Analysis of the Anisotropic Magnetocaloric Effect in RMn2O5 Single Crystals

Thanks to the strong magnetic anisotropy shown by the multiferroic RMn2O5 (R = magnetic rare earth) compounds, a large adiabatic temperature change can be induced (around 10 K) by rotating them in constant magnetic fields instead of the standard magnetization-demagnetization method. Particularly, the TbMn2O5 single crystal reveals a giant rotating magnetocaloric effect (RMCE) under relatively low constant magnetic fields reachable by permanent magnets. On the other hand, the nature of R3+ ions strongly affects their RMCEs. For example, the maximum rotating adiabatic temperature change exhibited by TbMn2O5 is more than five times larger than that presented by HoMn2O5 in a constant magnetic field of 2 T. In this paper, we mainly focus on the physics behind the RMCE shown by RMn2O5 multiferroics. We particularly demonstrate that the rare earth size could play a crucial role in determining the magnetic order, and accordingly, the rotating magnetocaloric properties of RMn2O5 compounds through the modulation of exchange interactions via lattice distortions. This is a scenario that seems to be supported by Raman scattering measurements.


Introduction
Functional magnetocaloric materials at room temperature have attracted worldwide interest over the last two decades due to their potential implementation as refrigerants in magnetic cooling systems [1][2][3][4][5][6][7][8][9][10][11][12][13].However, the search for materials with excellent magnetocaloric properties in the temperature range from about 2 to 30 K is of great interest from fundamental, practical, and economical points of view, due to their potential use as refrigerants in several low temperature applications such as the space industry, scientific instruments, and gas liquefaction [14][15][16][17][18][19][20][21][22][23][24][25].On the other hand, the development of new designs that can render magnetic cooling more competitive is also a key parameter for the commercialization of this emergent technology.Recently, Matsumoto et al. [14] have unveiled a reciprocating AMR magnetic cooling device which utilizes the Dy 2.4 Gd 0.6 Al 5 O 12 (DGAG) compound as a working refrigerant.However, this material exhibits a large specific heat which largely reduces its magnetocaloric effect (MCE) in terms of the adiabatic temperature change (1 to 2 K under 1 T) [14].
In this context, the RMn 2 O 5 (R = magnetic rare-earth element) multiferroics seem to be alternative candidates for magnetocaloric tasks around 10 K [15,16,[25][26][27][28][29].These compounds unveil complex crystalline and magnetic structures which results in a wide range of fascinating electrical and magnetic phenomena [25][26][27][28][29].At room temperature, they crystallize in the orthorhombic structure of the space group Pbam.Their unit cell consists of Mn 3+ O 5 pyramids and Mn 4+ O 6 octahedra which are connected to each other through oxygen atoms [25,26].The octahedra are aligned along the c-axis and share their edges.The formed ribbons are linked by pairs of corner-shared Mn 3+ O 5 pyramids within the ab-plane.The rare earth R 3+ ions are located in the empty interstitial sites surrounded by octahedra and pyramids.
Over the past fifteen years, the RMn 2 O 5 compounds have been widely studied because of the strong coupling between their electric and magnetic ordering parameters.Particularly, Hur et al. [13] have demonstrated that a reversible switching of electric polarization can be achieved in TbMn 2 O 5 using relatively low magnetic fields, opening ways for the design of new multiferroic devices.On the other hand, the competition between different magnetic exchange interactions in the orthorhombic RMn 2 O 5 compounds results in strongly frustrated systems.Consequently, a large MCE could be obtained by rotating them between their easy and hard-axes in constant magnetic fields (Figure 1), instead of the conventional magnetization-demagnetization process (via field variation) [15,16,30,31].This would enable the implementation of more compact and efficient magnetic refrigeration devices with a simplified design [1,15,16].However, as presented below, the RMCE shown by the RMn 2 O 5 oxides markedly depends on the rare earth element.In this paper, we try to understand the physics behind such differences by combining both magnetic measurements and Raman scattering data.
In this context, the RMn2O5 (R = magnetic rare-earth element) multiferroics seem to be alternative candidates for magnetocaloric tasks around 10 K [15,16,[25][26][27][28][29].These compounds unveil complex crystalline and magnetic structures which results in a wide range of fascinating electrical and magnetic phenomena [25][26][27][28][29].At room temperature, they crystallize in the orthorhombic structure of the space group Pbam.Their unit cell consists of Mn 3+ O5 pyramids and Mn 4+ O6 octahedra which are connected to each other through oxygen atoms [25,26].The octahedra are aligned along the c-axis and share their edges.The formed ribbons are linked by pairs of corner-shared Mn 3+ O5 pyramids within the ab-plane.The rare earth R 3+ ions are located in the empty interstitial sites surrounded by octahedra and pyramids.
Over the past fifteen years, the RMn2O5 compounds have been widely studied because of the strong coupling between their electric and magnetic ordering parameters.Particularly, Hur et al. [13] have demonstrated that a reversible switching of electric polarization can be achieved in TbMn2O5 using relatively low magnetic fields, opening ways for the design of new multiferroic devices.On the other hand, the competition between different magnetic exchange interactions in the orthorhombic RMn2O5 compounds results in strongly frustrated systems.Consequently, a large MCE could be obtained by rotating them between their easy and hard-axes in constant magnetic fields (Figure 1), instead of the conventional magnetization-demagnetization process (via field variation) [15,16,30,31].This would enable the implementation of more compact and efficient magnetic refrigeration devices with a simplified design [1,15,16].However, as presented below, the RMCE shown by the RMn2O5 oxides markedly depends on the rare earth element.In this paper, we try to understand the physics behind such differences by combining both magnetic measurements and Raman scattering data.It is worth noting that the magnetocaloric properties and particularly the RMCE were separately reported in RMn2O5 (R = Ho, Tb) multiferroics [15,16].However, in order to provide the reader with the big picture of the RMCE shown by these materials, we consider that it is important to firstly discuss and compare their magnetic and magnetocaloric properties in section 2. This will enable us to pave the way for the developed analysis in section 3 regarding the influence of the rare earth size on the RMCE in RMn2O5 single crystals.

