Junta Igarashi

Quentin Remy

Satoshi Iihama

Grégory Malinowski

Michel Hehn

Jon Gorchon

Julius Hohlfeld

Shunsuke Fukami

∥,⊥, #, ∇ , Hideo Ohno †, ∥,⊥, #, ∇ Stéphane Mangin

Engineering single-shot all-optical switching of ferromagnetic materials

Keywords: All-optical switching, single-shot all-optical switching, spin valve, spin current, ultrafast demagnetization, ultrafast laser

ABSTRACT

Since it was recently demonstrated in a spin-valve structure, magnetization reversal of a ferromagnetic layer using a single ultrashort optical pulse has attracted attention for future ultrafast and energy-efficient magnetic storage or memory devices. However, the mechanism and the role of the magnetic properties of the ferromagnet as well as the time scale of the magnetization switching are not understood. Here, we investigate single-shot all-optical magnetization switching in a GdFeCo/Cu/[CoxNi1-x/Pt] spin-valve structure. We demonstrate that the threshold fluence for switching both the GdFeCo and the ferromagnetic layer depends on the laser pulse duration and the thickness and the Curie temperature of the ferromagnetic layer. We are able to explain most of the experimental results using a phenomenological model. This work provides a way to engineer ferromagnetic materials for energy efficient single-shot all-optical magnetization switching.

MAIN TEXT

Magnetization manipulation using ultrashort optical pulses without the use of any magnetic field, namely all-optical switching (AOS), has attracted much attention because of the potential application for ultrafast and energy-efficient magnetic storage or memory devices [START_REF] Kimel | Writing Magnetic Memory with Ultrashort Light Pulses[END_REF][START_REF] Stanciu | All-Optical Magnetic Recording with Circularly Polarized Light[END_REF][START_REF] Alebrand | Light-Induced Magnetization Reversal of High-Anisotropy TbCo Alloy Films[END_REF][START_REF] Mangin | Engineered Materials for All-Optical Helicity-Dependent Magnetic Switching[END_REF][START_REF] Lambert | All-Optical Control of Ferromagnetic Thin Films and Nanostructures[END_REF][START_REF] El Hadri | Two Types of All-Optical Magnetization Switching Mechanisms Using Femtosecond Laser Pulses[END_REF][START_REF] Gorchon | Model for Multishot All-Thermal All-Optical Switching in Ferromagnets[END_REF][START_REF] Radu | Transient Ferromagnetic-like State Mediating Ultrafast Reversal of Antiferromagnetically Coupled Spins[END_REF][START_REF] Ostler | Ultrafast Heating as a Sufficient Stimulus for Magnetization Reversal in a Ferrimagnet[END_REF][START_REF] Bergeard | Ultrafast Angular Momentum Transfer in Multisublattice Ferrimagnets[END_REF][START_REF] Graves | Nanoscale Spin Reversal by Non-Local Angular Momentum Transfer Following Ultrafast Laser Excitation in Ferrimagnetic GdFeCo[END_REF][START_REF] Wienholdt | Orbital-Resolved Spin Model for Thermal Magnetization Switching in Rare-Earth-Based Ferrimagnets[END_REF][START_REF] Lalieu | Deterministic All-Optical Switching of Synthetic Ferrimagnets Using Single Femtosecond Laser Pulses[END_REF][START_REF] Gorchon | Single Shot Ultrafast All Optical Magnetization Switching of Ferromagnetic Co/Pt Multilayers[END_REF][START_REF] Iihama | Single-Shot Multi-Level All-Optical Magnetization Switching Mediated by Spin Transport[END_REF] . Two types of AOS have been observed. In the case of all-optical helicity-dependent switching (AO-HDS) magnetization can be switched by circularly polarized light pulses and the final magnetic state is determined by the light helicity. Recent experimental studies revealed that AO-HDS is observed for a large variety of magnetic materials such as rare earth (RE)-transition metal (TM) alloy and multilayers, RE-free synthetic ferrimagnetic heterostructures, ferromagnetic (FM) multilayers like [Co/Pt]N and granular recording media [START_REF] Stanciu | All-Optical Magnetic Recording with Circularly Polarized Light[END_REF][START_REF] Alebrand | Light-Induced Magnetization Reversal of High-Anisotropy TbCo Alloy Films[END_REF][START_REF] Mangin | Engineered Materials for All-Optical Helicity-Dependent Magnetic Switching[END_REF][START_REF] Lambert | All-Optical Control of Ferromagnetic Thin Films and Nanostructures[END_REF][START_REF] Liao | Controlling All-Optical Helicity-Dependent Switching in Engineered Rare-Earth Free Synthetic Ferrimagnets[END_REF] . However, unfortunately, multiple pulses are required to observe AO-HDS [START_REF] El Hadri | Two Types of All-Optical Magnetization Switching Mechanisms Using Femtosecond Laser Pulses[END_REF] , even if a drastic reduction of the number of pulses required has been recently shown [START_REF] Kichin | From Multiple-to Single-Pulse All-Optical Helicity-Dependent Switching in Ferromagnetic Co / Pt Multilayers[END_REF] . In the case of all-optical helicity-independent switching (AO-HIS), the magnetization can be switched with one single femto-second pulse whatever light helicity is used.

It has also been demonstrated using a single femto-second electron pulse [START_REF] Wilson | Ultrafast Magnetic Switching of GdFeCo with Electronic Heat Currents[END_REF][START_REF] Xu | Ultrafast Magnetization Manipulation Using Single Femtosecond Light and Hot-Electron Pulses[END_REF] .

Nonetheless, AO-HIS is observed only for specific ferrimagnetic materials. First, it was demonstrated only for GdCo alloys and then for a series of Gd-based alloys and multilayers. The number of material exhibiting AO-HIS is limited even if it has recently been observed for TbCo [START_REF] Avilés-Félix | Single-Shot All-Optical Switching of Magnetization in Tb/Co Multilayer-Based Electrodes[END_REF] and half-metallic compensated ferrimagnetic Heusler alloy Mn2RuxGa with crystallographically-inequivalent Mn sublattices [START_REF] Banerjee | Single Pulse All-Optical Toggle Switching of Magnetization without Gadolinium in the Ferrimagnet Mn2RuxGa[END_REF] . The mechanism behind AO-HIS still remains as a subject of intense debate [START_REF] Radu | Transient Ferromagnetic-like State Mediating Ultrafast Reversal of Antiferromagnetically Coupled Spins[END_REF][START_REF] Ostler | Ultrafast Heating as a Sufficient Stimulus for Magnetization Reversal in a Ferrimagnet[END_REF][START_REF] Bergeard | Ultrafast Angular Momentum Transfer in Multisublattice Ferrimagnets[END_REF][START_REF] Graves | Nanoscale Spin Reversal by Non-Local Angular Momentum Transfer Following Ultrafast Laser Excitation in Ferrimagnetic GdFeCo[END_REF][START_REF] Wienholdt | Orbital-Resolved Spin Model for Thermal Magnetization Switching in Rare-Earth-Based Ferrimagnets[END_REF][START_REF] Lalieu | Deterministic All-Optical Switching of Synthetic Ferrimagnets Using Single Femtosecond Laser Pulses[END_REF][START_REF] Avilés-Félix | Single-Shot All-Optical Switching of Magnetization in Tb/Co Multilayer-Based Electrodes[END_REF] . In GdFeCo, it was attributed to the presence of two exchange coupled magnetic sublattices (the RE and the TM one) showing different relaxation times after ultrafast laser excitation. In this model, the toggle effect is mediated by the antiferromagnetic exchange coupling between the Gd and the FeCo [START_REF] Radu | Transient Ferromagnetic-like State Mediating Ultrafast Reversal of Antiferromagnetically Coupled Spins[END_REF][START_REF] Ostler | Ultrafast Heating as a Sufficient Stimulus for Magnetization Reversal in a Ferrimagnet[END_REF][START_REF] Bergeard | Ultrafast Angular Momentum Transfer in Multisublattice Ferrimagnets[END_REF][START_REF] Graves | Nanoscale Spin Reversal by Non-Local Angular Momentum Transfer Following Ultrafast Laser Excitation in Ferrimagnetic GdFeCo[END_REF][START_REF] Wienholdt | Orbital-Resolved Spin Model for Thermal Magnetization Switching in Rare-Earth-Based Ferrimagnets[END_REF][START_REF] Lalieu | Deterministic All-Optical Switching of Synthetic Ferrimagnets Using Single Femtosecond Laser Pulses[END_REF] .

