Oleg I Utesov

Sébastien Burdin

Patrick Rosa

Mathieu Gonidec

Lorenzo Poggini

S V Andreev

Electric-field control of

Keywords:

published or not. The documents may come

I. INTRODUCTION

Spin crossover molecular compounds (SCO) have been intensively discussed during the past decades in connexion with data recording and sensing 1,2 . These systems switch between a low (LS) and a high-spin (HS) state as the temperature is increased. In some cases the conversion has a hysteretic behaviour characterized by heating and cooling characteristic temperatures, T ↑ c and T ↓ c , respectively. These temperatures can be easily made on the order of the room temperature. By applying temporary heating (e.g., a laser pulse) one can switch an initially LS state to a HS state. The latter will be preserved until cooling the device below the operational temperature.

At the microscopic level, the conversion is due to switching between two electronic states of molecules characterized by different occupation of e g and t 2g subsets of 3d metal orbitals. The LS state arises from the closedshell (t 6 2g ) and the HS state from the open-shell (t 4 2g e 2 g ) configurations 1 . These differ by magnetic, optical and structural properties and can be altered by pressure, temperature and light irradiation 3-7 which makes SCO promising for new functional materials. SCO complexes consist of transition metal ions surrounded by organic ligands. One may play with the SCO thermodynamics by carefully designing the ligands. At the spin crossover, the enthalpy remains essentially constant with temperature and the SCO phenomenon is driven by entropy. For the HS state the electronic contribution to entropy is higher than that of the LS state. As the SCO needs to be accompanied by a structural change of the complex resulting in weaker bonds in the HS state, the vibrational contribution to entropy for the latter is also higher than for the LS state. This situation leads to a thermal conversion from the LS state to HS state upon increasing temperature 8,9 .

A comprehensive theoretical description of the SCO physics, as demonstrated in numerous works [10][11][12][13][14][15][16][17][18] , can be done in terms of the Ising-like model:

Ĥ = ∆ N i=1 Ŝi z -J i,j Ŝi z Ŝj z , (1)
with the relevant parameters being the energy splittings between the LS and HS states 2∆ , and the coupling constant J > 0 describing the interaction between the nearest neighbours ("cooperativity effect"). Due to degeneracy of the open-shell t 4 2g e 2 g electronic configuration the HS state has larger statistical weight and thus stabilizes at sufficiently large temperatures.

The situation is less understood for thin films of SCO molecules. The studies of SCO films with thicknesses ranging from 5 to 1000 nm conclude that the thermally driven spin transition in such systems is similar to that of the bulk 8,[19][20][21][22][23][24][25][26][27] . However, when the thickness is decreased down to sub-monolayer or a few monolayers in coverage, the SCO behavior seems to be modified by the interaction with the substrate [28][29][30][31][32][33][34][35] . In particular, some of us have recently demonstated that a thick film of [Fe(H 2 B(pz) 2 ) 2 (bipy)] deposited by thermal sublimation on an organic ferroelectric substrate maintains the SCO behaviour 36 , whereas for thinner films (under 15 nm) the SCO behavior was controlled by the substrate polarization [36][37][38] .

On the general grounds, one may expect the substrate to modify the splitting ∆ between the spin states of the molecules. First, the splittings of molecules which constitute the boundary layer are clearly affected by microscopic Van-der-Waals interaction with the surface of the substrate. This effect seems to be responsible for the recent experimental observations 34,36,37 . Second, macroscopic electric field E produced by the ferroelectric substrate should modify the splittings in all layers according to the formula

∆(E) = ∆ 0 + 1 2 α,β=x,y,z υ αβ E α E β , (2)
where we assume the field being uniform over the sample, ∆ 0 is the bare splitting at E = 0 and υ αβ is some phenomenological symmetric tensor to be defined from the experiment. Existence of the coupling of the type (2) may be argued as follows. Due to the electrostriction the electric field would modify the pressure P acting on the system (or, alternatively, the system volume V ). The change in the pressure P can be written as

δP = 1 2 α,β ∂(α αβ V ) ∂V T E α E β , (3)
where α αβ is the polarizability of the sample. [START_REF] Landau | Electrodynamics of Continuous Media[END_REF] This change of the pressure, on the other hand, would modify the spin splittings due to an inverse "magnetostriction" effect,

∆ = ∆ 0 + ∂∆ ∂P δP =0 δP. (4)
What we call "magnetostriction" in the context of the model ( 1) is a phenomenological way to account for the fact that the average metal-ligand bond length is longer in the HS state than in the LS state [START_REF] Gallois | [END_REF]41 . For instance, the characteristic temperature of the crossover T 1/2 was shown to grow linearly with the pressure. 42,43 As we shall see, this experimental fact justifies the assumption (4) a posteriori and, therefore, supports existence of the relation (2). It is also worth to point out, that a relation of the type (2) has previously been obtained by microscopic considerations assuming dipolar coupling of SCO complexes to the electric field 44 . The calculated variation of T 1/2 in the applied electric field was in qualitative agreement with the experiment. Implementation of the coupling (2) would build a bridge between the field of spin transition polymers and ferroelectricity, and pave a way toward both temperature-and voltage-controllable organic memory. A crucial first step on this way is a theoretical analysis of implication of the hypothesis of a tunable ∆ on the physics of spin transitions as described by the Hamiltonian (1). This analysis is presented in our paper. We start by formulating the theoretical model we use in the present study. In Sec. II, under certain assumptions, we obtain the effective Hamiltonian of the system in the form (1). For the bulk problem its mean-field solution is given in Sec. III. The already established physics of thermal spin transitions and crossovers is presented in Subsec. III A. The main result of this subsection is the existence of the critical value of the ratio ∆/J above which the first-order thermal transition (hysteresis) turns to a smooth crossover. We obtain a simple analytical expression for this ratio and confirm it by numerics. In Subsec. III B we show that isothermal variation of ∆ can also lead to a hysteresis. Arguments, analogous to those presented in Subsec. III A, when applied to the spin transition induced by variation of ∆, yield the maximum and minimum temperatures at which the hysteresis under an electric field would be possible.

In Sec. IV we turn to the discussion of layered systems. We show that, for sufficiently weak coupling between the layers, it should be possible to observe a staircase in the fraction γ of molecules in the HS state as a function of ∆. We discuss such multistability in terms of a phase diagram of ∆ versus the ratio of inter-to intra-layer couplings for two layers. For sufficiently large inter-layer coupling the transition occurs in both layers simultaneously. This switching can be performed either as in bulk (by varying either temperature or ∆) or by variation of the energy splitting ∆ only in the boundary layer (due to, e.g., interaction with the surface of the substrate). This result of our theoretical model holds qualitatively for few layers (thin films). In contrast, in films with large number of layers, variation of ∆ in the boundary layer has no impact on γ. The situation here is similar to the bulk, in agreement with the experiment 36,37 .

