Large magnetocaloric effect in van der Waals crystal CrBr₃

Abstract

We study the magnetocaloric effect (MCE) in van der Waals (vdW) crystal CrBr₃. Bulk CrBr₃ exhibits a second-order paramagnetic-ferromagnetic phase transition with T_C=33 K. The maximum magnetic entropy change -\text{Δ}{S}_M near T_C is about 7.2 J·kg^-1·K^-1 with the maximum adiabatic temperature change \text{Δ}{T}_{\text{ad}}^{\text{max}}=2.37 K and the relative cooling power RCP=191.5 J·kg^-1 at {\mu }_{0}H=5 T, all of which are remarkably larger than those in CrI₃. These results suggest that the vdW crystal CrBr₃ is a promising candidate for the low-dimensional magnetic refrigeration in low temperature region.

Graphical abstract

Keywords

magnetocaloric effect / 2D magnetic materials

The discovery of two-dimensional (2D) van der Waals (vdW) materials has stimulated extensive research interest for basic science and applied technologies [1]. Owing to the reduced dimensionality, 2D materials with atomic thickness manifest unique physical properties, distinct from conventional bulk materials. For example, bulk MoS₂ is an indirect band gap semiconductor but it becomes a direct band gap one when thinning down to monolayer [2]. These features are utterly important for novel optoelectronic devices [1]. Among the various novel properties of 2D vdW materials, 2D ferromagnetism is a long-sought one. The absence of 2D vdW crystals with intrinsic magnetism has hindered the development of new magnetic, magnetoelectric and magneto-optic applications. Very recently, the long-range ferromagnetism with Curie temperature T_C of 45 K in the monolayer CrI₃ has been observed [3]. It indicates that the ferromagnetism in bulk materials can be retained even in monolayer ones. This discovery sheds light on exploring novel 2D ferromagnetic (FM) materials [3].

Layered chromium halides CrX₃ (X = Cl, Br, and I) have the same rhombohedral BiI₃-type structure (space group R\overline{3}, No. 148) at low temperatures [4, 5]. Taking CrBr₃ as an example [Fig. 1(a)], the edge-shared CrBr6 octahedra form a 2D honeycomb layers of Cr ions and these [CrBr] slabs are stacked along the c axis with vdW gaps in between. The cleavage energies of these three compounds are comparable to graphite and MoS₂ [4, 5]. Each of CrX₃ compounds is a magnetic semiconductor with a small band gap. But the different radii of halides alter the in-plane nearest-neighbor Cr-Cr distance and the vdW gap between [CrX] slabs, leading to the changes of magnetic interactions in these materials. As a result, CrCl₃ displays antiferromagnetic with Neel temperature T_N of 16.8 K, while CrBr₃ and CrI₃ show ferromagnetism with T_C=33 K and 68 K [4-6]. All of these materials are magnetic semiconductors.

Among various properties of FM materials, magnetocaloric effect (MCE) is an important one that can be used for magnetic refrigeration, a promising, environmentally friendly energy-conversion technology. Even the MCE of many materials have been studied for a long time, the MCE in the FM vdW materials are still rare. Fe_3-xGeTe₂ with T_C=225 K shows the maximum values of magnetic entropy change -\text{Δ}{S}_M^{\text{max}} is about 1.1 J·kg^-1·K^-1 at 5 T [7]. CrI₃ exhibits anisotropic -\text{Δ}{S}_M^{\text{max}} with the values of 4.24 and 2.68 J·kg^-1·K^-1 at 5 T for H//c and H//ab, respectively [8]. In this work, we carried out a study on the MCE of CrBr₃ single crystal. The CrBr₃ undergoes a second-order phase transition in the vicinity of T_C and the -\text{Δ}{S}_M^{\text{max}} is about 7.2 J·kg^-1·K^-1 at 5 T, much larger than that of the homologous series CrI₃. Due to such large MCE, this compound would be a promising candidate material for magnetic refrigeration at low temperature.

