Anisotropic magnetocaloric effect in Fe 3−x GeTe 2
aa r X i v : . [ c ond - m a t . s t r- e l ] A ug Anisotropic magnetocaloric effect in Fe − x GeTe Yu Liu , Jun Li , Jing Tao , Yimei Zhu , and Cedomir Petrovic Condensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, Upton, NewYork 11973, USA * [email protected] and [email protected] ABSTRACT
We present a comprehensive study on anisotropic magnetocaloric porperties of the van der Waals weak-itinerant ferromagnetFe − x GeTe that features gate-tunable room-temperature ferromagnetism in few-layer device. Intrinsic magnetocrystallineanisotropy is observed to be temperature-dependent and most likely favors the long-range magnetic order in thin Fe − x GeTe crsytal. The magnetic entropy change − ∆ S M also reveals an anisotropic characteristic between H//ab and
H//c , whichcould be well scaled into a universal curve. The peak value − ∆ S maxM of 1.20 J kg − K − and the corresponding adiabatictemperature change ∆ T ad of 0.66 K are deduced from heat capacity with out-of-plane field change of 5 T. By fitting of thefield-dependent parameters of − ∆ S maxM and the relative cooling power RCP, it gives − ∆ S maxM ∝ H n with n = 0 . and RCP ∝ H m with m = 1 . when H//c . Given the high and tunable T c , Fe − x GeTe crystals are of interest for fabricatingthe heterostructure-based spintronics device. Introduction
Intrinsic long-range ferromagnetism recently achieved in two-dimensional-limit van der Waals (vdW) crystals opens up greatpossibilities for both studying fundamental two-dimensional (2D) magnetism and engineering novel spintronic vdW heteros-tuctures. Fe GeTe is a promising candidate since its Curie temperature ( T c ) in bulk is high and depends on the concen-tration of Fe atoms, ranging from 150 to 230 K. Intrinsic magnetocrystalline anisotropy in few-layer counteracts thermalfluctuation and favors the 2D long-range ferromagnetism with a lower T c of 130 K. Most significantly, the T c can be ionic-gate-tuned to room temperature in few-layers which is of high interest for electrically controlled magnetoelectronic devices. The layered Fe − x GeTe displays a hexagonal structure belonging to the P6 /mmc space group, where the 2D layers ofFe − x Ge sandwiched between nets of Te ions are weakly connected by vdW bonding [Fig. 1(a)]. There are two inequivalentWyckoff positions of Fe atoms which are denoted as Fe1 and Fe2. The Fe1-Fe1 dumbbells are situated in the centre of thehexagonal cell in the honeycomb lattice, composed of covalently bonded Fe2-Ge atoms. No Fe atoms occupy the interlayerspace and Fe vacancies only occur in the Fe2 sites. Local atomic environment is also studied by the M¨ossbauer and X-rayabsorption spectroscopies.
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Partially filled Fe d orbitals results in an itinerant ferromagnetism in Fe − x GeTe , whichexhibits exotic physical phenomena such as nontrivial anomalous Hall effect, Kondo lattice behavior, strong electroncorrelations, and unusual magnetic domain structures.
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A second-step satellite transition T ∗ is also observed just below T c , and is not fully understood.
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Here we address the anisotropy in Fe − x GeTe as well as the magnetocaloric effect investigated by heat capacity and dcmagnetization measurements. The magnetocrystalline anisotropy is observed to be temperature-dependent. The magnetic en-tropy change ∆ S M ( T, H ) also reveals an anisotropic characteristic and could be well scaled into a universal curve. Moreover,the − ∆ S maxM follows the power law of H n with n = 0 . , and the relative cooling power RCP depends on H m with m = 1 . . Methods
High quality Fe − x GeTe single crystals were synthesized by the self-flux technique. The element analysis was performedusing energy-dispersive X-ray spectroscopy (EDX) in a JEOL LSM-6500 scanning electron microscope (SEM). The selectedarea electron diffraction pattern was taken via a double aberration-corrected JEOL-ARM200F operated at 200 kV. The dcmagnetization and heat capacity were measured in Quantum Design MPMS-XL5 and PPMS-9 systems with the field up to 5T.