II. THEORETICAL MODEL AND METHODS

Our starting point is the following phenomenological Hamiltonian

Ĥ = i Ĥi + i,j Vij (5)
FIG. 1. Switching of the spin state of a stack of n molecular thin films [Fe(H2B(pz)2)2bipy] (green rectangle) by the polarization of a ferroelectric substrate (blue rectangle). Each molecule can be in two possible states, "low spin" (LS) and "high spin" (HS) characterized by zero and non-zero spin projection on the growth axis, respectively. To describe the behavior of the system we use the model shown in the gray rectangle on the right (see the text). In the bottom panel we show the fraction of HS molecules γ as a function of the HS/LS splitting at the boundary layer calculated for two different temperatures T . At low T one has a first order transition (hysteresis) which turns to a crossover at high T . We used the model (32) with n = 2, σ = 0.5 and the following set of parameters: (i) t = 0.5, δ2 = 0.2 and (ii) t = 1, δ2 = 1.

where

Ĥi = E i 0 |0 i 0| i + E i 1 α=1..g |1 α i 1 α | i (6) and Vij = σ1,σ2,σ3,σ4 J σ1,σ2,σ3,σ4,i,j |σ 1 i ⊗ |σ 2 j σ 3 | j ⊗ σ 4 | i .
(7) The Hamiltonian ( 5) is a general model of an assembly of two-level systems with interaction. We attribute |0 i to the low-spin (LS) and |1 α i to the one of the g-fold degenerate high-spin (HS) states of the i-th molecule, respectively. By introducing the pseudo-spin operators

Ŝz = α |1 α 1 α | -|0 0|, Ŝ+ = Ŝx + i Ŝy = α |1 α 0|, Ŝ-= Ŝx -i Ŝy = α |0 1 α |, (8)
we rewrite the Hamiltonian (5) in the useful form

Ĥ = i ∆ i Ŝi z - i,j µ,ν=(+,-,z) Ŝi µ M µν Ŝj ν (9)
where we have introduced ∆ i = (E i 1 -E i 0 )/2 for the molecular energy splitting. The crucial assumption now is to take the second term in (9)

in the block form Vij = -(M zz Ŝi z Ŝj z +M +- Ŝi + Ŝj -+M -+ Ŝi - Ŝj + )
and assume the interaction between the nearest neighbors only. The problem is thus projected onto an effective Heisenberg XXZ model. The first term in the above equation describes the static interaction between the spins, whereas inclusion of the second term would allow to study the dynamical response to perturbations. In this work we shall examine the case M zz = J > 0 (ferromagnetic-like coupling) and use the static mean-field approximation < Ŝi z >= m and < Ŝi ± >= 0. Thus, the model is reduced to an effective Ising model (1) with "magnetic field" ∆.

To take into account the structure of the system (the layers are arranged on the top of each other along the growth direction) we shall further introduce J for the interlayer coupling and J ⊥ to describe interaction between the layers. The quantities z ⊥ and z will be the corresponding coordination numbers (see Fig. 1).

After the model Hamiltonian has been constructed, all the relevant thermodynamic quantities can be obtained starting from the partition function

Z = T r(e -β Ĥ ), (10)
where β = 1/k B T is the inverse temperature of the system. The free energy reads

F = -k B T ln(Z) (11)
and, considered as a function of the average magnetization m, can be used to describe transitions between different states, as we show below.

FIG. 2. Ways to switch the spin state of the system. In a certain range of parameters (see the main text) the transitions are characterized by hysteresis and can be accomplished by varying either the temperature or the energy splitting between the LS and HS states.

III. SINGLE LAYER

It is instructive to discuss first the simplest case of a homogeneous single-layer system (which is, of course, physically equivalent to the bulk). The diagram in Fig. 2 shows possible ways to switch between the spin states. Below we explain and discuss this scheme in more detail.

A. Thermal hysteresis

The Hamiltonian of the system reads

Ĥ1 = ∆ N i=1 Ŝi z - i,j J Ŝi z Ŝj z , (12)
where the summation in the second term is over the nearest neighbors and N is the total number of molecules in the layer. By introducing the coordination number z (the number of the nearest neighbors) and using the meanfield approximation we rewrite the above Hamiltonian in the form

Ĥ1 = N i=1 (∆ -Jzm) Ŝi z + 1 2 N i=1 Jzm 2 , ( 13
)
where Jzm is an effective Weiss field. The "magnetization" m is related to the fraction γ of the HS molecules by

γ = m + 1 2 . ( 14
)
Using Eq. ( 10), we calculate the free energy

F N = Jzm 2 2 -k B T ln ge -(∆-Jzm)/k B T + e (∆-Jzm)/k B T .
(15) Here g is the degeneracy of the HS state, discussed above.

It is convenient to introduce the dimensionless parameters t = k B T /Jz and δ = ∆/Jz. The dimensionless free energy per molecule then reads

f (m) = m 2 2 -t ln ge -(δ-m)/t + e (δ-m)/t . ( 16
)
Considered as a function of m the free energy can have either two minima separated by a barrier or one minimum. The latter situation is always realized at sufficiently large temperatures t. At moderate temperatures there can be two physically distinct scenarios depending on the value of δ: first order transition with hysteresis and a crossover. In order to describe these two scenarios analytically we first consider the low-temperature limit t 1 and δ ∼ t, where simple analytical expressions can be derived. Their region of validity will be discussed below. Near the m = 1 point one can neglect the second exponent in the logarithm in Eq. ( 16) and obtain the following form for the free energy :

f (m) = m 2 2 -m -t ln g + δ, (17)
which evidently yields a local minimum m = 1. Analogously, near m = -1,

f (m) = m 2 2 + m -δ, ( 18
)
and there is a local minimum at m = -1. There is also a maximum at m ≈ 0. So, the properties of the system are defined by three free energies

f (+1) ≈ -1/2 -t ln g + δ, f (-1) ≈ -1/2 -δ, f (0) = -t ln ge -δ/t + e δ/t . (19)
Obviously, at very low temperature the system will be in the LS state. From the condition f (+1) = f (-1) we can determine the temperature at which the ground state becomes doubly degenerate (we denote it t 1/2 since in the crossover regime at this temperature one has γ = 1/2). Simple calculation yields

t 1/2 = 2δ ln g . ( 20
)
Thus obtained formula is consistent with the well-known expression T 1/2 = ∆H/∆S, where ∆H is the enthalpy and ∆S is the entropy of the spin conversion 1, 45 . cases should be distinguished. The barrier height h(t) at the temperature t 1/2 can either exceed or be lower than this temperature. In the first case (upper panel of Fig. 3) the thermal fluctuations at t = t 1/2 are insufficient to induce a transition from LS to HS state. One has to attain some larger temperature t ↑ at which h(t ↑ ) = t ↑ in order to observe the transition. On the other hand, when decreasing t, an inverse transition from HS to LS state apparently cannot take place at t ↑ , so that one should define some t ↓ such that t ↓ < t ↑ , and a natural way to do it is to let t ↓ ≡ t 1/2 . In this case one may speak about a first-order like transition featuring hysteresis. Using equations above we can find the critical value δ c which separates the two different regimes: which solution gives

h(t 1/2 ) = f (0) -f (-1)| t=t 1/2 = t 1/2 , (21)
δ c = ln g 4(1 + ln 2) . (22)
For numerical estimates we take g = 5, which corresponds to the e g /t 2g splitting in the octahedral symmetry. One should bear in mind, however, that this value may be modified when taking into account molecular vibrations 18 and structural disorder 46 . We find δ c ≈ 0.24. For δ < 0.24 the barrier height h(t 1/2 ) > t 1/2 and one has a first order thermal spin transition characterized by a hysteresis loop. Indeed, after simple calculations one can derive equation for t ↑ :

