Analysis of the Anisotropic Magnetocaloric Effect in RMn₂O₅ Single Crystals

Abstract

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.

1. 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_2.4Gd_0.6Al₅O₁₂ (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 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 Mn³⁺O₅ pyramids and Mn⁴⁺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 Mn³⁺O₅ pyramids within the ab-plane. The rare earth R³⁺ 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.

2. 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 (632.8 nm) 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 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 Mn³⁺/Mn⁴⁺ 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 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 R³⁺ 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 RMn₂O₅. In the latter, the Mn³⁺/Mn⁴⁺ 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 Mn³⁺/Mn⁴⁺ 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 µ_B) 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 R³⁺ 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 hard-axes are plotted. Although the magnetic moments of Tb³⁺ and Ho³⁺ 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 T_ϴ in the case of HoMn₂O₅ reflects a paramagnetic behavior and/or a weak antiferromagnetic order of Ho³⁺ ions. In contrast, the relatively large positive value of T_ϴ as in the case of TbMn₂O₅ suggests a dominant ferromagnetic ordering of Tb³⁺ 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 Am²/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 Am²/kg (8.75 µ_B/f.u.), being close to the Tb³⁺ magnetic moment (9 µ_B). This indicates that the Tb³⁺ 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 (ΔS_R), associated with the rotation by an angle of 90° of HoMn₂O₅ (in the cb-plane) and TbMn₂O₅ (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) [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], ΔS_{R, max} is found to be 6.36 J/kg K for TbMn₂O₅ and only about 3 J/kg K for HoMn₂O₅. The improvement of ΔS_R in the TbMn₂O₅ compound is mainly attributed to the reinforcement of the magnetocrystalline anisotropy, as well as the enhancement of the magnetization (arising from Tb³⁺ ions) along the easy-axis. More interestingly, TbMn₂O₅ presents a rotating adiabatic temperature change (ΔT_{R, ad}) that is about five times larger than that obtained with HoMn₂O₅ under 2 T (Figure 3d). For both HoMn₂O₅ and TbMn₂O₅, ΔT_{R, ad} was evaluated using the equation $\Delta T_{R,ad}=-\frac{T}{C_P(H=0)}\Delta S_R$ 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 TbMn₂O₅ and only 1.6 K for HoMn₂O₅ under a constant magnetic field of 2 T. The giant ΔT_{R, ad} shown by TbMn₂O₅ is particularly due to its low specific heat and large rotating isothermal change. Around the ordering point of the rare earth moments, TbMn₂O₅ has a specific heat of about 6.8 J/kg K, being three times lower than that exhibited by HoMn₂O₅ [28]. In fact, the more ordered Tb³⁺ moments would reduce the magnetic part, and accordingly, the total specific heat.

3. Distinguished Features of the RMCE in RMn₂O₅: Hypothesis

It is worth noting that the fundamental mechanisms behind the coupling between the magnetic ordering, crystal structure, and magnetocaloric properties in RMn₂O₅ are still unclear. However, according to available data [25,26], we first speculate that the R³⁺ spins ordering, magnetic anisotropy, and accordingly, the strength of the rotating magnetocaloric effect in RMn₂O₅ 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 RMn₂O₅ crystallographic structure [25,26], the Mn³⁺ (S = 2) and Mn⁴⁺ (S = 3/2) spins are ordered within the ab-plane in loops of five Mn following the arrangement Mn⁴⁺-Mn³⁺-Mn³⁺-Mn⁴⁺-Mn³⁺. Based on the crystalline structure, the magnetic exchange interactions are mainly driven by the five nearest-neighbors of the Mn lattice identified as Mn⁴⁺-O2-Mn⁴⁺ (J₁), Mn⁴⁺-O3-Mn⁴⁺ (J₂), Mn⁴⁺-O4-Mn³⁺ (J₃), Mn⁴⁺-O3-Mn³⁺ (J₄), and Mn³⁺-O1-Mn³⁺ (J₅) [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 RMn₂O₅ (R = Ho, Tb) [26], it seems that J₃ and J₄ reinforce the ferromagnetic interactions of Mn⁴⁺ magnetic moments located in adjacent edge-shared octahedra, either side of the R³⁺ layer (with interaction J₁) [25,26]. This could explain the marked difference in terms of magnetic and magnetocaloric behaviours between TbMn₂O₅ and HoMn₂O₅ compounds. In fact, the interaction between the nearest Mn⁴⁺ spins is strongly modulated by the radius of the rare earth. As reported by Blake et al. [26], the Mn⁴⁺-O2-Mn⁴⁺ bond angle increases when increasing the R³⁺ 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 Mn⁴⁺-Mn⁴⁺ from 2.887 to 2.902 Å. Hence, the resulting interactions may play a role in determining the magnetic arrangement of R³⁺ via the local magnetic field produced by Mn⁴⁺ ions, and accordingly, the rotating magnetocaloric effect in RMn₂O₅ compounds. This scenario seems to be supported by Raman scattering investigations. The temperature dependences of the ~630 cm⁻¹ Ag mode of RMn₂O₅ (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 RMn₂O₅ (R = Tb, Ho and Bi) ($\Delta \omega \approx -\gamma ·{\omega }_0·\Delta V/V$) [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 TbMn₂O₅ (~1 cm⁻¹) is two times larger than its equivalent in HoMn₂O₅ (~0.5 cm⁻¹). This result underlines the importance of the lattice effect (R³⁺ size) on the Mn exchange interactions and therefore on the ordering of R³⁺ 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 R³⁺ spins. This scenario is currently being explored by our group.

4. 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).

5. 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 R³⁺ 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 promising family of multiferroics that can be implemented in numerous potential applications such as magnetic cooling and spintronic devices.