of the order parameter in the HTS as well as the emergence of the HTS.

In order to solve this unsettled problem, there have been numerous experiments such as photoelectron spectroscopy, NMR, specific heat measurement, etc. Unfortunately, the results were ambiguous, where some reports supported the d symmetry for the HTS but others supported the s symmetry. This muddy situation possibly originated from the indirect nature of the experimental evidence, as well as experimental issues such as sample quality, impurity scattering, twinning, etc.

Superexchange
Promising experimental results from various researchers in September 2022, including Weijiong Chen, J.C. Séamus Davis and H. Eisiaki revealed that superexchange of electrons is possibly the most probable reason for high-temperature superconductivity.

Previous studies on the symmetry of the HTS order parameter
The symmetry of the HTS order parameter has been studied in nuclear magnetic resonance measurements and, more recently, by angle-resolved photoemission and measurements of the microwave penetration depth in a HTS crystal. NMR measurements probe the local magnetic field around an atom and hence reflect the susceptibility of the material. They have been of special interest for the HTS materials because many researchers have wondered whether spin correlations might play a role in the mechanism of the HTS.

NMR measurements of the resonance frequency on YBCO indicated that electrons in the copper oxide superconductors are paired in spin-singlet states. This indication came from the behavior of the Knight shift, the frequency shift that occurs when the internal field is different from the applied field: In a normal metal, the magnetic moments of the conduction electrons in the neighborhood of the ion being probed align with the applied field and create a larger internal field. As these metals go superconducting, electrons with oppositely directed spins couple to form singlet states. In the anisotropic HTS, perhaps NMR measurements have found that the relaxation rate for copper depends on the direction of the applied static magnetic field, with the rate being higher when the static field is parallel to one of the axes in the copper oxide plane. While this observation by some group supported the d symmetry of the HTS, other groups could not observe it.

Also, by measuring the penetration depth, the symmetry of the HTS order parameter can be studied. The microwave penetration depth is determined by the superfluid density responsible for screening the external field. In the s wave BCS theory, because pairs can be thermally excited across the gap Δ, the change in superfluid density per unit change in temperature goes as exponential behavior, exp(-Δ/kBT). In that case, the penetration depth also varies exponentially with temperature T. If there are nodes in the energy gap as in the d symmetry HTS, electron pair can more easily be broken, the superfluid density should have a stronger temperature dependence, and the penetration depth is expected to increase as a power of T at low temperatures. If the symmetry is specially dx2-y2 then the penetration depth should vary linearly with T at low temperatures. This technique is increasingly being used to study superconductors and is limited in application largely by the quality of available single crystals.

Photoemission spectroscopy also could provide information on the HTS symmetry. By scattering photons off electrons in the crystal, one can sample the energy spectra of the electrons. Because the technique is sensitive to the angle of the emitted electrons one can determine the spectrum for different wave vectors on the Fermi surface. However, within the resolution of the angle-resolved photoemission spectroscopy (ARPES), researchers could not tell whether the gap goes to zero or just gets very small. Also, ARPES are sensitive only to the magnitude and not to the sign of the gap, so it could not tell if the gap goes negative at some point. This means that ARPES cannot determine whether the HTS order parameter has the d symmetry or not.

Junction experiment supporting the d-wave symmetry
There was a clever experimental design to overcome the muddy situation. An experiment based on pair tunneling and flux quantization in a three-grain ring of YBa2Cu3O7 (YBCO) was designed to test the symmetry of the order parameter in YBCO. Such a ring consists of three YBCO crystals with specific orientations consistent with the d-wave pairing symmetry to give rise to a spontaneously generated half-integer quantum vortex at the tricrystal meeting point. Furthermore, the possibility that junction interfaces can be in the clean limit (no defects) or with maximum zig-zag disorder was taken into account in this tricrystal experiment. A proposal of studying vortices with half magnetic flux quanta in heavy-fermion superconductors in three polycrystalline configurations was reported in 1987 by V. B. Geshkenbein, A. Larkin and A. Barone in 1987.