δ = - t ↑ 2 ln e 1 2t ↑ -1 -1 g , (23)
which yields t ↑ > t 1/2 at δ < δ c . We check the formulas ( 20), ( 22) and ( 23) numerically and find that they hold with excellent accuracy in the whole range of the relevant values of δ δ c . For δ > δ c the situation is very different. Now one has h(t 1/2 ) < t 1/2 (lower panel of Fig. 3), which means that the first order transition is replaced by a smooth crossover from LS to HS and vice versa along the same curve. The two distinct regimes are shown on the left (δ < 0.24) and right (δ > 0.24) sides of Fig. (4).

At δ ≈ 0.75 the barrier at t = t 1/2 ≈ 0.93 disappears, which means that the potential relief almost flattens and the two minima of f (m) merge. Below, we will use the value t 1/2 = 0.93 to quantify the situation where in the equation

m = tanh m t 1/2 , (24)
FIG. 4. Dependence of the barrier height h(t 1/2 ) (dashed line) and the characteristic temperature t 1/2 (open squares and solid line) on the parameter δ. The critical value δ = 0.24 is defined as a point at which h(t 1/2 ) = t 1/2 . For δ < 0.24 one has a regime of hysteresis (left area, see the text). For δ > 0.24 there is a smooth crossover between LS and HS states and vice versa along the same curve. For the t 1/2 dependence the open squares are used for the numerical result, whereas the solid line is the analytic expression (20). Note an excellent agreement between the two.

[which is the exact equation for extrema of the free energy ( 16) at t 1/2 (20)] the distinct roots at m ≈ ±1 disappear.

To close this subsection we notice that the obtained linear growth of t 1/2 with δ corroborates a posteriori the assumption (4) of the linear dependence of ∆ on the pressure. Indeed, linear growth of T 1/2 with the applied pressure has been previously reported in the experimental studies. 42,43

B. Isothermal switching

The above analysis may be put another way by fixing the temperature and considering variations of the parameter δ around

δ 1/2 ≡ t ln g 2 . ( 25
)
Here, again, the subscript 1/2 signifies an equal distribution of the molecules over the spin states in the crossover regime. The crossover occurs at high temperatures falling onto the right side of the diagram in Fig. 4 (previously classified as the thermal crossover region) and is characterized by smooth transition from the LS to the HS state as one decreases δ. This is sketched on the left side of Fig. 5. At low temperatures one has an isothermal hysteresis. This is illustrated on the right side of Fig. 5. Here, two well-defined characteristic values of δ exist, which we FIG. 5. Evolution of the free energy landscape in the course of isothermal crossover (on the left) and hysteresis (on the right) induced by variation of the energy splitting δ. Black double arrows indicate the temperature scale to be compared with the height of the potential barrier separating the two minima. Note that this temperature is fixed for each column comprising three graphs. However, the scale on each graph has been adjusted to better present the free energy profile, so the length of the arrows has been adjusted accordingly.

denote δ ↑ and δ ↓ . The point δ = δ ↑ corresponds to the situation where the global minimum of the free energy is the HS state and the thermal fluctuations (characterized by the magnitude of t) are sufficiently strong to jump into this state from the LS minimum. The point δ = δ ↓ corresponds to the transition from the HS to the LS state. By using Eqs. (20) and (23) one may obtain

δ ↑ -δ 1/2 = - δ 1/2 ln g ln e ln g/4δ 1/2 -1 -1 (26)
and

δ ↓ -δ 1/2 = δ 1/2 ln g ln e ln g/4δ 1/2 -1 -1 . ( 27
)
By requiring δ ↑ > 0, one obtains

δ 1/2 > ln g 4[ln (g + 1) + 1] ≈ 0.14. ( 28
)
Using Eq. ( 25) it can be rewritten as the following restriction on the temperature:

t > t min = 1 2[ln (g + 1) + 1] ≈ 0.18. ( 29
)
At lower temperatures even at δ = 0 the barrier remains too high for the transition from the LS to HS state could take place. In general, the higher the temperature, the smaller variation of δ around δ 1/2 is required to perform the switching.

The isothermal hysteresis and crossover regimes are separated by the point

t c = 2δ c ln g ≈ 0.29, ( 30
)
where δ c is given by (22). The low-temperature region where the hysteresis takes place is defined by t min < t < t c . The upper bound is consistent with the requirement δ ↓ > δ 1/2 . To summarize, in the temperature window specified above we find a hysteretic behaviour controlled by the energy splitting between LS and HS state. The splitting, in turn, may be controlled by the boundary strains and by the macroscopic electric field produced by the substrate as we have argued in the Introduction. Noteworthy, existence of the minimal temperature t min may explain the unidirectional character of the transition observed in micrometric samples 44 : at t < t min only a transition from the HS state to the LS state is possible by increasing δ. A full hysteresis cycle could possibly be realized at higher temperatures (but less than t c ). However, for the studied samples this would require stronger coupling to the electric field (to perform switching from the HS to the LS state).

IV. MULTILAYER PROBLEM. MULTISTABILITY

After having established the fundamentals of the thermal hysteresis/crossover in bulk, we now turn to investigation of a layered structure deposited on a ferroelectric substrate. As we have conjectured in the Introduction, the substrate primarily affects the value of the molecular energy splitting ∆ 1 at the boundary layer. In the frame of our model such coupling can be described by Eq. ( 4), where the pressure P is due to boundary effects (e.g., the epitaxial strain 34 or the thermal expansion mismatch). Clearly, such boundary strains are also affected by the electric polarization due to piezo-deformation of the substrate. However, in contrast to the bulk problem, existence of the relation of the type (3) here is not granted. We therefore merely assume a possibility of tuning ∆ 1 , leaving the detailed investigation of the underlying mechanisms for future studies. Increasing the ratio

σ = J ⊥ z J , (31)
drives the system to a cooperative regime, where the change in ∆ 1 results in switching of the spin state of the whole sample (simultaneous transition from LS to HS in both layers). To develop a feel of the effect it is instructive to consider first the case of two layers. ). The labels LS and HS denote the areas in the (m1, m2) plane where the entire system is in the low-/high-spin states, respectively. (Bottom) (σ, t) (left, δ1 = 0.1) and (σ, δ1) (right, t = 1) phase diagrams of a double-layer system. We take δ2 = 1. The color is the average magnetization m = (m1 + m2)/2: black corresponds to m = -1 and white to m = +1. For sufficiently large σ one can switch the spin state of the whole system by varying δ1 near some critical value δ1c.