Single crystals of CrBr₃ were grown by chemical vapor transport method with the mixture of polycrystal CrBr₃ (99%) powder. The starting materials were sealed in a silica tube under vacuum and then placed inside a two-zone horizontal tube furnace with temperature up to 890 K and 773 K for 7 days. The shiny black plate-like crystals with lateral dimensions up to several millimeters can be obtained. The X-ray diffraction (XRD) data were taken using a Bruker D8 X-ray diffractometer with Cu K_{\alpha } radiation (\lambda =0.15418 nm) at room temperature. The elemental analysis was performed using the energy-dispersive X-ray spectroscopy (EDX). Heat capacity was measured using a Quantum Design physical property measurement system (PPMS9). Magnetic properties were measured using a Quantum Design magnetic property measurement system (MPMS3). During the measurements, a piece of CrBr₃ single crystal was mounted in a plastic straw for both field directions. The crystal is about 0.6 mg with the sample geometry of 0.3 mm × 0.24 mm × 0.2 mm (a\times b\times c). For the M(H) measurement when H//c, the magnetic field has been corrected by using the formula {\mu }_{0}H={\mu }_{0}H-4\pi NM, where N is the demagnetization factor (~0.84). For the M(H) measurement when H//ab, the N is negligible (~0.07), thus the external magnetic field is not corrected.

As shown in Fig. 1(b), CrBr₃ single crystal has a plate-like morphology, consistent with its layered structure. The reflections in the XRD pattern of a single crystal [Fig. 1(c)] can be well indexed by the indices of (00l) lattice plane, indicating that the surface of crystal is perpendicular to the c axis (parallel to the ab plane). The EDX spectrum of a CrBr₃ single crystal confirms the existence of Cr and Br and the determined average atomic ratio of Cr to Br is 1:3.38(4), close to the chemical formula of CrBr₃. Moreover, the absence of other elements in the EDX spectrum also indicates the high purity of CrBr₃ crystals.

Figure 2(a) shows the temperature dependence of magnetization M(T) at {\mu }_{0}H=0.1 T for H//c and H//ab with zero-field-cooling (ZFC) and field-cooling (FC) modes. For both field directions, the M(T) curves exhibit rapid increase at low temperature, corresponding to the paramagnetic to FM phase transition and the T_C determined from the peak of derivative d\chi (T)/dT is about 33 K, close to that reported in the literature [6]. Moreover, it can be seen that when , the M(T) for H//ab drops gradually with decreasing temperature in contrast to the M(T) for H//c which is almost insensitive to temperature. Similar behavior has also been observed in CrI₃ [5], suggesting that the easy axis of magnetization is along the c axis. In addition, the ZFC and FC M(T) curves for both field directions are overlapped very well in the whole measuring temperature range, implying the absence of spin glassy behavior in CrBr₃. On the other hand, the magnetic susceptibility \chi (T) curve for H//c measured with FC mode was fitted by the modified Curie–Weiss law \chi ={\chi }_0+C/(T-\theta ) in the temperature range between 150 and 300 K (inset of Fig. 2(a)), where {\chi }_0 is a temperature-independent term, C is the Curie constant and θ is the Weiss temperature. The estimated value of θ is 49.7(1) K, confirming the FM interaction between Cr ions. Moreover, the obtained value of C is 0.1917(4) emu·K·mol^-1·T^-1, corresponding to the effective magnetic moment {\mu }_{\text{eff}}=3.906(4){\mu }_{\text{B}}/Cr. It is very close to the expected value {\mu }_{\text{eff}}=3.87{\mu }_{\text{B}} for spin-only Cr³⁺ ion (S=3/2). Figure 2(b) shows the isothermal M(H) curves measured at 2 K for both field directions. The values of saturation field is about 0.36 and 0.8 T for H//c and H//ab, respectively. The smaller value of the former indicates that the easy axis is the c axis, in agreement with the results of M(T) curves. But a small difference between two values implies that CrBr₃ does not have a strong uniaxial anisotropy, unlike that in CrI₃ [5]. Moreover, the quiet small remanet magnetizations and coercivity fields for both field directions suggest the soft ferromagnetism of CrBr₃, consistent with the weak magnetic anisotropy in this material. Importantly, this soft magnetism will lead to minimal hysteresis losses that would be detrimental to the cooling effect. On the other hand, the saturation moment at 2 K is about 2.85 {\mu }_{\text{B}}/Cr, close to the theoretical value gS=3{\mu }_{\text{B}} for Cr³⁺ ion with considering spin contribution only.

Figure 2(c) exhibits the initial isothermal magnetization curves M(H) in the magnetic field up to 5 T from 10 K to 58 K with a temperature step of 2 K. When T>T_C, the curves are almost linear, indicating a PM behavior. With decreasing temperature, the curves become bending with negative curvatures, suggesting an FM interaction appears. When T is far below T_C, there is a sharp increase in the M(H) curve in low-field region and then the magnetic moment saturates in high-field region, a typical feature of ferromagnet. In order to illustrate the order of PM–FM transition in CrBr₃, the relationship between M² and H/M, known as the Arrott plot, is shown in Fig. 2(d). Apparently, the slopes for all of curves in high-field region is positive, clearly indicating that the PM–FM phase transition is second-order [9, 10]. Moreover, these curves at various T are not parallel to each other with constant slope in the high-field region. It implies that the mean-field theory can not describe the critical behavior of CrBr₃ near T_C.