In the first tricrystal pairing symmetry experiment, the spontaneous magnetization of half flux quantum was clearly observed in YBCO, which convincingly supported the d-wave symmetry of the order parameter in YBCO. Because YBCO is orthorhombic, it might inherently have an admixture of s-wave symmetry. So, by tuning their technique further, it was found that there was an admixture of s-wave symmetry in YBCO within about 3%. Also, it was demonstrated by Tsuei, Kirtley et al. that there was a pure dx2-y2 order parameter symmetry in the tetragonal Tl2Ba2CuO6.

title: Unconventional superconductor


text:
Jefferson County

Jefferson County may refer to one of several counties or parishes in the United States, all of which are named directly or indirectly after Thomas Jefferson:

 * Jefferson County, Alabama
 * Jefferson County, Arkansas
 * Jefferson County, Colorado
 * Jefferson County, Jefferson Territory
 * Jefferson County, Florida
 * Jefferson County, Georgia
 * Jefferson County, Idaho
 * Jefferson County, Illinois
 * Jefferson County, Indiana
 * Jefferson County, Iowa
 * Jefferson County, Kansas
 * Jefferson County, Kentucky
 * Jefferson Parish, Louisiana
 * Jefferson County, Mississippi
 * Jefferson County, Missouri
 * Jefferson County, Montana
 * Jefferson County, Nebraska
 * Jefferson County, New York
 * Jefferson County, Ohio
 * Jefferson County, Oklahoma
 * Jefferson County, Oregon
 * Jefferson County, Pennsylvania
 * Jefferson County, Tennessee
 * Jefferson County, Texas
 * Jefferson County, Virginia, has existed twice; the two counties continue in existence as Jefferson County, Kentucky and Jefferson County, West Virginia
 * Jefferson County, Washington
 * Jefferson County, West Virginia
 * Jefferson County, Wisconsin

title: Jefferson County


text:
919

Year 919 (CMXIX) was a common year starting on Friday (link will display the full calendar) of the Julian calendar.

Byzantine Empire

 * March 25 – Romanos Lekapenos, admiral (droungarios) of the Byzantine navy, seizes the Boukoleon Palace in Constantinople. He is named megas hetaireiarches (head of the imperial guard). Lekapenos consolidates his position and becomes regent of Emperor Constantine VII. He marries his 9-year-old daughter Helena Lekapene to Constantine and assumes the new title of basileopator (one of the highest offices in the Byzantine Empire).

Europe

 * May 24 – The nobles of Franconia and Saxony elect Henry the Fowler at the Imperial Diet in Fritzlar as ruler of the East Frankish Kingdom. He recognizes the stem duchies (uniting them in a German confederation) and all their sovereign privileges. Two of the four most influential duchies, Bavaria and Swabia, do not accept his rule. Henry fortifies Magdeburg against the Magyars.
 * Summer – Arnulf, Duke of Bavaria ("the Bad"), is elected as anti-king by the East-Frankish nobles in opposition to Henry I. Burchard II, duke of Swabia, submits to Henry's rule — allowing him to retain administrative control over his duchy. After an absence of nearly 15 years, the Magyars raid Bavaria and Northern Italy again, sacking the Po Valley (see Hungarian invasions of Europe).
 * September 14 – Battle of Islandbridge: High King Niall Glúndub is killed while leading an Irish coalition against the Dublin-based Vikings of Uí Ímair, led by King Sitric Cáech.

Britain

 * Lady Ælfwynn of the Mercians is brought to the court of her uncle, King Edward the Elder, and deprived of her authority in Mercia. Edward formally annexes the kingdom, ending independent Mercian rule.
 * Ragnall ua Ímair, a Viking chief from Ireland, takes control of the Norse Kingdom of York (also referred to as Jórvik) and the English-ruled Earldom of Northumbria. He establishes himself as king at York.

Africa

 * April 5 – The Fatimid Caliphate of Ifriqiya (modern-day Tunisia) launch the second Fatimid invasion of Egypt (919–921) in an attempt to seize Egypt from its Abbasid rulers. The expedition fails and the Fatimids will be forced to retreat.
 * Following his death, Mara Takla Haymanot is succeeded by his eldest son Tatadim as ruler (negus) of the Zagwe Dynasty in Ethiopia.