Results and Discussion
The average stoichiometry of our flux-grown Fe − x GeTe single crystals was determined by examination of multiple points.The actual concentration is determined to be Fe . Ge . Te [Fig. 1(b)], and it is referred to as Fe − x GeTe throughout igure 1. (Color online). (a) Crystal structure and (b) X-ray energy-dispersive spectrum of Fe − x GeTe single crystal. Insetshows a photograph of Fe − x GeTe single crystal on a 1 mm grid. (c) X-ray diffraction (XRD) pattern of Fe − x GeTe . Insetshows the electron diffraction pattern taken along the [001] zone axis direction. (d) Temperature dependence of the reducedmagnetization with out-of-plane field of Fe − x GeTe fitted using spin-wave (SW) model and single-particle (SP) model.Inset shows the temperature dependence of zero-field-cooling (ZFC) magnetization of Fe − x GeTe measured at H = 1 Tapplied along the c axis.this paper. The as-grown single crystals are mirror-like and metallic platelets with the crystallographic c axis perpendicular tothe platelet surface with dimensions up to 10 millimeters [inset in Fig. 1(b)]. In the 2 θ X-ray diffraction pattern [Fig. 1(c)],only the (00 l ) peaks are detected, confirming the crystal surface is normal to the c axis. The corresponding electron diffractionpattern [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 − x GeTe with out-of-plane field us-ing both spin-wave (SW) model and single-particle (SP) model. The temperature dependence of zero-field-cooling (ZFC)magnetization M ( T ) for Fe − x GeTe 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: ∆ MM (0) = M (0) − M ( T ) M (0) = AT / + BT / + ..., (1)where A and B are the coefficients. The M (0) is the magnetization at 0 K, which is usually estimated from the extrapolationof M ( T ) . The T / term stems from harmonic contribution and the T / term is a high-order contribution in spin-wavedispersion relation. In an itinerant magnetism, it is a result of excitation of electrons from one subband to the other. Thesingle-particle excitation is: ∆ MM (0) = M (0) − M ( T ) M (0) = CT / exp − ∆ k B T , (2)where C , ∆ and k B are fit coefficient, the energy gap between the Fermi level and the top of the full subband and the Boltzmannconstant, respectively. It can be seen that the SW model gives a better fit than the SP model up to 0.9 T c [Fig. 1(d)], indicatingpossible localized moment, in agreement with the bad-metallic resistivity of Fe − x GeTe . It is also understandable thatthe SP model fails due to strong electron correlation in Fe − x GeTe . The fitting yields A = 8 . × − K − / , B =1 . × − K − / , C = 3 . × − K − / and ∆ = 3 . meV.Figure 2(a) shows the temperature dependence of heat capacity C p for Fe − x GeTe 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 isgradually suppressed in fields. The entropy S ( T, H ) can be determined by S ( T, H ) = Z T C p ( T, H ) T dT. (3)
00 120 140 160 180 200220240260280 100 120 140 160 180 2000.00.40.81.2 100 120 140 160 180 2000.00.20.40.6
H // c
T (K) C p ( J kg - K - ) (a) - S M ( J kg - K - ) (c) T a d ( K ) T (K)
Figure 2. (Color online). Temperature dependences of (a) the specific heat C p , (b) the magnetic entropy change − ∆ S M ,and (c) the adiabatic temperature change ∆ T ad for Fe − x GeTe with out-of-plane field changes of 2 and 5 T.The magnetic entropy change ∆ S M ( T, H ) can be approximated as ∆ S M ( T, H ) = S M ( T, H ) − S M ( T, . In addition,the adiabatic temperature change ∆ T ad caused by the field change can be derived by ∆ T ad ( T, H ) = T ( S, H ) − T ( S, atconstant total entropy S ( T, H ) . Figures 2(b) and 2(c) present the temperature dependence of − ∆ S M and ∆ T ad estimatedfrom heat capacity with out-of-plane field. They are asymmetric and attain a peak around T c . The maxima of − ∆ S M and ∆ T ad increase with increasing field and reach the values of 1.20 J kg − K − and 0.66 K, respectively, with the field change of5 T. Since a large magnetic anisotropy is observed in Fe − x GeTe , it is of interest to further calculate its anisotropic magneticentropy change.Figures 3(a) and 3(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 beobtained from dc magnetization measurement as: ∆ S M ( T, H ) = Z H (cid:20) ∂S ( T, H ) ∂H (cid:21) T