RMCE in RMn2O5 (R = Tb and Ho): Comparative Study
Figure 2 shows the Raman spectra of RMn2O5 (R = Tb and Ho) at 5 K obtained with incident light (632.8nm) polarized in the xy-plane.The analysis of different Raman excitations confirms that the high-quality crystals under study form in an orthorhombic symmetry with the Pbam space group.It It is worth noting that the magnetocaloric properties and particularly the RMCE were separately reported in RMn 2 O 5 (R = Ho, Tb) multiferroics [15,16].However, in order to provide the reader with the big picture of the RMCE shown by these materials, we consider that it is important to firstly discuss and compare their magnetic and magnetocaloric properties in Section 2. This will enable us to pave the way for the developed analysis in Section 3 regarding the influence of the rare earth size on the RMCE in RMn 2 O 5 single crystals.

RMCE in RMn 2 O 5 (R = Tb and Ho): Comparative Study
Figure 2 shows the Raman spectra of RMn 2 O 5 (R = Tb and Ho) at 5 K obtained with incident light (632.8nm) polarized in the xy-plane.The analysis of different Raman excitations confirms that the high-quality crystals under study form in an orthorhombic symmetry with the Pbam space group.It is worth noting that the competition between different magnetic exchange interactions makes RMn 2 O 5 systems highly frustrated.Consequently, consecutive magnetic and ferroelectric phase transitions occur at around 45, 38, 20, and 10 K [25][26][27][28][29]. Usually, the Mn 3+ /Mn 4+ spins order in an incommensurate antiferromagnetic (AFM) state at T N1 ~45 K, becoming commensurate with decreasing temperature at a lock-in transition point (T L = 33 K).A second magnetic phase transition at which the AFM ordering of Mn moments becomes incommensurate takes place at T N2 ~20 K.The onset of ferroelectric order was observed slightly below T N1 , at T C ~38 K, while the rare earth moments usually order below 15 K [25][26][27][28][29].The temperature dependence of the magnetization for both HoMn 2 O 5 and TbMn 2 O 5 compounds under a low magnetic field of 0.1 T applied along their easy-axes is reported in Figure 3a.As shown, only the magnetic transition related to the R 3+ spin ordering is clearly visible at low temperatures around 10 K.The phase transitions involving the manganese sublattice and occurring at T N1 , T C , and T N2 cannot be clearly seen in the thermomagnetic curves shown in Figure 3a, but their presence can be easily identified from specific heat measurements, as reported in Reference [28].This mainly arises from the complex arrangement of the Mn moments in RMn 2 O 5 .In the latter, the Mn 3+ /Mn 4+ magnetic moments are strongly AFM-coupled within the ab-plane, building zigzag chains in a direction along the a-axis, regardless of the presence of the rare-earth 4f-magnetic moments [25,26].This makes the contribution of the Mn 3+ /Mn 4+ moments to the total magnetization marginal, being a common property of RMn 2 O 5 multiferroics [25][26][27][28][29]. On the other hand, the large magnetic moment of the rare earth ions (~10 µ B ) tends to overshadow the features resulting from the Mn sublattice.
Magnetochemistry 2017, 3, 36 3 of 8 is worth noting that the competition between different magnetic exchange interactions makes RMn2O5 systems highly frustrated.Consequently, consecutive magnetic and ferroelectric phase transitions occur at around 45, 38, 20, and 10 K [25][26][27][28][29]. Usually, the Mn 3+ /Mn 4+ spins order in an incommensurate antiferromagnetic (AFM) state at TN1 ~ 45 K, becoming commensurate with decreasing temperature at a lock-in transition point (TL = 33 K).A second magnetic phase transition at which the AFM ordering of Mn moments becomes incommensurate takes place at TN2 ~ 20 K.The onset of ferroelectric order was observed slightly below TN1, at TC ~ 38 K, while the rare earth moments usually order below 15 K [25][26][27][28][29].The temperature dependence of the magnetization for both HoMn2O5 and TbMn2O5 compounds under a low magnetic field of 0.1 T applied along their easy-axes is reported in Figure 3a.As shown, only the magnetic transition related to the R 3+ spin ordering is clearly visible at low temperatures around 10 K.The phase transitions involving the manganese sublattice and