China

 * Battle of Langshan Jiang: The Wuyue navy (500 dragon ships) under Prince Qian Yuanguan who is preparing an invasion to attack the Wu Kingdom, defeats the naval forces of General Peng Yanzhang on the Yangtze River. Due to the use of flamethrower ships (using gunpowder to ignite petrol, like Greek fire) Qian Yuanguan manages to destroy 400 enemy ships and captures 7,000 prisoners.

Mesoamerica

 * The Ancestral Puebloans, living in the Four Corners, begin construction at Pueblo Bonito, in modern-day New Mexico's Chaco Canyon (approximate date).

Religion

 * The Bulgarian Orthodox Church is declared as autocephalous and elevated to the rank of patriarchate at an ecclesiastical council.

Births

 * January 29 – Shi Zong, emperor of the Liao Dynasty (d. 951)
 * García I, king of Pamplona (d. 970)
 * Li Cheng, Chinese painter (d. 967)
 * Meng Chang, emperor of Later Shu (d. 965)
 * Xu Jingqian, official and regent of Wu (d. 937)
 * Theinhko, king of the Pagan dynasty (d. 956)

Deaths

 * January 28 – Zhou Dewei, Chinese general
 * August 11 – Dhuka al-Rumi, Abbasid governor of Egypt
 * August 28 – He Gui, Chinese general (b. 858)
 * September 14 – Niall Glúndub, High King of Ireland
 * December 18 – Lady Wu, wife of Qian Liu (b. 858)
 * Justan III, ruler of the Justanid Dynasty (Iran)
 * Khusrau Firuz, ruler of the Justanid Dynasty
 * Mara Takla Haymanot, ruler of Ethiopia
 * Solomon III, bishop of Constance

title: 919


text:
918

Year 918 (CMXVIII) was a common year starting on Thursday (link will display the full calendar) of the Julian calendar.

Europe

 * December 23 – King Conrad I, injured at one of his battles with Arnulf I (the Bad), dies at his residence in Weilburg Castle after a 7-year reign. On his deathbed Conrad persuades his younger brother Eberhard III to offer the East Frankish crown to Henry the Fowler, the duke of Saxony. Conrad is buried in Fulda Cathedral (also the burial place of Boniface) in Germany.

Britain

 * Battle of Corbridge: High-Reeve Ealdred I persuades King Constantine II of Scotland to help him reclaim his position in Bernicia. They mount an invasion of his now Norse controlled lands. The Vikings under Ragnall ua Ímair (or Rægnald) defeat the Scots and their allies at Corbridge (Northern Northumbria), but take heavy casualties themselves.
 * Summer – Lady Æthelflæd of Mercia begins to intrigue with disaffected factions within the Norse Kingdom of York (also referred to as Jórvik). Mercian troops ravage the local countryside and peacefully overrun the fortress of Leicester (belonging to the Five Boroughs of the Danelaw), while her brother, King Edward the Elder, takes Stamford.
 * June 12 – Æthelflæd dies at Tamworth while campaigning against the Vikings. She is buried with her husband Æthelred in St. Oswald's Priory at Gloucester. Æthelflæd is succeeded by her only daughter Ælfwynn.
 * Kings Idwal Foel of Gwynedd and Hywel ap Cadell, and Prince Clydog of Deheubarth (Wales) submit to the overlordship of Edward the Elder. The Vikings raid Anglesey.

Asia

 * July 25 – Wang Kon, a Korean general, overthrows the government of the short-lived state Ho Goguryeo and ascends the throne at Cheorwon. He founds the Goryeo dynasty and makes Song'ak his capital.
 * Emperor Taizu of the Khitan Empire occupies a newly walled city called Shangjing (modern-day Inner Mongolia), meaning Supreme Capital. It becomes the residence of the Chinese Liao dynasty.

Births

 * Minamoto no Hiromasa, Japanese nobleman (d. 980)

Deaths

 * January 21 – Liu Zhijun, Chinese general
 * June 12 – Æthelflæd, lady of Mercia (b. c.870)
 * July 6 – William I, duke of Aquitaine (b. 875)
 * September 10 – Baldwin II, Frankish margrave
 * October 1 – Zhou, empress of Former Shu
 * December 23 – Conrad I, Frankish king
 * Gung Ye, king of Hu Goguryeo (Korea)
 * Husayn ibn Hamdan, Abbasid general
 * Lady Ren Neiming, Chinese noblewoman (b. 865)
 * Miyoshi Kiyotsura, Japanese scholar (b. 847)
 * Ottir (the Black), Norse Viking chieftain
 * Tan Quanbo, Chinese warlord (approximate date)
 * Wang Jian, emperor of Former Shu (b. 847)
 * Xu Zhixun, Chinese governor and regent
 * Zhu Jin, Chinese warlord (b. 867)

title: 918


text:
917

Year 917 (CMXVII) was a common year starting on Wednesday (link will display the full calendar) of the Julian calendar.

