# Fileset

[MLF_AR2022.pdf](https://mdr.nims.go.jp/filesets/20322053-275d-4a34-a0bb-dc88fc52c18a/download)

## Creator

[N. Terada](https://orcid.org/0000-0002-8676-5586), H. Mamiya, H. Saito, T. Nakajima, T. D. Yamamoto, K. Terashima, H. Takeya, O. Sakai, S. Itoh, Y. Takano, M. Hase, H. Kitazawa

## Rights

[In Copyright](http://rightsstatements.org/vocab/InC/1.0/)

## Other metadata

[Crystal Electric Field Level Scheme Behind Giant Magnetocaloric Effect for Hydrogen Liquefaction](https://mdr.nims.go.jp/datasets/b4177e35-1d0f-491f-a605-045a6465281f)

## Fulltext

MLF_AR20221. IntroductionMagnetic refrigeration, which is known as a cool-ing method using a magnetic !eld, has been actively researched so far mainly for application to near room temperature or extremely low temperatures below 1 K [1]. On the other hand, recently, magnetic refrigera-tion in the intermediate temperature range (on the or-der of several tens of K) has been attracting attention as a new cooling method for e#ciently cooling liquid hydrogen [2]. Magnetic refrigeration for the purpose of hydrogen liquefaction requires e#cient cooling in the temperature range from the hydrogen liquefaction temperature of 20 K to around 77 K (assuming precool-ing with liquid nitrogen). In magnetic refrigeration, the magnetic entropy change (ΔSM) of a magnetic material when a magnetic !eld is excited or demagnetized is an important factor in developing an e#cient magnetic refrigeration system. For the purpose of obtaining high performance MCE materials, heavy rare earth compounds become the most promising candidates. Because, as a poten-tial maximum magnetic entropy is defined as SM = R ln (2J + 1), where R is the gas constant and J is total an-gular momentum quantum number. However, in most of the cases, such potentially large SM does not exist at several tens degrees of Kelvin temperature range that could be useful for hydrogen liquefaction, due to the crystal electric !eld reducing the large entropy even in zero magnetic !eld condition. Such temperature range of several tens degrees of Kelvin is generally comparable to the crystal electric !eld (CEF) energy levels for heavy rare earth ions (schematic illustration is presented in Fig. 1). Magnetic entropy change (ΔSM) strongly depends on the degeneracy of the CEF ground state, which is lift-ed by external magnetic !eld through Zeemann split-ting, leading to MCE. In this context, understanding the CEF level scheme for heavy rare earth compounds is important for designing the MR materials for hydrogen liquefaction.2. Inelastic neutron scattering of HoB2In inelastic neutron scattering (INS) experiments, the energy levels of the CEF can be determined by measuring the energy spectrum of the purely para-magnetic phase, because there is no internal magnetic !eld induced by ferromagnetic long-range order. As an example, we selected the MR material HoB2 with a huge MCE to evaluate the CEF energy level scheme. HoB2 was recently discovered to exhibit a very large |ΔSM| value near the hydrogen liquefaction temperature [2]. INS ex-periments were performed using the High-Resolution Chopper Spectrometer (HRC) beamline. The experimen-tally determined CEF level scheme shown in Fig. 2(a) was illustrated, which reproduces the experimental INS spec-trum. (Fig. 2(b)). In order to calculate magnetic entropy change with the determined CEF parameters, we con-ducted the mean-!eld calculation, which successfully reproduced the ΔSM, observed in previous magnetiza-tion measurement [2] (Fig. 2(c)). Here, we discuss how the CEF states of the obtained HoB2 a$ect the magnetic entropy change ΔSM when a magnetic !eld is applied. When the temperature of the system is assumed to be 20 K, the energy gap between the ground state (Γ1B) and the excited states Γ6C and Γ6B can be considered pseudo-degenerated with respect to the system temperature. When applying magnetic !elds along a principal axis, the pseudo-degeneracy is lifted, leading to such a large |ΔSM| (Fig. 2(d)). 3.  