Giant low-field reversible magnetocaloric effect in HoCoGe compound

Abstract

Magnetic properties and magnetocaloric effects (MCEs) of the HoCoGe compound have been investigated by magnetization and heat capacity measurements. The HoCoGe compound undergoes a second-order ferromagnetic–paramagnetic phase transition around the Curie temperature T_C = 7.6 K and exhibits a giant reversible MCE. For a field change of 0–5 T, the maximum values of magnetic entropy change (−ΔS_M) and adiabatic temperature change (ΔT_ad) are 23.9 J kg⁻¹ K⁻¹ and 10.9 K, respectively. A large refrigerant capacity of 402 J kg⁻¹ is also observed. In particular, the maximum values of −ΔS_M and ΔT_ad are high, at 17.1 J kg⁻¹ K⁻¹ and 6.0 K respectively, for a field change of 0–2 T. These results show that the HoCoGe compound with excellent magnetocaloric effects can be expected to have effective applications in low temperature magnetic refrigeration.

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1. Introduction

The consequent changes in the entropy and temperature of a material with magnetic field are known as magnetocaloric effect (MCE).¹ W. Thomson predicted this effect first.² P. Weiss and A. Piccard discovered it experimentally.³ Magnetic refrigeration based on MCE has been widely employed in ultra-low temperatures.^4,5 Recently, researchers anticipate it to be a promising alternative technology available to high temperature and even room temperature.^6,7 Many excellent magnetocaloric materials, such as Gd₅(Si, Ge)₄,⁸ La(Fe, Si)₁₃,^9,10 MnAs,^11,12 MnFe(P, As),¹³ Ni₂MnGa,¹⁴ and Gd⁷ etc., have been successively reported. However, systems exhibiting large MCEs at low temperatures are also important for basic research as well as special technological applications, such as space science and liquefaction of hydrogen in the fuel industry.^6,7 Therefore, it is important to develop magnetic advanced refrigerants applicable in the low temperature range.

Paramagnetic salts such as Gd₃Ga₅O₁₂, GdLiF₄, and GdF₃ have been applied to achieve temperature lower than 20 K.^15,16 But the MCEs of the paramagnetic salts are small and largely depend on the temperature. In contrast, rare-earth based compounds with large magnetic entropy change (ΔS_M, an important parameter for evaluating MCE) can be expected as valuable alternatives. In addition, a large MCE for low field change is desirable for the fulfillment of a magnetic refrigerator simply by using permanent magnets, which can currently only provide a field less than 2 T. Therefore, we should explore magnetic refrigerant materials possessing giant MCE for low field change at low temperatures.

The RTX (R = rare earth, T = transition metal, and X = p-metal) family with different crystal structures show rich magnetic and electrical properties.^17–19 Some are promising for low temperature magnetic refrigeration for their large MCE.^20–28 Only a few reports on RCoGe have been published.^29–33 RCoGe (R = La–Nd, Sm) compounds crystallize in the tetragonal CeFeSi-type structure.^31,32 LaCoGe is a Pauli paramagnet, whereas CeCoGe and PrCoGe are Curie–Weiss paramagnets.³² NdCoGe shows ferromagnetic Nd layers antiferromagnetically coupled below Néel temperature T_N = 8 K.³² RCoGe (R = Gd–Lu) compounds crystallize in the orthorhombic TiNiSi-type structure.^29,30,33 RCoGe (R = Gd–Yb) are Curie–Weiss-type paramagnets by magnetic susceptibility measurement within 77–300 K.²⁹ Neutron diffraction reports³³ of TbCoGe show the coexistence of a dominant noncollinear ferromagnetic (FM) structure with a sine-modulated ordering at low temperatures. However, the magnetic property of HoCoGe has only been researched by magnetic susceptibility so far.²⁹ In this paper, we report on the magnetic properties and giant MCE of the HoCoGe compound. In particular, it exhibits a large −ΔS_M of 17.1 J kg⁻¹ K⁻¹ and a large adiabatic temperature change ΔT_ad of 6.0 K for a low field change of 0–2 T in the low temperature range.