Byzantine Empire

 * August 20 – Battle of Achelous: A Byzantine expeditionary force (62,000 men) under General Leo Phokas (the Elder) is routed by the Bulgarians at the Achelous River near the fortress of Anchialos (modern Pomorie) on the Black Sea coast. Phokas flees to Mesembria (modern Nesebar) and escapes by boarding a ship. Tsar Simeon I (the Great) becomes de facto ruler of the whole Balkan Peninsula, except the well-protected Byzantine capital of Constantinople and the Peloponnese.
 * Fall – Battle of Katasyrtai: The Bulgarian army under Simeon I marches southwards to Constantinople. Leo Phokas, who survived at Anchelous, gathers the last Byzantine troops to intercept the Bulgarians before they reach the capital. The two armies meet near the village of Katasyrtai, just outside Constantinople. After a surprise night attack, the Byzantines are completely routed from the battlefield.

Europe

 * Bulgarian–Serbian War: Simeon I sends a Bulgarian expeditionary force under Theodore Sigritsa and Marmais to Serbia. The two persuade Petar Gojniković, a Serbian prince who formed an anti-Bulgarian coalition, to meet for a peace agreement. They seize him and send the rebellious prince to the Bulgarian capital of Preslav, where he dies in prison. Simeon replaces Petar with Pavle Branović, a grandson of prince Mutimir, who lives in Preslav. Serbia becomes a puppet state until 921.
 * The Hungarians, after attacking Swabia, sack and burn Basel (modern Switzerland). They invade Lorraine in Lotharingia, destroying Verdun and Moyenmoutier, and many monasteries in Alsace. Duke Arnulf I (the Bad) with Hungarian military aid, reconquers his land from King Conrad I of the East Frankish Kingdom. After this event, Bavaria and Swabia agree to pay tribute to the Hungarians.
 * Battle of Confey: The Norse Vikings under Sigtrygg Caech defeat and kill King Augaire mac Ailella of Leinster in battle. Sigtrygg re-captures Dublin and establishes himself as king, while his kinsman Ragnall ua Ímair returns to England to become King of Northumbria.

Britain

 * Summer – Lady Æthelflæd of Mercia cements an alliance with King Constantine II of Scotland against Norse York. She captures the fortress at Derby (belonging to the Five Boroughs of the Danelaw), while her brother, King Edward the Elder, takes Towcester. Æthelflæd's armies also ravage Brycheiniog (Wales) in revenge for killing the Mercian abbot Ecbryht (see 916).
 * Battle of Tempsford: The English army led by Edward the Elder defeats the Danish Vikings at Tempsford. They storm the fortified burh and kill King Guthrum II of East Anglia, along with the Danish Jarls Toglos and Manna.

Islamic Empire

 * Battle of San Esteban de Gormaz: Umayyad forces under Abi-Abda besiege the repoblación of San Esteban de Gormaz (Northern Spain). King Ordoño II of León (supported by his brother Fruela II of Asturias) allies himself with Sancho I, king of Pamplona, and defeats the Moors. Abi-Abda is captured and executed by decapitation.

Asia

 * September 5 – The Great Yue Kingdom, later renamed Southern Han, is founded by Liu Yan, former governor and military advisor, in Panyu (modern Guangdong) and Guangxi. Liu Yan declares himself emperor, and gives his niece Liu Hua in marriage to Wang Yanjun, a son of his rival Wang Shenzhi (Prince of Min), to cement a relationship between the two states.