In addition, AO-HIS had never been observed for a single ferromagnetic layer. However, single laser pulse switching has been demonstrated for a ferromagnetic [Co/Pt] multilayers in an exchange coupled GdFeCo/[Co/Pt] bilayer as well as in GdFeCo/Cu/[Co/Pt] spin-valve structure without exchange coupling between the two magnetic layers [START_REF] Gorchon | Single Shot Ultrafast All Optical Magnetization Switching of Ferromagnetic Co/Pt Multilayers[END_REF][START_REF] Iihama | Single-Shot Multi-Level All-Optical Magnetization Switching Mediated by Spin Transport[END_REF] . In the latter case, the [Co/Pt] switching would result from the combined effect of the spin current generated by the AO-HIS of the GdFeCo layer and the laser-induced heating of the ferromagnet [START_REF] Iihama | Single-Shot Multi-Level All-Optical Magnetization Switching Mediated by Spin Transport[END_REF] .

From the later work it was suggested that a single femto-second spin current pulse can induce the switching of the magnetization of a ferromagnetic layer [START_REF] Iihama | Single-Shot Multi-Level All-Optical Magnetization Switching Mediated by Spin Transport[END_REF] , many questions remain unanswered. For instance, how much polarized current is needed? How much heat needs to be brought to the ferromagnetic layer? What type of ferromagnet can be switched? What are the key ferromagnet characteristics needed to observe the switching? Does the Curie temperature of the FM play a role in the switching? What sets the fluence and the pulse duration needed to observe the single pulse reversal?

In this study, we investigate the switching of [CoxNi1-x/Pt] in GdFeCo/Cu/[CoxNi1-x/Pt] spinvalve structure. [CoxNi1-x/Pt] is a model system showing perpendicular anisotropy with a Curie temperature (TC) that can be tuned from 400 K to close 850 K by adjusting the CoxNi1-x concentration. From the experimental results and using a three temperature model, we can demonstrate that the ferromagnetic layer needs to be sufficiently demagnetized to ensure its switching when the spin current generated by the GdFeCo demagnetization reaches the FM layer. This highlights the fact that the FM Curie temperature has a significant role in the observed switching.

RESULTS

Film fabrication and Curie temperature

Ta (5)/Gd23.3FeCo76.7 (5)/Cu (10)/[CoxNi1-x (1)/Pt (1)]4/Pt (3)/Ta (5) stacks were deposited on glass substrate by dc/rf magnetron sputtering as shown in Figure 1a. The numbers in parentheses are nominal thicknesses in nm. FeCo rich composition is used for the GdFeCo layer, meaning that net magnetization of the alloy is parallel to the magnetization of the FeCo sublattice. We prepared several samples with different Co compositions x (= 0.2, 0.3, 0.4, 0.6, 0.8, 1.0) in [CoxNi1-x] to tune its Curie temperature TC [START_REF] Hashimoto | Adding Elements to the Co Layer in Co/Pt Multilayers[END_REF] . The temperature dependence of the magnetization of Ta (5)/Cu (10)/[CoxNi1-x (1)/ Pt (1)]4/Pt (3)/Ta (5) was measured by a vibrating sample magnetometer with an oven. The increase of the TC as the Co concentration increases in CoxNi1-x is shown in Figure 1b. From previous reports [START_REF] Ostler | Crystallographically Amorphous Ferrimagnetic Alloys: Comparing a Localized Atomistic Spin Model with Experiments[END_REF][START_REF] Gorchon | Role of Electron and Phonon Temperatures in the Helicity-Independent All-Optical Switching of GdFeCo[END_REF] , GdFeCo exhibits a Curie Temperature around 540 K, which corresponds to the Curie temperature of a [CoxNi1-x /Pt] multilayer for x between 0.3 and 0.4. Figure 1c shows one example of the magneto-optic Kerr effect (MOKE) signal (θK) as a function of the magnetic field (H) applied perpendicularly to the film plane for the sample with x = 0.6. We confirm that four magnetic configurations (P+, AP+, AP-, P-) can be accessed by applying a field except for the sample with x = 0.2. The four magnetic configurations are the one for which the two magnetization configurations are parallel P+, P-, or anti-parallel AP+, AP-. P+ and AP+ correspond to the cases for which the magnetization of the [CoxNi1-x/Pt] is along the positive field direction. Red and blue triangle symbols in Fig. 1c

All-optical switching

Figure 2a shows MOKE images obtained after shooting one, then two, three, and four single femto-second laser pulses starting from a saturated P+ state for different samples. Here, the sample is irradiated from the capping layer side and MOKE images are obtained from the substrate side. The fluence used in the measurements shown in the figure are between 14 and 21 mJ/cm 2 . The laser pulse duration is fixed to 35 fs. When the MOKE images are changed from dark red (P+) to light red (AP+) it indicates that only the GdFeCo layer magnetization has been switched. This transition is observed, for an outer ring, after a single pulse for all samples concentration. After every pulse the GdFeCo magnetization switches. This is an AO-HIS. The change of MOKE contrast from dark red (P+) to dark blue (P-) proves that both the GdFeCo and the [CoxNi1-x/Pt] magnetization are switched. The later is observed after one single pulse in the case of x = 0.4, 0.6, 0.8. For those samples, the single pulse reversal of both layers is possible as already observed by Iihama et al. [START_REF] Iihama | Single-Shot Multi-Level All-Optical Magnetization Switching Mediated by Spin Transport[END_REF] . This effect can be explained by the generation of a spin current pulse, whose polarization is parallel to the initial Gd magnetization, due to the change in magnetization (-dM/dt) generated by the GdFeCo layer AO-HIS. The generated spin current can then switch the [CoxNi1-x/Pt]. We also observe a white spot at the center at high power, corresponding to the formation of random domain states due to high energy density (Shown in Supporting Information S3, and ref. (15)). In the case of x = 1.0, although both layers are impacted by the laser beam, no full switching of the layers is observed. To determine the laser pulse energy Ep required for switching, the radius of the switched domain ri (where i indicates the type of reversal) is evaluated (see Supporting Information S3). Assuming a Gaussian spatial distribution of the laser pulse as follow: Fpi = 2Ep/(πw0 2 )exp(-2ri 2 /w0 2 ), where Fpi and 2w0 are the threshold fluence and the 1/e 2 spot size respectively (details are shown in Supporting Information S3). Figure 2b shows the obtained Fpi versus TC. We do not observe any effect of the FM composition on the critical fluence required to switch the GdFeCo layer. On the other hand, the threshold fluence for the switching of both layers (Fboth) and the generation of multi-domain states (Fmulti) increases with the increasing TC of the FM layer. Figure 2c shows the difference between the fluence to obtain the multi-domain state and the fluence to switch both layers (Fmulti -Fboth) as a function of TC. Fmulti -Fboth increases with increasing TC up to ~ 800 K, indicating that there is a certain fluence window that allows the switching of both layers without generating a multi-domain state. Note that other parameters such as saturation magnetization, perpendicular anisotropy, refractive indices, moreover, the probability of spin-flipping, also depends on x and may affect the FM layer switching since it changes the amount of angular momentum transfer to the magnetization (see Supporting Information S1, S4, and S5). This latter comment is out of the scope of this study. In Figure 2, calculated fluence to switch the interface layer (Fint) and to fully demagnetize at the end of the FM layer (Fend) are shown. These will be discussed later. Finally, we performed single pulse switching measurements for various pulse durations ranging from 35 fs to 3 ps. The sample is the same as in the previous experiment with tCo = 0.6 nm. Figure 4a shows MOKE images after irradiation of laser pulse with different pulse durations.

Clear single-shot switching of the [Co/Pt] layer is observed for a pulse duration of up to 500 fs.

Note that in the case of a single-layer GdFeCo, single-shot AO-HIS up to 1 ~ 10 ps was observed depending on the Gd composition [START_REF] Gorchon | Role of Electron and Phonon Temperatures in the Helicity-Independent All-Optical Switching of GdFeCo[END_REF] . Figure 4b shows the threshold fluence for the GdFeCo switching (FGdFeCo), both layers switching (Fboth) and formation of multi-domain states (Fmulti) plotted as a function of the laser pulse duration. For the GdFeCo switching and both layers switching, the threshold fluence does not change when increasing the pulse duration up to 200 fs, then it increases with increasing the pulse duration up to 1(3) ps for Fboth (FGdFeCo). On the other hand, the evolution of Fmulti as a function of the pulse duration is different from the evolution of Fboth and FGdFeCo. Fmulti is constant for pulse durations up to 100 fs, then it starts to decrease with increasing pulse duration up to 2 ps.

