E Burgos-Parra

N Bukin

S Sani

A I Figueroa

G Beutier

M Dupraz

S Chung

P D Ürrenfeld

Q Tuan Le

S M Mohseni

A Houshang

S A Cavill

R J Hicken

J ˚akerman

G Van Der Laan

F Y Ogrin

Investigation of magnetic droplet solitons using x-ray holography with extended references

A dissipative magnetic soliton, or magnetic droplet, is a structure that has been predicted to exist within a thin magnetic layer when non-linearity is balanced by dispersion, and a driving force counteracts the inherent damping of the spin precession. Such a soliton can be formed beneath a nano-contact (NC) that delivers a large spin-polarized current density into a magnetic layer with perpendicular magnetic anisotropy. Although the existence of droplets has been confirmed from electrical measurements and by micromagnetic simulations, only a few attempts have been made to directly observe the magnetic landscape that sustains these structures, and then only for a restricted set of experimental parameter values. In this work we use and x-ray holography technique HERALDO, to image the magnetic structure of the [Co/Ni]x4 multilayer within a NC orthogonal pseudo spin-valve, for different range of magnetic fields and injected electric currents. The magnetic configuration imaged at -33 mA and 0.3 T for devices with 90nm NC diameter reveals a structure that is electrically and spatially consistent with a droplet soliton. We also report the magnetisation configurations observed at lower DC currents in the presence of fields (0-50 mT), where it is expected to observe regimes of the unstable droplet formation..

Introduction

A typical spin valve structure is a trilayer film consisting of a magnetic pinned layer (PL), a non-magnetic spacer layer, and a magnetic free layer (FL). The FL is magnetically softer than the PL and therefore more able to change its magnetisation state when small magnetics fields are applied. The main attraction of spin valves is that a relative change in the orientation of the magnetisation in the FL and PL produces large changes in the resistance due the giant magnetoresistance effect, making it ideal for sensing very small magnetic fields [START_REF] Smith | Magnetic field sensing utilizing GMR materials[END_REF] . However, when large electrical current densities (≥ 10 7 A/m 2 ) are applied, these devices can also behave as spin transfer oscillators (STOs) [START_REF] Tsoi | Excitation of a Magnetic Multilayer by an Electric Current[END_REF] . In a STO a DC electrical current may be converted to a microwave signal when the angular momentum carried by a spin polarized current exerts a torque on the magnetisation of the FL. As was first shown by Slonczewski 3,[START_REF] Slonczewski | Excitation of spin waves by an electric current[END_REF] this spin transfer torque (STT) can then lead either to the suppression of the damping in the FL and therefore a persistent precession of the magnetisation vector, or to a total reversal of the magnetisation. In order to obtain the large current density needed, point-contacts are often used to inject the current into the multilayer sample stack. The size of such point contacts ranges from tens to hundreds of nanometres, in what is known as a nano-contact spin transfer oscillator (NC-STO). In a NC-STO the NC is positioned on the top of the FL. In the orthogonal NC-STO [START_REF] Rippard | Spin-transfer dynamics in spin valves with out-of-plane magnetized CoNi free layers[END_REF][START_REF] Mohseni | High frequency operation of a spin-torque oscillator at low field[END_REF] studied here, the magnetisations of the PL and FL are almost completely orthogonal to each other in the remanent state. While the PL magnetisation lies in plane, the FL has perpendicular magnetic anisotropy so that its magnetisation points out of the plane. The STT associated with the injected DC current excites sustained and stable oscillations of the magnetisation in an area localized beneath the NC. Due to its high tunability, high quality factor, and the ease by which it can be combined with conventional semiconductor technology, the NC-STO promises to be a corner stone for the development of future technologies such as magnetic memories, microwave nano-emitters, and neuromorphic computing among others [START_REF] Chen | Spin-Torque and Spin-Hall Nano-Oscillators[END_REF] .

The NC-STO provides an ideal environment in which to nucleate a dissipative magnetic soliton, which we refer to as a droplet from here on. A droplet is a localized excitation sustained by STT, with magnetisation opposite of the rest of the free layer, for which the amplitude of precession decays exponentially towards its boundaries [START_REF] Hoefer | Theory for a dissipative droplet soliton excited by a spin torque nanocontact[END_REF] . Similar to theoretically predicted conservative solitons [START_REF] Ivanov | Bound states of a large number of magnons in a ferromagnet with a single-ion anisotropy[END_REF] , magnetic droplets can be sustained by balancing exchange with anisotropy energies and through the opposing effects of the damping and STT.

In 2013, an experimental study led by J. Åkerman 10 showed that a magnetic droplet can be created and maintained within a NC-STO. Further investigations based on transport measurements and micro-magnetic simulations of these systems [START_REF] Macià | Stable Magnetic Droplet Solitons in Spin Transfer Nanocontacts[END_REF][START_REF] Iacocca | Confined dissipative droplet solitons in spin-valve nanowires with perpendicular magnetic anisotropy[END_REF][START_REF] Mohseni | Magnetic droplet solitons in orthogonal nano-contact spin torque oscillators[END_REF][START_REF] Lendínez | Observation of droplet soliton drift resonances in a spin-transfer-torque nanocontact to a ferromagnetic thin film[END_REF][START_REF] Chung | Magnetic droplet solitons in orthogonal spin valves[END_REF][START_REF] Wills | Deterministic drift instability and stochastic thermal perturbations of magnetic dissipative droplet solitons[END_REF][START_REF] Chung | Magnetic droplet nucleation boundary in orthogonal spin-torque nano-oscillators[END_REF][START_REF] Xiao | Merging droplets in double nanocontact spin torque oscillators[END_REF][START_REF] Xiao | Parametric autoexcitation of magnetic droplet soliton perimeter modes[END_REF][START_REF] Slobodianiuk | Eigenmodes of two-dimensional conservative droplet soliton[END_REF] revealed a rich dynamic structure, promising a range of applications in microwave technology. However, few experimental techniques allow the magnetisation of these structures to be imaged with adequate resolution (≤ 32 nm) while the necessary external magnetic field is applied. Therefore only a few direct images have been obtained [START_REF] Backes | Direct Observation of a Localized Magnetic Soliton in a Spin-Transfer Nanocontact[END_REF][START_REF] Bonetti | Direct observation and imaging of a spin-wave soliton with $p-$like symmetry[END_REF][START_REF] Chung | Direct observation of magnetic droplet solitons in all-perpendicular spin torque nano-oscillators[END_REF] of magnetic solitons confined with NC-STO devices, so that the different dynamic regimes of the system remain largely unexplored.

