Anisotropic magnetocaloric effect in Fe3−xGeTe2

We present a comprehensive study on anisotropic magnetocaloric porperties of the van der Waals weak-itinerant ferromagnet Fe3−xGeTe2 that features gate-tunable room-temperature ferromagnetism in few-layer device. Intrinsic magnetocrystalline anisotropy is observed to be temperature-dependent and most likely favors the long-range magnetic order in thin Fe3−xGeTe2 crsytal. The magnetic entropy change ΔSM also reveals an anisotropic characteristic between H//ab and H//c, which could be well scaled into a universal curve. The peak value \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-\Delta {S}_{M}^{{\max }}$$\end{document}−ΔSMmax of 1.20 J kg−1 K−1 and the corresponding adiabatic temperature change ΔTad of 0.66 K are deduced from heat capacity with out-of-plane field change of 5 T. By fitting of the field-dependent parameters of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-\Delta {S}_{M}^{{\max }}$$\end{document}−ΔSMmax and the relative cooling power RCP, it gives \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-{\rm{\triangle }}{S}_{M}^{{\max }}$$\end{document}−∆SMmax ∝ Hn with n = 0.603(6) and RCP ∝ Hm with m = 1.20(1) when H//c. Given the high and tunable Tc, Fe3−xGeTe2 crystals are of interest for fabricating the heterostructure-based spintronics device.


Results and Discussion
The average stoichiometry of our flux-grown Fe 3−x GeTe 2 single crystals was determined by examination of multiple points. The actual concentration is determined to be Fe 2.64(6) Ge 0.87(4) Te 2 [ Fig. 1(b)], and it is referred to as Fe 3−x GeTe 2 throughout this paper. The as-grown single crystals are mirror-like and metallic platelets with the crystallographic c axis perpendicular to the platelet surface with dimensions up to 10 millimeters [inset in Fig. 1(b)]. In the 2θ X-ray diffraction pattern [ Fig. 1(c)], only the (00l) peaks are detected, confirming the crystal surface is normal to the c axis. The corresponding electron diffraction pattern [inset in Fig. 1(c)] also confirms the high quality of single crystals. Figure 1(d) presents the low temperature thermal demagnetization analysis for Fe 3−x GeTe 2 with out-of-plane field using both spin-wave (SW) model and single-particle (SP) model. The temperature dependence of zero-field-cooling (ZFC) magnetization M(T) for Fe 3−x GeTe 2 measured in H = 1 T applied along the c axis is shown in the inset of Fig. 1(d). Localized-moment spin-wave excitations can be described by a Bloch equation [24][25][26] : where A and B are the coefficients. The M(0) is the magnetization at 0 K, which is usually estimated from the extrapolation of M(T). The T 3/2 term stems from harmonic contribution and the T 5/2 term is a high-order contribution in spin-wave dispersion relation. In an itinerant magnetism, it is a result of excitation of electrons from one subband to the other. The single-particle excitation is 24 : . It is also understandable that the SP model fails due to strong electron correlation in Fe 3−x GeTe 2 21 . The fitting yields A = 8.4(7) × 10 −5 K −3/2 , B = 1.24(5) × 10 −6 K −5/2 , C = 3.4(1) × 10 −4 K −3/2 and Δ = 3.9(4) meV. www.nature.com/scientificreports www.nature.com/scientificreports/ Figure 2(a) shows the temperature dependence of heat capacity C p for Fe 3−x GeTe 2 measured in zero-field and out-of-plane field of 2 and 5 T, respectively. The ferromagnetic order anomaly at T c = 153 K in the absence of magnetic field is gradually suppressed in fields. The entropy S(T, H) can be determined by  Figure 2(b,c) present the temperature dependence of −ΔS M and ΔT ad estimated from heat capacity with out-of-plane field. They are asymmetric and attain a peak around T c . The maxima of −ΔS M and ΔT ad increase with increasing field and reach the values of 1.20 J kg −1 K −1 and 0.66 K, respectively, with the field change of 5 T. Since a large magnetic anisotropy is observed in Fe 3−x GeTe 2 , it is of interest to further calculate its anisotropic magnetic entropy change. Figure 3(a,b) present the magnetization isotherms with field up to 5 T applied in the ab plane and along the c axis, respectively, in temperature range from 100 to 200 K with a temperature step of 4 K. The magnetic entropy change can be obtained from dc magnetization measurement as 27 : ) , it can be rewritten as 28 : M H H 0 When the magnetization is measured at small temperature and field steps, ΔS M (T, H) is approximated: The asymmetry of −ΔS M (T, H) is more apparent in the temperature dependence of −ΔS M R [ Fig. 3(e)]. Furthermore, there is a slight shift of −ΔS M maximum towards higher temperature when the field varies from 1 to 5 T [ Fig. 3(c,d)]. This shift of T peak excludes the mean field model but could be reproduced by the Heisenberg model due to its discrepancy with T c 29 .
Around the second order phase transition 30 , the magnetic entropy maximum change is −ΔS M max = aH n 31 , where a is a constant and n is 32   Figure 4(a) shows the temperature dependence of n(T) in various fields. All the n(T) curves follow an universal behavior 33 . At low temperatures, n has a value close to 1. At high temperatures, n tends to 2 as a consequence of the Curie-Weiss law. At T = T c , n has a minimum. Additionally, the exponent n at T c is related to the critical exponents 30 : c where β, γ, and δ are the critical exponents related to the spontaneous magnetization M s below T c , the inverse initial susceptibility H/M above T c , and the isotherm M(H) at T c , respectively. Relative cooling power (RCP) could be used to estimate the cooling efficiency 34 :