DISCUSSION

We have demonstrated in this work that three parameters can have a strong impact on the single pulse switching of a ferromagnetic multilayer [CoxNi1-x/Pt] in a GdFeCo/Cu/[CoxNi1-x/Pt] spin-valve: the concentration of the CoNi alloys, the thickness of the interface ferromagnetic layer in contact with the Cu and the laser pulse duration.

From those measurements, one can reach the following general understanding of the mechanism behind the two-layer switching with one single light pulse: The laser pulse interacts with the GdFeCo leading to its switching, this is AO-HIS. During the reversal, the magnetization relaxation of the two sublattices leads to two distinct spin current pulses separated in time as described by Choi et al [START_REF] Choi | Laser-Driven Spin Generation in the Conduction Bands of Ferrimagnetic Metals[END_REF] . The first one is generated mainly by the TM sublattice, a few femtoseconds after the laser pulse, and is polarized along the TM magnetization direction. The second one is generated and polarized by the Gd after 1 ps. We believe that in order for the FM layer to switch, this second spin current pulse has to interact with the FM layer when the FM is sufficiently demagnetized. Based on angular momentum conservation, our hypothesis is that the FM switching will take place only if the remaining magnetization of the interfacial FM layer reaches a threshold value which corresponds to the amount of angular momentum transferred by the spin current originating from the Gd sublattice. We do not consider the first current pulse as it interacts with the FM layer while its demagnetization has barely started. However, the second pulse reaches the FM layer typically 1 ps after the FM started demagnetizing. The demagnetization is mainly generated by the direct laser irradiation plus possibly by some hot electrons generated in the structure [START_REF] Bergeard | Hot-Electron-Induced Ultrafast Demagnetization in Co / Pt Multilayers[END_REF] . To observe the multi-domain state, we presume that the full CoNi/Pt layer needs to be demagnetized for a long period such that the system can no longer "remember" the polarization of the Gd polarized current.

The influence of the CoNi concentration on the fluence needed for the ferromagnetic switching and the multi-domain formation is then consistently explained by the fact that demagnetized states can be reached with less energy as the TC of the FM layer is lower. Similarly, the significant change in the fluence needed to switch a Co/Pt multilayer as a function of the thickness of the interface Co layer deposited next to the Cu layer can be explained with a similar argument. In a Co/Pt multilayer, the exchange coupling inside the Co layer is strong and it is weaker between the Co layers because of the Pt layer [START_REF] Gottwald | Asymmetric Magnetization Reversal in Dipolarly Coupled Spin Valve Structures with Perpendicular Magnetic Anisotropy[END_REF] . The exchange coupling inside the Co layer also depends on its thickness [START_REF] Liao | Controlling All-Optical Helicity-Dependent Switching in Engineered Rare-Earth Free Synthetic Ferrimagnets[END_REF] . If the interface Co layer is thin, the effective exchange coupling inside the layer will be weak and it will require less energy to be partly demagnetized.

It will then be easier to reach the demagnetization threshold and consequently to be switched. If the interface layer switches, the switching of the rest of the multilayer can then be explained by the propagation of the reversal due to the exchange coupling between the layer as observed in several systems [START_REF] Gorchon | Single Shot Ultrafast All Optical Magnetization Switching of Ferromagnetic Co/Pt Multilayers[END_REF][START_REF] Beens | Comparing All-Optical Switching in Synthetic-Ferrimagnetic Multilayers and Alloys[END_REF] .

Concerning the experiments for which the laser pulse duration is tuned, we observed that the fluence needed for the GdFeCo switching increases monotonically as the pulse duration increases, as has been reported previously [START_REF] Gorchon | Role of Electron and Phonon Temperatures in the Helicity-Independent All-Optical Switching of GdFeCo[END_REF][START_REF] Steil | All-Optical Magnetization Recording by Tailoring Optical Excitation Parameters[END_REF] . In our spin-valve samples, the threshold for switching both the GdFeCo and the ferromagnet's magnetization follows a similar trend of monotonic increase. Both these increases can be simply explained by the fact that, as the pulse duration becomes longer more energy is lost to the lattice that does not contribute to the demagnetization or the switching. Surprisingly, the threshold energy to generate a multi-domain state decreases with increasing pulse duration, which cannot be understood in the frame of the above discussion. This has never been reported in single GdFeCo layers [START_REF] Gorchon | Role of Electron and Phonon Temperatures in the Helicity-Independent All-Optical Switching of GdFeCo[END_REF] and is certainly due to our spin-valve structure. We believe thus that such decrease in threshold fluence with pulse duration maybe due to (mutual) spin currents (stronger for short pulses) that stabilize the magnetization of the remote layer.

In order to be more quantitative, we first evaluate the amount of angular momentum or magnetic moment transfer from the GdFeCo (during its reversal) to the CoNi/Pt multilayer.

Considering Choi et al [START_REF] Choi | Laser-Driven Spin Generation in the Conduction Bands of Ferrimagnetic Metals[END_REF] work, we can assume that the change in magnetization at the Cu/FM interface, due to the generated spin accumulation, can reach a maximum value of about M = 1000 A/m at 1 ps since the laser pulse we are using is ten time more energetic. This M value is a very rough estimate since we consider that the same magnetization is transferred to the first layer of the ferromagnetic multilayer. Moreover, we do not take into account the time dependence of the angular momentum transfer and the nonuniformity of the resulting magnetization in the first CoNi layer. We can now define a criterion to observe the switching of the FM multilayer: "To generate the switching of the FM, the magnetization of the first CoNi layer at the interface with Cu should reach the value M 1 ps after the laser pulse irradiation".

We then assume that after the first layer has switched the rest of the layer will reverse because of the exchange coupling as in ref. (13), (14). Note that with the above criterion, switching is observed when the normalized magnetization of the interface layer m = M/MS reaches around 10 - 3 . A better model would consider the rate of transfer of angular momentum through an s-d model [START_REF] Beens | S -d Model for Local and Nonlocal Spin Dynamics in Laser-Excited Magnetic Heterostructures[END_REF] , although this is out of the scope of this study. The criterion for the appearance of the multidomain state should be the complete demagnetization of the full multilayer. However, because a zero magnetization depends on the numerical precision and because it does not lead to qualitative changes, we assume that it is the case when the magnetization of the last layer of the FM reaches 10% of M.

Then, in order to determine the time evolution of m at the interfacial CoNi layer and in the last CoNi layer, due to the laser pulse, we have modeled the magnetization dynamics of the FM layer with a microscopic three temperature model (M3TM) for a spin 1/2 ferromagnetic system, considering heat diffusion and realistic light absorption profiles in the full structure. Information on the calculation procedure can be found in Supporting Information S5 [START_REF] Koopmans | Explaining the Paradoxical Diversity of Ultrafast Laser-Induced Demagnetization[END_REF] . Several parameters used for the calculation, shown in the Supporting Information, are determined either experimentally or from the literature [START_REF] Gorchon | Role of Electron and Phonon Temperatures in the Helicity-Independent All-Optical Switching of GdFeCo[END_REF][START_REF] Bergeard | Hot-Electron-Induced Ultrafast Demagnetization in Co / Pt Multilayers[END_REF][START_REF] Kittel | Introduction to Solid State Physics[END_REF] . Using the above criterion, we can then calculate the fluence to switch the interface layer Fint and compare with the experimentally determined fluence needed to switch both layers (Fboth). Similarly, the calculated fluence to demagnetize the last FM Fend is compared to the experimentally determined fluence needed to observe a multi-domain state (Fmulti) as shown in Figure 2b, 3c and 4b.

In Figure 2b, one can see the evolution of the calculated fluences (Fend and Fint) as a function of the CoNi Curie temperature. We can see that the calculation reproduces accurately the experimental trend. With no adjustment, we find about a factor two difference, which is reasonably good for such a simple model. In Figure 3c The evolution of the fluence as a function of the interface Co layer thickness is also well reproduced and the same factor two is observed.

In Figure 4b, showing the evolution of the fluence for both layer switching (Fboth and Fint) as a function of the pulse duration, a good agreement is observed between calculations and experiments. However, the evolution of the multi-domain fluence (Fend and Fmulti) as a function of the pulse duration is following the opposite trend. This could be a hint that the spin current from the GdFeCo demagnetization not only induce the FM switching but tends to avoid its demagnetization. Indeed if the laser pulse is longer, we expect the spin current to decrease because the GdFeCo relaxation will be longer (-dM/dt will decrease). Consequently, the fluence needed for the switching of both layers should increase and this spin current should no longer be as efficient in maintaining the magnetization direction once it has switched. Thus, the fluence needed to observe the multi-domain state should decrease.