In the present work we report the first direct measurement of the magnetic structures in the FL of an orthogonal NC-STO for different combinations of external magnetic field and applied DC current. In order to obtain magnetic information from the sample we combined holography with extended reference autocorrelation by linear differential operator (HERALDO) [START_REF] Guizar-Sicairos | Holography with extended reference by autocorrelation linear differential operation[END_REF][START_REF] Guizar-Sicairos | Direct image reconstruction from a Fourier intensity pattern using HERALDO[END_REF] with the magnetic contrast provided by X-ray magnetic circular dichrosim (XMCD). The latter, being element-specific, allows probing different layers separately. Our implementation of magnetic HERALDO allows to access both the perpendicular and parallel components of the magnetization [START_REF] Duckworth | Magnetic imaging by x-ray holography using extended references[END_REF][START_REF] Duckworth | Holographic imaging of interlayer coupling in Co/Pt/NiFe[END_REF][START_REF] Burgos Parra | Holographic Magnetic Imaging of Single-Layer Nanocontact Spin-Transfer Oscillators[END_REF][START_REF] Bukin | Time-resolved imaging of magnetic vortex dynamics using holography with extended reference autocorrelation by linear differential operator[END_REF] . Here we work in perpendicular X-ray incidence geometry, which provides the perpendicular component of magnetization [START_REF] Duckworth | Holographic imaging of interlayer coupling in Co/Pt/NiFe[END_REF] A particular advantage in this case is also that the magnetisation can be imaged beneath the electrical contacts. Studies of the magnetisation both around and underneath the nano-contact are crucial for understanding the importance of the effects produced by Oersted field in the nucleation and subsequent drift of the droplets. In this study the sample fabrication process does not allow the exact location of the NC to be known, however as we show below, the area of the NC can be identified by the unique structure of the domains nucleated by the Oersted field of the DC current. Imaging the magnetic structure at different values of the magnetic field and electric current shows a significant variation in the domain structure around the NC. We demonstrate that at certain conditions, correlated with the intensity spectra observed in transport measurements, a localised magnetic structure with opposite polarisation to surrounding magnetisation can be observed. We suggest that this visualisation is in direct agreement with magnetic droplet formation at the field and current values expected from electrical measurements.

Results

Electrical transport measurements and time-averaged imaging of the dynamics of the out-of-plane magnetisation within an orthogonal NC-STO were performed for samples with NC diameter of 90 nm and 110 nm for different combinations of applied magnetic field and DC injected current. Figure 1(a) shows a schematic of the multi-layered device and the intended position of the NC within the sample. The fabrication, electrical characterization, and HERALDO measurements carried out on these samples are described in detail in the Methods section.

Transport measurements

Figure 2 shows the power spectral density (PSD) with a ∼-0.4 T external magnetic field applied to a device with 90 nm nano-contact diameter. Microwave emission occurs at a frequency of 15 ± 0.1 GHz from -27 to -30.5 mA, which then drops to 8.2 GHz, as the emitted power increases by a factor of about 5. Furthermore, emission at a lower frequency of a few hundreds of MHz is also detected once the threshold current for the nucleation of the droplet is reached (not shown here). This is in agreement with previous results where the appearance of lower frequency (hundreds of MHz) dynamics, simultaneous drop in frequency and an increase in emitted power of the principal microwave mode occurred as a droplet was formed [START_REF] Lendínez | Observation of droplet soliton drift resonances in a spin-transfer-torque nanocontact to a ferromagnetic thin film[END_REF][START_REF] Mohseni | Temperature-dependent interlayer coupling in Ni/Co perpendicular pseudo-spin-valve structures[END_REF] . Considering also the stability map presented in reference [START_REF] Lendínez | Observation of droplet soliton drift resonances in a spin-transfer-torque nanocontact to a ferromagnetic thin film[END_REF] , the device with a 90 nm NC diameter is a good candidate for imaging current-induced magnetisation dynamics in a range of magnetic fields. The device with 110 nm NC diameter also revealed similar electrical features but the magnetic field needed to image a magnetic droplet lies outside of the range that could be achieved within theused experimental set-up, which was 0.35 T.

Holographic measurements

Figure1(b) shows a SEM image of a standard sample used in HERALDO measurements. In this case, the device is built on one side of a Si 3 N 4 membrane while the other side of the membrane is covered by a Au layer of ∼ 600 nm thickness. A reference slit and an aperture are milled into the Au layer using a focused ion beam, which together generate the diffraction pattern produced by cohenrent x-rays passing through and captured by the CCD camera, as shown in the schematic of the set-up in Figure 1(c).

The magnetic domain configurations found within both samples at zero current are the characteristic maze-like domain pattern well described in the literature for samples with perpendicular magnetic anisotropy (PM(a). Figure 3 shows four magnetic domain patterns corresponding to four different points on the hysteresis curve. It is evident how the the balance between magnetic domains of opposite polarisation changes as the magnetic field is increased. Even though the total thickness of the Ni layer is only ∼ 3.2 nm, and imaged behind a 500 nm copper contact, the magnetic contrast is remarkably good.

An out-of-plane external field of 0.05 T was first applied to magnetically saturate the Co/Ni multilayer. DC currents ranging from -10 to -35 mA were then injected into the nano-contact at zero external magnetic field. It was observed that a single magnetic domain formed with magnetisation opposite to that of the rest of the sample. It is not possible to locate the exact position of the NC by optical or electronic means after the device is finished, but the location of the NC, and hence the maximum Oersted field generated by the current, is expected to be within the region where the reverse domains are nucleated. For the sample with 90 nm (110 nm) NC diameter this reverse domain first appears at -10 mA (-15 mA). Figure 4(a) shows how this domain grows in size as the amplitude of the DC current is increased. Due to the size of the magnetic domain formed, we suggest that its growth is driven by the Oersted field generated by the current passing through the NC. This field is large enough to locally modify the magnetisation as shown in Figure 4. This effect was also seen for positive current values. In contrast, the STT is not expected to contribute to domain formation outside of the NC region.

Afterwards, to magnetically saturate the FL again, an out-of-plane field of 0.05 T was applied and then removed. A constant current of -33 mA was then applied to the sample with a 110 nm NC diameter at zero field. Small fields ranging from 20 to 50 mT were applied in the same out-of-plane direction to explore the interplay between the current and the external applied field. Under these conditions, a small C-shaped domain is observed at 20 mT that we infer to be nucleated from the NC. As the magnetic field was increased, the magnetic domain collapsed to a small region that was observed through all field steps. The same experiment performed instead with a current of -25 mA injected into the 110 nm contact (Fig. 4(b), bottom panel ) showed a similar domain to that observed before at 25 mT and -33 mA, but in this case at 20 mT. This reverse domain vanished when the magnetic field was increased to 30 mT, such that the sample appeared to be in a state of uniform magnetic saturation (Figure 4(b), bottom panel for 40 and 50 mT).

