Large reversible magnetocaloric effect in antiferromagnetic Ho2O3 powders

Giant magnetocaloric materials are highly promising for technological applications in magnetic refrigeration. Although giant magnetocaloric effects were discovered in first-order magnetic transition materials, it is accompanied by some non-desirable drawbacks, such as important hysteretic phenomena, irreversibility of the effect, or poor mechanical stability, which limits their use in applications. Here, we report the discovery of a giant magnetocaloric effect in commercialized Ho2O3 oxide at low temperature (around 2 K) without hysteresis losses. Ho2O3 is found to exhibit a second-order antiferromagnetic transition with a Néel temperature of 2 K. At an applied magnetic field change of 5 T and below 3.5 K, the maximum value of magnetic entropy change \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(-\Delta {{\rm{S}}}_{M}^{max})$$\end{document}(-ΔSMmax), the refrigerant capacity (RC) were found to be 31.9 J.K−1.kg−1 and 180 J.K−1, respectively.

Cryocoolers able of cooling at low temperature (1.8-20 K) are widely utilized in different applications. As examples, they are used in hydrogen and helium liquefactions, superconducting quantum interference device (SQUID), medical instrumentation and diverse scientific research technologies. Superconducting magnet materials producing strong magnetic fields are broadly utilized in medicine and laboratories for scientific aims. Generally, liquid helium is used for cooling them, due to the fact that superconducting magnets exhibit low superconducting order temperature transition. However, liquid helium is expensive and scarcer which is not convenient from the economic point of view. Consequently, low-energy consumption cryocoolers are required. Magnetic refrigeration based on magnetocaloric effect (MCE) is a promising solution for refrigeration at low temperature [1][2][3][4][5][6][7] . Recently, considerable efforts were devoted to rare-earth based intermetallic compounds for low temperature magnetic refrigeration and some of them exhibit good MCE properties [8][9][10][11][12][13][14][15][16] . One of the main challenges in developing magnetic cryocoolers is to find a suitable working temperature range, large reversible magnetocaloric effect with low magnetic hysteresis losses. To date, the common used materials for cryogenic refrigeration 17-19 based on magnetocaloric effect [20][21][22] are hydrated salts. Such materials are used in low temperature cooling systems for detectors in space mission or laboratory facilities. The performance of an adiabatic demagnetization refrigerator (ADR) 23 is critically dependent on the design and construction of these salt pills that produce cooling. However, the only available salts refrigerants present some drawbacks because they are hydrated, which requires to be encapsulated in a hermetic container to prevent dehydration. Furthermore, hydrated salts are fabricated by growth which is not appropriate with industrial processes because it is very time consuming.
One can notice that for room temperature applications giant magnetocaloric effects (MCE) were reported in materials with a first-order magnetic transition (FOMT) such as LaFe 13−x Si x 24-29 Gd 5 (Si,Ge) 4 6 and others [30][31][32] . However, FOMTs occur in a narrow temperature window and are often accompanied with some non-desirable drawbacks such as the irreversibility of the MCE, very large thermal and magnetic-field hysteresis losses 33 and their high material cost. We note that very recently, the irreversibility of the MCE has been overcome in FOMT FeRh thin films 34 using dual-stimulus multicaloric cycle. It is known that magnetic materials with a second-order magnetic transition (SOMT) lack a very large (−ΔS M ), [35][36][37][38][39][40] but they do present some advantages such as low magnetic hysteresis and tunable order temperature by varying composition. In this work, we found that commercialized Ho 2 O 3 powders presents a giant magnetocaloric effect without magnetic hysteresis losses at low temperature.