M max FWHM
where −ΔS M max is the entropy change maximum around T c and δT FWHM is the width at half maximum. The RCP also depends on the field as RCP = bH m , where b is a constant and m is related to the critical exponent δ: Figure 4(b) presents the field-dependent −ΔS M max and RCP. The RCP is 113.3 J kg −1 within field change of 5 T for Fe 3−x GeTe 2 . This is one half of those in manganites and much lower than in ferrites 35,36 . Fitting of the −ΔS M max and RCP gives n = 0.603 (6) and m = 1.20 (1), which are close to the values estimated from the critical exponents ( Table 1).
The scaling of magnetocaloric data is constructed by normalizing all the −ΔS M curves against the maximum −ΔS M max , namely, ΔS M /ΔS M max by rescaling the temperature t below and above T c as defined in:  www.nature.com/scientificreports www.nature.com/scientificreports/  Fig. 4(c). In the phase transition region, the scaling analysis of −ΔS M can also be expressed as  Fig. 4(d)]. The good overlap of the experimental data points clearly indicates that the obtained critical exponents for Fe 3−x GeTe 2 are not only in agreement with the scaling hypothesis but also intrinsic.   When H//ab, the anisotropy becomes maximal. We estimated the saturation magnetization M s by using a linear fit of M(H) above a magnetic field of 2.5 T with in-plane field [ Fig. 5(b)], which monotonically decreases with increasing temperature. Then we determined the saturation field H s as the intersection point of two-linear fits, one being a fit to the saturated regime at high fields and one being a fit of the unsaturated linear regime at low fields. The value of H s increases at low temperature, which is possibly related to a spin reorientation transition 15 , and then decreases with increasing temperature [Fig. 5(c)]. Figure 5(d) presents the temperature evolution of K u for Fe 3−x GeTe 2 , which can not be described by the l(l + 1)/2 power law 40,41 . The value of K u for Fe 3−x GeTe 2 is about 69 kJ cm −3 at 10 K, slightly increases to 78 kJ cm −3 at 50 K, and then decrease with increasing temperature, which are comparable to those for CrBr 3 , but smaller than those for CrI 3 42 . The decrease of K u with increasing temperature is also observed in CrBr 3 and CrI 3 42 , arising from a large number of local spin clusters 43,44 . In a pure two-dimensional system, materials with isotropic short-range exchange interactions can not magnetically order. The long-range ferromagnetism in few-layers of Fe 3−x GeTe 2 could possibly be favored by the large magnetocrystalline anisotropy.

conclusion
In summary, we have investigated in detail the magnetocaloric effect of Fe 3−x GeTe 2 single crystals. The large magnetocrystalline anisotropy is found to be temperature-dependent and probably establishes the long-range ferromagnetism in few-layers of Fe 3−x GeTe 2 . The magnetic entropy change −ΔS M also reveals an anisotropic characteristic and could be well scaled into a universal curve independent on temperature and field. By fitting of the field-dependent parameters of −ΔS M max and the relative cooling power RCP, it gives −ΔS M max ∝H n with n = 0.603 (6) and RCP ∝ H m with m = 1.20 (1) when H//c. Considering its tunable room-temperature ferromagnetism and hard magnetic properties in nanoflakes, further investigation on the size dependence of magnetocaloric effect is of interest. www.nature.com/scientificreports www.nature.com/scientificreports/