occurring at TN1, TC, and TN2 cannot be clearly seen in the thermomagnetic curves shown in Figure 3a, but their presence can be easily identified from specific heat measurements, as reported in Reference [28].This mainly arises from the complex arrangement of the Mn moments in RMn2O5.In the latter, the Mn 3+ /Mn 4+ magnetic moments are strongly AFM-coupled within the abplane, building zigzag chains in a direction along the a-axis, regardless of the presence of the rareearth 4f-magnetic moments [25,26].This makes the contribution of the Mn 3+ /Mn 4+ moments to the total magnetization marginal, being a common property of RMn2O5 multiferroics [25][26][27][28][29]. On the other hand, the large magnetic moment of the rare earth ions (~10 µB) tends to overshadow the features resulting from the Mn sublattice.The magnetic and magnetocaloric properties (particularly RMCE) are very sensitive to the nature of the R 3+ ions.In Figure 3b, the isothermal magnetization curves of the RMn2O5 (R = Ho, Tb) single crystals measured at 2 K as a function of the magnetic field applied along their easy and hardaxes are plotted.Although the magnetic moments of Tb 3+ and Ho 3+ are almost similar, the magnetic behaviors of both TbMn2O5 and HoMn2O5 show significant deviations.The data in Figure 3b indicate that the magnetic easy-direction of TbMn2O5 is along the a-axis, while that of HoMn2O5 is along the b-axis.From the linear fit of the inverse magnetic susceptibility (not shown here), the paramagnetic Curie-Weiss temperatures along the easy axes were found to be about 0.9 K for HoMn2O5 and 20 K for TbMn2O5.The weak value of Tϴ in the case of HoMn2O5 reflects a paramagnetic behavior and/or The magnetic and magnetocaloric properties (particularly RMCE) are very sensitive to the nature of the R 3+ ions.In Figure 3b, the isothermal magnetization curves of the RMn 2 O 5 (R = Ho, Tb) single crystals measured at 2 K as a function of the magnetic field applied along their easy and hard-axes are plotted.Although the magnetic moments of Tb 3+ and Ho 3+ are almost similar, the magnetic behaviors of both TbMn 2 O 5 and HoMn 2 O 5 show significant deviations.The data in Figure 3b indicate that the magnetic easy-direction of TbMn 2 O 5 is along the a-axis, while that of HoMn 2 O 5 is along the b-axis.From the linear fit of the inverse magnetic susceptibility (not shown here), the paramagnetic Curie-Weiss temperatures along the easy axes were found to be about 0.9 K for HoMn 2 O 5 and 20 K for TbMn 2 O 5 .The weak value of T θ in the case of HoMn 2 O 5 reflects a paramagnetic behavior and/or a weak antiferromagnetic order of Ho 3+ ions.In contrast, the relatively large positive value of T θ as in the case of TbMn 2 O 5 suggests a dominant ferromagnetic ordering of Tb 3+ moments.This leads to a marked difference in the behavior of the field dependence of magnetization along the easy-axes of RMn 2 O 5 (R = Ho, Tb), as shown in Figure 3b.With an increasing field, the HoMn 2 O 5 magnetization increases slightly with a weak tendency to saturate even under high magnetic fields (127 Am 2 /kg under 7 T).For TbMn 2 O 5 , the magnetization easily reaches the saturation state under relatively low magnetic fields of about 2 T. The magnetization saturation is found to be about 140 Am 2 /kg (8.75 µ B /f.u.), being close to the Tb 3+ magnetic moment (9 µ B ).This indicates that the Tb 3+ magnetic moments in TbMn 2 O 5 can be completely aligned using magnetic fields higher than 2 T, since the contribution of the Mn sublattice to the full magnetization is negligible.
Magnetochemistry 2017, 3, 36 4 of 8 a weak antiferromagnetic order of Ho 3+ ions.In contrast, the relatively large positive value of Tϴ as in the case of TbMn2O5 suggests a dominant ferromagnetic ordering of Tb 3+ moments.This leads to a marked difference in the behavior of the field dependence of magnetization along the easy-axes of RMn2O5 (R = Ho, Tb), as shown in Figure 3b.With an increasing field, the HoMn2O5 magnetization increases slightly with a weak tendency to saturate even under high magnetic fields (127 Am 2 /kg under 7 T).For TbMn2O5, the magnetization easily reaches the saturation state under relatively low magnetic fields of about 2 T. The magnetization saturation is found to be about 140 