A. Two layers

The dimensionless free energy of the double-layer system reads

f (m 1 , m 2 ) = 1 2 m 2 1 + m 2 2 + 2σm 1 m 2
-t ln ge -e1/t + e e1/t + ln ge -e2/t + e e2/t ,

where

e 1,2 = δ 1,2 -m 1,2 -σm 2,1 (33)
and g = 5 accounts for the 5-fold degeneracy of the HS state. We have introduced the following notations: f = F/N J z , N being the number of molecules in one layer,

t = k B T /J z , δ α = ∆ α /J z .
We start from the similar to the previous section analysis of the free energy at low temperatures. We shall refer to states with different m 1 and m 2 as (m 1 , m 2 ).

Near (+1, +1) point we have the free energy in the form

f ≈ m 2 1 + m 2 2 + 2σm 1 m 2 2 -(1 + σ)(m 1 + m 2 ) -2t ln g + (δ 1 + δ 2 ). (34)
This function evidently has minimum at (+1, +1). The same analysis can be also performed for (-1, -1), (-1, +1) and (+1, -1) points. It shows that (-1, -1) is a local minimum. However, two other points (-1, +1) and (+1, -1) can be minima only if σ < σ c < 1, where σ c is dependent on t, δ 1 , δ 2 and will be determined below.

Corresponding free energies read

f (-1, -1) ≈ -1 -σ -(δ 1 + δ 2 ), (35) f (+1, +1) ≈ -1 -σ -2t ln g + (δ 1 + δ 2 ). (36)
At σ < σ c we have additional minima with free energy

f (+1, -1) ≈ σ -1 -t ln g + δ 1 -δ 2 , ( 37
) f (-1, +1) ≈ σ -1 -t ln g + δ 2 -δ 1 . (38)
These additional minima make the transition from the LS in both layers (-1, -1) to HS (+1, +1) indirect, for example sequence (-1, -1) → (+1, -1) → (+1, +1) can arise. We shall refer to this case as multistability.

It is seen from the equations above, that at low temperatures (-1, -1) state is the global minimum. At

t (2) c = δ 1 + δ 2 ln g (39)
we have f (+1, +1) = f (-1, -1), thus it is the temperature when the ground state is doubly degenerate. We also notice a possibility for (+1, -1) or (-1, +1) to be a global minimum in some temperature interval of temperatures near t

(2) c . Indeed, one can see from Eqs. (35) and Eqs. (37)

that if 2σ < δ 1 -δ 2 then f (-1, +1) < f (-1, -1) at t (2) c .
At high enough interlayer interaction (σ > σ c ) the transition from LS to HS occurs simultaneously in both layers. In this case the minima at (+1, -1) and (-1, +1) disappear in the critical temperature t

(2) c vicinity. In order to quantify σ c we rewrite (32) using new variables, m I = m 1 + σm 2 and m II = m 2 + σm 1 . We obtain the free energy in the form

f (m 1 , m 2 ) = m 2 I + m 2 II -2σm I m II 2(1 -σ 2 )
-t ln(ge (m I -δ1)/t + e (δ1-m I )/t ) + ln(ge (m II -δ2)/t + e (δ2-m II )/t ) .

In a special case of δ 1 = δ 2 at t

(2) c the system of equations which defines free energy minima reads (cf. Eq. ( 24))

m I -σm II 1-σ 2 = tanh (m I /t (2) c ), m II -σm I 1-σ 2 = tanh (m II /t (2) c ). ( 41
)
At small enough t

(2) c all the right hand sides of these equations can be substituted by ±1 and the system gives previously discussed solutions, but written in new variables: (-1 -σ, -1 -σ), (1 + σ, 1 + σ), (1 -σ, σ -1) and (σ -1, 1 -σ). From Eq. ( 24) we saw that if the tanh argument becomes small enough (≈ 1) the potential relief near the minimum flattens. Here the tanh argument is multiplied either by 1 + σ or by 1 -σ. Thus, the minima for LS and HS in both layers are much more stable, and the minima with opposite spin states can be destroyed by large enough σ. Corresponding equation reads

1 -σ c t (2) c ≈ 1 ⇔ σ c ≈ 1 - 2δ ln g . (42)
It is also applicable if (δ 1 -δ 2 )/(δ 1 + δ 2 ) 1. At σ > σ c barrier height at t

(2) c is defined with good accuracy by f (+1, -1) -f (-1, -1) or f (-1, +1)f (-1, -1). It gives h = 2σ-(δ 2 -δ 1 ) or h = 2σ-(δ 1 -δ 2 ), correspondingly. At δ 1 = δ 2 the minimal barrier height is 2σ c ≈ 2 -2t

(2) c . Thus, at t

(2) c < 2/3 the first order transition takes place. At t

(2) c > 2/3 the character of the transition depends on σ.

As in the one-layer problem, by variation of δ in both layers the system can be switched from LS to HS state and vice versa.

However, we notice a new feature with respect to the one-layer problem. One can tune the splitting δ 1 at one layer, due to the interaction with the substrate, keeping the splitting at the other one δ 2 and the temperature t fixed. This idea is illustrated in Fig. (6), where the phase diagram of the system in (σ, t) plane is mapped onto the corresponding phase diagram in (σ, δ 1 ) plane. Variation of δ 1 around

δ 1,c = t ln g -δ 2 . (43)
allows one to switch from LS to HS and vice versa simultaneously in both layers, i.e. to induce a spin transition in one layer by its interaction with another layer.

B. Multiple layers

Let us now consider some general results for n layers. The free energy in this case has the form:

f (m 1 , ..., m n ) = 1 2 (m 2 1 + ... + m 2 n + 2σm 1 m 2 + 2σm 2 m 3 + ... + 2σm n-1 m n )
-t ln(ge (m1+σm2-δ1)/t + e (δ1-m1-σm2)/t ) + ln(ge (m2+σ(m1+m3)-δ2)/t + e (δ2-m2-σ(m1+m3))/t ) + ... + ln(ge (mn-1+σ(mn-2+mn)-δn-1)/t + e (δn-1-mn-1-σ(mn-2+mn)/t ) + ln(ge (mn+σmn-1-δn)/t + e (δn-mn-σmn-1)/t ) .