dH. (4)With the Maxwell’s relation h ∂S ( T,H ) ∂H i T = h ∂M ( T,H ) ∂T i H , it can be rewritten as: ∆ S M ( T, H ) = Z H (cid:20) ∂M ( T, H ) ∂T (cid:21) H dH. (5)When the magnetization is measured at small temperature and field steps, ∆ S M ( T, H ) is approximated: ∆ S M ( T, H ) = R H M ( T + ∆ T ) dH − R H M ( T ) dH ∆ T . (6)Figures 3(c) and 3(d) show the calculated − ∆ S M ( T, H ) as a function of temperature in various fields up to 5 T applied inthe ab plane and along the c axis, respectively. All the − ∆ S M ( T, H ) curves feature a pronounced peak around T c , similarto those obtained from heat capacity [Fig. 2(b)], and the peak broadens asymmetrically on both sides with increase in field.Moreover, the value of − ∆ S M ( T, H ) increases monotonically with increase in field; the peak − ∆ S M reaches 1.26 J kg − K − with in-plane field change and 1.44 J kg − K − with out-of-plane change of 5 T, respectively. We calculated the rotatingmagnetic entropy change ∆ S RM as ∆ S RM ( T, H ) = ∆ S M ( T, H c ) − ∆ S M ( T, H ab ) . (7)The asymmetry of − ∆ S M ( T, H ) is more apparent in the temperature dependence of − ∆ S RM [Fig. 3(e)]. Furthermore, thereis a slight shift of − ∆ S M maximum towards higher temperature when the field varies from 1 to 5 T [Figs. 3(c) and 3(d)].This shift of T peak excludes the mean field model but could be reproduced by the Heisenberg model due to its discrepancywith T c . Around the second order phase transition, the magnetic entropy maximum change is − ∆ S maxM = aH n , where a is aconstant and n is n ( T, H ) = dln | ∆ S M | /dln ( H ) . (8)
00 120 140 160 180 2000.00.40.81.2 100 120 140 160 180 2000.00.40.81.21.6 100 120 140 160 180 2000.00.10.20.3
H // ab
T (K) - S M ( J kg - K - ) (c) H // c (d) T (K) - S M ( J kg - K - ) H // ab H // c (e) - S R M ( J kg - K - ) T (K)
200 K M ( e m u m o l - ) H (T)(a) H // ab 100 K 200 K100 KH // c(b) M ( e m u m o l - ) H (T)
Figure 3. (Color online). Initial isothermal magnetization curves from T = 100 to 200 K with temperature step of T = 4 Kmeasured with (a) in-plane and (b) out-of-plane fields. Temperature dependence of magnetic entropy change − ∆ S M obtained with (c) in-plane and (d) out-of-plane field changes, and (e) the difference − ∆ S RM . -2 -1 0 1 2 3 40.00.30.60.91.2 -0.2 -0.1 0.0 0.1 0.20.00.20.40.6100 120 140 160 180 2000.60.91.21.51.8 0 1 2 3 4 50.00.51.01.5 D S M / D S m a x M t(c) H // c H // c(d) - D S M / H n e/H b + g ) n = 1 + (b - 1)/(b + g) -2 0 201 H // ab D S M / D S m a x M t H // c(a) n T (K) n = 0.603(6) - D S m a x M ( J kg - K - ) H (T)(b) H // c -DS maxM -DS maxM = aH n m = 1.20(1) R C P ( J kg - ) RCPRCP = bH m Figure 4. (Color online). (a) Temperature dependence of n in various fields. (b) Field dependence of the maximummagnetic entropy change − ∆ S maxM and the relative cooling power RCP with power law fitting in red solid lines. (c) Thenormalized ∆ S M as a function of the rescaled temperature t with out-of-plane field and in-plane field (inset). (d) Scalingplot based on the critical exponents β = 0.372 and γ = 1.265. igure 4(a) shows the temperature dependence of n ( T ) in various fields. All the n ( T ) curves follow an universal behavior. 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: n ( T c ) = 1 + (cid:18) β − β + γ (cid:19) = 1 + 1 δ (cid:18) − β (cid:19) , (9)where β , γ , and δ are the critical exponents related to the spontaneous magnetization M s below T c , the inverse initial suscep-tibility 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: RCP = − ∆ S maxM × δT F W HM , (10)where − ∆ S maxM is the entropy change maximum around T c and δT F W HM is the width at half maximum. The RCP alsodepends on the field as
RCP = bH m , where b is a constant and m is related to the critical exponent δ : m = 1 + 1 δ . (11)Figure 4(b) presents the field-dependent − ∆ S maxM and RCP. The RCP is 113.3 J kg − within field change of 5 T forFe − x GeTe . This is one half of those in manganites and much lower than in ferrites.
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Fitting of the − ∆ S maxM andRCP gives n = 0 . and m = 1 . , which are close to the values estimated from the critical exponents (Table I).Technique β γ δ n m − ∆ S maxM Table 1.