2. Experimental details

Several polycrystalline HoCoGe compounds were synthesized by arc melting the stoichiometric mixture of constituent elements Ho with purity above 99.9 wt%, Co with purity above 99.9 wt% and Ge with purity above 99.99 wt%, under high-purity argon atmosphere. Ho, Co and Ge raw materials are fully polished in order to eliminate their oxide coating before they are weighed according to stoichiometric proportion. Three atomic percent excessive Ho was added to compensate the weight loss during the arc melting. Sample chamber was pumped to 3.6 × 10⁻³ Pa and was then filled with high-purity argon atmosphere. This process was repeated three times before arc melting to prevent oxidation of the samples as much as possible. The samples were turned over and re-melted four times to ensure their homogeneity. The as-casts were wrapped with molybdenum foil and sealed in a quartz tube filled with high-purity argon atmosphere, which had been evacuated to avoid the oxidation of the samples, annealed at 973 K for two weeks and then quenched in liquid nitrogen. Powder X-ray diffraction (XRD) using Cu Kα radiation was employed to identify the crystal structure. The morphology and chemical compositions of one sample were measured by using an EVO18 scanning electron microscopy (SEM) (Zeiss) equipped with energy disperse X-ray spectrometer (EDS) (Bruker). Magnetizations were carried out on a commercial MPMS SQUID VSM magnetometer and a commercial MPMS-XL SQUID magnetometer (Quantum Design). Ac magnetic susceptibility and heat capacity were measured by using a commercial PPMS-14H physical property measurement system (Quantum Design).

3. Results and discussion

Fig. 1 shows the Rietveld refined powder XRD patterns of HoCoGe at room temperature. Almost all the diffraction peaks can be indexed to an orthorhombic TiNiSi-type structure (space group Pnma; no. 62, Z = 4). Ho, Co and Ge atoms occupy the 4(c) [0.0018, 0.25, 0.7005], 4(c) [0.1691, 0.25, 0.0889] and 4(c) [0.2989, 0.25, 0.3943] sites respectively, with the occupation factor of 0.5. The lattice parameters are determined to be a = 6.863(3) Å, b = 4.208(1) Å, and c = 7.259(5) Å, which are almost in agreement with the previous report.³⁰ The R-factors of Rietveld refinement are R_P = 19.7% and R_WP = 25.5%. These large values may be influenced by a small amount of impurity phase marked by “*” in the pattern of Fig. 1. The insets of Fig. 1 show the typical SEM back scattered electron images of HoCoGe in different regions. The molar ratio of Ho/Co/Ge obtained from EDS results is 1 : 1.08 : 0.99 for matrix phase characterized by grey area, which almost accord with our nominal ratios. The white area is of Ho-rich impurity phase Ho1.8Ge, which may be caused by the excessive addition of Ho. The black area corresponds to microcracks and holes due to the fast-cooling of our sample during the preparation process. Moreover, the proportion of impurity phase is confirmed to be lower than 5% by MATLAB software based on SEM images. However, we could not determine the content of impurity phase after searching ICDD data.

Fig. 1 Rietveld refined powder XRD pattern of HoCoGe compound at room temperature. The observed data are indicated by crosses, and the calculated profile is the continuous line overlying them. The short vertical lines indicate the angular positions of the Bragg peaks of HoCoGe. The lower curve shows the difference between the observed and calculated intensity. Left and right insets: the SEM images of HoCoGe in different regions.

Fig. 2(a) displays the zero-field cooling (ZFC) and field-cooling (FC) temperature dependences of magnetizations for HoCoGe compound under 0.01 T. The Curie temperature (T_C) determined by the minimum of dM/dT is equal to 7.6 K. The FC curve is typical for ferromagnetic materials and the good thermal magnetic reversibility between the ZFC and FC curves around T_C indicates a second order phase transition. However, a distinct discrepancy between the ZFC and FC branches appears below T_C. This thermomagnetic irreversibility (TI) can be observed in many cases, such as spin-glass systems,³⁴ materials with competing magnetic interaction,³⁵ and ferromagnetic materials with high anisotropy.^27,36 In order to investigate the origin of this irreversibility, the ac susceptibilities χ′ of HoCoGe have been measured in various frequencies ranging from 10 to 9997 Hz (see top inset of Fig. 2(a)). The peak position of χ′ does not show any obvious frequency dependence, suggesting that the irreversibility is not related to the spin-glass system.³⁴ Neutron diffraction and/or magnetic measurements investigations have determined that RNiSi (R = Tb–Er) compounds and the HoCoSi compound with the same TiNiSi-type structure show strong magnetocrystalline anisotropy at low temperatures.^37,38 Previous research indicates that in materials with high anisotropy and low ordering temperature, the domain wall width could be comparable to that of lattice space, thus resulting in a large pinning effect.³⁶ Considering the magnetic anisotropy and low T_C for HoCoGe, it is reasonable that the TI is attributed to the narrow domain wall pinning effect. In addition, neutron diffraction studies revealed a coexistence of noncollinear FM and a sine-modulated antiferromagnetic (AFM) ordering for TbCoGe.³³ Considering the existence of FM and AFM interactions in HoCoGe obtained from the reciprocal magnetic susceptibility (see below), the competition of FM and AFM interactions may contribute to the TI. Thus, we conclude that the TI stems from the narrow domain wall pinning effect and the competition of FM and AFM interactions.