Due to the available size and orientation of the magnetic field, all the former measurements were made on devices with a PL magnetized mostly in plane and a FL magnetically saturated out of plane. It was shown above that, for a NC of 110 nm diameter, the Oersted field generated by a current of -33 mA nucleated a reverse domain at zero field within a saturated sample, as shown in Figure 4. When an external field is applied, this effect is still visible but the size of the domain nucleated by the current is smaller than for the zero field case. As the external field is increased, it begins to dominate and the effect of the Oersted field is only seen at shorter distances from the nano-contact. The interplay between the external field and the Oersted field produced by the DC current modifies the local magnetic free energy, and therefore the reverse domain might still appear even for fields where the FL would otherwise be saturated, as can be seen in Figure 4(b).

In order to work within the magnetic field range where transport measurements showed the nucleation of a droplet, an external field of -0.3 T was applied perpendicular to the plane of the sample with a 90 nm diameter NC. A localized reversal of the magnetisation was observed at -35 mA injected current at the location inferred for the NC (Figure 5 (b). This structure was not present in the images taken at smaller current values, while the value of -35 mA is in good agreement with that expected (∼ -33 m(a), from theory and transport measurements, for nucleation of a droplet in a 90 nm NC subject to a field of 0.3 T. In order to confirm the correlation between the structure observed and the nano-contact position, a yellow dashed line denoting the edge of a domain formed in the vicinity of the nano-contact at -10 mA without external field (Figure 5 We notice that the observed magnetic structure does not have the symmetrical circular shape expected of a droplet. It has been reported that canted magnetisation of the PL as well as the influence of the Oersted field [START_REF] Hoefer | Theory for a dissipative droplet soliton excited by a spin torque nanocontact[END_REF][START_REF] Wills | Deterministic drift instability and stochastic thermal perturbations of magnetic dissipative droplet solitons[END_REF][START_REF] Mohseni | Temperature-dependent interlayer coupling in Ni/Co perpendicular pseudo-spin-valve structures[END_REF] might affect the stability of the droplet so that it may extend beyond the region immediately beneath the NC or even drift away from it completely. It is possible that Figure 5(c) and(d) are showing the time averaged trajectory of the droplet as it deviates from the centre of the NC, but further measurements performed at different values of current and external field are needed to confirm this conjecture.

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Conclusions.

The results shown in this paper are consistent with the local modification of the magnetisation around and beneath the NC due to the DC current. At zero field, and due to the size of the domains, we suggest that the modification of the magnetisation is due to the Oersted field produced by the DC current. When a small magnetic field is applied perpendicular to the sample plane, the interplay between the external field and the Oersted field modifies the size of the domains and erases them altogether when the external field becomes dominant, as can be seen in Figure 4. Finally, when the external field and the DC current are set to 0.3 T and -35 mA respectively, the magnetic contrast shows a magnetic structure with reversed magnetisation which we suggest is a droplet soliton. Since the exact position of the NC is unknown it is not possible to state unequivocally that the observed magnetic structure lies beneath the NC. However, the size of the structure, its position relative to the domains induced at other DC current values, and the correlation with separate electrical measurements, suggest that the nucleation of a droplet soliton has occurred.

Methods

Sample fabrication

50×250 µm 2 rectangular patterns were exposed and developed on standard 4-inch thermally oxidized Si wafers using an optical lithography technique. A pseudo-spin-valve structure of composition Co (6 nm)/Cu (6 nm)/Co (0.2 nm)[Ni (0.8 nm)/Co (0.3 nm)]×4, was then deposited by confocal magnetron sputtering onto a Ta (4 nm)/Cu (11 nm)/Ta (4 nm) seed layer and capped with a Cu (2 nm)/Pd (2 nm) bilayer. The lift-off process was completed by the removal of the remaining photo resist, and followed by the deposition of a 30 nm-thick SiO 2 dielectric film by chemical vapour deposition. Nano-pores of different size were formed within the SiO 2 using electron beam lithography and highly selective reactive ion etching. The device fabrication was completed by the deposition of a 400 nm Cu/100 nm Au top electrode using a combination of lift-off lithography and sputtering.

Device Characterization

In order to electrically characterize the NC-STO, the sample was mounted in a custom probe station and a DC bias current from a Keithley 6221 current source was passed through the NC and between the signal and ground lines of the surrounding coplanar waveguide (CPW) structure. The current was swept from 0 to -40mA under a fixed external field of 0.3 T at room temperature. In order to decouple and amplify the a.c. signal from the device, a bias-T and a 2 -18 GHz AtlanTec(AS7265) amplifier were used respectively . The amplified a.c signal was recorded by an Agilent E448A spectrum analyser.

HERALDO measurements.

The measurements presented in this paper were taken on beamlines I06 and I10 of the Diamond Light Source using a continuous filling pattern (∼300 mA). To perform x-ray magnetic circular dichroism measurements on the samples, left and right-circularly polarised x-rays were applied with a photon energy of 851.1 eV coinciding with the Ni L 3 absorption edge. The interference pattern of the direct and diffracted x-rays for each polarisation was recorded on a CCD camera positioned behind a beam stop, that blocked the direct non-diffracted beam, at a distance of 60 cm from the sample, resulting in a minimum spatial resolution of 32 nm. To obtain holographic images the sample had a reference slit that was isolated from the imaged area by a distance of twice the aperture diameter but remained within the x-ray tranverse coherence length (∼25 µm). Holograms recorded for left and right polarisations were subtracted and then processed using directional derivatives and Fourier transformed in order to obtain the real-space image.

  (a) is superimposed upon Figure 5(b). Figures 5(c)and (d) are a close-up of the region enclosed within the red square in Figure 5(b), where the black dashed line represents the possible position of a NC of 90 nm diameter.

Figure 1 .