Am 2 /kg (8.75 µB/f.u.), being close to the Tb 3+ magnetic moment (9 µB).This indicates that the Tb 3+ magnetic moments in TbMn2O5 can be completely aligned using magnetic fields higher than 2 T, since the contribution of the Mn sublattice to the full magnetization is negligible.As a result, an enhancement of the magnetocrystalline anisotropy is observed in TbMn2O5 (Figure 3b).When changing the magnetic field direction from the easy-axis to the hard-axis, the magnetization under a magnetic field of 7 T is reduced by 94% in the case of TbMn2O5 and 70% for HoMn2O5.In Figure 3c, we report the temperature dependence of the rotating entropy change (ΔSR), associated with the rotation by an angle of 90° of HoMn2O5 (in the cb-plane) and TbMn2O5 (in the caplane) between their easy and hard-axes.ΔSR can be written as ΔSR = ΔS (H//easy-axis) − ΔS (H//hardaxis) [1], where ΔS (H//easy-axis) and ΔS (H//hard-axis) are the entropy changes resulting from the application of the magnetic field along the easy and hard-axes, respectively.Both quantities can be well calculated from isothermal magnetization curves using the Maxwell relation since the hysteresis effect in these multiferroic materials is negligible [32,33].As can be seen in Figure 3c, TbMn2O5 unveils a rotating entropy change that is about two times larger than that shown by HoMn2O5.Under a constant magnetic field of 2 T which is accessible via permanent magnets [34,35], ΔSR, max is found to be 6.36 J/kg K for TbMn2O5 and only about 3 J/kg K for HoMn2O5.The improvement of ΔSR in the TbMn2O5 compound is mainly attributed to the reinforcement of the magnetocrystalline anisotropy, as well as the enhancement of the magnetization (arising from Tb 3+ ions) along the easy-axis.More As a result, an enhancement of the magnetocrystalline anisotropy is observed in TbMn 2 O 5 (Figure 3b).When changing the magnetic field direction from the easy-axis to the hard-axis, the magnetization under a magnetic field of 7 T is reduced by 94% in the case of TbMn 2 O 5 and 70% for HoMn 2 O 5 .In Figure 3c, we report the temperature dependence of the rotating entropy change (∆S R ), associated with the rotation by an angle of 90 • of HoMn 2 O 5 (in the cb-plane) and TbMn 2 O 5 (in the ca-plane) between their easy and hard-axes.∆S R can be written as ∆S R = ∆S (H//easy-axis) − ∆S (H//hard-axis) [1], where ∆S (H//easy-axis) and ∆S (H//hard-axis) are the entropy changes resulting from the application of the magnetic field along the easy and hard-axes, respectively.Both quantities can be well calculated from isothermal magnetization curves using the Maxwell relation since the hysteresis effect in these multiferroic materials is negligible [32,33].As can be seen in Figure 3c, TbMn 2 O 5 unveils a rotating entropy change that is about two times larger than that shown by HoMn 2 O 5 .Under a constant magnetic field of 2 T which is accessible via permanent magnets [34,35], ∆S R, max is found to be 6.36 J/kg K for TbMn 2 O 5 and only about 3 J/kg K for HoMn 2 O 5 .The improvement of ∆S R in the TbMn 2 O 5 compound is mainly attributed to the reinforcement of the magnetocrystalline anisotropy, as well as the enhancement of the magnetization (arising from Tb 3+ ions) along the easy-axis.More interestingly, TbMn 2 O 5 presents a rotating adiabatic temperature change (∆T R, ad ) that is about five times larger than that obtained with HoMn 2 O 5 under 2 T (Figure 3d).For both HoMn 2 O 5 and TbMn 2 O 5 , ∆T R, ad was evaluated using the equation ∆T R,ad = − T C P (H=0) ∆S R where C p is the specific heat.C p values were taken from Reference [28].
Considering initially the magnetic field parallel to the hard-axis, the rotation motion around the intermediate-axis by an angle of 90 • induces a maximum temperature change larger than 8 K for TbMn 2 O 5 and only 1.6 K for HoMn 2 O 5 under a constant magnetic field of 2 T. The giant ∆T R, ad shown by TbMn 2 O 5 is particularly due to its low specific heat and large rotating isothermal change.Around the ordering point of the rare earth moments, TbMn 2 O 5 has a specific heat of about 6.8 J/kg K, being three times than that exhibited by HoMn 2 O 5 [28].In fact, the more ordered Tb 3+ moments would reduce the magnetic part, and accordingly, the total specific heat.