In summary, we have studied femto-second single-shot all-optical magnetization switching for the various ferromagnetic layers (FM) in GdFeCo/Cu/FM spin valves and various pulse durations. The results shed light on the mechanism leading to this single laser pulse switching of a ferromagnet where FM layer thickness, Curie temperature, and pulse duration play decisive roles. Based on this finding, we developed a phenomenological criterion, and confirmed that it reproduces most of the experimental results. We also find that AOS of ferromagnetic layer is observed in a wide range of stack structures and pulse duration ranging from 35 fs to 1 ps, indicating robustness of the phenomenon. This work will provide us a way to engineer ferromagnetic materials for single-shot all-optical magnetization switching.

MATERIALS AND METHODS

Sample Preparation

All samples were prepared by physical vapor deposition. The base pressure used to deposit multilayer film was about 1 × 10 -7 Torr. Basic stacking structures used in this study for the spinvalve structure were as follows:

  are minor loops corresponding to the magnetization reversal of the GdFeCo layer. No shift of the minor loop indicates no coupling between GdFeCo and [CoxNi1-x /Pt] magnetic layers (The results for other x are shown in supplementary Supporting Information S2).

Figure 1 .

 1 Figure 1. Stacking structure and magnetic properties. (a). Stacking structure for the spin-valve

Figure 2 .

 2 Figure 2. All-optical magnetization switching for ferromagnetic materials with different Curie

Figure

  Figure3bshows MOKE images after irradiation of fs-laser pulses for the samples with different

Figure 3 .

 3 Figure 3. All-optical magnetization switching experiment by engineering thickness of

Figure 4 .

 4 Figure 4. All-optical magnetization switching experiment on spin-valve structure with

Ta ( 5 )

 5 /Gd23.3FeCo76.7 (5)/Cu (10)/[CoxNi1-x (1)/Pt (1)]4/ Pt (3)/Ta (5)/glass sub. (thickness in nm). The different composition x of Co were 0.2, 0.3, 0.4, 0.6, 0.8 and 1.0. Ta (5)/Gd23.3FeCo76.7 (5)/Cu (10)/Co (tCo)/Pt (1)/[Co (0.6)/Pt (1)]3/Pt (3)/Ta (5)/glass sub. The different top Co thicknesses tCo in [Co/Pt] were 0.2, 0.6 and 1.0 nm. AOS Measurement Ti: sapphire fs-laser source and regenerative amplifier were used for the pump laser beam in AOS measurement. Wavelength and repetition rate of the fs laser was 800 nm and 5 kHz, respectively. The 1/e 2 spot size 2w0 is ≈ 94 μm. MOKE images were obtained from the other side of the film. LED light source with a wavelength of 628 nm was used for taking MOKE images. ASSOCIATED CONTENT Supporting Information. The Supporting Information is available free of charge at XXX. Magnetic properties of [CoxNi1-x/Pt], MOKE Hysteresis loop, Determination of threshold fluence, Absorption profile, and M3TM calculation for the spin-valve structure. (PDF)

ACKNOWLEDGMENT The authors thank T. Ferté for technical support. This work was supported in part by JST-OPERA, JSPS KAKENHI (JP19J12926), DIARE, the French PIA project "Lorraine Université d'Excellence" reference ANR-15-IDEX-04-LUE, the Institut Carnot ICEEL, the Sakura Program, the JSPS Bilateral Program and the Tohoku University-Université de Lorraine Matching Funds. This work is part of the project PLUS supported by the "FEDER-FSE Lorraine et Massif Vosges 2014-2020", a European Union Program. J.I. acknowledges support from GP-Spin.

AUTHOR INFORMATION

Corresponding Author

* Stéphane Mangin -stephane.mangin@univ-lorraine.fr Author Contributions J.I., S.I., and S.M. planned study. M.H. performed sample fabrication. J.I., S.I., and Q.R. performed experiments, G.M. and J.G. helped for measurement. J.I. analyzed data. J.I., Q.R., and J.H. performed the calculation. J.I., Q.R., S.I., and S.M. wrote the manuscript with inputs from G.M., J.G., and S.F. All authors contributed to discuss the measurement results.

Notes

The authors declare no competing financial interest.


Basile Coutens

Céline Derreumaux

François Labaste

Vincent Minville

Dr Bruno Pierre Guiard
email: bruno.guiard@univ-tlse3.fr

Lionel Moulédous

Vincent Bounes

Anne Roussin

Bernard Frances

Editing Bruno

Pierre Guiard

: Supervision

Editing Lionel Moulédous

Editing Vincent Bounes

Editing Anne Roussin

Editing Bernard Francès

Efficacy of multimodal analgesic treatment of severe traumatic acute pain in mice pretreated with chronic high dose of buprenorphine inducing mechanical allodynia

Keywords: Conceptualization, Methodology, Investigation and Formal analysis. Céline Derreumaux : Conceptualization, Methodology, Investigation and Formal analysis. François Labaste : Conceptualization, Methodology. Vincent Minville : Validation, Writing -Review Hyperalgesia, Multimodal analgesia, Opioid, Buprenorphine

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.

Efficacy of multimodal analgesic treatment of severe traumatic acute pain in mice pretreated with chronic high dose of buprenorphine inducing mechanical allodynia 1 Introduction

Buprenorphine medication for maintenance treatment of opioid use disorder is available in most countries (INCB 2018). Abuse and misuse of prescription opioids has resulted in an opioid crisis with many patients developing opioid use disorder, particularly in the U.S. where efforts have been recently undertaken to expand access to buprenorphine [START_REF] Ghertner | trends in the supply of providers with a waiver to prescribe buprenorphine for opioid use disorder in 2016 and 2018[END_REF].

Whereas formulations of buprenorphine at low dosages are marketed for pain relief, there are controversies concerning pharmacological treatments of severe acute pain in patients receiving high doses of buprenorphine for opioid maintenance treatment. [START_REF] Jonan | Buprenorphine Formulations: Clinical Best Practice Strategies Recommendations for Perioperative Management of Patients Undergoing Surgical or Interventional Pain Procedures[END_REF] have recently discussed various pharmacological strategies of perioperative pain treatment in patients under buprenorphine for opioid maintenance treatment. These strategies are already described in many clinical guidelines and depend of elective versus emergency surgery and the need of intermediate or high postoperative opioid requirement. Multimodal analgesia is recommended in all scenari with non-opioid adjuvants as Non-Steroidal Anti-Inflammatory Drugs (NSAIDs) or N-methyl-D-aspartate (NMDA) receptor antagonists, regional anesthesia and local anesthetic infiltration. Several pharmacological features of buprenorphine could explain why a multimodal analgesia is required in case of severe acute pain. Buprenorphine is an opioid with a complex pharmacological profile. Indeed, this agent displays mixed agonistantagonist activity at classical opioid receptors. In particular evidence demonstrates that buprenorphine activates mu and kappa receptors while inhibiting the functional activity of delta receptors [START_REF] Cowan | Buprenorphine: new pharmacological aspects[END_REF]. Moreover, the existing data show that buprenorphine displays a 10-fold lower affinity for the delta receptor as compared to the mu and kappa. It should be also noted that buprenorphine has been shown to activate the opioid receptor-like (ORL-1; also known as NOP) receptor (Lufty and [START_REF] Lutfy | Buprenorphine: a unique drug with complex pharmacology[END_REF]. These properties hinder the use of full µ-opioid receptor agonists for severe acute pain relief in patients under buprenorphinemaintenance treatment. Moreover, opioid-induced hyperalgesia (OIH) can occur under opioid chronic treatment as well as in patients under opioid-maintenance treatment. OIH refers to the development of hypersensitivity to painful stimuli observed upon chronic opioid administration and includes two major manifestations i.e. allodynia and hyperalgesia [START_REF] Simonnet | Opioid-induced hyperalgesia: abnormal or normal pain?[END_REF]. OIH is highly prevalent (nearby 30%) with a long-term treatment with opioids for chronic pain [START_REF] Katz | Review of the performance of quantitative sensory testing methods to detect hyperalgesia in chronic pain patients on long-term opioids[END_REF]. For patients under opioid replacement therapy, randomized controlled trials aimed at identifying OIH in nonsurgical setting have been conducted. It has been observed a lower pain tolerance with buprenorphine-or methadone-maintained individuals compared to control [START_REF] Compton | Pain responses in methadone-maintained opioid abusers[END_REF][START_REF] Compton | Hyperalgesia in heroin dependent patients and the effects of opioid substitution therapy[END_REF][START_REF] Doverty | Hyperalgesic responses in methadone maintenance patients[END_REF][START_REF] Athanasos | Buprenorphine Maintenance Subjects Are Hyperalgesic and Have No Antinociceptive Response to a Very High Morphine Dose[END_REF]. All these experimental studies have been performed in patients dependent to a full µ-opioid receptor agonist before entry in maintenance therapy. However, whereas buprenorphine can represent the first opioid substance having led to a substance use disorder in some individuals, only few studies have been aimed to investigate if buprenorphine itself could induce hyperalgesia. A pioneer study [START_REF] Wala | Buprenorphine-induced hyperalgesia in the rat[END_REF] examined responsiveness to an ultra-low sub-analgesic dose and a higher analgesic dose of buprenorphine following acute and repeated administration in rat.