Mean-field calculation with CEF and exchange parametersWe also calculated the ideal CEF level scheme for general heavy rare earth ions with site symmetries, cubic Oh and hexagonal D6h by using mean-field cal-culations. Figure 3(a) shows one example, crystal !eld parameter dependence of |ΔSM| (5 T, 20 K) for cubic Oh. Figure 1.   Schematic illustration of complicated crystal electric field (CEF) energy level splitting in heavy rare earth ions (with schematic drawings of electrons wave func-tions in each energy level), and Zeemann splitting of the CEF levels resulting in a large magnetocalo-ric effect. For several tens degrees of Kelvins energy scale, CEF splittings are generally comparable to the system temperature in heavy rare earth system. Crystal Electric Field Level Scheme Behind                         Giant Magnetocaloric E!ect for Hydrogen Liquefaction37MLF Annual Report 2022     Research and Development HighlightsN. Terada1, H. Mamiya1, H. Saito2, T. Nakajima2, 3, T. D. Yamamoto1, K. Terashima1, H. Takeya1, O. Sakai4, S. Itoh5, 6, Y. Takano1, M. Hase1, and H. Kitazawa11National Institute for Materials Science; 2Institute for Solid State Physics, The University of Tokyo; 3RIKEN Center for Emergent Matter Science (CEMS); 4Neutron Science and Technology Center, CROSS; 5 Institute of Materials Structure Science, KEK; 6Materials and Life Science Division, J-PARC CenterThe |ΔSM| in%uences signi!cantly the crystal !eld param-eters. It is important to note that this does not neces-sarily show that |ΔSM| is largest when the crystal !eld is zero. In this way, in addition to the degree of degeneracy of the pseudo ground state of the crystal !eld, the de-gree of how much the ground state is isolated when a magnetic !eld is also an important factor in producing a large |ΔSM|. The calculation results are summarized in Fig. 3(c). The maximum |ΔSM| for Ho3+ with the hexagonal sym-metry for powder case, corresponding to HoB2 case, is 10.1 J mol–1 K–1, which is 30% larger than that of HoB2. We, therefore, found that there is still room to improve |ΔSM | even in one of the largest MCE materials, HoB2.4. Concluding remarksThe relationship between ΔSM and crystal !eld pa-rameters derived in this study provides new guidelines for searching for compounds with larger magnetoca-loric e$ects near the hydrogen liquefaction tempera-ture. Recent advancements in density functional theory calculations have unlocked the possibility of predicting CEF parameters for rare-earth systems based on the crystal information. A combination of DFT calculations and the relationships between |ΔSM| and the CEF param-eters derived in this study would accelerate the search for compounds with a large MCE and help to design more magnetic refrigeration materials.References[1] T. Numazawa, et. al., Cryogenics 62,185 (2014).[2] P. Baptista de Castro, et. al., NPG Asia Mater. 12, 35 (2020).[3] N. Terada, et. al., Communications Materials 4 13 (2023).Figure 3.   Contour map of magnetic entropy change of Ho3+ in the cubic Oh symmetry at T = 20 K in magnetic field change from 0 to 5 T along [100] direction. (b) Zeemann splitting in magnetic field along [100] direction at T = 25 K for the set of CEF parameters indicated by the star symbol in (a). (c) Heavy rare earth ion dependence of the maximum magnetic entropy change, predicted by the present mean-field calculations for the cubic Oh and hexagonal D6h symmetries. The experimental value of HoB2 at 15 K is also plotted [3].Figure 2.   (a) Crystal electric field (CEF) level scheme in HoB2 was determined by the present neutron scattering experiment. (b) The neutron intensity (open circle) was successfully explained by theoretical calcula-tion curve (solid line) with the CEF parameters. (c) Magnetic field and temperature dependence of magnetic entropy change (open circle) is roughly consistent with those calculated with the mean-field calculation with the determined CEF param-eters. (solid line) The data were taken from Ref. [3]. (d) Calculated Zeemann splitting for HoB2 in mag-netic field perpendicular to the c-axis.38Research and Development Highlights     MLF Annual Report 2022