Fig. 2 (a) Temperature dependences of ZFC and FC magnetizations of HoCoGe under 0.01 T. (b) Isofield χ⁻¹–T curves around the cusp transformed from our measured isothermal magnetization curves. The top inset of (a) shows the temperature dependence of ac susceptibilities of HoCoGe collected at various frequencies under a zero dc field. The bottom inset of (a) displays the temperature variations of the ZFC inverse susceptibility χ⁻¹ under different magnetic fields. The solid line to inverse susceptibility shows the CW fit under 2 T. The inset of (b) displays ac susceptibilities collected at various frequencies around the cusp under zero dc field.

The reciprocal dc magnetic susceptibilities χ⁻¹ versus temperatures for HoCoGe under the fields of 0.01 T, 0.5 T, 2 T and 5 T are shown in the bottom inset of Fig. 2(a). The χ⁻¹–T curve displays a cusp around 134 K under 0.01 T, resulting from the small cusp around 170 K on the M–T curve. In order to confirm this phenomenon, several HoCoGe compounds were prepared the same way as described in the experimental section. SQUID magnetometer and SQUID VSM magnetometer were carried out to repeat the M–T measurements under 0.01 T. These results revealed that all samples exhibit the same cusp phenomenon. Moreover, magnetizations of possible impurities Ho or Ho–Ge compounds with high Ho content reported do not show an anomaly around 170 K. Thus we speculate that the anomaly is an inherent character of HoCoGe. We get the isofield χ⁻¹–T curves around the cusp by transforming from our measured isothermal magnetization curves (see Fig. 2(b)). The cusp decreases gradually with the increase of field and disappears completely at 0.2 T. The temperature dependences of χ′ around the cusp at several frequencies are displayed in the inset of Fig. 2(b). There were no significant observations around the cusp. The inverse magnetic susceptibility of HoCoGe above 50 K under 0.5 T, 2 T and 5 T obeys the Curie–Weiss (CW) law, whereas it deviates from the CW law under low magnetic fields. This magnetic deviation from the CW law above T_C under low magnetic fields is characteristic of a Griffiths-like phase, which implies the formation of finite-sized FM clusters in the matrix of the PM phase. Similar deviations have been found in other intermetallic compounds such as Tb₅Si₂Ge₂,³⁹ Gd₅Ge₄,⁴⁰ ErCo₂ (ref. 41) and La_0.6Bi_0.4MnO₃.⁴² The effective magnetic moment (μ_eff) of the HoCoGe compound, evaluated from the slope of 1/χ in the PM region under the field of 2 T (see bottom inset of Fig. 2(a)), is equal to 11.0 μ_B/f.u. The value of μ_eff is close to the free Ho³⁺ ion value (10.6 μ_B), suggesting that 4f electrons are well localized and that there is no appreciable moment from Co, as all neutron reports on RCoGe compounds.^32,33 The PM Curie temperature (θ_P) is determined to be 2.7 K, further confirming that a FM–PM phase transition takes place around T_C for HoCoGe. It is much lower than that reported.²⁹ Meanwhile, the value of μ_eff we obtained is a little higher than that reported. We assume that large differences of θ_P and μ_eff from the results in ref. 29 may be mainly caused by the different heat treatment techniques (30 days at 1070 K in ref. 29), which might influence the homogeneity of samples and result in different compositions of the matrix phase. In addition, the lower θ_P is reasonable when considering the existence of AFM interaction in HoCoGe at low temperatures. The TbCoGe compound with the same TiNiSi-type structure has been reported to contain antiferromagnetic ordering at low temperatures.³³

The isothermal magnetization curves for HoCoGe compound were measured in applied fields up to 5 T in the vicinity of T_C. Fig. 3 presents the typical magnetization curves of the HoCoGe compound. The HoCoGe exhibits typical FM nature at temperatures lower than T_C. However, the magnetization does not reach saturation at 5 K even when magnetic field goes up to 5 T. The saturation magnetic moment per Ho atom is calculated to be 8.5 μ_B by using the magnetization under 5 T at 5 K, which is smaller than that expected for the free Ho³⁺ ion saturated moment (10 μ_B). This may result from the crystalline field effect, which leads to the large anisotropy of HoCoGe. The inset of Fig. 3 displays the corresponding Arrott-plots for the HoCoGe compound. According to the Banerjee's criterion,⁴³ the positive slope of the Arrott-plots confirms a characteristic of the second-order FM–PM phase transition for HoCoGe.