Distinguished Features of the RMCE in RMn 2 O 5 : Hypothesis
It is worth noting that the fundamental mechanisms behind the coupling between the magnetic ordering, crystal structure, and magnetocaloric properties in RMn 2 O 5 are still unclear.However, according to available data [25,26], we first speculate that the R 3+ spins ordering, magnetic anisotropy, and accordingly, the strength of the rotating magnetocaloric effect in RMn 2 O 5 multiferroics could be strongly controlled by the atomic radius of the magnetic rare earth ions.This can be well understood when considering the interplay between lattice distortions and exchange interactions.Looking at the RMn 2 O 5 crystallographic structure [25,26], the Mn 3+ (S = 2) and Mn 4+ (S = 3/2) spins are ordered within the ab-plane in loops of five Mn following the arrangement Mn 4+ -Mn 3+ -Mn 3+ -Mn 4+ -Mn 3+ .Based on the crystalline structure, the magnetic exchange interactions are mainly driven by the five nearest-neighbors of the Mn lattice identified as Mn 4+ -O2-Mn 4+ (J 1 ), Mn 4+ -O3-Mn 4+ (J 2 ), Mn 4+ -O4-Mn 3+ (J 3 ), Mn 4+ -O3-Mn 3+ (J 4 ), and Mn 3+ -O1-Mn 3+ (J 5 ) [25,26].According to the Goodenough-Kanamori-Anderson rules [36][37][38] and the Mn-O-Mn bond angles associated with the exchange interactions in RMn 2 O 5 (R = Ho, Tb) [26], it seems that J 3 and J 4 reinforce the ferromagnetic interactions of Mn 4+ magnetic moments located in adjacent edge-shared octahedra, either side of the R 3+ layer (with interaction J 1 ) [25,26].This could explain the marked difference in terms of magnetic and magnetocaloric behaviours between TbMn 2 O 5 and HoMn 2 O 5 compounds.In fact, the interaction between the nearest Mn 4+ spins is strongly modulated by the radius of the rare earth.As reported by Blake et al. [26], the Mn 4+ -O2-Mn 4+ bond angle increases when increasing the R 3+ size.At 60 K, it was found to increase from 97.10 • in the case of R = Ho to 97.45 • for Tb, consequently increasing the corresponding interatomic distance Mn 4+ -Mn 4+ from 2.887 to 2.902 Å.Hence, the resulting interactions may play a role in determining the magnetic arrangement of R 3+ via the local magnetic field produced by Mn 4+ ions, and accordingly, the rotating magnetocaloric effect in RMn 2 O 5 compounds.This scenario seems to be supported by Raman scattering investigations.The temperature dependences of the ~630 cm −1 Ag mode of RMn 2 O 5 (R = Tb and Ho) are reported in Figure 4.For both, the frequency of this phonon (Mn-O stretching mode) deviates from the regular anharmonic behavior and hardens below T* ~65 K.According to early studies [39][40][41], T* is a characteristic temperature attributed to the short magnetic correlations often observed just above the Néel transition temperature [39][40][41].This frequency hardening is due to the reduction of the unit cell volume below T* and T N previously observed in RMn 2 O 5 (R = Tb, Ho and Bi) (∆ω ≈ −γ•ω 0 •∆V/V) [39][40][41].This volume contraction was attributed to the Mn-Mn exchange-striction [39][40][41].The frequency hardening of the 630 cm −1 mode in TbMn 2 O 5 (~1 cm −1 ) is two times larger than its equivalent in HoMn 2 O 5 (~0.5 cm −1 ).This result underlines the importance of the lattice effect (R 3+ size) on the Mn exchange interactions and therefore on the ordering of R 3+ magnetic moments.However, the crystalline field effect on the 4f magnetic moments ground state manifold may also play a role in the magnetic configuration of the R 3+ spins.This scenario is currently being explored by our group.