Births

 * September 20 – Kyunyeo, Korean poet (d. 973)
 * Ibn Battah al-Ukbari, Arab theologian (d. 997)
 * Kamo no Yasunori, Japanese spiritual advisor (d. 977)
 * Theophylactus, patriarch of Constantinople (d. 956)

Deaths

 * January 21 – Erchanger, East Frankish nobleman
 * August 5 – Euthymius I, patriarch of Constantinople
 * August 20 – Constantine Lips, Byzantine admiral
 * Al-'Abbas ibn 'Amr al-Ghanawi, Abbasid governor
 * Augaire mac Ailella, king of Leinster (Ireland)
 * Frederuna, West Frankish queen (b. 887)
 * Guthrum II, king of East Anglia (England)
 * Hasan al-Utrush, emir of Tabaristan (Iran)
 * Nicholas Picingli, Byzantine general
 * Petar Gojniković, Serbian prince
 * Radboud, archbishop of Utrecht
 * Sindeok, king of Silla (Korea)

title: 917


text:
916

Year 916 (CMXVI) was a leap year starting on Monday (link will display the full calendar) of the Julian calendar.

Europe

 * Sicilian Berbers in Agrigento revolt and depose the independent Emir Ahmed ibn Khorob. They offer Sicily to the Fatimid Caliphate in Ifriqiya (modern Tunisia). Caliph Abdullah al-Mahdi Billah welcomes this turn of events, but refuses to grant the Berber rulers their autonomy. He sends a Fatimid expeditionary force under Abu Said Musa which lands in Sicily and, with some difficulty, takes control of the island. Abdullah al-Mahdi Billah appoints Salam ibn Rashid as the emir of Sicily. Ahmed ibn Khorob is dispatched to Raqqada and executed.

Britain

 * Lady Æthelflæd, daughter of the late King Alfred the Great and the widow of Earl Æthelred of Mercia, sends an army into Brycheiniog to avenge the murder of the Mercian abbot Ecbryht and his companions. They seize and burn the royal fort of King Tewdr of Brycheiniog at Llangorse Lake (Wales), and take the queen and thirty-three others captive.

Asia

 * Abaoji, Khitan ruler and founder of the Liao Dynasty, adopts Chinese court formalities in which he declares himself emperor in the Chinese style and adopts an era name, Taizu of Liao. He names his eldest son Yelü Bei as heir apparent, a first in the history of the Khitan. Abaoji leads a campaign in the west, conquering much of the Mongolian Plains.

Religion

 * Clement of Ohrid, Bulgarian scholar, writer and enlightener of the Slavs, dies. He is regarded as the first bishop of the Bulgarian Orthodox Church and the founder of the first Slavic Literary School. Clement is buried in his monastery, Saint Panteleimon, in Ohrid (modern North Macedonia).

Births

 * June 22 – Sayf al-Dawla, Hamdanid emir (d. 967)
 * Theodoric I, German nobleman (approximate date)
 * Yuan Zong, emperor of Southern Tang (d. 961)

Deaths

 * March 27 – Alduin I, Frankish nobleman
 * May 25 – Flann Sinna, king of Meath
 * Anarawd ap Rhodri, king of Gwynedd
 * Bencion, Frankish nobleman
 * Clement of Ohrid, Bulgarian scholar
 * Ge Congzhou, Chinese general
 * Mór ingen Cearbhaill, queen of Laigin
 * Tighearnach ua Cleirigh, king of Aidhne
 * Theodora, Roman politician
 * Theodoric I, bishop of Paderborn
 * Ziyadat Allah III, Aghlabid emir

title: 916


text:
915

Year 915 (CMXV) was a common year starting on Sunday (link will display the full calendar) of the Julian calendar.

Europe

 * Summer – Battle of Garigliano: The Christian League, personally led by Pope John X, lays siege to Garigliano (a fortified Arab camp in the area of Minturno), which is blockaded from the sea by the Byzantine navy. After three months of siege, plagued by hunger, the Saracens decide to break out of Garigliano and find their way back to Sicily by any means possible. Christian hunting parties fall on the fleeing Arabs, and all are captured and executed.
 * July – The Magyars (Hungarians), led by Zoltán, only son of the late Grand Prince Árpád, attack Swabia, Franconia and Saxony. Small units penetrate as far as Bremen, burning the city.

Religion

 * December 3 – John X crowns the Italian sovereign Berengar I as the Holy Roman Emperor in Rome. Berengar returns to northern Italy, where Friuli is threatened by the Hungarians.