Critical exponents of Fe − x GeTe . The MAP, KFP and CI represent the modified Arrott plot, the Kouvel-Fisherplot and the critical isotherm, respectively.The scaling of magnetocaloric data is constructed by normalizing all the − ∆ S M curves against the maximum − ∆ S maxM ,namely, ∆ S M / ∆ S maxM by rescaling the temperature t below and above T c as defined in: t − = ( T peak − T ) / ( T r − T peak ) , T < T peak , (12) t + = ( T − T peak ) / ( T r − T peak ) , T > T peak , (13)where T r and T r are the temperatures of two reference points corresponding to ∆ S M ( T r , T r ) = ∆ S maxM . All the − ∆ S M ( T, H ) curves collapse onto a single curve regardless of temperature and field, as shown in Fig. 4(c). In the phasetransition region, the scaling analysis of − ∆ S M can also be expressed as − ∆ S M a M = H n f ( εH / ∆ ) , (14)where a M = T − c A δ +1 B with A and B representing the critical amplitudes as in M s ( T ) = A ( − ε ) β and H = BM δ , ∆ = β + γ , and f ( x ) is the scaling function. If the critical exponents are appropriately chosen, the − ∆ S M ( T ) curvesshould be rescaled into a single curve, consistent with normalizing all the − ∆ S M curves with two reference temperatures.By using the values of β = 0.372 and γ = 1.265 obtained by the Kouvel-Fisher plot, we have replotted the scaled − ∆ S M for Fe − x GeTe [Fig. 4(d)]. The good overlap of the experimental data points clearly indicates that the obtained criticalexponents for Fe − x GeTe are not only in agreement with the scaling hypothesis but also intrinsic.Then we estimated the magnetocrystalline anisotropy of Fe − x GeTe . By using the Stoner-Wolfarth model a value for themagnetocrystalline anisotropy constant K u can be estimated from the saturation regime in isothermal magnetization curves[Fig. 5(a)]. Within this model the magnetocrystalline anisotropy in the single domain state is related to the saturationmagnetic field H s and the saturation moment M s with µ is the vacuum permeability: K u M s = µ H sat . (15)
20 40 60 80 100 120 1400.81.01.21.41.60 20 40 60 80 100 120 1403040506070800 1 2 3 4 50.00.51.01.50 20 40 60 80 100 120 1401.01.21.4 M s ( e m u m o l - ) (b)(d) K u ( k J m - )
140 KH // ab(a) M ( e m u m o l - )
10 KT = 10 K H s ( T ) (c) Figure 5. (Color online). (a) Initial isothermal magnetization curves from T = 10 to 140 K with in-plane fields. Temperatureevolution of (b) the saturation magnetization M s , (c) the saturation field H s , and (d) the anisotropy constant K u .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 regimeat 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, and then decreases with increasing temperature [Fig. 5(c)]. Figure5(d) presents the temperature evolution of K u for Fe − x GeTe , which can not be described by the l ( l + 1) / power law.
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The value of K u for Fe − x GeTe is about 69 kJ cm − at 10 K, slightly increases to 78 kJ cm − at 50 K, and then decreasewith increasing temperature, which are comparable to those for CrBr , but smaller than those for CrI . The decrease of K u with increasing temperature is also observed in CrBr and CrI , arising from a large number of local spin clusters.
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Ina pure two-dimensional system, materials with isotropic short-range exchange interactions can not magnetically order. Thelong-range ferromagnetism in few-layers of Fe − x GeTe could possibly be favored by the large magnetocrystalline anisotropy. Conclusion
In summary, we have investigated in detail the magnetocaloric effect of Fe − x GeTe single crystals. The large magnetocrys-talline anisotropy is found to be temperature-dependent and probably establishes the long-range ferromagnetism in few-layersof Fe − x GeTe . The magnetic entropy change − ∆ S M also reveals an anisotropic characteristic and could be well scaled intoa universal curve independent on temperature and field. By fitting of the field-dependent parameters of − ∆ S maxM and therelative cooling power RCP, it gives − ∆ S maxM ∝ H n with n = 0 . and RCP ∝ H m with m = 1 . when H//c .Considering its tunable room-temperature ferromagnetism and hard magnetic properties in nanoflakes, further investigationon the size dependence of magnetocaloric effect is of interest.
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We thank J. Warren for help with the scanning electron microscopy (SEM) measurement. Work at Brookhaven NationalLaboratory is supported by the US DOE, Contract No. DE-SC0012704.
Author contributions statement
Y.L. and C.P. designed this study and synthesized crystals; Y. L. performed magnetization and heat capacity measurements.J.L, J.T. and Y.Z. contributed TEM measurement. Y.L. and C.P. organized and wrote the paper with input from all collaborators.This manuscript reflects the contribution and ideas of all authors.
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