Similar to previous section calculations give minima at (+1, ..., +1) and (-1, ..., -1) with free energies

f (-1, ..., -1) ≈ -n/2 -(n -1)σ -nδ, (45)
f (+1, ..., +1) ≈ -n/2 -(n -1)σ -nt ln g + nδ, (46) where δ = (δ 1 + ...δ n )/n is mean value of δ α . From these equation we get

t (n) c = 2δ ln g . (47)
Conditions of other possible minima stability (they have the form (±1, ..., ±1)) at t (n) c are similar to the discussed above. They depend on the value of arguments in tanh functions:

tanh m 1 + σm 2 t (n) c , (48)
tanh m i + σ(m i-1 + m i+1 ) t (n) c , ( 49
) tanh m n + σm n-1 t (n) c . (50)
Let's start from (-1, ..., -1) state. If we flip some layer in the middle we will have condition of this texture stability in form (1 -2σ)/t

(n) c

> 1. However textures with (-1, ..., -1, +1, ..., +1) -"domain walls"are much more stable, the corresponding condition reads 1/t (n) c > 1. Thus, we can estimate the barrier height at t (n) c as f (-1, ..., -1, +1, ..., +1) -f (-1, -1, ..., -1). For the (-1, ..., -1, +1, ..., +1) state the potential relief for layers at the "domain wall" are almost flat at 1/t (n) c > 1 and the average spin of the corresponding layers is zero. So, we obtain for equal δ i case:

f (-1, ..., -1, +1, ..., +1) ≈ - n -2 2 -(n -2)δ -(n -3)σ - 4δ ln g (ln 2 √ g) , (51)
Thus, the barrier height reads

h ≈ 1 + 2σ -2t (n) c ln 2. ( 52
)
This quantity can be used for estimating whether we have the first order transition or smooth crossover. As in the previous Subsec. IV A we notice a possibility of switching the spin state of the whole system by variation of δ 1 . However, it is seen from Eq. (47) that the impact of δ 1 has an additional factor 2/n in comparison with (39), which makes it rather weak for n 1. Thus, the interaction of the first layer with the substrate, which is important in the double-layer problem, is almost negligible. So, similar to the one-layer problem, the spin state of the whole sample can be switched by the temperature or by the δ variation in all the layers, by means of e.g. external electric field. An important issue, which should be taken into account is the existence of the domain walls, which are metastable at low temperatures.

V. SUMMARY AND CONCLUSION

To conclude, we theoretically address the problem of spin transitions in the systems consisting of molecular layers. In the framework of the mean-field approach we obtain the already established physics of this systems, which includes the first-order-like thermal phase transitions with hysteresis and smooth crossovers from the low spin state of the system to the high spin state. We further consider the possibility of isothermal switching by means of an electric field, which is provided by, e.g., ferroelectric substrate. For the bulk problem (single layer) we determine the conditions under which the hysteresis due to the variation of the energy splitting between the LS and HS states can appear. Experimental observation of such hysteresis would be a crucial step toward technological implementation of SCO films in nanoelectronics.

In the case of layered structures we find that two qualitatively different situations should be distinguished: the system consisting of few layers (n ∼ 1) and multilayer systems with n 1. In both cases it should be possible to observe a staircase in the total magnetization as a function of the electric field in a certain range of parameters. We call such phenomenon multistability. For n ∼ 1, provided the interlayer coupling is sufficiently large, all the layers can be switched simultaneously by switching only the first layer by, e.g., microscopic interaction with the surface of the substrate. We believe this effect to be relevant to the experimental findings 36,37 . In contrast, multilayer systems with n 1 behave analogously to the bulk: the boundary plays no role and the total magnetization of the film can be controlled either by temperature or by the macroscopic electric field produced by the substrate. The latter must be sufficiently strong for the coupling (2) could come into play. One should also take care of highly stable intermediate states -"domain walls" -which should be avoided in the switching process. Detailed investigation of this phenomenon is beyond the scope of this paper, and will be given elsewhere.

FIG. 3 .

 3 FIG.3. Free energy profiles at the characteristic temperatures t ↑ , t ↓ in the hysteresis (upper panel) and t 1/2 in the crossover (lower panel) regimes distinguished by the values of δ (see also Fig.4). Black double arrows indicate the temperature scale to be compared with the height of the potential barrier separating the two minima.

FIG. 6 .

 6 FIG.6. (Top) Schematic illustration of a two-layer setting and the corresponding free energy landscape f (m1, m2). The labels LS and HS denote the areas in the (m1, m2) plane where the entire system is in the low-/high-spin states, respectively. (Bottom) (σ, t) (left, δ1 = 0.1) and (σ, δ1) (right, t = 1) phase diagrams of a double-layer system. We take δ2 = 1. The color is the average magnetization m = (m1 + m2)/2: black corresponds to m = -1 and white to m = +1. For sufficiently large σ one can switch the spin state of the whole system by varying δ1 near some critical value δ1c.

ACKNOWLEDGMENTS

S. V. thanks A. Cano for helpful discussions and acknowledges the financial supports by CNRS and by Russian Science Foundation (Grant No. 18-72-00013). Contribution to the work by O. I. Utesov was funded by RFBR according to the research project 18-02-00706.


Emile Boyer

Bénédicte Martin

Sandrine Le Gall-David

Bing Shao

Yves Fong

Martine Deugnier

Vincent Bonnaure-Mallet

Meuric

; Shao

Bing Fong

Yves Deugnier

Martine Bonnaure-Mallet

Vincent Meuric
email: vincent.meuric@univ-rennes1.fr

Chapple, I. L. C M Kilian

Periodontal pathogens and clinical parameters in chronic periodontitis

Keywords: Genetics < Oral Microbiology, Periodontal Disease, Ecology

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

predicting the mean pocket depth was microbial dybiosis using the dysbiosis ratio taxa formula. While further studies are needed to assess the validity of these results on the general population, such a dysbiosis ratio could be used in the future to monitor the subgingival microbiota. Periodontitis is a worldwide health problem and the 6 th most common disease globally 42 [START_REF] Frencken | Global 374 epidemiology of dental caries and severe periodontitis -a comprehensive review[END_REF]. It is a chronic inflammation produced in response to a diseaseassociated multispecies bacterial community with intermittent episodes of remission and as a signature of periodontitis that could score the dysbiosis of the subgingival microbiota 63 (Meuric, Le Gall-David, et al., 2017). However, its relationship with the global periodontal status 2

Materials and methods

Participants and collection of clinical data The participants corresponded to a group of 75 patients with hemochromatosis and chronic 87 periodontitis previously studied by [START_REF] Meuric | Periodontal status and serum biomarker levels in HFE hemochromatosis patients. A case 437 series study[END_REF]. This case study as a confounding factor. As described previously, periodontitis through mean PD was associated 302 with transferrin saturation in the two models [START_REF] Meuric | Periodontal status and serum biomarker levels in HFE hemochromatosis patients. A case 437 series study[END_REF] found in health (Meuric, Le Gall-David, et al., 2017). This result is independent from the 307 transferrin saturation (reflecting the iron status of the hemochromatosis disease). Thus, the 308 dysbiosis ratio confirmed its utility in exploring the microbial dysbiosis to explain periodontal 309 disease (Meuric, Le Gall-David, et al., 2017). Similar microbial dysbiosis ratios have also been 310 calculated in Crohn's disease (Gevers et al., 2014) and in peri-implantitis [START_REF] Kröger | The severity of human peri-implantitis lesions correlates with the level of submucosal 422 microbial dysbiosis[END_REF].