Births

 * January 13 – Al-Hakam II, Umayyad caliph (d. 976)
 * Abu Shakur Balkhi, Persian poet
 * Adalbert I, Frankish nobleman (approximate date)
 * Al-Mutanabbi, Muslim poet (d. 965)
 * Boleslaus I, duke of Bohemia (approximate date)
 * Burchard III, Frankish nobleman (d. 973)
 * Hasdai ibn Shaprut, Jewish diplomat (d. 970)
 * Sunifred II, Frankish nobleman (d. 968)
 * William III, Frankish nobleman (d. 963)

Deaths

 * April 23 – Yang Shihou, Chinese general
 * November 4 – Zhang, Chinese empress (b. 892)
 * Abu Salih Mansur, Samanid governor
 * Adalbert II, Lombard nobleman
 * Al-Nasa'i, Muslim scholar and hadith compiler
 * Bi'dah al-Kabirah, was a songstress, and had been a slave of Arib. She died on 10 July 915. Abu Bakr ibn al-Muhtadi led the funeral prayers. She was also concubine of Abbasid caliph Al-Mamūn (r. 813–833)
 * Bertila of Spoleto, queen of Italy
 * Cutheard, bishop of Lindisfarne
 * Domnall mac Áeda, king of Ailech (Ireland)
 * Gonzalo Fernandez, count of Castile
 * Gregory IV, duke of Naples
 * Jing Hao, Chinese painter
 * Leoluca, Sicilian abbot (approximate date)
 * Li Yanlu, Chinese warlord
 * Ratbod, archbishop of Trier
 * Reginar I, Frankish nobleman
 * Regino of Prüm, German abbot
 * Spytihněv I, duke of Bohemia
 * Sunyer II, Frankish nobleman
 * Tuotilo, German composer (approximate date)

title: 915


text:
914

Year 914 (CMXIV) was a common year starting on Saturday (link will display the full calendar) of the Julian calendar.

Byzantine Empire

 * Spring – Empress Zoe Karbonopsina leads a palace coup at Constantinople and, with the support of the magistros John Eladas, overthrows Patriarch Nicholas Mystikos as regent over her son, Emperor Constantine VII. She allows Nicholas to remain as patriarch, repudiates the title granted to Simeon I of Bulgaria (see 913) and nullifies the marriage plans (with a Bulgarian princess) made for her son by Nicholas.
 * Summer – Byzantine–Bulgarian War: Simeon I, with the Bulgarian army, invades the themes of Thrace and Macedonia. Simultaneously, the Bulgarian troops penetrate into the regions of Dyrrhachium and Thessalonica to the west. Thrace's largest and most important city, Adrianople (modern Turkey), is besieged and captured. However, the Byzantines promptly regain the city in exchange for a huge ransom.

Europe

 * January 19 – King García I dies at Zamora (Spain) after a 4-year reign. He is succeeded by his brother Ordoño II, who becomes king of Galicia and León. Ordoño continues his expansion and settles his court in León.
 * Summer – Saracens from Garigliano establish advanced strongholds in Lazio at Trevi (in the Sabine Hills, near Palestrina) and Sutri. From here, they encroach on the papal cities of Orte, Narni and Nepi with impunity.
 * Viking raiders establish a settlement near Waterford (Ireland) led by Ottir (the Black). The Dublin Vikings are forced to pay tribute to the Irish kings of Meath and Leinster as the price to keeping their independence.
 * In Al-Andalus a drought leads to a terrible famine in the Iberian Peninsula, which continues in 915. In his centralization effort, the Umayyad caliph Abd al-Rahman III, reconquers Seville from the Banu Hajjaj clan.

Britain

 * Vikings devastate the Welsh coast and move up the Severn River. They capture Bishop Cyfeilliog of Ergyng, and he is ransomed by King Edward the Elder. The Vikings are defeated by levies from Hereford and Gloucester.
 * Æthelflæd, Lady of the Mercians, a daughter of King Alfred the Great, builds a burh or fortified dwelling at Warwick and repairs Eddisbury hill fort. She leads the Mercians in their fight against the Danish invaders.

