# Fileset

[ar2022_highlight_TERADA_revised_v2.pdf](https://mdr.nims.go.jp/filesets/3921d77d-0dd0-4bed-9df2-1c08cf73ee65/download)

## Creator

[寺田 典樹](https://orcid.org/0000-0002-8676-5586)

## Rights

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

## Other metadata

[Crystal electric field leading to giant magnetocaloric effect for hydrogen liquefaction](https://mdr.nims.go.jp/datasets/ab15cedc-b401-428a-8b60-d86bb0c32146)

## Fulltext

Crystal electric field leading to giantmagnetocaloric effect for hydrogen liquefactionLiquid hydrogen (LH2) is widely expected toserve as medium for storing renewable energy re-sources. Although LH2 can store hydrogen at thehighest density in all the media, there is a seri-ous technical bottleneck on cooling method withconventional gas compression technique wherethe cooling efficiency near hydrogen condensa-tion temperature, 20 K, is much lower than am-bient temperature. Recently, magnetic refrig-eration (MR) has been extensively studied asan alternative technique to the conventional gascompression cooling in hydrogen liquefaction[1].The MR materials, which have a large magne-tocaloric effect (MCE) identified by magnetic en-tropy change with the application of magneticfield ∆SM , are the most important factor in MRcooling system.Heavy rare earth compounds are the mostpromising MR material candidates. Because, alarge magnetic entropy is potentially caused bythe large number of states due to the magneticentropy obeying SM = R ln(2J + 1), where Ris the gas constant and J is total angular mo-mentum quantum number. Unlike MR for ex-tremely low temperature (T < 1 K) or for aroundroom temperature range, MR for hydrogen lique-faction is for the target temperature range from20 K (hydrogen condensation temperature) to 77K (liquid nitrogen temperature for pre-cooling).Such several tens of kelvin temperature rangeis generally comparable to the crystal electricfield (CEF) energy levels for heavy rare earthions. (schematic picture is illustrated in Fig. 1)Magnetic entropy change (∆SM ) is strongly re-lated to degeneracy of CEF ground state, whichis lifted by external magnetic field through Zee-Fig. 1. Schematic illustration of complicatedcrystal electric field (CEF) energy level splittingin heavy rare earth ions (with schematic draw-ings of electrons wave functions in each energylevel), and Zeemann splitting of the CEF levelsgiving a large magnetocaloric effect. For severaltens of kelvins energy scale, CEF splittings aregenerally comparable to system temperature inheavy rare earth system.mann splitting, leading to MCE. In this context,understanding the CEF level scheme for heavyrare earth compounds is important for designingthe MR materials for hydrogen liquefaction.In inelastic neutron scattering (INS) experi-ment, one can purely see the CEF energy levelsby measuring the energy spectrum in the para-magnetic phase due to absence of internal mag-netic field induced by the ferromagnetic long-range ordering. As an example, we chose theMR material HoB2 with giant MCE to evaluatethe CEF energy level schame. HoB2 has been re-cently discovered to show very large |∆SM | valuenear hydrogen liquefaction temperature[2]. TheINS experiment was carried out with the HighResolution Chopper spectrometer (HRC) beam-line. The experimentally determined CEF levelscheme shown in Fig. 2(a) successfully explainedFig. 2. (a)Crystal electric field (CEF) levelscheme in HoB2 was determined by the presentneutron scattering experiment. (b)The neutronintensity (open circle) was successfully explainedby theoretical calculation curve (solid line) withthe CEF parameters. (c)Magnetic field and tem-perature dependence of magnetic entropy change(open circle) is roughly consistent with those cal-culated with the mean-field calculation with thedetermined CEF parameters. (solid line) Thedata were taken from Ref. [3].the measured energy spectrum (Fig. 2(b)). Inorder to calculate magnetic entropy change withthe determined CEF parameters, we conductedthe mean-field calculation, which successfully re-produced the ∆SM , observed in previous mag-netization measurement[2](Fig. 2(c)).We also have calculated the ideal CEF levelschemes for general heavy rare earth ions withsite symmetries, cubic Oh and hexagonal D6h, toobtain the largest |∆SM | with the applied mag-netic field of 5 T at 20 K, by using the mean-fieldcalculations. The calculation results are sum-marized in Fig. 3. The maximum |∆SM | forHo3+ with the hexagonal symmetry for powderFig. 3. Heavy rare earth ion dependence of themaximum magnetic entropy change for the cubic(Oh) and hexagonal D6h symmetries. The crosssymbol denotes the experimental value of HoB2.The data were taken from Ref. [3].case, corresponding to HoB2 case, is 10.1 J mol−1K−1, which is 30 % larger than that of HoB2.We therefore found that there is still room toimprove |∆SM | even in one of the largest MCEmaterials, HoB2.Finally, we have studied the CEF level schemeand MCE for the special case of HoB2 and gen-eral heavy rare earth ions, which provided idealCEF parameters leading to a large ∆SM . It ishoped that the relationships presented here givesadditional guideline for searching compoundswith a large MCE and the further MR-materialsdesign.References[1] T. Numazawa, et. al., Cryogenics 62,185(2014).[2] P. Baptista de Castro, et. al., NPG AsiaMater. 12, 35 (2020).[3] N. Terada, et. al., Communications Materials4 13 (2023).