Materials and Methods
The RMn2O5 (R = Ho, Tb) single crystals were synthesized by the high temperature solutions growth method using PbO-PbF2-B2O3 flux, as described in Reference [29].The RMn2O5 (R = Ho, Tb) polycrystalline samples were obtained first by mixing the R2O3 (R = Ho, Tb) and MnO2 oxides in stoichiometric proportions using a standard solid-state reaction method.The resulting products were subjected to heat treatment in open air at 1150 °C for 48 h.Powders of RMn2O5 (R = Ho, Tb) were then mixed with PbO-PbF2-B2O3 flux and pre-melted in a Pt crucible at 1225 °C for 48 h in oxygen atmosphere.The single crystal growth was achieved by reducing the growth temperature from 1225 °C to 1000 °C at a rate of 1 °C/h for TbMn2O5 and from 1225 °C to 950 °C at a rate of 0.5 °C/h for HoMn2O5 [29].The crystals' crystallographic symmetry was analyzed based on Raman scattering.Micro-Raman spectra were collected using a Labram-800 equipped with a microscope, He-Ne laser, and a nitrogen-cooled charge coupled device detector (CCD).The magnetization measurements were carried out with a superconducting quantum interference devices (SQUID) magnetometer from Quantum Design (MPMS XL).

Conclusions
In summary, we have discussed the MCE features of RMn2O5 (R =Ho, Tb) single crystals with the support of both magnetization and Raman scattering data.This preliminary study particularly aims to clarify the origin of the marked difference between their RMCEs.According to Raman scattering data combined with magnetic measurements and early reported neutron diffraction experiments, it seems that the rare earth size could impact the RMn2O5 magnetocaloric properties.This could occur via the fine tuning of the magnetic exchange interactions involving the Mn sublattice because of structural distortions.The new established interactions would affect the ordering state of R 3+ magnetic moments, and accordingly, the RMCE.However, this is not the only hypothesis to be considered since additional factors such as the crystalline field contribution must be taken into account.The latter is currently under investigation and any relevant result will be published in the future.Additionally, to get the "big picture" of the RMn2O5 magnetocaloric features, this study must be completed by considering other rare earth elements such as Dy, Gd, Er, Pr…etc.With the present work, we particularly aim at opening the door for further fundamental investigations of this

Materials and Methods
The RMn 2 O 5 (R = Ho, Tb) single crystals were synthesized by the high temperature solutions growth method using PbO-PbF 2 -B 2 O 3 flux, as described in Reference [29] [29].The crystals' crystallographic symmetry was analyzed based on Raman scattering.Micro-Raman spectra were collected using a Labram-800 equipped with a microscope, He-Ne laser, and a nitrogen-cooled charge coupled device detector (CCD).The magnetization measurements were carried out with a superconducting quantum interference devices (SQUID) magnetometer from Quantum Design (MPMS XL).