According to the classical thermodynamical and the Maxwell’s thermodynamic relation, the isothermal magnetic entropy change -\text{Δ}{S}_M(T) associated with the external field is given by [11, 12]

\begin{array}{}\text{(1)}& \text{Δ}{S}_M(T\mathrm{,}H)={\displaystyle {\int }_0^H}{\left(\frac{\partial S}{\partial H}\right)}_T\text{d}H={\displaystyle {\int }_0^H}{\left(\frac{\partial M}{\partial T}\right)}_H\text{d}H\mathrm{,}\end{array}

where {\left(\frac{\partial S}{\partial H}\right)}_T={\left(\frac{\partial M}{\partial T}\right)}_H is based on Maxwell’s relation. Under discrete magnetization and temperature measurements, -\text{Δ}{S}_M can be approximated written as

\begin{array}{}\text{(2)}& |\text{Δ}{S}_M(T\mathrm{,}H)|=-{\displaystyle \sum }\left[\frac{(M_{i+1}-M_i)}{T_{i+1}-T_i}\right]\text{Δ}{H}_i\mathrm{,}\end{array}

where M_i and M_{i+1} are the magnetization at T_i and T_{i+1} under the same magnetic field, respectively [11, 12]. The evolution of isothermal magnetic entropy changes -\text{Δ}{S}_M as functions of magnetic field and temperature is presented in Fig. 3(a). The curve of -\text{Δ}{S}_M at certain field shows a peak in the vicinity of T_C and the absolute value of -\text{Δ}{S}_M becomes larger with increasing field. The maximum value of magnetic entropy changes -\text{Δ}{S}_M^{\text{max}} at {\mu }_{0}H=5 T is about 7.2 J·kg^-1·K^-1 (33.0 mJ·cm^-3·K^-1). Recent studies proposed that for a second-order PM–FM transition, there is a scaling behavior between normalized magnetic entropy change -\text{Δ}{S}_M/-\text{Δ}{S}_M^{\text{max}} and rescaled temperature [13, 14]. The temperature axis was rescaled in a different way below and above T_C with an imposed constraint that the position of the two reference points of each curve corresponds to \theta =\pm 1,

\begin{array}{}\text{(3)}& \theta =\{\begin{array}{cc}-(T-T_C)/(T_{r1}-T_C)\mathrm{,}& \text{for }T\le T_C\mathrm{,}\\ (T-T_C)/(T_{r2}-T_C)\mathrm{,}& \text{for }T\text{>}{T}_C\mathrm{,}\end{array}\end{array}

where the reference temperatures T_{r1} and T_{r2} are chosen in order to make -\text{Δ}{S}_M(T_{r1}\mathrm{,}{T}_{r2})=-\mathrm{1/2}\text{Δ}{S}_M^{\text{max}}. It can be clearly seen that the curves of -\text{Δ}{S}_M(T\mathrm{,}H) at different fields fall onto a single curve [inset of Fig. 3(a)], i.e., exhibiting a scaling behavior. It confirms the feature of second-order PM–FM transition in CrBr₃.

Another parameter to characterize the potential magnetocaloric effect of materials is the relative cooling power (RCP). It can be calculated using the expression [12]

\begin{array}{}\text{(4)}& \text{RCP}=\left|\text{Δ}{S}_M^{\text{max}}\right|\times \delta T_{\text{FWHM}}\mathrm{,}\end{array}

where the FWHM means the full width at half maximum of -\text{Δ}{S}_M curve. The \delta T_{\text{FWHM}} representing the temperature range of magnetic entropy change play an important role in the refrigeration capacity. The value of RCP reaches a maximum value of 191.5 J·kg^-1 (0.877 J·cm^-3) at {\mu }_{0}H=5 T [Fig. 3(b)]. In addition, the field dependence of -\text{Δ}{S}_M^{\text{max}} and RCP can be fitted very well by using the power-law relations -\text{Δ}{S}_M^{\text{max}}\propto a{H}^n and RCP \propto b{H}^m [Fig. 3(b)]. The fitted n and m is 0.60(1) and 1.15(2), respectively, deviating from the mean-field values 2/3 and 1.33, but close to the values for 3D XY or 3D Ising models [8, 13-15].