311

These results are based on a specific population suffering from haemochromatosis.

312

Extrapolations outside of this population need to be validated, though the iron status of the 313 patients has been included as a confounding variable in statistical models. Nonetheless, these 314 results are in accordance with the existing view that periodontitis or peri-implantitis are 315 orchestrated by a bacterial consortium rather than a single pathogen [START_REF] Darveau | Periodontitis: A polymicrobial disruption of host homeostasis[END_REF]. 124. 125. 126. 130. 133. 134. 136. 137. 138. 139. 146. 149. 388. 442. 478. 479. 481. 501. 639. 892. 919. 920. 936 4: Multiple linear adjusted regression models with bacteria positively associated before or dysbiosis ratio and Aggregatibacter as predictors of mean periodontal pocket depth, adjusted for age, sex, smoking status, alcohol intake, transferrin saturation, plaque index, gingival index and bleeding index. Characteristics of the model 1: multiple R 2 = 0.4573, adjusted R 2 = 0.3798, F-statistic = 5.899, P-value = 0.0001569. (42 degrees of freedom) Characteristics of the model 2: multiple R 2 = 0.5349, adjusted R 2 = 0.4868, F-statistic = 11.12, P-value = 3.219e-08. (58 degrees of freedom)

  In this specific population, we found that the best model in predicting the mean 34 pocket depth was microbial dybiosis using the dysbiosis ratio taxa formula. While further studies 35 are needed to assess the validity of these results on the general population, such a dysbiosis ratio 36 could be used in the future to monitor the subgingival microbiota.

88

  series was approved by the local ethical committee (CPP Ouest V -10/02-744). The informed 89 consent for study participation has been obtained from all patients and all research was performed 90 in accordance with relevant guidelines and regulations. These patients were recruited at the 91 University Hospital of Rennes and benefited from a full-mouth periodontal examination, 92 including PD, CAL, papillary bleeding index, gingival index, plaque score(Barnett, Ciancio, & 93 Mather, 1980;[START_REF] Lobene | A modified 428 gingival index for use in clinical trials[END_REF] Silness & Loe, 1964) and 94 evaluation of periodontitis severity according to the case definitions from the Centers for Disease 95 Control and Prevention and the American Association of Periodontology (CDC/AAP) (Eke, 96 Page, Wei, Thornton-Evans, & Genco, 2012). For the 2018 classification, the algorithms 97 considered the interdental CAL on two non-adjacent teeth and tooth loss (Graetz et al., 2019; 98 Tonetti, Greenwell, & Kornman, 2018). The exclusion criteria were pregnancy, periodontal 99 therapy within the last 12 months and treatment with either systemic antibiotics or drugs known 100 to cause gingival hyperplasia within the last 3 months. Clinical data recorded at the time of dental 101 examination included smoking status, alcohol consumption (non-drinkers, former drinkers, 102 occasional drinkers and regular drinkers evaluated quantitatively in dose/day), number of dental 103 visits per year and transferrin saturation. The assays of serum iron and transferrin were performed 104 on an automated analyzer AU2700 Olympus (Beckman Coulter). Serum iron levels were 105 measured by a standard colorimetric method that used TPTZ[2,4,6-Tri-(2-pyridyl)-5-triazine] as a 106 chromogen and serum transferrin concentrations were quantified by immunoturbidimetry. Test 107 procedures were conducted as described in the manufacturer's standard operating manual. Total 108 iron binding capacity (TIBC) was calculated using the formula: (transferrin in g/l x 25) and 109 transferrin saturation is calculated as follows: (iron in µmol/l / TIBC) × 100.

  gingival plaque removal, sterile endodontic paper points (Henry Schein, France) were 112 inserted into one of the deepest periodontal pockets for 30s. The material was transferred into a 113 sterile tube with 100 µL of sterile distilled water and kept at 4°C overnight before DNA supernatants was performed using QIAamp DNA Mini Kit (Qiagen, 117 France) according to the manufacturer's recommendations. DNA was then kept frozen at -80°C 118 until amplification. The V3-V4 regions of the 16S rRNA gene were amplified with the primers 119 338F (5'-ACTCCTACGGGAGGCAGCAG-3') (Huse et al., 2008) and 802R (5'-120 TACNVGGGTATCTAATCC-3') (Claesson et al., 2009) using 25 amplification cycles with an 121 annealing temperature of 45°C. PCR products were sequenced with the Illumina MiSeq of the 122 Get-PlaGe platform (Toulouse, France

  Desulfobulbus, Treponema and Porphyromonas genera were also found 203 significantly correlated with these periodontal data. Significant inverse correlations were found 204 for the taxa of Campylobacter, Aggregatibacter and Rothia. No correlation was found between the outcome variable -the percentage of sites with PD ≥ 4 mm -, the 225 dysbiosis ratio (p < 0.001 -TableS2) remained as the most significant predictor. Fretibacterium was not detected in our Caucasian population. As for the 244 other five remaining taxa, we have confirmed that they were not detected in this population.