Animals displayed hyperalgesia with repeated analgesic doses and immediate hyperalgesia at ultra-low dose [START_REF] Wala | Buprenorphine-induced hyperalgesia in the rat[END_REF].

Here, we developed a model of severe acute pain based on a closed tibial fracture in mouse treated during nine days by high dose of buprenorphine (BUP HD) or its vehicle (Saline). The dose range of buprenorphine used for opioid maintenance treatment in human is higher than the one used to treat pain. In mouse, the range for analgesic dose does not exceed 100 µg/kg.

In this way, we chose to assess a higher buprenorphine dose (i.e. 2x200 µg/kg). The efficacy of multimodal analgesic approach was then tested in this original model to relieve postoperative pain.

Materials and methods

Animals

The study was approved by the French ethical committee in animal experimentation of the Region Midi-Pyrenees (France) project n° 2015101214598332 and conducted according to the European Convention for the Protection of Vertebrate Animals used for Experimental and Other Scientific Purposes (Strasbourg, 1986), in an accredited laboratory under the supervision of an authorized researcher. The animals were housed in cages with solid floor covered with 3 cm of soft bedding and were fed and watered ad libitum. There were five animals in each cage, living on a 12 h light-dark cycle. Three-four months old C57BL/6 male mice weighting between 20-25g (Janvier Labs, Saint-Berthevin, France) were used for all the experiments.

Protocol (Fig. 1)

Groups

A control group was included in all experiments; i.e. Saline (NaCl 0.9%, twice a day for 9 days; i.p.). [START_REF] Wala | Buprenorphine-induced hyperalgesia in the rat[END_REF] showed that buprenorphine at a dose of 2x100 µg/kg for ten days enhanced pain sensitivity in mice. Since opioid substitution treatment by buprenorphine involves higher daily doses than those used for analgesia, we decided to focus on a higher dosage (2x200 µg/kg / day for 9 days) of buprenorphine to generate the BUP HD group. For all drug administrations, the volume of injection was the same: 100 µl of solution were injected for 10g of mice.

The experimental protocol was defined in order to evaluate both allodynia and hyperalgesia during a chronic treatment, and hyperalgesia following a painful surgical intervention. It was therefore divided in three parts:

The first part (named "pre-fracture") lasted 9 days and involved the chronic treatment of mice, divided in two groups: Saline and BUP HD. Pain tests were performed before any treatment (baseline, D0) and thirty min after saline or buprenorphine administration on the 5th (D5) and the 9th day (D9). On the 10th day, a bone fracture was performed (see Fig. 1).

The second part of the protocol (named "post-fracture") involved pain tests conducted 2 (H2), 4 (H4) and 24 h (H24) after the fracture. An antinociceptive effect of 3 mg/kg morphine one day after the same consolidated tibial fracture has been previously observed in mice [START_REF] Minville | Opioid-induced hyperalgesia in a mice model of orthopaedic pain: preventive effect of ketamine[END_REF]. In the present study, morphine (4.5 mg/kg; i.p.) was administered 30 min before the H4 and H24 tests.

In order to avoid the possibility of a "cage effect", treatments were randomly assigned to each mouse before the beginning of first Von-Frey Test. Mice were then housed by group of five, so each cage contained mice injected with Saline and Buprenorphine treatment.

The third part was devoted to multimodal analgesia, 48h after surgery. Each group was divided in 3 subgroups: morphine (4.5mg/kg i.p.), morphine (4.5mg/kg i.p.) + ketamine (10mg/kg i.p.) or morphine (4.5mg/kg i.p.) + (ketoprofen 50mg/kg i.p.). Ketamine was chosen owing to its ability to antagonize NMDA receptors and have an opioid-sparing effect by reducing pain transmission and by preventing the development of OIH [START_REF] Crumb | Emerging Trends in Pain Medication Management: Back to the Future: A Focus on Ketamine[END_REF].

Ketoprofen was chosen as representative of the class of Non-Steroidal Anti-Inflammatory Drugs (NSAIDs).

Surgery: Bone fracture

A bone fracture was performed in all mice according to the validated technique described by [START_REF] Minville | Mouse model of fracture pain[END_REF]. Mice were anesthetized with 4% sevoflurane delivered via cone nose.

After antiseptic preparation of the right paw using povidone iodine, an unilateral closed fracture was made in the right tibia using a blunt guillotine (specially designed fracture apparatus). The fracture apparatus consists of four parts: a frame, an animal support system, a guillotine ramming system, and a 300-g weight. The support anvil was made with an adjustable foot rest that ensures that all of the fractures are at the same level by positioning the mouse leg on the anvil with the foot against the foot rest. For the intramedullary pinning using a sterile technique, a hole was made above the tibial tuberosity percutaneously using a 27-gauge needle (Becton Dickinson and Company, Drogheda, Ireland). Then the needle was directed into the medullary canal. By rotating the needle, the canal was reamed to 5 mm up to the ankle joint. The end of the needle was cut as short as possible so that the skin could roll over and cover it. No suture was used. Then, the mouse was placed with the leg on the anvil so that the blunt guillotine lined up with the proximal third of the tibia. The 300-g weight was dropped from a height of 9-10 cm, fracturing the tibia shaft. Radiography confirmed the fracture.

Mechanical nociception

Animals were placed on an elevated mesh floor surrounded by a clear plastic enclosure (10 X 10 X 10 cm) and allowed to acclimate to this environment for at least 15 min before testing.

We used the manual VonFrey filaments, according to the protocol described by [START_REF] Hache | Antinociceptive activity of the new triple reuptake inhibitor NS18283 in a mouse model of chemotherapy-induced neuropathic pain[END_REF]. Mechanical sensitivity was then assessed using three VonFrey filaments with bending force of 0.6g, 1.4g and 4g (Bioseb Inc., Vitrolles France). Each filament was applied in a growing strength for a duration of 2 sec to the mid-plantar area of each hind paw ten times, with 3 sec between each application. Rapid retraction, shaking and/or licking of the hind paw were considered to represent nociceptive specific behaviors and only one of these responses needed to be displayed to be considered as a positive withdrawal response. Applications were done to both hind paws, counted and then expressed as an overall percentage of paw withdrawal response (i.e. 50% for five paw withdrawals after 10 stimuli).

In basal conditions, filament inducing less than 40% of paw withdrawals is considered as painless while filament inducing more than 40% is considered as painful. Filaments were chosen in order to assess allodynia (painless filament 0.6g and 1.4g) and hyperalgesia (painful filament 4.0g) in basal condition (pre-fracture experiment). However, after bone fracture (post-fracture experiment) , all filaments were considered as painful.

Statistical analysis

Data were presented as mean ± S.E.M. Statistical significance was set at P< .05. For data presented on Fig. 234, two-way analyses of variance (ANOVAs) [Time x Treatment] were applied. Significant main effects were followed by Tukey post hoc analysis. For data presented on Fig. 4, one-way ANOVA follow by Dunnett's test were also realized in order to compare results to H2 tests. Comparisons and significant results are summarized in Supplemental Tables 1 and2.

Results

In the VonFrey filament test, the 0.6g and the 1.4g filaments were used to search for eventual allodynia whereas the application of the 4.0g filament which represents a painful stimulus,

was used to reveal a potential hyperalgesia.