Figure 3(c) exhibits temperature dependence of heat capacity C_p at different fields. At zero field, there is a sharp jump at about 32 K, clearly indicating a bulk PM–FM transition in CrBr₃. It is consistent with the M(T) results. With increasing field, the jump starts to broaden and shifts to higher temperatures. This is a typical behavior of PM–FM transition. The entropy S(T\mathrm{,}H) can be calculated from the heat capacity as

\begin{array}{}\text{(5)}& S(T\mathrm{,}H)={\displaystyle {\int }_0^T}\frac{C_p(T\mathrm{,}H)}{T}\text{d}T+S_0(H)\mathrm{,}\end{array}

where S_0(H) is the zero-temperature entropy, which can be neglected in a condensed system [11]. If assuming the heat capacities of electronic and lattice are not sensitive to field, the -\text{Δ}{S}_M can be obtained using the formula -\text{Δ}{S}_M=S_M(T\mathrm{,}H)-S_M(T\mathrm{,0}). As shown in the inset of Fig. 3(c), the -\text{Δ}{S}_M(T) show similar temperature dependence to those derived from M(H) curves and the -\text{Δ}{S}_M^{\text{max}} at 5 T (~6.91 J·kg^-1·K^-1) is also in agreement with that value obtained from magnetization data. The adiabatic temperature change \text{Δ}{T}_{\text{ad}}(=T(S\mathrm{,}H)-T(S\mathrm{,0})) caused by the field change during the isentropic process can be estimated from the heat capacity measurements. The temperature dependence of \text{Δ}{T}_{\text{ad}} shows a peak close to the T_C, similar to the -\text{Δ}{S}_M curves [Fig. 3(d)]. The \text{Δ}{T}_{\text{ad}}^{\text{max}} increases with increasing field and the \text{Δ}{T}_{\text{ad}}^{\text{max}} at 5 T is about 2.37 K.

The -\text{Δ}{S}_M^{\text{max}} of CrBr₃ is significantly smaller than that of well-known magnetic refrigerating materials with first-order magnetic phase transition, such as Gd₅Si₂Ge₂, LaF_13-xSi_x, and MnP_1-xAs_x [16]. However, the first-order magnetic phase transition always accompanies by the lattice expansion and magnetic thermal hysteresis, that may reduce the physically achievable efficiency and hinders practical application. In contrast, the MCE parameters of CrBr₃ are comparable or even larger than those magnetic refrigerating materials with second-order phase transition. For example, the -\text{Δ}{S}_M^{\text{max}} of RE₆Co_1.67Si₃ (RE = Pr, Gd, and Tb) are 6.9, 5.2 and 7.0 J·kg^-1·K^-1 at 5 T, and for the sulfospinels CdCr₂S₄, this value is 7.0 J·kg^-1·K^-1 at the same field [17]. Importantly, when compared to these materials, CrBr₃, as a binary compound, does not include costly rare-earth elements and is also easy to synthesis. It is worth noting that the values of -\text{Δ}{S}_M^{\text{max}}, RCP and \text{Δ}{T}_{\text{ad}}^{\text{max}} of CrBr₃ are also much larger than those values in CrI₃ at same field (~ 4.24 J·kg^-1·K^-1, 122.6 J·kg^-1, and 1.5 K at 5 T) [8]. Even using the unit of mJ·cm^-3·K^-1 which is meaningful for practical application, the -\text{Δ}{S}_M^{\text{max}} of CrBr₃ (33.0 mJ·cm^-3·K^-1) is still larger than that of CrI₃ (22.6 mJ·cm^-3·K^-1). This result shows that the variation of anions may have a significant influence not only on the T_C but also on the MCE. Thus, CrBr₃ could be a promising candidate for cryogenic magnetic refrigerating materials. Moreover, combining with the unique features of layered CrX₃, such as easy exfoliation down to a few layers or monolayer, persistence of 2D FM, maneuverable magnetism by using the external electric field [18-20], these kinds of vdW materials pave a way to study on the low-dimensional MCE and the interplay between MCE and other physical properties in 2D materials, especially in 2D heterostructures.

In summary, the magnetism and MCE of bulk CrBr₃ single crystal are comprehensively studied in the vicinity of the PM–FM transition. The PM–FM transition is second-order, confirmed by the analysis of Arrot plot and scaling behavior of -\text{Δ}{S}_M. The CrBr₃ displays larger magnetic entropy changes near T_C and the -\text{Δ}{S}_M reaches the maximum values of 7.2 J·kg^-1·K^-1 for \text{Δ}H=5 T, much larger than that in CrI₃. Combining with the easy exfoliation down to monolayer and large MCE, CrX₃ provides a new ingredient for the study of 2D materials.

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