Conclusions
In summary, we have discussed the MCE features of RMn 2 O 5 (R =Ho, Tb) single crystals with the support of both magnetization and Raman scattering data.This preliminary study particularly aims to clarify the origin of the marked difference between their RMCEs.According to Raman scattering data combined with magnetic measurements and early reported neutron diffraction experiments, it seems that the rare earth size could impact the RMn 2 O 5 magnetocaloric properties.This could occur via the fine tuning of the magnetic exchange interactions involving the Mn sublattice because of structural distortions.The new established interactions would affect the ordering state of R 3+ magnetic moments, and accordingly, the RMCE.However, this is not the only hypothesis to be considered since additional factors such as the crystalline field contribution must be taken into account.The latter is currently under investigation and any relevant result will be published in the future.Additionally, to get the "big picture" of the RMn 2 O 5 magnetocaloric features, this study must be completed by considering other rare earth elements such as Dy, Gd, Er, Pr . . .etc.With the present work, we particularly aim at opening the door for further fundamental investigations of this promising family of multiferroics that can be implemented in numerous potential applications such as magnetic cooling and spintronic devices.

Figure 1 .
Figure 1.(a) Generation of the MCE by rotating the single crystals between their easy and hard-axes; (b) Full entropy as a function of temperature along the easy and hard-axes.

Figure 1 .
Figure 1.(a) Generation of the MCE by rotating the single crystals between their easy and hard-axes; (b) Full entropy as a function of temperature along the easy and hard-axes.

Figure 2 .
Figure 2. Micro Raman spectra at 5 K for the orthorhombic single crystals RMn2O5 (R = Ho, Tb).The narrow excitations demonstrate the high quality of the crystals and confirm the orthorhombic symmetry.

Figure 2 .
Figure 2.Micro Raman spectra at 5 K for the orthorhombic single crystals RMn 2 O 5 (R = Ho, Tb).The narrow excitations demonstrate the high quality of the crystals and confirm the orthorhombic symmetry.

Figure 3 .
Figure 3. (a) Temperature dependence of magnetization under a magnetic field of 0.1 T applied along the easy-axes for TbMn2O5 and HoMn2O5.(b) Isothermal magnetization curves of RMn2O5 (R = Ho, Tb) measured at 2 K under magnetic fields applied along their easy and hard-axes.(c) Temperature dependence of the rotating isothermal entropy change in RMn2O5 (R = Ho, Tb) under 2 T. (d) Associated adiabatic temperature change under 2 T.

Figure 3 .
Figure 3. (a) Temperature dependence of magnetization under a magnetic field of 0.1 T applied along the easy-axes for TbMn 2 O 5 and HoMn 2 O 5 .(b) Isothermal magnetization curves of RMn 2 O 5 (R = Ho, Tb) measured at 2 K under magnetic fields applied along their easy and hard-axes.(c) Temperature dependence of the rotating isothermal entropy change in RMn 2 O 5 (R = Ho, Tb) under 2 T. (d) Associated adiabatic temperature change under 2 T.
. The RMn 2 O 5 (R = Ho, Tb) polycrystalline samples were obtained first by mixing the R 2 O 3 (R = Ho, Tb) and MnO 2 oxides in stoichiometric proportions using a standard solid-state reaction method.The resulting products were subjected to heat treatment in open air at 1150 • C for 48 h.Powders of RMn 2 O 5 (R = Ho, Tb) were then mixed with PbO-PbF 2 -B 2 O 3 flux and pre-melted in a Pt crucible at 1225 • C for 48 h in oxygen atmosphere.The single crystal growth was achieved by reducing the growth temperature from 1225 • C to 1000 • C at a rate of 1 • C/h for TbMn 2 O 5 and from 1225 • C to 950 • C at a rate of 0.5 • C/h for HoMn 2 O 5