ON THE ROTATING MAGNETOCALORIC EFFECT IN MULTIFERROIC RMn 2 O 5 COMPOUNDS

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1 ON THE ROTATING MAGNETOCALORIC EFFECT IN MULTIFERROIC RMn 2 O 5 COMPOUNDS M. Balli *, S. Mansouri, B. Roberge, S. Jandl, P. Fournier (a,b), D. Z. Dimitrov (c,d) Département de Physique,Université de Sherbrooke,J1K 2R1, QC, Canada Canadian Institute For Advanced Research, Ontario M5G 1Z8, Canada (c) Institute of Solid state Physics, Bulgarian Academy of Science, Sofia 1184, Bulgaria (c) Institute of Optical Materials and Technologies, Bulgarian Academy of Sciences, 1113 Sofia, Bulgaria * Corresponding author. mohamed.balli@usherbrooke.ca ABSTRACT Thanks to the strong magnetic anisotropy shown by RMn 2 O 5 compounds, a large magnetocaloric effect can be induced (around 10 K) by rotating them in constant magnetic fields instead the standard magnetizationdemagnetization method. Particularly, the TbMn 2 O 5 single crystal reveals a giant rotating magnetocaloric effect (RMCE) under relatively low constant magnetic fields reachable by permanent magnets. On the other hand, it was found that the RMCE in RMn 2 O 5 crystals strongly depends on the R 3+ ion nature. Under a constant magnetic field of 2 T, the maximum rotating adiabatic temperature change exhibited by TbMn 2 O 5 is more than 5 times larger than that presented by HoMn 2 O 5. The rare earth ion size could play a crucial role in the determination of the magnetic and magnetocaloric properties of RMn 2 O 5 compounds through the modulation of exchange interactions via lattice distortions, a scenario that seems to be supported by Raman scattering. Keywords: RMn 2 O 5, Multiferroics, Anisotropy, Single crystals, Magnetocaloric effect. DOI: /iir.thermag INTRODUCTION 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. This is mainly due to their potential use as refrigerants in several low temperature applications such as space industry, scientific instruments and gas liquefaction [1]. On the other hand, the development of new designs which are able to render the magnetic cooling more competitive is also a key parameter for the commercialization of this emergent technology. In this context, the RMn 2 O 5 (R = magnetic rare earth) multiferroics seem to be promising candidates for magnetocaloric tasks around 10 K [2-8].Usually, the competition between different magnetic exchange interactions in the orthorhombic RMn 2 O 5 compounds results in strongly frustrated systems. Consequently, a large magnetocaloric effect (MCE) could be obtained in RMn 2 O 5 crystals by rotating them between their easy and hard axes in constant magnetic fields, instead the conventional magnetization-demagnetization process (via field variation). At room temperature, this kind of materials crystallizes in the orthorhombic structure of space group Pbam. As shown in Fig.1-a, their unit cell consists of Mn 3+ O 5 pyramids and Mn 4+ O 6 octahedra which are connected each to other through oxygen atoms [2, 3]. The octahedra are aligned along the c-axis with sharing 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. In this paper, we discuss the magnetic and anisotropic magnetocaloric properties of RMn 2 O 5 compounds, recently studied in Sherbrooke [6, 7]. 2. RESULTS AND DISCUSSION Figure 1-b shows the Raman spectra of RMn 2 O 5 (R = Tb and Ho) at 5 K obtained with an incident light (632.8 nm) polarized in the xy-plane. The analysis of different Raman excitations confirms that the crystals under study form in a high quality orthorhombic crystallographic structure with 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 [2-5]. Usually, the Mn 3+ /Mn 4+ spins order in an incommensurate antiferromagnetic (AFM)

2 state at T N1 45 K becoming commensurate with decreasing temperature at a lock-in transition point ( T L = 333 K). A second magnetic phase transition at which AFM ordering of Mn moments becomes incommensuratee takes place at T N2 20 K. The onset of ferroelectric order was observed slightly beloww T N1, at T C 38 K, while Figure 1. Crystal structure of RMn 2 O 5 compounds [2]. Micro Raman spectra at 5 K for the orthorhombic single crystals HoMn 2 O 5 and TbMn 2 O 5. the rare earth moments usually order bellow 155 K [2-5]. The temperature dependence of the magnetization n for a typical RMn 2 O 5 (R = magnetic rare earth) multiferroic (HoMn 2 O 5 ) under a low magnetic field of 0.15 T applied along its easy axis b is reported in Fig.2-a (for example). As shown, onlyy the magnetic transitionn related to the Ho 3+ spins ordering is clearly visible at low temperatures around 10 K. For TbMn 2 O 5, the ordering point of Tb 3+ moments (not shown in Fig.2) was observed around 5 K, which is in good agreement with early works [4, 5]. However, the phase transitions involving the manganese m sublattice and occurring at T N1, T C and T N2 cannot be clearly seen in the thermomagnetic curves shown in Fig.2-a but their presence can be easily identified from specific heat measurements as reported in Ref. R 5. This mainly arises from the Figure 2. Temperature dependence of magnetization under a magneticc field of 0.15 T applied along the b axis for HoMn 2 O 5. Isothermal magnetization curves of RMn 2 O 5 (R = Ho, H Tb) measured at 2 K under magnetic fields applied along their easy and hardd axes. complex arrangement of the Mn moments in RMn 2 O 5 [2-5]. The magnetic and magnetocaloric properties (particularly RMCE) are very sensitive to the nature of the R 3+ ions (Figs.( 2b to 4). The data in Fig.2-b indicate that the magnetic easy direction of TbMn 2 O 5 is along the a axiss 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 orderr of Ho 3+ ions. In contrast, the relatively large positive valuee 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 HoMn 2 O 5 and TbMn 2 O 5, as shown in Fig. 2-b. With increasing field, thee 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 Seventh IIF-IIR International Conference on Magnetic Refrigeration at Room R Temperature, Thermag VII