	the species level was assigned using the "Quantitative Insights Into Microbial Ecology" (QIIME 1.9.1) package software (Caporaso et al., 2010) with the default parameters (script: pick_open_reference_otus.py, uclust as the clustering method) and the Human Oral Microbiome Database (HOMD, version 15.1) as the reference database (Chen et al., 2010). The mean periodontal measure as 226 133 134 135 202 224 of species considered as periodontal pathogens (from previous studies) and continuous 250 periodontal measures, in haemochromatosis patients with periodontitis to assess the current 295 refined with the stepwise method (Venables & Ripley, 2002) adjusted with the clinical and 296 demographic data as for example, alcohol intake, which is considered as a risk factor for 297 periodontitis (Wang, Lv, Wang, & Jiang, 2016) and a worsened mean PD in our population. respectively). 205 the sampled pocket depth and any of the bacterial taxa. Finally, the calculated dysbiosis ratio 227 4 Discussion 251 weight of their implication in the disease. Adjusted regression models were then used to 298 Since the patients come from a sub-cohort of a previous study where high transferrin saturation
	136 206 228 252 299	unassigned reads per sample was 6.4 % ± 6.2 %. These reads have been excluded from further corresponding to (%Porphyromonas + %Treponema + %Tannerella) / (%Rothia + Owing to decades of oral microbiology studies, some species are well known for their determine the best bacterial biomarkers of periodontitis severity. Taxa already well described as (specifically for the hemochromatosis disease) was implicated in explaining clinical severity of
	159
	137 207 229 253 300	species analyses. To challenge the assignment capacities used in this study, the V3V4 sequences %Corynebacterium) showed the highest correlation with mean PD (r=0.37, p=0.001) and with periodontal pathogenicity. Culture-independent and molecular-based approaches to bacterial implicated in the disease were found correlated with the mean PD or the percentage of sites with periodontitis, we have added the transferrin saturation into the multiple linear regression models
	138 160 208 230 254 301	of each taxon were extracted from the HOMD and entered in the previously described pipeline. 3 Results the percentage of sites with PD ≥ 4 mm (r=0.35, p=0.0017), as compared with individual taxa. identification has highlighted new putative periodontal pathogens, that were found increased in PD ≥ 4 mm: P. gingivalis and T. forsythia (red complex) and E. nodatum (orange complex)
	139 140 161	F o Only three species (Mogibacterium timidum, Anaeroglobus geminatus and Enterococcus faecalis) could not be correctly classified by the pipeline, among all the putative periodontal F o -Clinical data F o F o F o F o F o F o
			r r r r r r r r
	141	pathogens described.	R R R R R R R R
	142	Statistics	e v i e e e e e e e v i v i v i v i v i v i v i
	143 144 214 215	e w Data were studied using R (version 3.3.3) (R. Core Team, 2015) with the RStudio software (RStudio Team, 2016). Statistical tests were considered significant for p<0.05. Results of the e w e w e w e e e e -Multiple linear regression analyses w w w w
	124 145 146	gov/Traces/ study/) under BioProject O accession number PRJNA416501 and PRJNA517671. n descriptive analysis are presented as mean ± standard error (SE) and with prevalence (%). Distribution of continuous variables was assessed using the Shapiro-Wilk test. The mean PD was O n O n O n O n O n O n O n
	125 147	Microbiological analysis analyzed according to the demographic and clinical data using the Mann-Whitney test. l y l y l y l y l y l y l y l y
	148	Correlations between taxa relative abundance and clinical parameters were calculated using
	126	Taxonomy at the genus level was assigned using the "Visualization and Analysis of Microbial
	149 220	Spearman correlation coefficient. Multiple linear regression models were used to study the genera (β=-0.053, -0.063 and 0.051, respectively, p<0.05) in the first model (adjusted R 2 =
	127	Population Structures" (VAMPS) analysis pipeline web tool (Huse et al., 2014). Default
	128 150 197 221	parameters were used for assignment to the genus level with the Ribosomal Database Project association between periodontal parameters (i.e. mean PD and percentage of site with PD≥4mm) 0.3798, p<0.001). The most significant data were obtained in the second model using the
	129 151 174 198 222	(RDP) classification (Cole et al., 2014). Through the Global Alignment for Sequence Taxonomy and bacterial taxa presenting a significant correlation (r≥0.20, p<0.05) or the dysbiosis ratio -Microbiological correlation with periodontal data dysbiosis ratio and Aggregatibacter as independent variables with β=0.062 (p<0.001) and β=-
	130 152 175 199 223 245	(GAST) process of VAMPS, the best taxonomic hit was assigned for each read. Reads identified (% Porphyromonas + % Treponema + % Tannerella) / (% Rothia + % Corynebacterium) -Prevalence and proportion of bacteria Analysis showed that the species exhibiting significant correlations with periodontal clinical data 0.053 (p<0.01) respectively and an adjusted R 2 = 0.4868 (p<0.00001) (Table 4). By using another Thus, different population could carry different taxon associated with periodontitis. However,
	131	as Archaea, Eukarya, Organelle and unknown were excluded from further analysis. Taxonomy at
			8 11 12 13 14 15

). The sequence data were submitted to the NCBI 123 Sequence Read Archive (https://www.ncbi.nlm.nih.

153 described in

Meuric et al. 2017

(Meuric, Le Gall-David, et al., 2017)

, adjusted for confounding 154 factors including age, gender, smoking status, alcohol intake, plaque index, transferrin saturation, 9 155 gingival and bleeding index. The stepwise AIC algorithm was performed using the 'MASS' 156 package for R

(Venables & Ripley, 2002)

. Final regression coefficients, standard errors (SE) and 157 statistics for each variable adjusted for confounding factors, with the characteristics of the models 158 (adjusted R 2 , p-value) are presented.

162

Based on the CDC/AAP case definition

[START_REF] Eke | Update of the case 371 definitions for population-based surveillance of periodontitis[END_REF]

, all patients presented periodontitis; 163 44.3 % and 54.4 % had moderate and severe periodontitis, respectively. On average, 50.

164

0±1.96 % of sites per mouth had CAL ≥ 3 mm, 10.7±1.43 % of sites had CAL ≥ 5 mm, and 165 12.5±1.15 % of sites had PD ≥ 4 mm. The full description of the periodontal measures is 166 available in Table

S1

. According to the 2018 classification, and using CAL and tooth loss as the 167 main available criteria, 3/75 (4%) patients were classified as stage II, 59/75 (79%) as stage III 168 and 13/75 (17%) as stage IV

(Tonetti et al., 2018)

. A minority (9/75, 12%) was classified as 169 localized. The average age was 50.6 ± 8 years. Males represented 56 %, and former or current smokers and drinkers were 62.6 % and 80 %, respectively. Most of the patients visited their dentist at least once a year (78.6 %). Table

1

presents the statistics exploring the potential impact 172 of each demographic on the mean PD. The mean PD was increased in former or current drinkers, compared to patients who had never experienced alcohol abuse (p=0.028).

176

The average of reads per sample was 14 980 ± 740 (minimum = 5 298 reads). From the 74 genera and species related to periodontitis and described by

Socransky et al.,

belonging to the orange and red complexes described by Socransky et al. were found. The lowest 180 prevalence was Fusobacterium periodonticum (6.4 %), while Fusobacterium nucleatum and T. 181 forsythia were found in all patients. For the 8 species which have been reported as highly 182 implicated in periodontitis (reported by ≥ 4 studies according to the systematic review of the 183 literature by Pérez-Chaparro et al.), five of them were found: i.e. Porphyromonas endodontalis 184 (prevalence = 88.6 %), Treponema lecithinolyticum (62 %), Treponema medium (55.7 %), 185 Filifactor alocis (40.5 %) and Eubacterium saphenum (11.4 %), while two were not detected 186 (Fretibacterium OT360 and Selenomonas sputigena). For the taxa cited 3 times, the following 187 were not detected: Bacteroidales OT274, Peptostreptococcus stomatis, Desulfobulbus OT041 188 and phylum TM7. Species with lower evidence of implication with periodontitis (cited only by 189 two studies) or belonging to the purple or green complex (Actinomyces odontolyticus, Veillonella 190 parvula and Eikenella corrodens respectively) were not, or hardly detected (Table 2). 191 Mogibacterium timidum, Anaeroglobus geminatus and Enterococcus faecalis were not found due 192 to methodological limitations. 193 The most abundant genus was Fusobacterium (mean = 26.1±1.7 %) followed by Prevotella 194 (12±1 %), Porphyromonas (7±0.8 %), Streptococcus (5.8±0.7 %), Treponema (5.6±0.6 %) and 195 Tannerella (5.4±0.6 %). The most abundant species were F. nucleatum (15.3±1.4 %) followed by 196 T. forsythia (4.5±0.5 %), P. endodontalis (3.1±0.4 %), and P. gingivalis (2.8±0.6 %). 200 were P. gingivalis (r=0.33 and 0.41, with mean PD and percentage of sites with PD≥4 mm, 201 respectively), T. forsythia (r=0.25 and 0.30, respectively), and E. nodatum (r=0.35 and 0.34, 209 Table

3

presents all the significant results of the correlation between bacterial/clinical data and 210 mean PD, which were further used in the following statistical experiments. As shown in Table

3

, 211 the periodontal indices rating the plaque, gingival inflammation and bleeding on probing, were 212 found significantly correlated with the mean PD. Therefore, they were also used in the statistical 213 models as confounding variables.