 1 Figure 1. (a) Schematic of a section of the 16×8 µm 2 mesa layer containing the nano-contact orthogonal pseudo spin-valve, where the Co/Ni multilayer acts as the free layer and the Co layer as the pinned layer. In this work devices with nano-contacs of 90 and 110 nm diameter were studied. The red arrows indicate the magnetic anisotropy of the magnetic layers. (b) Au layer covering one side of the Si 3 N 4membrane. An aperture of 5 µm diameter and a reference slit of 6 µm in length and ∼ 60 nm width were milled using a focused ion beam. The pseudo spin-valve is located on the opposite side of the Si 3 N 4 membrane (c) Schematic set up for HERALDO measurements with an external magnetic field. The sample is positioned in the middle of a portable octupole magnet system (POMS) and the coherent x-rays from the synchrotron source pass through the aperture and the reference slit. The resulting diffraction pattern is captured by a CCD camera at a distance ∼ 60 cm behind the sample, at the end of the beam-line. The coplanar waveguide (CPW) supplies the DC current that passes through the magnetic layers and generates the STT required to form the droplet soliton.

Figure 2 .

 2 Figure 2.Power spectral density (PSD) is represented by the colour scale for an orthogonal pseudo spin-valve with a nano-contact of 90 nm diameter with a magnetic field of 0.4 T applied perpendicular to the sample plane. When the threshold current for the nucleation of the droplet is reached ( ∼-30.5 mA), a sudden drop in in the emission frequency of ∼ 8 GHz occurs in addition to a dramatic increase of the emitted power, as is shown in (a) and (b).The additional structure is an artifact due to standing waves in one or more of the cables between the microwave components in the measurement chain.

7 / 10 Figure 3 .

 7103 Figure 3. Magnetic domains formed on Ni within the free layer on the orthogonal pseudo spin-valve. The sample was saturated in theŷ direction before an external magnetic field was applied in the + ŷ direction (defined in inset of Figure1(c))with a magnitude of (a) 15 mT, (b) 20 mT, (c) 27.5 mT, and (d) 35 mT. The brighter (darker) regions correspond to magnetisation with a component in the ŷ (-ŷ) direction. Bright regions overcome dark regions as expected as the magnetic field saturates the sample magnetisation in the + ŷ direction.

Figure 4 . 10 Figure 5 .

 4105 Figure 4. Magnetic structures observed for different fields and applied current values. The samples were saturated by an out-of-plane field of 0.05 T that was then reduced to zero. (a) The darker regions are the magnetic domains created by passing a DC current of -10, -15, -25, -30 and -35 mA through NCs of 90 (upper panel) and 110 nm diameter (lower panel) with zero external magnetic field. The nucleation of the domain is followed by small increments in its size as the amplitude of the DC current is increased. (b) The samples were magnetically saturated at 0.05 T and the field was then removed. The DC current injected through the 110 nm NC was fixed at values of -33 (upper panel) and -25 mA (lower panel) and HERALDO measurements were made with fields of 20, 25, 40 and 50 mT applied perpendicular to the sample plane in the direction of the initial saturation, parallel to the direction of the x-rays. The domain size decreases as the external magnetic field is increased, vanishing when the external magnetic field is sufficient to overcome the influence of the Oersted field produced by the current.

10/10

Acknowledgements (not compulsory)

We acknowledge financial support from the Engineering and Physical Sciences Research Council (EPSRC) of the United Kingdom, via the EPSRC Centre for Doctoral Training in Metamaterials (Grant No. EP/L015331/1), the CONICyT-Becas Chile, the ERC Starting Grant 307144 "Mustang", the Swedish Foundation for Strategic Research (SSF) Successful Research Leaders program, the Swedish Research Council (VR), the Göran Gustafsson foundation, and the Knut and Alice Wallenberg Foundation.

Author contributions statement

Additional information

Competing financial interests

The author(s) declare no competing financial interests.


Influences between logic programming and proof theory

by Dale Miller, Inria-Saclay, January 1, 2018 The earliest and most popular use of logic in computer science views computation as something that happens independent of logic: e.g., registers change, tokens move in a Petri net, messages are buffered and retrieved, and a tape head advances along a tape. Logics (often modal or temporal logics) are used to make statements about such computations. Model checkers and Hoare proof systems employ this computation-as-model approach.

Early in the 20th century, some logicians invented various computational systems, such as Turing machines, Church's λ-calculus, and Post correspondence systems, which were shown to all compute the same set of recursive functions. With the introduction of high-level programming languages, such LISP, Pascal, Ada, and C, it was clear that any number of ad hoc computation systems could be designed to compute these same functions. Eventually, the large number of different programming languages were classified via the four paradigms of imperative, object-oriented, functional, and logic programming. The latter two can be viewed as an attempt to make less ad hoc computational systems by relying on aspects of symbolic logic. Unlike most programming languages, symbolic logic is a formal language that has well-defined semantics and which has been studied using model theory [START_REF] Tarski | Contributions to the theory of models I,II[END_REF], category theory [START_REF] Lambek | Introduction to Higher Order Categorical Logic[END_REF][START_REF] Lawvere | Functorial semantics of algebraic theories[END_REF], recursion theory [START_REF] Gödel | On formally undecidable propositions of the principia mathematica and related systems[END_REF][START_REF] Kleene | A theory of positive integers in formal logic. part I[END_REF], and proof theory [START_REF] Gentzen | Investigations into logical deduction[END_REF][START_REF] Girard | Linear logic[END_REF]. The computation-as-deduction approach to programming languages takes as its computational elements objects from logic, namely, terms, formulas, and proofs. This approach has the potential to allow the direct application of logic's rich metatheory to proving properties of specific programs and entire programming languages.

The influence of proof theory on logic programming

The first thing that proof theory has offered to the logic programming paradigm is a clean and straightforward means to differentiate itself from functional programming. From the proof theory perspective, functional programs correspond to proofs (usually in natural deduction), and computation corresponds to proof normalization: that is, programs correspond to non-normal proofs and computation is seen as a series of normalization steps (using either β-convergence or cut-elimination). This programs-as-proof correspondence is known as the Curry-Howard isomorphism [START_REF] Heine | Lectures on the Curry-Howard Isomorphism[END_REF]. In contrast, proof search is a good charactorization of computation in logic programming. Here, quantificational formulas are used to encode both programs and goals (think about the rules and queries in database theory). Sequents are used to encode the state of a computation and (cut-free) proofs are used to encode computation traces: changes in sequents model the dynamics of computation. Although cut-elimination is not part of computation, it can be used to reason about computation. Also. the prooftheoretic notions of inference rule, schematic variable, proof checking, and proof search are directly implementable. The proof-normalization and the proof-search styles of computational specification remain distinct even in light of numerous recent developments in proof theory: for example, linear logic, game semantics, and higher-order quantification have all served to illustrate differences and not similarities between these two styles.