Pre-fracture: A prolonged treatment with a high dose of buprenorphine induced mechanical allodynia

Before the initiation of the different treatments (Saline and BUP HD), groups of mice were balanced and their average percentages of hind paw retraction/withdrawal were similar (Fig. 2 A, B, C). As expected, the nociceptive response induced by the application of the 0.6g (Fig. 2A), 1.4g (Fig. 2B) and 4.0g (Fig. 2C) filaments did not vary with the day of treatment in the Saline group. In comparison with D0 values and also with those obtained with saline group, for the group of mice treated by BUP HD, the application of the 0.6g filament revealed significant allodynia from D5 (Fig. 2A -Suppl Table 1). The application of the 1.4g filament gave the same results since a significant increase in paw withdrawal percentage, evoking allodynia, was observed at D5 and D9 (Fig. 2B -Suppl Table 1). The application of the 4.0g filament induced intense response (about 60% of paw withdrawal) throughout the Saline and BUP HD. At D9, a significant increase in paw withdrawal percentage was observed in the mice from the BUP HD group in comparison with the Saline group (Fig. 2C -Suppl Table 1).

These observations indicate that chronic buprenorphine treatment led to the development of mechanical allodynia and a potential hyperalgesia.

Post-fracture: Loss of anti-allodynia and of analgesic effects of morphine in BUP HD group 24h and 48h after surgery

A closed tibial fracture was performed in all mice on the tenth day in order to induce severe acute pain. An acute injection of morphine (4.5 mg/kg; i.p.) was performed 30 min before the application of the 0.6g, 1.4g and 4.0 g filaments at H4, H24 and H48 post-fracture. The application of the 0.6g filament induced significant mechanical allodynia at H2 after surgery (significant increase of percentage of paw withdrawal in comparison with D0) that was no more observed in saline group after acute administration of morphine at H4 and H24 and H48 and also not observed in the BUP HD group but only at H4 (Fig. 3A -Suppl Table 1). After acute administration of morphine, the percentage of paw withdrawals was significantly higher in the BUP HD group at H24 and H48 post-fracture compared to Saline group. Overall, the application of the 1.4g filament provided the same results (Fig. 3B -Suppl Table 1). The application of the 4.0g filament induced a high level of pain (about 50% of paw withdrawal) since the beginning of the experiments and whatever the group of mice. As for the 0.6g and 1.4g Von Frey filaments, the percentage of paw withdrawals was significantly higher in the BUP HD group compared to Saline group at H24 and H48 after surgery, suggesting a loss of antiallodynic/analgesic effect of morphine (Fig. 3C -Suppl Table 1).

Post-fracture: multimodal analgesia is efficient to reduce pain in the BUP HD group

The third part of the protocol (named "multimodal analgesia") involved mechanical pain tests at H48 after the closed tibial fracture in mice from the two groups. Before testing, mice were injected with morphine (4.5 mg/kg; i.p.) alone or in combination with either ketamine (10 mg/kg; i.p.) or ketoprofen (50 mg/kg; i.p.).

In the Saline group, the evoked response was very low with the three filaments in the VonFrey test (similar to pre-injection values) and thus significantly lower than the pain sensitivity at H2 (Fig. 4A-C -Suppl Table 2). Addition of ketamine or ketoprofen to morphine did not change the nociceptive response.

In the BUP HD group, after injection of morphine alone, pain was also similar to the postfracture value, whereas a reduced pain response was observed in comparison to H2 when ketamine or ketoprofen was combined to morphine (Fig. 4A-C -Suppl Table 2). In addition, two-way ANOVA revealed that addition of ketoprofen is efficient to reduce pain response for both 0.6g and 1.4g filaments (Fig. 4A-B). In the same way, addition of ketamine reduced pain response only for the 0.6g filament (Fig. 4A).

Discussion

The main findings of this study are that a daily treatment of mice with a high dose of buprenorphine (2x200 µg/kg / day; i.p.) induces a significant mechanical allodynia evidenced at five and nine days of treatment. In a marked contrast, changes in thermal sensitivity were not observed in response to buprenorphine (see Fig. S1A-C). Interestingly, morphine exerts anti-allodynic and analgesic effects 24h and 48h after a severe pain induced by traumatic orthopedic surgery in the buprenorphine treated mice for nine days compared to saline controls on mechanical nociception. Reduced pain response was also observed when ketamine or ketoprofen was combined with morphine two days after the surgery. Finally, an increase in pain sensation was observed one and two days after a closed tibial fracture despite a single injection of morphine (which was analgesic in the Saline group).

Prescriptions of buprenorphine have markedly increased of 75.2% between 2011 and 2016 in the USA [START_REF] Piper | Trends in Medical Use of Opioids in the U.S., 2006-2016[END_REF]. Buprenorphine is now the most prescribed substitution drug for opioid addicts. In these patients, the management of intense acute pain as in case of orthopedic surgery is difficult and controversial. This is likely due to the high affinity and very low dissociation of buprenorphine from µ-opioid receptors that hinders the use of common opioid analgesics.

In this study, we pretreated mice during nine days with a high dose of buprenorphine (2x200 µg/kg / day; i.p.) to be as close as possible to clinical conditions of substitution treatment. We based our study on the work of [START_REF] Wala | Buprenorphine-induced hyperalgesia in the rat[END_REF] showing that an acute administration of 100 to 200 µg/kg buprenorphine produced anti-nociception in rats.

One of the most original results of our work is that a chronic treatment with buprenorphine induced mechanical allodynia in pain-free mice (pre-fracture experiments). Whereas not well known, as a subset of OIH, allodynia represents a potential complication of opioid therapy and has been first described after opioid intrathecal administration in rats and also in humans [START_REF] Hayes | A comprehensive clinical review of opioid-induced allodynia: Discussion of the current evidence and clinical implications[END_REF]. Several mechanisms of action of buprenorphine could have been involved in the emergence of allodynia. Activation of the mu opioid receptor, resulting in a classical form of OIH, is of course the primary suspect. However, buprenorphine is a partial agonist on mu opioid receptor but also an antagonist on kappa receptor, and, although with a lower affinity, can also activate nociceptin receptor at high doses. The fact that buprenorphine also binds and activates the nociceptin (NOP) receptor (Lufty and [START_REF] Lutfy | Buprenorphine: a unique drug with complex pharmacology[END_REF] raises the possibility of a contribution of this system to the allodynia observed herein. Indeed, nociceptin has been shown to induce tactile allodynia following intrathecal administration in mice [START_REF] Hara | Characterization of nociceptin hyperalgesia and allodynia in conscious mice[END_REF]). Moreover, it has been recently suggested that buprenorphine could also act as an inverse agonist on CB1 receptor and also as an activator of monoamine transporters [START_REF] Olson | Comprehensive molecular pharmacology screening reveals potential new receptor interactions for clinically relevant opioids[END_REF]. The modulation of these targets could also participate in the observed allodynia through a reduction in endocannabinoid [START_REF] Booker | The fatty acid amide hydrolase (FAAH) inhibitor PF-3845 acts in the nervous system to reverse LPS-induced tactile allodynia in mice[END_REF] and monoamine [START_REF] Nagakura | Biogenic amine depletion causes chronic muscular pain and tactile allodynia accompanied by depression: A putative animal model of fibromyalgia[END_REF] tone.

Of particular note, chronic buprenorphine treatment did not affect thermal sensitivity using the Thermal Place Preference or the Hargreaves tests (Fig. S1) suggesting that OIH could be selective to mechanical stimuli. Such a distinction between mechanical and thermal sensitivity has been already reported in response to acutely administered buprenorphine [START_REF] Siemian | Antinociceptive Interactions between the Imidazoline I2 Receptor Agonist 2-BFI and Opioids in Rats: Role of Efficacy at the mu-Opioid Receptor[END_REF]. It was also reported that a single administration of buprenorphine produced a greater analgesic effect on mechanical nociception compared to thermal nociception in a polyneuropathic rat model [START_REF] Christoph | Broad analgesic profile of buprenorphine in rodent models of acute and chronic pain[END_REF]. It is well known that sensory nerve fibers differ with respect to their sensory modalities and conduction velocities but also to their relative roles for pain hypersensitivity [START_REF] Draxler | VGluT3(+) primary afferents play distinct roles in mechanical and cold hypersensitivity depending on pain etiology[END_REF]. Based on the present results, it is plausible that pharmacological agents specifically influence mechanical or thermal sensitivity.

Some few clinical experimental data suggest that buprenorphine maintenance subjects display hyperalgesia and are resistant to analgesic effects of high doses of morphine [START_REF] Athanasos | Buprenorphine Maintenance Subjects Are Hyperalgesic and Have No Antinociceptive Response to a Very High Morphine Dose[END_REF]. In the latter study, pain-free subjects were recruited and maintained under daily buprenorphine treatment (dose range = 2-22 mg; no dose change for 1.5-12 month).