Results and Discussion
The XRD pattern of Ho 2 O 3 powders is displayed in Fig. 1. Different diffraction peaks can be observed, indicating a polycrystalline character of the sample. All the diffraction peaks can be indexed according to the bixbyite structure, which is in agreement with the data found in the literature 41 . The lattice parameters were determined using Rietveld refinement and were found to be a = b = c = 10.6186 Å with R WP = 10.1%, R P = 12.18% and χ 2 = 4.82. The absence of any additional peak in the XRD pattern demonstrates that there are no spurious phases in the detection limit of XRD experiments. Figure 2 displays the temperature dependence of the magnetic susceptibility recorded at an applied magnetic field of 0.05 T for the Ho 2 O 3 compound. As can be observed, the sample shows a decrease in magnetic susceptibility with increasing temperature which is associated with the antiferromagnetic interaction in Ho 2 O 3 in agreement with previous reports 41 . In order to determine the Néel temperature (T N ), we display in the inset of Fig. 1(a) the χ = .
θ − C T P versus T plot. The T N is defined as the inflection point of derivative and it is around 2 K. Inset of Fig. 2 shows the change of magnetic susceptibility (χ −1 ) as a function of temperature. In the paramagnetic region, χ −1 (T) was fitted using the classical Curie-Weiss law: where C is the Curie constant and θ p is the Curie-Weiss temperature. From the linear fit, the C and θ p parameters were obtained. The negative (θ p = −7 K) value confirms the presence of an antiferromagnetic interaction. The C constant is related to the effective paramagnetic moment by the where N A = 6.023 10 23 mol −1 is the Avogadro number, µ B = 9.274 10 −24 (A/m 2 ) is the Bohr magneton and k B is the Boltzmann constant. From the determined C parameter, we have deduced the real effective moment of Ho value which was found to be µ eff exp = 11.8 µ B . The experimental effective paramagnetic moment µ eff exp is higher than the theoretical value (µ eff the = 10.6 µ B ), which could be attributed to the crystal field effects which favors a high spin configuration 41 . Figure 3 shows the temperature dependence of the magnetization at different applied magnetic fields. We display in the inset of Fig. 3 the magnetic field dependence of transition temperature. As shown, the magnetic transition is sensitive to the high magnetic field. Sharp change of the M(T) curve can be observed with increasing temperature at low magnetic field, while the increase of the applied field leads to a broader distribution of the M (T) curve. With increasing applied magnetic field more magnetic moments are forced to follow the direction of the applied field, which induced a broader distribution of the M(T) curve.
Isothermal magnetization curves were measured at various temperatures (Fig. 4). The gradual evolution of these curves to linear behavior characterizes an increase of the paramagnetic contribution above T N . Figure 4(b) presents the magnetic hysteresis loop of the Ho 2 O 3 powder recorded at 2 K. The hysteresis loop is closed and completely reversible. These properties are highly suitable for magnetic refrigeration 42 . In order to investigate the nature of the magnetic phase transition, Arrott plots (H/M versus M 2 ) were studied (Fig. 5). According to the Banerjee criterion 43 , a magnetic transition is the first-order when the slope of Arrott curves is negative, whereas it will be second-order when the slope is positive. As can be observed, positive slopes are observed for all temperatures which show that the H 2 O 3 compound undergoes a SOMT.
The magnetocaloric effect can be related to the magnetic properties of the material through the thermodynamics Maxwell's relation. It has been calculated in terms of isothermal magnetic entropy change using isothermal magnetization obtained at various temperatures (Fig. 5). According to the thermodynamically theory 6 , the isothermal magnetic entropy changes associated with a magnetic field change is given by:

T H
One can obtain the following expression Where µ 0 H max is the maximum external field. Figure 6 displays the temperature dependence of the magnetic entropy change of Ho 2 O 3 powders obtained at different applied magnetic field changes (1, 2, 3, 4, and 5 T). For all fields, the (−ΔS M ) curves show a maximum at around 3 K, which it is close to T N . We note that for a second-order phase transition the (−ΔS M )(T) should show a peak with a maximum around T N , however, since the T N of the sample is too low (2 K), we only observe half peak of (−ΔS M )(T). The peak magnitude increases when ΔH increases, from 8.2 to 31.9 J/kgK with increasing applied magnetic field change from 1 to 5 T, respectively. The large magnetocaloric effect in H 2 O 3 can be understood by its high magnetization associated with its sharp magnetization change at the antiferromagnetic-paramagnetic and the presence of crystal field effects above the transition. ΔT ad can be calculated from magnetization and heat capacity measurements C p  The temperature dependence of ΔT ad and heat capacity for magnetic field changes of 1 T is shown in Fig. 7 Table 1. Magnetic ordering temperature (T N,C ), maximum values of (−ΔS M max ) and refrigerant capacity (RC) under the magnetic field change of 5 T of the Ho 2 O 3 compound and some potential magnetic refrigerant materials.
compound is smaller than the other materials. We note that the RC factor is comparable or smaller than those of the materials reported in Table 1. The giant values of (−∆S M ), the low-cost and fast way of preparation suggest that this compound is one suitable candidate as a magnetic refrigerant in low temperature range (around 2 K).

Conclusion
In this paper, we have studied the magnetic and magnetocaloric properties of Ho 2 O 3 powders. Magnetic measurements have shown the presence of an antiferromagnetic-paramagnetic transition around 2 K and a giant magnetic entropy change with second-order magnetic transition. Strong influence of crystal field effect is also observed in magnetic properties as well as magnetocaloric effect. Our study demonstrates that the Ho 2 O 3 material could be considered as a potential candidate for magnetic refrigeration applications at low temperature (around 2 K).