In the early days of logic programming, say from 1972-1985, the entire logic programming paradigm was described using just one particular logic: that of the first-order Horn theories in classical logic [START_REF] Kowalski | Logic programming in the 1970s[END_REF]. Also, the process of proof search was paradoxically described as refutation (using the resolution rule). Gentzen invented the sequent calculus for the explicit purpose of unifying proofs in classical and intuitionistic logic. Girard showed that the sequent calculus can naturally account for linear logic proofs as well [START_REF] Miller | Uniform proofs as a foundation for logic programming[END_REF][START_REF] Miller | Overview of linear logic programming[END_REF]. As a result of this unity, the sequent calculus provided logic programming a natural framework in which proof-search could be described for much richer logics (first-order and higher-order versions of classical, intuitionistic, and linear logics) than that underlying Prolog.

Another feature of the sequent calculus is its support for abstraction: that is, it provides mechanism for allowing some aspects of a program's specification to be hidden while other aspects are made explicit. The cut-elimination theorem can be used to match abstractions from actual implementations. In programming language terminology, such abstractions provide logic programming with modularity, abstract datatypes, and higher-order programming. The use of abstractions can significantly aid in establishing formal properties of programs.

The influence of logic programming on proof theory

Logic programming has also influenced proof theory. To explain Prolog's operational behaviour, resolution was restricted to SLD-resolution [START_REF] Apt | Contributions to the theory of logic programming[END_REF]. Similarly, sequent calculus proofs were restricted to goal-directed (or uniform) proofs in order to provide a general framework for logic programming. Such goal-directed programs were structured with alternating phases of inference rules: one phase reduced the goal formula (using right-introduction rules), and one phase performed backchaining steps (using left-introduction rules) [START_REF] Miller | A logic programming language with lambda-abstraction, function variables, and simple unification[END_REF][START_REF] Miller | Uniform proofs as a foundation for logic programming[END_REF]. The resulting sequent calculus framework provided justifications for the design of logic programming languages within both classical and intuitionistic logics. After Girard's introduction of linear logic [START_REF] Girard | Linear logic[END_REF] in 1987, Andreoli defined focused linear logic proofs [START_REF] Andreoli | Logic programming with focusing proofs in linear logic[END_REF] in which cut-free proofs were restricted to alternating phases but this time, such proofs applied to all of linear logic. The completeness of focused proofs provided a complete analysis of which subsets of linear logic made good logic programming languages [START_REF] Miller | Overview of linear logic programming[END_REF]. Several subsequent efforts have been made to provide flexible, focused proof systems for classical and intuitionistic logic all of which are captured by the LKF and LJF focused proofs system [START_REF] Liang | Focusing and polarization in linear, intuitionistic, and classical logics[END_REF].

Logic programming makes heavy use of term structures and quantification. Thus a comprehensive analysis of the proof theory of logic programs forced proof theory to look beyond its usual concentration on propositional connectives and to look hard at quantification. For example, Skolemization is seldom a natural and efficient means for addressing quantifier alternation in a proof theory setting. Instead, the sequent calculus supports the concept of mobility of binders [START_REF] Miller | Bindings, mobility of bindings, and the ∇-quantifier[END_REF] in which term-level bindings are capable of moving to formula-level quantifiers which are then capable of moving to proof-level eigenvariables. Furthermore, the proof-theoretic treatment of inductive reasoning applied to logic programming specifications has lead to the appearance of the ∇-quantifier that is capable of capturing generic quantification [START_REF] Miller | A proof theory for generic judgments[END_REF].


Raimundo Gonçalves De Oliveira-Júnior

Christiane Adrielly

Alvez Ferraz

Michelle Cruz Pontes

Noelly Bastos Cavalcante

Edigênia Cavalcante Da

Cruz Araújoa

Ana Paula De Oliveira

Laurent Picot

Larissa Araújo Rolim

Jackson Roberto

Guedes Da

Silva Almeida

Christiane Adrielly Alvez

Alves Ferraz

Edigênia Cavalcante Da Cruz Araújo

Jackson R G S Almeida

Antibacterial activity of terpenoids isolated from Cnidoscolus quercifolius Pohl (Euphorbiaceae), a Brazilian medicinal plant from Caatinga biome

Keywords: Cnidoscolus, medicinal plant, triterpene, diterpene, antibacterial activity

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

The use of antibiotics is widely described in many clinical situations, including in the control of infections during invasive surgeries, in cancer chemotherapy and in the treatment of immune-compromised patients [START_REF] Hughes | Discovery and preclinical development of new antibiotics[END_REF]. In recent years, antibiotic resistance has become a serious health problem, leading to the emergence of microorganisms resistant to conventional chemotherapy [START_REF] Srivastava | Antimicrobial resistance (AMR) and plant-derived antimicrobials (PDAms) as an alternative drug line to control infections[END_REF].

In this sense, infectious diseases caused by antibiotic resistant microorganisms have been frequently reported [START_REF] Ventola | The Antibiotic Resistance Crisis, Part 1: Causes and Threats[END_REF][START_REF] Blair | Molecular mechanisms of antibiotic resistance[END_REF]. For this reason, the search for new antimicrobial molecules from natural products remains an effective alternative [START_REF] Chandra | Antimicrobial Resistance and the Alternative Resources with Special Emphasis on Plant-Based Antimicrobials-A Review[END_REF][START_REF] Brown | New natural products as new leads for antibacterial drug discovery[END_REF][START_REF] Moloney | Natural Products as a Source for Novel Antibiotics[END_REF].

Euphorbiaceae is a pantropical family containing approximately 300 genera and 7000 species, including trees, shrubs and herbs, of which 70 genera and 1000 species occur in Brazil [START_REF] Souza | Botânica Sistemática: guia ilustrado para identificação das famílias de Angiospermas da flora brasileira[END_REF].