3 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 closer 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 [2-7]. On the other hand, an enhancement of the magnetocrystalline anisotropy is observed in TbMn 2 O 5 (Fig. 2-b). 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. The observed difference in the magnetic behavior of both HoMn 2 O 5 and TbMn 2 O 5 single crystals, leads to a significant deviation between their MCEs represented by the isothermal entropy change as shown in Fig.3-a,b. Since the hysteresis effect is negligible in HoMn 2 O 5 and TbMn 2 O 5 compounds, their isothermal entropy changes ΔS can be accurately determined by using the well-known Maxwell relation [9]. Figure 3. Isothermal entropy changes of RMn 2 O 5 (R = Ho, Tb) as a function of temperature along their easy and hard axes for a magnetic field changing from 0 to 2 T. In Fig.4-a, we report the temperature dependence of the rotating entropy change (ΔS 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. ΔS R can be written as ΔS R = ΔS (H//easy axis) - ΔS (H//hard axis) [6, 7], 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. As can be seen in Fig. 4-a, TbMn 2 O 5 unveils a rotating entropy change that is about 2 times larger than that shown by HoMn 2 O 5. Under a constant magnetic field of 2 T, ΔS R is found to be 6.36 J/kg K for TbMn 2 O 5 and only 3 J/kg K for HoMn 2 O 5. The improvement of ΔS R in the 2 T 2 T Figure 4. Temperature dependence of the rotating isothermal entropy change in RMn 2 O 5 (R = Ho, Tb) under 2 T. Associated adiabatic temperature change under 2 T. Both compounds show a maximum RMCE at different temperatures, corresponding to the ordering points of Ho 3+ ( 10 K) and Tb 3+ ( 5 K) spins. TbMn 2 O 5 compound is mainly attributed to the reinforcement of the magnetocrystalline anisotropy as well as the enhancement of the isothermal entropy change (arising from Tb 3+ ions) along the easy axis (Fig.3-a). More interestingly, TbMn 2 O 5 presents a rotating adiabatic temperature change [6, 7] which is about 5 times

4 larger than that obtained with HoMn 2 O 5 under 2 T (Fig. 4-b). 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. On the other hand, the ΔT ad, R shown by TbMn 2 O 5 is much larger than that exhibited by the garnets DGAG ( 1 to 2 K/T), usually used in low temperature applications such in the hydrogen liquefaction [1]. The giant ΔT ad, R 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 3 times lower than that exhibited by HoMn 2 O 5 [5]. It is worth noting that the fundamental mechanisms behind the nature of the coupling between the magnetic ordering, crystal structure and magnetocaloric properties in RMn 2 O 5 are still unclear. However, according to available data [2, 3], we first speculate that the R 3+ spins ordering, magnetic anisotropy and consequently the strength of the rotating magnetocaloric effect in multiferroic RMn 2 O 5 could be strongly controlled by the atomic radius of the rare earth ions. This can be well understood when taking into account the interplay between lattice distortions and exchange interactions. Looking at the RMn 2 O 5 crystallographic structure reported in Fig. 1-a, 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 crystal structure, the magnetic exchange interactions are mainly driven by five nearest-neighbors of Mn lattice identified as Mn 4+ -O2-Mn 4+ (J1), Mn 4+ -O3-Mn 4+ (J2), Mn 4+ -O4-Mn 3+ (J3), Mn 4+ -O3-Mn 3+ (J4) and Mn 3+ -O1-Mn 3+ (J5) [2, 3]. According to the Goodenough-Kanamori- Anderson rules [10-12] and the Mn-O-Mn bond angles associated with the exchange interactions in HoMn 2 O 5 and TbMn 2 O 5 [3], it seems that J3 and J4 reinforce the ferromagnetic interactions of the Mn 4+ magnetic moments located in adjacent edge-shared octahedra, either side of the R 3+ Figure 5. Temperature dependence of the Raman-active phonon ~ 630 cm -1 A g for HoMn 2 O 5 and TbMn 2 O 5. layer (J1), as shown in Fig. 1-a. This could explain the marked difference in the magnetic and magnetocaloric behaviours of RMn 2 O 5 since the interaction between nearest Mn 4+ spins are strongly modulated by the radius of the rare earth. As reported by Blake et al [3], the Mn 4+ -O2-Mn 4+ bond angle increases with increasing the R 3+ size. At 60 K, it was found to increase from in the case of R = Ho to for Tb, increasing consequently the corresponding interatomic distance Mn 4+ -Mn 4+ from to Å. The resulting interactions may play a role in the determination of the magnetic arrangement of R 3+ via the local magnetic field produced by Mn 4+ ions, and consequently the rotating magnetocaloric effect in RMn 2 O 5. This scenario seems to be supported by Raman scattering investigations. The temperature dependences of ~ 630 cm -1 A g mode of RMn 2 O 5 (R = Tb and Ho) are reported in Fig.5. 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 [13-15], T* is a characteristic temperature attributed to the short magnetic correlations often observed just above the Néel transition temperature [13-15]. This frequency hardening retraces the reduction of the unit cell volume below T* and T N previously observed in RMn 2 O 5 (R = Tb, Ho and Bi) ( Δ ω γ. ω0. ΔV V ) [13-15]. The volume contraction was attributed to the Mn-Mn exchange-striction [13-15]. The frequency hardening of the considered mode in TbMn 2 O 5 (~1 cm -1 ) is 2 times larger than its equivalent in HoMn 2 O 5 (~ 0.5 cm -1. This result underlines the important lattice effect (R 3+ size) on the Mn exchange interactions and therefore the ordering of the 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 explored by our group (Mansouri et al). 3. CONCLUSIONS In summary, we have investigated the magnetic and magnetocaloric properties of HoMn 2 O 5 and TbMn 2 O 5 single crystals. Around the ordering temperature of the R 3+ moments ( 5 and 10 K), the two compounds show