Fig. 3 Typical magnetic isothermals measured during field increasing for HoCoGe around T_C. The inset shows its Arrott-plots.

The temperature dependences of the heat capacities for HoCoGe under the fields of 0 T, 2 T and 5 T are shown in Fig. 4. The zero field heat capacity shows a λ-type peak, which suggests the second order phase transition nature. The magnetic transition temperature (T_C = 7.7 K) calculated from the first derivative of heat capacity is equal to that estimated from the magnetization data. With the increase of magnetic field, the peak gradually becomes broader and lower. At the same time, it also shifts slightly toward higher temperature, a typical characteristic of ferromagnets.⁶ The appearance of the zero-field heat-capacity peak is attributed to the absorption of a large amount of heat, which is consumed in randomizing the magnetic moments near T_C. When a magnetic field is applied, the process of randomization of moments would take place at temperatures above T_C, thereby broadening the heat capacity peak.⁴⁴

Fig. 4 Temperature dependences of heat capacities for HoCoGe under 0, 2, and 5 T. The top inset shows magnetic entropy changes of HoCoGe calculated from magnetizations (solid symbols) and heat capacity measurements (solid lines) as a function of temperature for different magnetic field changes up to 5 T. The bottom inset displays adiabatic temperature changes of HoCoGe as a function of temperature for the field changes of 0–2 T and 0–5 T.

As is well known, there are two methods to calculate the ΔS_M value, one using the Maxwell relation based on the magnetization isotherms, the other based on the heat capacity data.⁴⁵ However, we need to make some modifications to the second method because the starting temperature of the heat capacity measurement for HoCoGe (4.5 K) is not as ideal as 0 K. The Curie temperature is so low (only 7.6 K) that the specific heat values at 4.5 K are obviously different under different magnetic fields. The key point of modification is to replace the reference temperature of 0 K with 45 K.⁴⁶ Thus, we obtain the expressions of entropy with/without magnetic field as follows:

Substituting ΔS_M(45 K)_0–H = S(45 K)_H − S(45 K)_{0 T}, we get

Finally, we can obtain the expression of magnetic entropy change for a field change of 0–H as follows:

We choose 45 K (37 K higher than T_C) as the reference temperature since the magnetic ground state and magnetic transition are clearly known at this temperature which is far above T_C. That is, HoCoGe is paramagnetic at 45 K. Moreover, 45 K is also the highest temperature at which we measured M–H data. Obviously, the values of ΔS_M(45 K)_{0–2 T} and ΔS_M(45 K)_{0–5 T} are not zero. However, ΔS_M values calculated from magnetizations and heat capacities in the paramagnetic region are almost equal under the same temperature and magnetic field condition.^27,47,48 So we can use the values of ΔS_M(45 K)_{0–2 T} and ΔS_M(45 K)_{0–5 T} obtained from magnetizations. The ΔS_M values from heat capacity data can be obtained based on eqn (4). For comparison, the ΔS_M values were determined from both methods as shown in the top inset of Fig. 4, and it is clear that ΔS_M curves obtained from both methods match well. The peak broadens asymmetrically toward higher temperatures with the increase of magnetic field, confirming the presence of magnetic field-induced FM correlation above T_C.^21,49,50 The maximum values of −ΔS_M reach 17.1 J kg⁻¹ K⁻¹ and 23.9 J kg⁻¹ K⁻¹ for the field changes of 0–2 T and 0–5 T, respectively. Moreover, no magnetic hysteresis is found for the magnetization isotherms in the field increasing and decreasing processes, which leads to reversible magnetic entropy change. This also illustrates that the influence of TI on MCE is negligible. Refrigerant capacity (RC) is considered another important parameter to quantify the heat transferred between the hot and cold sinks in an ideal refrigeration cycle. It was estimated with the approach , where T_cold and T_hot are the temperatures corresponding to both sides of the half maximum value of ΔS_M peak.⁵¹ RC values are 137 J kg⁻¹ and 402 J kg⁻¹ for the field changes of 0–2 T and 0–5 T, respectively. As mentioned before, the magnetic field of 2 T can be provided by a permanent magnet. Therefore, this large MCE of HoCoGe under low field change is favorable to practical applications.