The neotropical genus Cnidoscolus Pohl is represented by 70 species [START_REF] Webster | Systematics of the Euphorbiaceae[END_REF][START_REF] Gordillo | Los géneros de la familia Euphorbiaceae en México[END_REF]. In Brazil, there are 42 Cnidoscolus species distributed in different geographical areas, such as Cerrado, Atlantic Forest, Amazon and Caatinga biome [START_REF] Melo | O gênero Cnidoscolus Pohl (Crotonoideae-Euphorbiaceae) no estado de Pernambuco, Brasil[END_REF][START_REF] Wurdack | Malpighiales phylogenetics: Gaining ground on one of the most recalcitrant clades in the angiosperm tree of life[END_REF]. Hoffm.) is a Brazilian medicinal plant from Caatinga biome, popularly known as "favela", "faveleira" and "urtiga-branca". In folk medicine, its leaves and stem barks are used to treat injury, urinary tract infections and inflammatory processes [START_REF] Albuquerque | Medicinal plants of the Caatinga (semi-arid) vegetation of NE Brazil: a quantitative approach[END_REF]. Previous pharmacological investigations evaluated the antinociceptive [START_REF] Gomes | Antinociceptive activity of the ethanolic extract from barks and leaves of Cnidoscolus quercifolius (Euphorbiaceae) in mice[END_REF], anti-inflammatory [START_REF] Gomes | Phytochemical screening and anti-inflammatory activity of Cnidoscolus quercifolius (Euphorbiaceae) in mice[END_REF], antioxidant [START_REF] Peixoto-Sobrinho | Phenolic content and antioxidant capacity of four Cnidoscolus species (Euphorbiaceae) used as ethnopharmacologicals in Caatinga, Brazil[END_REF][START_REF] Paredes | Screening of Bioactivities and Toxicity of Cnidoscolus quercifolius Pohl[END_REF], antiproliferative [START_REF] Paula | Constituintes Químicos e Atividade Citotóxica de Cnidoscolus phyllacanthus[END_REF][START_REF] Peixoto-Sobrinho | Antiproliferative activity of species of the genus Cnidoscolus against HT-29, Hep-2 and NCI-H292 cells[END_REF] and antibacterial [START_REF] Paredes | Screening of Bioactivities and Toxicity of Cnidoscolus quercifolius Pohl[END_REF][START_REF] Peixoto-Sobrinho | Phytochemical screening and antibacterial activity of four Cnidoscolus species (Euphorbiaceae) against standard strains and clinical isolates[END_REF] effects of crude extracts from C. quercifolius.

Cnidoscolus quercifolius

From a phytochemical point of view, lupane-type triterpenes and bis-nor-diterpenes have been reported in C. quercifolius [START_REF] Lemos | Terpenoids from Cnidoscolus phyllacanthus Pax et Hoff[END_REF]. New tricyclic benzocyclohepten diterpenes, called favelins, were isolated from stem barks extracts [START_REF] Ohta | Absolute stereochemistry of benzocycloheptenone derivatives from Cnidoscolus phyllacanthus[END_REF]. New cyclopropane and cyclobutene tetracyclic derivatives, such as favelanone and neofavelanone, respectively, were also described in previous phytochemical studies [START_REF] Endo | Favelanone, a novel tetracyclic clyclopropane derivative from the Brazilian plant, Cnidoscolus phyllacanthus[END_REF][START_REF] Endo | Neofavelanone, a novel tetracyclic cyclobutene derivative from the Brazilian plant, Cnidoscolus phyllacanthus[END_REF]. Apparently, these diterpenes occur exclusively in C. quercifolius.

Although C. quercifolius extracts have been investigated for their antibacterial potential, there are no reports on the antibacterial activity of compounds isolated from this species.

Considering the popular use of this plant for the treatment of infections, the present study describes the antibacterial activity of terpenoids isolated from the stem barks of C. quercifolius against pathogenic strains.

Materials and methods

Plant material

Extraction and isolation

The dried and pulverized stem barks (534 g) were extracted with hexane (2.0 L, four times), followed by methanol (2.0 L, four times), yielding 8.7 and 18.5 g of hexane and methanol extracts (Hex-Cq and MeOH-Cq, respectively) after removal of the solvents under vacuum. An aliquot of Hex-Cq (7.0 g) was fractionated by chromatography column, using silica gel 60 (Sigma-Aldrich ® , 230-240 mesh) as stationary phase. Hexane, chloroform (CHCl 3 ), ethyl acetate (AcOEt) and methanol (MeOH) were used as eluents, in increasing order of polarity. In total, 42 fractions (125 ml each) were collected and reunited in 13 different groups (groups A-M), after TLC analysis.

Group D (eluted with hexane/CHCl 3 2.5:7.5, v/v) showed the formation of white crystals (635 mg) soluble in chloroform, which was subsequently identified as a mixture of two compounds (1 and 2).

Group F (eluted with CHCl 3 ) was fractionated by preparative TLC, using hexane/AcOEt (9:1, v/v) as eluent, leading to the isolation of compound 3 (13.7 mg, yellow crystals soluble in chloroform).

Spectroscopic analysis

NMR spectra ( 1 H, 13 C, DEPT-135, COSY, HSQC and HMBC) were recorded on a Bruker Ascend ® (400 MHz for 1 H and 100 MHz for 13 C) spectrometer, at 25 °C and with CDCl 3 as solvent (internal standard 0.05% TMS, Tedia ® , Brazil). Chemical shifts are given in ppm values (δ) and coupling constants (J) in Hz. In addition, retention factor (R f ) was calculated for each compound, through TLC analysis, using the same eluent (hexane/AcOEt, 9.5:0.5, v/v). TLC plates were visualized in UV chamber (254 and 365 nm) and, subsequently, revealed with 1% sulfuric vanillin solution.

Antibacterial activity 2.4.1. Bacteria strains assay

Reference bacterial strains were obtained from National Institute of Quality Control in Health (INCQS/FIOCRUZ, Brazil). The pathogenic microorganisms used were Enterococcus faecalis (ATCC ® 19433), Escherichia coli (ATCC ® 25922), Klebsiella pneumoniae (ATCC ® 13883), Serratia marcescens (ATCC ® 13880) and Staphylococcus aureus (ATCC ® 25923).

Determination of minimum inhibitory concentration (MIC)

Antibacterial activity was evaluated by the microdilution method, as recommended by National Committee for Clinical Laboratory Standards [START_REF]Metodologia dos testes de sensibilidade a agentes antimicrobianos por diluição para bactérias de crescimento aeróbico: norma aprovada[END_REF]. Stock solutions of extracts (Hex-Cq and MeOH-Cq, 20 mg.ml -1 ) and isolated compounds (1/2 and 3, 2 mg.ml -1 ) were prepared in 2% DMSO (v/v). Subsequently, 100 µl of this solution was added to microplates containing 100 µl of Müller-Hinton broth, in order to obtain final concentrations of 10 -0.16 mg.ml -1 (for extracts) and 1 -0.008 mg.ml -1 (for isolated compounds). Gentamicin was used as positive control (final concentrations of 1.6 -0.012 mg.ml -1 ). Wells were reserved for sterility control of the broth (negative control). Finally, an inoculum containing 5 x 10 5 CFU.ml -1 (0.5 in McFarland scale) was added to each well and microplates were maintained under aerobic conditions (37 °C, during 18-24 hours). After incubation, 10 μl of 2% 2,3,5-triphenyl-tetrazolium (CTT) solution (v/v) were added to each well to detect the color change of the CTT (colorless) to red, reflecting the bacterial metabolism active. MIC was defined as the lowest concentration of extracts or compounds that visibly inhibited the bacterial growth in three independent experiments.