5 a gigantic magnetic anisotropy leading to a large rotating magnetocaloric effect. However, the reported values of the RMCE in TbMn 2 O 5 were found to exceed largely those shown by HoMn 2 O 5. The giant RMCE shown by TbMn 2 O 5 can be mainly attributed to the colossal anisotropy of the isothermal entropy change, the enhancement of the Tb 3+ magnetization under relatively low magnetic fields (enhancement of ΔS) along the easy axis and the low specific heat. The R 3+ size seems to have a role in the control of the magnetocaloric properties via the configuration of the magnetic exchange interactions in RMn 2 O 5. On the other hand, the large RMCE shown by RMn 2 O 5 opens new avenues for the design of new cryomagnetocaloric devices. ACKNOWLEDGMENTS The authors thank M. Castonguay and S. Pelletier for technical support. We acknowledge the financial support from NSERC (Canada), FQRNT (Québec), CFI, CIFAR, Canada First Research Excellence Fund (Apogée Canada) and the Université de Sherbrooke. REFERENCES [1] K. Matsumoto, T. Kondo, S. Yoshioka, K. Kamiya and T. Numazawa, J. Phys.: Conference Series. 150, (2009). [2] Y. Noda, H. Kimura, M. Fukunaga, S. Kobayashi, I. Kagomiya and K. Kohn, J. Phys.: Condens. Matter 20, (2008). [3] G. R. Blake, L. C. Chapon, P. G. Radaelli, S. Park, N. Hur, S-W. Cheong and J. Rodríguez-Carvajal, Phys. Rev. B 71, (2005). [4] N. Hur, S. Park, P.A. Sharma, J. S. Ahn, S. Guha and S-W. Nature. 429, 392 (2004). [5] N. Hur, S. Park, P. A. Sharma, S. Guha, and S-W. Cheong, Phys. Rev.Lett. 93, (2004). [6] M. Balli, S. Jandl, P. Fournier, M. M. Gospodinov, Appl. Phys. Lett. 104, (2014). [7] M. Balli, S. Jandl, P. Fournier, M. M. Gospodinov, Appl. Phys. Lett. 108, (2016) [8] B. Mihailova, M. M. Gospodinov, B. Güttler, F. Yen, A. P. Litvinchuk, and M. N. Iliev, Phys. Rev. B. 71, (2005). [9] M. Balli, D. Fruchart, D. Gignoux and R. Zach, Appl. Phys. Lett. 95, (2009). [10] J. B. Goodenough, Phys. Rev. 100, 564 (1955). [11] J. Kanamori, J. Phys. Chem. Solids 10, 87 (1959). [12] P. W. Anderson, Solid State Phys. 14, 99 (1963). [13] A. F. Garcia-Flores, E. Granado, H. Martinho, R. R. Urbano, C. Rettori, E. I. Golovenchits, V. A. Sanina, S. B. Oseroff, S. Park and S-W. Cheong, Phys. Rev. B 73, (2006). [14] L. C. Chapon, G. R. Blake, M. J. Gutmann, S. Park, N. Hur, P. G. Radaelli, and S.-W.Cheong, Phys. Rev. Lett. 93, (2004). [15] E. Granado, M. S. Eleotério, A. F. Garcia-Flores, J. A. Souza, E. I. Golovenchits, and V. A. Sanina, Phys. Rev. B 77, (2008).