216

The multiple linear regression was performed with the stepwise method which selects the most 217 significant variables affecting the mean pocket depth. After adjustment for age, sex, smoking 218 status, alcohol status, plaque index, transferrin saturation, bleeding index and gingival index, the 219 mean PD was found independently associated with Aggregatibacter, Rothia and Porphyromonas 231 periodontitis patients. However, few studies assess the correlation between the severity of 232 periodontal disease and the abundance of these taxa. The identification of taxa that are 233 significantly associated with the periodontal status is the first step in the search for biomarkers 234 that could predict the onset of the disease. 235 Most of the periodontal pathogens were identified in the analyses due to the sequencing 236 depth. However, six species were not detected. Bacteroidales OT274, Peptostreptococcus 237 stomatis, Desulfobulbus OT041, Fretibacterium sp., TM7 and Selenomonas Sputigena could not 238 be found while they are highly cited (≥3 times) in the literature as being implicated in 239 periodontitis. Only three (Mogibacterium timidum, Anaeroglobus geminatus and Enterococcus 240 faecalis) could not be identified through the pipeline of assignation, due to methodological 241 limitations. The lack of detection of Fretibacterium is surprising since it was proposed as a 242 diagnostic bacterial biomarker for periodontitis screening in a Japanese population (Khemwong 243 et al., 2019). Indeed, 246 previous works on periodontitis microbiota analysis through NGS have used a binary approach 247

(healthy or disease) to determine in which condition taxon are increased

[START_REF] Abusleme | The subgingival microbiome in health and periodontitis and its relationship with 345 community biomass and inflammation[END_REF] 255 (Socransky et al., 1998)

. From the newly identified putative periodontal pathogen, only

256

Desulfobulbus genus

[START_REF] Pérez-Chaparro | Newly identified pathogens associated with periodontitis: A systematic review[END_REF]

was found correlated with the mean pocket 257 depth. Correlation coefficients between periodontal data and bacterial taxa remained inferior to 258 0.4, similarly to other microbiota analyses in chronic periodontitis

(Khemwong et al., 2019;

259

[START_REF] Lourenço | Microbial signature profiles of periodontally healthy and diseased patients[END_REF] Silva-Boghossian, Cesário, Leão, & Colombo, 2018)

. Finding associations 260 is especially more difficult when looking at the species level. However, it is not surprising as this 261 disease is a multifactorial pathology, as each taxon might be partially implicated in the disease.

262

For instance, T. denticola which belongs to the red complex

(Socransky et al., 1998)

, was not 263 correlated with the mean PD. Nevertheless, the Treponema genus, which contains T. denticola 264 and other species highly suspected to be periodontal pathogens (i.e. T. vincentii, 265 T. lecithinolyticum and T. medium, as reported in the systematic review by Pérez-Chaparro et al.), 266 was found correlated with the PD measures.

267 Surprisingly, Campylobacter was negatively associated with the mean PD, while 268 Campylobacter species are mainly classified as periodontal pathogens (i.e.: C. showae, 269 C. gracilis, and C. rectus belonging to the orange complex and C. concisus to the green complex 270 (Socransky

et al., 1998)

). However, this repartition of species is controversial: C. gracilis belongs 271 to the orange complex, though it was found increased in healthy subjects

(Henne, Fuchs, Kruth,

Table 1 :

 1 In this study, we have confirmed that most of the well-described and newly identified 320 periodontal pathogens can be found in the deepest periodontal pocket of patients suffering from 321 haemochromatosis and periodontitis. Yet, only few taxa were correlated to mean pocket depth. Silness, J., & Loe, H. (1964). Periodontal disease in pregnancy. II. Correlation between oral 453 hygiene and periodontal condition. Acta Odontologica Scandinavica, 22, 121-135. Mean probing depth (PD) according to demographic data. Data are presented as mean ± standard error (SE). Bold p-values indicate significant Mann-Whitney test.

	316
	317

325

previously described dysbiosis ratio -(% Porphyromonas + % Treponema + % Tannerella) / (% 326 Rothia + % Corynebacterium) -was the most reliable biomarker to predict periodontitis severity 327 in our patients. Longitudinal studies in patients with no systemic disease, as well as several 328 sampling sites and time points during the episodes of disease-active periodontitis should be 329 considered to further validate and generalize the findings of this study.

Table 2 :

 2 Taxonomy and dysbiosis ratio (PTT/RC) implicated in chronic periodontitis, with the mean, standard error (SE) and occurrence of the bacterial taxa and of the dysbiosis ratio in the present study. ND: not detected

	Perez-Chapparo	2014	2 studies	ND
	. 937

Table 3 :

 3 Correlation between mean probing depth (PD) and bacterial or clinical data. Only significant correlations are presented. Dysbiosis ratio: (%Porphyromonas+%Treponema+%Tannerella)/(%Rothia+%Corynebacterium); SE: standard error. Plaque index from Silness & Loe. 1964, Gingival index from[START_REF] Lobene | A modified 428 gingival index for use in clinical trials[END_REF] and Papillary bleeding index from[START_REF] Barnett | The Modified Papillary Bleeding Index-348 Comparison with Gingival Index During the Resolution of Gingivitis[END_REF]

	F o r R e v i e w	O n l y
		26

Molecular Oral Microbiology

Meuric et al., 47 taxa (64.4 %) have been identified in this study (Table2). All the bacteria

Horz, & Conrads, 2014) and decreased in severe periodontitis[START_REF] Macuch | Campylobacter species in health, gingivitis, and 433 periodontitis[END_REF]. Finally,

meta-analysis. Journal of ClinicalPeriodontology, 43(7),[572][573][574][575][576][577][578][579][580][581][582][583]

Acknowledgments:

The authors are indebted to the medical and nursing staff for participating in 331 the recruitment and follow-up of patients. We thank the GeT-PlaGe facility and the NED team

Data availability: The sequence data were deposited to the NCBI Sequence Read Archive 338 (https://www.ncbi.nlm.nih.gov/Traces/study/) under BioProject accession numbers

the Campylobacter genus was still negatively associated with percentage of PD ≥ 4mm in the 274 regression model.

275

This analytical approach is also interesting when focused on the prevalence or occurrence 276 of periodontal pathogens in patients. Taxa are not found in all patients. Even the prevalence of 277 P. gingivalis, which is well described as one of the keystone pathogens in the disease (George (Kato, Imai, Ochiai, & Ogata, 2013) and not higher than 281 79% in chronic periodontitis (Griffen et al., 1998). The chronic nature and clinical course of the S3.