Buprenorphine subjects were hyperalgesic in the cold pressor test in comparison with controls. Subjects were tested at about the time of putative trough plasma buprenorphine concentrations. To our knowledge, the publication of [START_REF] Athanasos | Buprenorphine Maintenance Subjects Are Hyperalgesic and Have No Antinociceptive Response to a Very High Morphine Dose[END_REF] is the first work examining also the effect of added morphine to buprenorphine-substituted patients who were pain-free at the time of study. Very high doses of morphine (55 mg) failed to provide antinociception in either the electrical stimulation or cold pressor tests, irrespective of maintenance buprenorphine dose.

Since sedation could have represented a bias in the interpretation of the results, we decided to address this point by evaluating the locomotor activity of mice at baseline and after 9 days of saline or buprenorphine injection (see Fig S2). As expected, there was no locomotor activity difference between the two groups before injection of saline or buprenorphine (D0), showing a good balance in term of locomotor activity. Interestingly after 9 days of treatment, we observed a significant increase in locomotor activity following buprenorphine injection thereby ruling out the possibility that this pharmacological compound elicited sedative-like effects. Effect on locomotion was well described after opioid administration as shown by [START_REF] Allouche | Different patterns of administration modulate propensity of methadone and buprenorphine to promote locomotor sensitization in mice[END_REF] where locomotor sensitization was observed after buprenorphine and morphine injection.

Some limitations of our study must be pointed out. In our model, mice chronically treated with buprenorphine were not pre-treated with an opioid agonist like heroin, so our model is not representative of a substitution treatment of opioid dependence. This choice relies on the fact that heroin is also known to induce hyperalgesia [START_REF] Compton | Hyperalgesia in heroin dependent patients and the effects of opioid substitution therapy[END_REF] and we wanted to address the specific effects of buprenorphine.

Another important point that has yet to be solved is to determine whether it is necessary to discontinue/withdraw buprenorphine treatment in patients that undergo major elective surgery. So far, there is no consensus on this question although recommendations exist on perioperative optimal acute pain management strategies for patients taking buprenorphine.

However, reduction or even stopping buprenorphine should be differentially considered regarding previous use of buprenorphine for chronic pain treatment or for substance in patients with opioid use disorder [START_REF] Goel | Perioperative Pain and Addiction Interdisciplinary Network (PAIN): protocol of a practice advisory for the perioperative management of buprenorphine using a modified Delphi process[END_REF]. [START_REF] Anderson | To Stop or Not, That Is the Question: Acute Pain Management for the Patient on Chronic Buprenorphine[END_REF] suggested to continue buprenorphine in patients undergoing surgeries with only mild pain expected postoperatively, or patients at high risk for perioperative substance abuse relapse, because of the anxiety and possible destabilization caused by the cessation. In patients taking buprenorphine for chronic pain or if it is anticipated that postoperative pain may be difficult to control, buprenorphine may be discontinued preoperatively and replaced with opioid agonists in the interim. In our model, we decided to interrupt buprenorphine treatment before the orthopedic surgery.

Tibial fracture was chosen to induce a major orthopedic pain [START_REF] Minville | Mouse model of fracture pain[END_REF]. Among orthopedic surgery patients, preoperative opioid use is associated with increased postoperative pain, higher postoperative opioid requirements, and continued use of opioids in the weeks to months after surgery [START_REF] Hayhurst | Differential Opioid Tolerance and Opioid-induced Hyperalgesia: A Clinical Reality[END_REF][START_REF] Smith | Impact of Preoperative Opioid Use on Total Knee Arthroplasty Outcomes[END_REF][START_REF] Rozell | Preoperative Opiate Use Independently Predicts Narcotic Consumption and Complications After Total Joint Arthroplasty[END_REF].

In our study, using the VonFrey test, we found that a dose of morphine (4.5 mg/kg) usually analgesic such as in the Saline group, was not efficient to alleviate pain in BUP HD group one and two days after the orthopedic surgery whichever the hind paw stimulated (fractured vs non-fractured paw). However, in the peri-operative period (H4) morphine was effective to produce analgesia, no difference was observed between Saline and BUP HD groups. It cannot also be excluded that at H24 or H48 apparent hyperalgesia (i.e. the loss of morphine effect) could represent withdrawal-induced hyperalgesia, a well-known phenomenon following the abrupt cessation of opioid [START_REF] Stein | New concepts in opioid analgesia[END_REF] or tolerance to the antinociceptive effect of morphine.

In fact, it is difficult to anticipate whether a higher dose of morphine would have produced analgesic or hyperalgic responses. On these grounds, it could have been interesting to compare the pain levels after surgery with and without morphine injection, to know if hyperalgesia is observed or not but also to evaluate the evolution of pain/recovery all along post-fracture experiment. We did not perform this control group for ethical reasons but also to fit with clinical practice in which pain must be relieved as soon as possible. Moreover, we do believe that tests at H2 represent valuable controls in post-fracture experiment and allow us to provide reliable conclusions only by evoking a loss of sensitivity to morphine and not hyperalgesia.

The efficacy of multimodal analgesic approach was then tested to relieve postoperative pain.

We tested pharmacological substances now recommended for the perioperative pain treatment in human.

The combination of opioids and nonsteroidal anti-inflammatory drugs (NSAIDs) may provide synergistic analgesia. Evidence suggests a role for COX-2 inhibitors in the modulation of OIH in humans [START_REF] Angst | Short-term infusion of the mu-opioid agonist remifentanil in humans causes hyperalgesia during withdrawal[END_REF][START_REF] Koppert | Differential modulation of remifentanil-induced analgesia and postinfusion hyperalgesia by S-ketamine and clonidine in humans[END_REF]. Thus, it is suggested that there is a possible role for prostaglandins in sensitizing the nociceptive system before pathologic activation, and that it probably has a less important role than the N-methyl-D-aspartate receptor (NMDA) system, at least in human experimental pain models after acute opioid exposure [START_REF] Lee | A comprehensive review of opioidinduced hyperalgesia[END_REF]. Therefore, we assessed multimodal analgesia two days after surgery to alleviate pain observed in VonFrey test despite morphine (4.5 mg/kg) administration. Our results showed that the combination of morphine with ketoprofen, a nonsteroidal anti-inflammatory drug (NSAID), was able to alleviate pain in BUP HD group in comparison with morphine alone.

These results suggest that the combination of opioids and NSAIDs may provide additive analgesia and alleviate OIH. Multimodal analgesia with ketoprofen associated to morphine was efficient to reduce pain in post-fracture experiments in the BUP HD group.

Minville and colleagues (2010) investigated the effects of the NMDA-receptor antagonist ketamine on postoperative hyperalgesia in a mouse model of orthopedic pain. These experiments showed that mice given intraoperative opioid analgesia (i.e. sufentanil) and high dose ketamine had significantly less thermal hyperalgesia (measured as the amount of time a hind paw could remain on a hot plate before withdrawal) for the first 4 postoperative days as compared to mice treated with sufentanil alone. Prior research with ketamine had shown similar results. Indeed, ketamine enhanced the earlier response (analgesia) and prevented the development of long-lasting enhancement in pain sensitivity in fentanyl-treated rats [START_REF] Celerier | Long-lasting hyperalgesia induced by fentanyl in rats: preventive effect of ketamine[END_REF]. The NMDA receptor antagonist MK-801 also prevented both heroin-induced long-lasting enhancement in pain sensitivity, suggesting that hyperalgesia is issued from a neuroadaptive process in which NMDA systems play a critical role [START_REF] Celerier | Evidence for opiate-activated NMDA processes masking opiate analgesia in rats[END_REF]2001;[START_REF] Laulin | The role of ketamine in preventing fentanyl-induced hyperalgesia and subsequent acute morphine tolerance[END_REF]. On this context, we assessed the combination of morphine with ketamine.

Our results showed that this combination was able to alleviate pain in BUP HD group in comparison with morphine alone. We chose not to evaluate the effect of ketamine and ketoprofen alone because it would have been necessary to split groups and we would have to reduce the number of mice per group. In fact, these results suggest that the combination of opioids and NMDA-receptor antagonist may provide additive analgesia and alleviate OIH compare to morphine alone.

While it is unrealistic to expect that the diversion and misuse of opioid analgesics can be entirely eradicated, the effects of these drugs on public health need to be acknowledged, tracked, and mitigated. Important research gaps exist in such areas and intensive efforts worldwide (from basic science to drug development) must be directed toward understanding the neurobiology of acute/chronic pain and the mechanism of action of related treatments based on the manipulation of opioid receptors. This will likely help provide new therapeutic options with safer and more effective profile. In this prospect, three main strategies are currently under investigation: mu-opioid receptors biased agonists, multiple opioid receptor mixed agonists, and blockade of the catabolism of endogenous peptides (Turnaturi et al., 2019, Noble and[START_REF] Noble | Management of Opioid Addiction With Opioid Substitution Treatments: Beyond Methadone and Buprenorphine[END_REF].