Determination of minimum bactericidal concentration (MBC)

To determine MBC, an aliquot (10 µl) was withdrawn from each well containing extracts or isolated compounds and transferred to Petri dishes containing agar Müller-Hinton. Plates were incubated for 24 h in the same conditions previously described. The absence of bacterial colony for a given concentration indicates that it was able to kill 99.9% or more of bacterial inoculum used.

MBC was defined as the lowest concentration of extracts or compounds that visibly inhibited the bacterial colony production in three independent experiments.

Results

Structural characterization of isolated compounds

TLC analysis revealed a good degree of purity for the isolated compounds. Compound 3 showed fluorescence at 365 nm, suggesting the presence of an aromatic ring in its structure. In addition, TLC analysis using sulfuric vanillin revealed the presence of purple spots, indicating that these compounds were terpenes (Fig. 1).

After careful NMR (1D and 2D) analysis, as well as comparison with spectral data reported in the literature [START_REF] Paula | Constituintes Químicos e Atividade Citotóxica de Cnidoscolus phyllacanthus[END_REF][START_REF] Lemos | Terpenoids from Cnidoscolus phyllacanthus Pax et Hoff[END_REF], we identified compounds 1 and 2 as lupeol-3β-O-cinnamate and lupeol-3β-O-dihydrocinnamate, respectively. The presence of a lupeol unit in both molecules was recognized by chemical shifts and multiplicity of all 1 H and 13 C NMR signals. 1 H NMR spectra showed two broad singlet signals for two ethylenic protons (H-29, δ 4.70 and 4.58), and two singlet signal attributed to methyl groups (H-30, δ 1.69 for compound 1, and δ 1.68 for compound 2), compatible for lupeol units. 13 C NMR spectra displayed signals at δ 172.8 and 166.9, indicating the presence of an ester function for both compounds. Two signals for carbinolic protons (H-3) at δ 4.63 (dd, J = 10.4 and 5.2 Hz) and 4.48 (dd, J = 10.4 and 5.6 Hz) suggested that the site of esterification was at C-3 (A ring of the basic skeleton of lupeol). 1 H NMR spectra also indicated a cinnamyl group for compound 1 through the signals at δ 7.28-7.53 (m, H-2'/6', H-3'/5' and H-4'), 7.67 (d, J = 16 Hz, H-7') and 6.45 (d, J = 16 Hz, H-8'). A 7',8'-dihydrocinnamyl group corresponding to the major component 2 was indicated by the signals δ 2.96 (t, H-7') and 2.63 (t, H-8') [START_REF] Lemos | Terpenoids from Cnidoscolus phyllacanthus Pax et Hoff[END_REF]. The intensities (revealed integration) of the signals at δ 7.67 (H-7' for compound 1) and 2.96 (H-7' for compound 2) were used to estimate the relative proportions of them in the mixture: 25% of 1 (approximately 159 mg) and 75% of 2 (approximately 476 mg). 1 H NMR spectra for compound 3 displayed two singlets at δ 7.62 (H-1) and 6.59 (H-4), attributed to two protons para-related, and another singlet signal at 6.29 (H-11), attributed to a vinyl hydrogen. 13 C NMR spectra showed a signal at δ 201.5, attributed to a ketone group, suggesting the presence of an acetophenone unit. 1 H NMR spectra also revealed signals for two methyl groups attached to a quarternary sp 3 carbon [δ 0.75 (s, H-16) and 1.12 (s, H-17)], and one methyl group attached to a sp 2 carbon [δ 2.18 (s, H-18)]. The identification of a methoxy group [δ 3.87 (s, H-19)] led to the molecular formula C 18 H 21 O for the basic skeleton, compatible for a bis-nor-diterpene.

Homonuclear and heteronuclear shift correlations ( 1 H-1 H COSY and 13 C-1 H HMBC, respectively) confirmed the substitution pattern of the aromatic ring and all 1 H and 13 C assignments. These data allowed the unambiguous structural characterization of compound 3 as the bis-nor-diterpene phyllacanthone [START_REF] Lemos | Terpenoids from Cnidoscolus phyllacanthus Pax et Hoff[END_REF]. All the spectra data obtained for each compound are shown in the supplementary material.

Antibacterial activity

The MIC values determined for the samples are presented in Table 1. Cq-Hex and Cq-MeOH displayed weak antibacterial activity. However, compounds 1/2 and 3 showed MIC values ten and twenty times lower (0.5 and 0.25 mg.ml -1 , respectively) than those verified for both extracts (5.0 mg.ml -1 ) against all bacteria strains. Furthermore, the isolated compounds demonstrated MBC values between 0.25 and 0.5 mg.ml -1 , suggesting that these molecules also exert a bactericidal effect (Table 2). In this case, compound 3 was more effective than gentamicin against E. faecalis and E. coli.

Table 1. Minimum inhibitory concentration (MIC, mg.ml -1 ) of extracts (Hex-Cq and MeOH-Cq) and isolated compounds (1/2 and 3) from C. quercifolius.

Discussion

Compounds 1 and 2 have previously been described in C. quercifolius [START_REF] Paula | Constituintes Químicos e Atividade Citotóxica de Cnidoscolus phyllacanthus[END_REF][START_REF] Lemos | Terpenoids from Cnidoscolus phyllacanthus Pax et Hoff[END_REF]. In fact, these compounds are frequently obtained as a mixture, due to its structural similarity. This mixture has also been reported in C. vitifolius [START_REF] Brum | Acyl lupeols from Cnidoscolus vitifolius[END_REF]. Other lupane-type triterpenes were reported in C.