Africa

 * January 24 – The Fatimid general, Hubasa ibn Yusuf of the Kutama Berber tribe, marches out with his troops to invade Egypt. He follows the coastline, and takes possession of the only two towns of any size Syrte and Ajdabiya, without a struggle. The garrisons of the two towns—the westernmost outposts of the Abbasid Caliphate—have already fled.
 * February 6 – Hubasa takes Barqah (modern-day Benghazi), the ancient capital of Cyrenaica. The Abbasid governor withdraws to Egypt, before the superior strength of the Fatimids. With this rich, fertile province fallen into his hands, it provides Hubāsa with 24,000 gold dinars in annual revenues from taxes, as well as 15,000 dinars paid by Christians.
 * July 11 – Al-Qa'im bi-Amr Allah, son of the Fatimid caliph Abdullah al-Mahdi Billah, leaves Raqqada at the head of an army, which is composed of Kutama warriors and the Arab jund (personal guard) in an attempt to conquer Egypt. He sends orders to Hubāsa to wait for him, but driven by ambition Hubāsa is already on his way to Alexandria.
 * August 27 – Hubasa captures Alexandria, after a victorious encounter with Egyptian troops near al-Hanniyya (modern-day El Alamein). The Abbasid governor Takin al-Khazari refuses to surrender and asks for reinforcements, which reach him in September. Shortly after al-Qa'im bi-Amr Allah enters Alexandria, with the rest of his army.
 * December – The Fatimid army under Hubasa leaves Alexandria, followed by al-Qa'im bi-Amr Allah. The Abbasid troops hold Fustat and begin a counter-offensive against the invaders. The Kutama cavalry suffers heavy losses to the Turkish archers.

Arabian Empire

 * January 12 – Ahmad Samani, emir of the Samanid Empire, is murdered (decapitation) while sleeping in his tent at Bukhara (modern Uzbekistan) by some of his slaves. He is succeeded by his 8-year-old son, Nasr II, under the regency of Vizier Abu Abdallah al-Jayhani. The Abbasids try, in vain, to benefit from the turmoil to reconquer Sistan.
 * Sajid invasion of Georgia: A Muslim army under Yusuf ibn Abi'l-Saj campaigns in the Georgian principalities. He makes Tiflis his base for operations, and invades Kakheti. Yusuf proceeds to Kartli, where the fortifications of Uplistsikhe are demolished. He besieges and captures the fortress of Q'ueli, putting its defender Gobron to death.
 * Hasan al-Utrush re-establishes Zaydid rule over the province Tabaristan (Northern Iran), after 14 years of Samanid occupation. He becomes the new ruler (emir) and Zaydid noblemen accept his authority.

Asia

 * February 4 – The Belanjong pillar is established on Bali.
 * In India Emperor Indra III of the Rashtrakuta Dynasty, a grandson of Krishna II, begins his rule (until 929).

Religion

 * March or April – Pope Lando dies at Rome after a reign of less than a year. He is succeeded by John X, archbishop of Ravenna, as the 122nd pope of the Catholic Church.

Births

 * Al-Muti, Abbasid caliph (d. 974)
 * Chen Hongjin, Chinese warlord (d. 985)
 * Li Conghou, emperor of Later Tang (d. 934)
 * Luitgarde, duchess consort of Normandy (d. 978)
 * Shi Chonggui, emperor of Later Jin (d. 974)
 * Valtoke Gormsson, Viking nobleman (d. 985)

Deaths

 * January 12 – Ahmad Samani, Samanid emir
 * January 19 – García I, king of León (Spain)
 * February 12 – Li, empress of Yan
 * December 31 – Ibn Hawshab, founder of the Isma'ili community in Yemen
 * Abu Sa'id al-Jannabi, founder of Bahrain (or 913)
 * Aedh mac Ailell, abbot of Clonfert
 * Bárid mac Oitir, Viking leader
 * Gobron, Georgian military commander
 * Idalguer, Frankish bishop
 * John Eladas, Byzantine regent
 * Krishna II, Indian ruler
 * Lando, pope of the Catholic Church
 * Li Jihui, Chinese governor
 * Liu Rengong, Chinese warlord
 * Liu Shouguang, Chinese warlord
 * Mu'nis al-Fahl, Abbasid general
 * Plegmund, archbishop of Canterbury (or 923)

title: 914


text:
912

Year 912 (CMXII) was a leap year starting on Wednesday (link will display the full calendar) of the Julian calendar.