To conclude, our findings showed for the first time that a chronic treatment with a high dose of buprenorphine is able to induce an allodynia on pain-free mice model and that our model of closed tibia fracture will allow to study new protocols of pain management of peri-and postoperative severe acute pain management for patients suffering from OIH.

Thermal nociception

The protocol of the Thermal Place Preference Test was as described by [START_REF] Hache | Antinociceptive effects of fluoxetine in a mouse model of anxiety/depression[END_REF].

Mice were placed in an enclosure in which the floor is composed by two adjoining thermoelectric computer-managed metal plates (Bioseb Inc., Vitrolles France), and first were allowed to freely explore the area for 5 min daily, for 2 days (habituation). Both plates were enclosed by an opaque Plexiglas box (Bioseb Inc., Vitrolles France). Low illumination was used for each compartment. Preliminary experiments determined that 'naïve' animals spent a similar amount of time on the two plates when they were set to 25°C, suggesting that there is no bias towards one compartment. Subsequently, in the present work, the floor of one compartment was maintained at 25°C and the other plate was set at 20°C (moderate cold).

This latter temperature is well within the threshold range of channel complexes localized within the terminal endings of sensory neurones that are capable of responding to cooling and cold. The animals were videotaped from above for 5 min, and the time spent on each plate was automatically recorded. The number of transitions between the two plates and the total mobility time were recorded as well, to check the good walking ability of the animals in the post-fracture time.

Paw withdrawal latency in response to radiant heat was measured using the Hargreaves equipment (Ugo Basile, Varese, Italy). Mice were placed in a clear plastic chamber on a glass floor, and allowed to acclimate to this environment for at least 15 min before testing. Then the radiant heat source was positioned under the glass floor directly beneath the right hind paw, and a trial commenced by a switch which activated the radiant heat source and started an electronic timer. The radiant heat source consisted of a high intensity projector lamp bulb located around 12 cm under the glass floor, so as to create a temperature of 45°C on the hind paw. The heat beam was switched off when the mouse lifted or licked its hind paw, signs of pain, and the electronic timer stopped automatically. A cut-off time of 20 sec was used to avoid tissue damage. Two measures, separated by a 5 min interval, were performed and the mean of the two values was kept.

Locomotor Activity

Mice were tested in the Open Field test in order to evaluate the effect of Saline and BUP HD

-Results

Lack of evidence of allodynia or hyperalgesia in thermal nociceptive tests

The percentages of time spent on the 20°C plate in the Thermal Place Preference Test on D0

were undistinguishable between both groups such as the paw withdrawal latencies in response to radiant heat (Hargreaves' test). After the 9-days chronic treatments (pre-fracture), buprenorphine-treated mice showed a marked decrease of time spent on 20°C plate but it was not significant (Figure S1A) and the paw withdrawal latencies were similar (Figure S1C) in both groups. In this case, the chronic treatment with high doses of buprenorphine did not induce any allodynia or hyperalgesia thereby demonstrating different sensibilities of mice to mechanical or thermal stimuli.

In the Thermal Place Preference Test, the level of pain was higher in both groups two and four h (H2 and H4) after the surgery without highlighting any consequences of the chronic treatments, nor of morphine administration (figure S1B). Two-way ANOVA only showed a significant effect of BUP HD treatment at H2 with an increase of pain sensitivity while 4.5 mg/kg of morphine reversed this effect at H24 (D0 vs H2, P=0.009; H2 vs H24, P=0.021). As observed previously in mechanical experiment, the chronic treatment with BUP HD did not induce any allodynia/hyperalgesia 24 h after surgery, again demonstrating different sensibilities of mice to mechanical or thermal stimuli. In the Hargreaves test, the pain threshold remained stable throughout the experiments (Figure S1D).

Chronic buprenorphine treatment promotes locomotor activity

As expected, the results of locomotor activity test at D0 showed that there is no difference in distance travelled between both groups which were well balanced in term of locomotor activity. Interestingly after 9 days of treatment, two-way ANOVA [Treatment x Day] showed a significant effect of interaction (F(1:16)=38.6, P< 0.001), Day factor (F(1:16)=17.2, P<0.001)

and Treatment factor (F(1:16)=23;6, P<0.001). Indeed, we observed a significant increase in locomotor activity in buprenorphine-injected mice after nine days of chronic treatment compared to their respective baseline (D9 vs. D0: P<0.001).

FIGURE S1

Figure 1 -

 1 Figure 1 -Experimental protocol. Pain tests: VonFrey filament test.

Figure 2 -

 2 Figure 2 -Pre-fracture: A prolonged treatment with a high dose of buprenorphine induced mechanical allodynia and hyperalgesia Mechanical nociception test using von Frey filaments with bending force (A) 0.6g, (B) 1.4g, and (C) 4.0g. Tests were performed at baseline (D0), after five and nine days of chronic treatment (D5-D9). Results are expressed in percentage of withdrawal ± S.E.M. for Saline (n=17, white bar) and BUP group (n=22, black bar). *** P<0.001 significantly different from their respective baseline (D0); $ P< 0.05 and $$$ P<0.001 significantly different from Saline group at the corresponding day.

Figure 3 -

 3 Figure 3 -Post-fracture: Loss of anti-allodynia and analgesic effects of morphine in the BUP HD group 24h and 48h after surgery Mechanical nociception test using von Frey filaments with bending force (A) 0.6g, (B) 1.4g, and (C) 4.0g. Tests were performed at baseline (D0); pre-fracture (Fig. 2), two (H2), four (H4), twenty-four (H24) and forty-eight h (H48) after a closed tibial fracture. Results are expressed in percentage of withdrawal ± S.E.M. for Saline (n=17, white bar) and BUP group (n=22, black bar). For H48 tests, both groups were divided in subgroups for multimodal analgesia (Saline n=8; BUP HD n=6). For each result $ P< 0.05, $$ P< 0.01 and $$$ P<0.001 significantly different from their respective value assessed two h after fracture (H2). * P< 0.05 and *** P<0.001 significantly different from baseline (D0), ° P<0.05, °°P<0.01 and °°° P<0.001 significantly different from their respective Saline group.

Figure 4 -

 4 Figure 4 -Post-fracture: multimodal analgesia is efficient to reduce pain in the BUP HD group Mechanical nociception test using von Frey filaments with bending force (A) 0.6g, (B) 1,4g and (C) 4.0g. Tests were assessed two h (H2; Fig. 3) and 2 days after a closed tibial fracture (H48). Results were expressed in percentage of withdrawal ± S.E.M. for Saline (white histogram) and BUP HD group (black bar). Respective results of H2 tests were represented by horizontal solid line (Mean) and discontinuous line (S.E.M.). All groups were divided in subgroups to assess different multimodal analgesia: Saline (Morphine, n=8; Morphine+Ketamine, n=4; Morphine+Ketoprofene, n=5), and BUP HD (Morphine, n=6; Morphine+Ketamine, n=8; Morphine+Ketoprofene, n=10). For each result * p<0.05, ** P< 0.01 and *** P<0.001: significantly different from Morphine condition. For each result $ P<0.05, $$ P< 0.01 and $$$ P<0.001: significantly different from respective H2 tests.

  Figure 1

  treatment on locomotion at D0 and D9 in pre-fracture experiment. The circular field dimensions were 40 x 30 cm. The tests were conducted in the morning, following habituation in room experimentation (1 h in the homecage). Mice were tracked by video tracking (Ethovision Noldus, Wageningen, The Netherlands). Before the beginning of chronic treatment and 30 min after the last drug administration, each animal was placed in the center of the open field then locomotor activity was recorded during 10 min. The open field was cleaned with 30% ethanol between animals. Locomotor activity score was expressed as distance travelled (in cm).

  FIGURE S2

Figure 4C MOR

 4C Figure 4C

Figure S2 -

 S2 Figure S2 -Chronic Buprenorphine increases locomotor activity. Data are mean ± S.E.M. of distance travelled (in cm) in the open-field for 10 min before (D0) and after (D9) injection of saline (n=5) or BUP (n=5). ***p< 0.001 significantly different from the corresponding group of mice tested at D0 respective baseline (D0). ### P< 0.001 significantly different from the group of mice injected with saline at D9.