quercifolius, such as lupeol [START_REF] Lemos | Terpenoids from Cnidoscolus phyllacanthus Pax et Hoff[END_REF] and lupeol-3β-O-nanoate [START_REF] Paula | Constituintes Químicos e Atividade Citotóxica de Cnidoscolus phyllacanthus[END_REF]. Compound 3 is a bis-nor-diterpene commonly found in C. quercifolius [START_REF] Paula | Constituintes Químicos e Atividade Citotóxica de Cnidoscolus phyllacanthus[END_REF][START_REF] Lemos | Terpenoids from Cnidoscolus phyllacanthus Pax et Hoff[END_REF][START_REF] Endo | Favelines, novel tricyclic benzocycloheptenes with cytotoxic activities from Brazilian plant, Cnidoscolus phyllacanthus[END_REF]. Also known as faveline-methyl-ether, phyllacanthone (3) was one of the first isolated substances from this plant. To date, there are no reports of other species that present this chemical constituent in its composition, being considered of exclusive occurrence in C. quercifolius. A recent study demonstrated the cytotoxic potential of phyllacanthone (3) against human pro-myelocytic leukemia (HL-60), human lung carcinoma (NCI-H292) and human breast adenocarcinoma (MCF-7) cells [START_REF] Paula | Constituintes Químicos e Atividade Citotóxica de Cnidoscolus phyllacanthus[END_REF]. However, these compounds have not been sufficiently investigated for their biological activities.

In this paper, we evaluated the antibacterial activity of extracts (Hex-Cq and MeOH-Cq) and isolated compounds (1/2 and 3) against pathogenic bacteria strains. In general, compounds 1/2 and 3 were effective against all the microorganisms used. Interestingly, compound 3 was more effective than the standard drug (gentamicin) against E. faecalis and E. coli strains. Although it is present in the human gastrointestinal microbiota, E. faecalis is considered an opportunistic pathogen associated with hospital-acquired wound, bloodstream, and urinary tract infections [START_REF] Tien | Enterococcus faecalis Promotes Innate Immune Suppression and Polymicrobial Catheter-Associated Urinary Tract Infection[END_REF]. Similarly, E. coli is also among the most frequent pathogens found in urinary tract infections. These microorganisms are able to persist in the host for long periods through formation of biofilm that prevents phagocytosis by immune system cells [START_REF] Castro | Escherichia coli and Enterococcus faecalis are able to incorporate and enhance a pre-formed Gardnerella vaginalis biofilm[END_REF]. In addition, both microorganisms have developed multidrug resistance mechanisms in recent years, making it difficult to control associated infections [START_REF] Miller | Mechanisms of antibiotic resistance in enterococci[END_REF][START_REF] Rasheed | Antimicrobial drug resistance in strains of Escherichia coli isolated from food sources[END_REF]. In this context, the search for bioactive molecules that can treat E. faecalis and E. coli infections remains a current challenge.

Terpenoids are admittedly used in the treatment of bacterial infections. Due to their lipophilic character, terpenoids can easily interact with the bacterial wall, interfering with the biosynthesis of its components. Furthermore, these compounds penetrate the bacterial cell and may also interfere with protein synthesis and DNA replication and repair mechanisms. In recent years, terpenoids have shown ability to enhance the effect of conventional antibacterial drugs. This has been an extremely useful strategy in controlling antibiotic resistance. These molecules have modulated the effect of antibacterial agents either by promoting direct cytotoxicity or by increasing their residence time in the cell, ensuring greater pharmacological activity at lower concentrations [START_REF] Zacchino | Plant phenolics and terpenoids as adjuvants of antibacterial and antifungal drugs[END_REF]. In this sense, compounds isolated from C. quercifolius may play an important role not only in the control of bacterial infections, especially those caused by E. faecalis and E. coli, but also in the control of multidrug resistance mechanisms. In vivo studies should be performed to determine the toxicity of these molecules, as well as their pharmacokinetic properties, associated or not with other antibacterial agents.

Peixoto-Sobrinho et al. [START_REF] Peixoto-Sobrinho | Phytochemical screening and antibacterial activity of four Cnidoscolus species (Euphorbiaceae) against standard strains and clinical isolates[END_REF] have reported the antibacterial activity of four Cnidoscolus quercifolius) using the agar diffusion method. In this study, C. quercifolius extracts were the most bioactive, showing a relevant bacteriostatic effect against S. aureus. However, this was a preliminary study conducted with crude extracts. In the present paper, we report the isolation of antibacterial compounds from C. quercifolius extracts for the first time. We believe that these compounds are responsible, at least in part, for the antibacterial potential observed for the extracts.

These findings suggest that this plant may be considered a promising source of new antibacterial agents and further studies should be performed in order to characterize their mode of action.

Conclusions

In this phytochemical investigation, we report the isolation and characterization of three

  Pohl (syn.: Cnidoscolus phyllacanthus (Mull. Arg.) Pax & L.

Fig. 1 .

 1 Fig. 1. Chemical structures (A) and analytical TLC plates (eluent: hexane-ethyl acetate, 95:5) of

*

  Absence of bacterial growth in all tested concentrations (n=3).

  species (C. infestus Pax and K. Hoffman, C. pubescens Pohl, C. urens (L.) Arthur and C.

  terpenoids from the stem barks of C. quercifolius: lupeol-3β-O-cinnamate (1), lupeol-3β-Odihydrocinnamate and phyllacanthone (3). The isolated substances showed significant antibacterial activity, mainly compound 3. These results indicate that C. quercifolius has antibacterial potential, supporting its use in folk medicine in the treatment of urinary tract infections.

  Stem barks of C. quercifolius were collected in the city of Petrolina (coordinates 09° 24' 40.97" S and 40° 32' 49.19" W), state of Pernambuco, Brazil, in February 2015. A voucher specimen (n° 19202) has been deposited at the Herbário do Vale do São Francisco (HVASF), of the Universidade Federal do Vale do São Francisco (UNIVASF).

Table 2 .

 2 Minimum bactericidal concentration (MBC, mg.ml -1 ) of extracts (Hex-Cq and MeOH-Cq) and isolated compounds (1/2 and 3) from C. quercifolius.

	Microorganism			MBC (mg.ml -1 )
		Cq-Hex	Cq-MeOH	1/2	3	Gentamicin
	E. faecalis	> 10	> 10	0.5	0.25	0.40
	E. coli	> 10	> 10	0.5	0.25	0.40
	K. pneumoniae	> 10	> 10	0.5	0.25	0.05
	S. marcescens	> 10	> 10	0.5	0.25	0.025
	S. aureus	> 10	> 10	0.5	0.25	0.025
	> 10 indicates bacterial growth in all tested concentrations (n=3).

Acknowledgment

The authors thank FACEPE (Fundação de Amparo à Ciência e Tecnologia do Estado de Pernambuco) and CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) for the financial support.

Conflict of interests

All authors declare that there is no conflict of interest for the publication of this manuscript.