Byzantine Empire

 * May 11 – Emperor Leo VI (the Wise) dies after a 26-year reign in which he has completed the Byzantine code of laws (Basilika). He is succeeded by his brother Alexander III as emperor (basileus) alongside Leo's 6-year-old son Constantine VII. Alexander becomes de facto ruler of the Byzantine Empire and expels Empress Zoe Karbonopsina, the mother of Constantine, from the palace and exiles her to a nunnery.

Europe

 * German dukes Henry the Fowler of Saxony and Arnulf I (the Bad) of Bavaria claim themselves to be sovereign princes, not recognizing the authority of their overlord, King Conrad I of the East Frankish Kingdom, as he is not a Carolingian. Duke Erchanger II of Swabia and Conrad's brother, Duke Eberhard III of Franconia, support the Conradines.
 * Orso II Participazio becomes the doge of Venice. He sends his son Pietro to Constantinople in order to re-establish the relationship with Alexander III.
 * King Ordoño II of Galicia continues his expansion of the Christian polity. He sacks the cities of Mérida and Évora.

Britain

 * Lady Æthelflæd expands her policy by building defensive burghs at Shrewsbury and Bridgnorth. The fortifications are needed to protect Mercia against plundering Vikings from the Danelaw (Danish territory in England).

Arabian Empire

 * October 16 – Abd al-Rahman III succeeds his grandfather Abdullah ibn Muhammad (after his execution) and becomes emir of Córdoba (Al-Andalus).
 * The second rebellion in two years, of the Kutama tribesmen against the Fatimid Caliphate, occurs.

China

 * July 18 – Emperor Taizu (Zhu Wen) is murdered in the imperial palace at Kaifeng by his eldest living son Zhu Yougui after a 5-year reign. He succeeds his father as the ruler of Later Liang.

Religion

 * Euthymius I is deposed as Patriarch of Constantinople, and Nicholas Mystikos is restored.

Births

 * November 23 – Otto I, emperor of the Holy Roman Empire (d. 973)
 * Alberic II, princeps and duke of Spoleto (d. 954)
 * Frederick I, duke of Upper Lorraine (approximate date)
 * Hyejong, king of Goryeo (Korea) (d. 945)
 * Ma Xichong, governor and ruler of Chu (d. 951)
 * Minamoto no Mitsunaka, Japanese nobleman and samurai (d. 997)
 * Nakatsukasa, Japanese waka poet (d. 991)
 * Nikephoros II, emperor of the Byzantine Empire (d. 969)
 * Pelagius of Córdoba, Christian martyr (d. 926)
 * Ryōgen, Japanese monk and abbot (d. 985)
 * Willa of Tuscany, queen consort of Italy (or 911)
 * Xue Juzheng, Chinese scholar-official and historian (d. 981)

Deaths

 * May 11 – Leo VI, emperor of the Byzantine Empire (b. 866)
 * May 25 – Xue Yiju, chancellor of Later Liang
 * July 18 – Zhu Wen, emperor of Later Liang (b. 852)
 * August 15 – Han Jian, Chinese warlord (b. 855)
 * October 15 – Abdullah ibn Muhammad, Muslim emir (b. 844)
 * October 25 – Rudolph I, king of Burgundy (b. 859)
 * November 30 – Otto I, duke of Saxony
 * Ahmad ibn Yusuf, Muslim mathematician (b. 835)
 * Guanxiu, Chinese Buddhist monk and poet (b. 832)
 * Hermenegildo Gutiérrez, Galician nobleman
 * Hyogong, king of Silla (Korea) (b. 885)
 * Ibn Khordadbeh, Persian geographer
 * Notker the Stammerer, Benedictine monk
 * Oleg of Novgorod, Varangian prince
 * Pietro Tribuno, doge of Venice (approximate date)
 * Qusta ibn Luqa, Syrian Melkite physician (b. 820)
 * Rudalt, Breton nobleman (approximate date)
 * Smbat I, king of Armenia (approximate date)
 * Wilferth, bishop of Lichfield (approximate date)
 * Zhang Ce, chancellor of Later Liang
 * Zhu Youwen, prince of Later Liang

title: 912