In order better understand the application potential of the HoCoGe compound, we have also calculated the MCE in terms of ΔT_ad by using the equation ΔT_ad(ΔH, T) = [T(S)_H − T(S)₀]_S.⁵² Firstly, S(T)_{0 T} is obtained from eqn (1) and S(45 K)_{0 T} is set to zero. Secondly, S(T)_{2 T} and S(T)_{5 T} are obtained from eqn (3), and ΔS_M(45 K)_{0–2 T} and ΔS_M(45 K)_{0–5 T} by using the results calculated from magnetizations. Thirdly, T(S)_{0 T}, T(S)_{2 T,} and T(S)_{5 T} are acquired by exchanging the corresponding T and S axes. The bottom inset of Fig. 4 shows the temperature dependences of ΔT_ad of HoCoGe for the field changes of 0–2 T and 0–5 T. The maximum values of ΔT_ad are 6.0 K and 10.9 K for the field changes of 0–2 T and 0–5 T, respectively. For comparison, the magnetocaloric properties of HoCoGe and some other refrigerant materials with a similar magnetic ordering temperature are listed in Table 1.^{20,22–24,48,53–56} It is clear that HoCoGe shows giant MCE, especially under the low magnetic field change. Therefore, the HoCoGe compound is a very attractive candidate for magnetic refrigeration in the low temperature range.

Table 1 The ordering temperature (T_ord), the magnetic entropy change −ΔS_M, the adiabatic temperature change ΔT_ad, and the refrigerant capacity RC for HoCoGe and some other refrigerant materials with a similar magnetic ordering temperature

Material	Tord (K)	−ΔSM (J kg^−1 K^−1)		ΔTad (K)		RC (J kg^−1)		Ref.
		0–2 T	0–5 T	0–2 T	0–5 T	0–2 T	0–5 T
a Field change (ΔH) = 6 T.b The RC values were estimated from the temperature dependence of ΔSM in the reference literatures.
HoCoAl	10	12.5	21.5	—	—	170^b	448^b	20
HoCuSi	7	16.7	33.1	—	—	117	385	22
ErCuAl	7	14.7	22.9	—	—	98	321	23
ErRuSi	8	15.2	21.2	—	—	124^b	340^b	24
EuHo2O4	5	8.6	22.8	2.8	10.0^a	71	282	53
TmGa	11.5/15	20.6	34.2	5.0	9.1	149	364	48
ErMn2Si2	4.5	20.0	25.2	5.4	12.9	96^b	271^b	54
TmMn2Si2	5.5	15.3	22.7	5.0	10.1	75^b	197^b	55
TmZn	8	19.6	26.9	3.3	8.6	57^b	210^b	56
HoCoGe	7.6	17.1	23.9	6.0	10.9	137	402	This paper

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4. Conclusions

In conclusion, the HoCoGe compound crystallizes in TiNiSi-type orthorhombic structure. A giant reversible MCE and large RC in HoCoGe compound were observed due to its second-order FM–PM phase transition around T_C = 7.6 K. For a field change of 0–5 T, the maximum values of −ΔS_M and ΔT_ad are 23.9 J kg⁻¹ K⁻¹ and 10.9 K, respectively. A large RC of 402 J kg⁻¹ is also obtained. In particular, the maximum values of −ΔS_M and ΔT_ad reach 17.1 J kg⁻¹ K⁻¹ and 6.0 K respectively, for a low field change of 0–2 T, which can be realized by permanent magnet; RC reaches 137 J kg⁻¹. The excellent performances in low magnetic field make the HoCoGe compound an attractive candidate for magnetic refrigeration in the low temperature range.

Acknowledgements

This work is supported by the National Basic Research Program of China (973 program, Grant No. 2014CB643700), the National Natural Science Foundation of China (Grant No. 51471111, 11274357, and 51531008, 51271196), General Program of Science and Technology Development Project of Beijing Municipal Education Commission, the Strategic Priority Research Program B (Grant No. XDB07030200), and the Key Research Program of the Chinese Academy of Sciences.

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