Large Low-Field Reversible Magnetocaloric Effect in Itinerant-Electron Hf1−xTaxFe2 Alloys

First-order isostructural magnetoelastic transition with large magnetization difference and controllable thermal hysteresis are highly desirable in the development of high-performance magnetocaloric materials used for energy-efficient and environmental-friendly magnetic refrigeration. Here, we demonstrate large magnetocaloric effect covering the temperature range from 325 K to 245 K in Laves phase Hf1−xTaxFe2 (x = 0.13, 0.14, 0.15, 0.16) alloys undergoing the magnetoelastic transition from antiferromagnetic (AFM) state to ferromagnetic (FM) state on decreasing the temperature. It is shown that with the increase of Ta content, the nature of AFM to FM transition is gradually changed from second-order to first-order. Based on the direct measurements, large reversible adiabatic temperature change (ΔTad) values of 2.7 K and 3.4 K have been achieved under a low magnetic field change of 1.5 T in the Hf0.85Ta0.15Fe2 and Hf0.84Ta0.16Fe2 alloys with the first-order magnetoelastic transition, respectively. Such remarkable magnetocaloric response is attributed to the rather low thermal hysteresis upon the transition as these two alloys are close to intermediate composition point of second-order transition converting to first-order transition.


Introduction
Magnetic refrigeration, as an alternative cooling technology with the promises of high-efficiency and environment-friendly, has been recognized as a competitive substitute to replace the conventional gas-compression based refrigeration technology. Magnetic refrigeration is designed on the basis of magnetocaloric effect (MCE) [1], which is an intrinsic magneto-thermodynamic property of magnetic materials, using the isothermal magnetic entropy change (∆S M ) or the adiabatic temperature change (∆T ad ) on exposure to a magnetic field as the performance index. From the viewpoint of practical applications, highperformance magnetocaloric materials, especially those with large reversible MCE actuated at relatively low magnetic field (no more than 2 T), are highly sought in accelerating the commercialization process of magnetic refrigeration. In recent years, the utilization of first-order magnetic transition with large magnetization jump to achieve giant MCE has become the focus of discussion. Several representative alloy systems, such as La-Fe-Si [2][3][4], Mn-Fe-P-As (Ge, Si) [5][6][7], Gd-Si-Ge [8,9] and Heusler type Ni-Mn-based alloys [10][11][12][13][14][15], have been well developed.
In general, the first-order magnetic transition can be categorized into two types [16,17]. One is the magnetostructural transition, where the crystal structure is simultaneously changed in association with the magnetic transition, and the other is the magnetoelastic transition without symmetry breaking. In the case of magnetostructural transition, it is frequently observed that giant magnetocaloric response is achieved for the first application

Materials and Methods
The polycrystalline alloys with the nominal compositions of Hf 1−x Ta x Fe 2 (x = 0.13, 0.14, 0.15, 0.16) were prepared by arc-melting under the protection of high purity argon atmosphere, using the high-purity (4N) metal elements as the raw materials. For achieving a good composition homogeneity, each alloy was melted four times. The as-cast alloys were then encapsulated into vacuumed quartz tubes and isothermally annealed at 1273 K for one week, followed by quenching into water.
The crystal structure analyses were performed by X-ray diffraction (XRD) with Cu-Kα radiation in a Rigaku SmartLab diffractometer (Rigaku, Tokyo, Japan,) equipped with a temperature control attachment. The iso-field (M(T) curves) and iso-thermal (M(H) curves) magnetization measurements were carried out in a Quantum Design MPMS-3 system (Quantum Design, San Diego, CA, USA,), using the disc shaped samples with the dimension of Φ3 × 1 mm and the weight of~0.09 g. To reduce the influence of internal demagnetization field, the magnetic field was applied along circular plane. The specific heat capacity (C p ) was measured by the modulated differential scanning calorimetry (DSC) Materials 2021, 14, 5233 3 of 11 technology (TA- DSC 25). Direct measurements of adiabatic temperature change (∆T ad ) induced by magnetic field change were performed in a self-designed experimental device. The temperature range for such device is 223-343 K and the magnetic field, produced by NbFeB permanent magnet in Halbach array, is 1.5 T. Since the magnetic field is stationary, the adiabatic magnetization and demagnetization processes are realized through moving the sample into and out of the uniform magnetic field region, where the sample is placed in a movable rod controlled by servo motor. The time for move-in or move-out is 1 s. Thus, the rate of magnetic field change is 1.5 T s −1 . The temperature change of the sample (dimension: Φ10 × 2 mm,~2 g) induced by magnetic field change applied along circular plane was measured by a thermocouple directly attached to the sample surface. Figure 1a shows the powder XRD patterns for the Hf 1−x Ta x Fe 2 (x = 0.13, 0.14, 0.15, 0.16) alloys measured at the room temperature. It is seen that all the alloys present the characteristic of hexagonal MgZn 2 -type structure, with the space group of P6 3 /mmc (C14 Laves phase). In the lattice, Fe atoms are expected to be located at 2a and 6h sites and Hf/Ta atoms at 4f site [19]. Figure 1b shows the compositional dependence of lattice parameters for the Hf 1−x Ta x Fe 2 alloys as determined from the XRD patterns. With the increase of Ta content, the lattice parameters a and c almost linearly decrease. The decrease in lattice parameters a and c indicates the shrink of lattice volume, which should be attributed to the relatively lower atomic radius of Ta (1.43 Å) with respect to that of Hf (1.56 Å). heat capacity (Cp) was measured by the modulated differential scanning calorimetry (DSC) technology (TA- DSC 25). Direct measurements of adiabatic temperature change (ΔTad) induced by magnetic field change were performed in a self-designed experimental device. The temperature range for such device is 223-343 K and the magnetic field, produced by NbFeB permanent magnet in Halbach array, is 1.5 T. Since the magnetic field is stationary, the adiabatic magnetization and demagnetization processes are realized through moving the sample into and out of the uniform magnetic field region, where the sample is placed in a movable rod controlled by servo motor. The time for move-in or move-out is 1 s. Thus, the rate of magnetic field change is 1.5 Ts −1 . The temperature change of the sample (dimension: Ф10 × 2 mm, ~2 g) induced by magnetic field change applied along circular plane was measured by a thermocouple directly attached to the sample surface. Figure 1a shows the powder XRD patterns for the Hf1-xTaxFe2 (x = 0.13, 0.14, 0.15, 0.16) alloys measured at the room temperature. It is seen that all the alloys present the characteristic of hexagonal MgZn2-type structure, with the space group of P63/mmc (C14 Laves phase). In the lattice, Fe atoms are expected to be located at 2a and 6h sites and Hf/Ta atoms at 4f site [19]. Figure 1b shows the compositional dependence of lattice parameters for the Hf1-xTaxFe2 alloys as determined from the XRD patterns. With the increase of Ta content, the lattice parameters a and c almost linearly decrease. The decrease in lattice parameters a and c indicates the shrink of lattice volume, which should be attributed to the relatively lower atomic radius of Ta (1.43 Å) with respect to that of Hf (1.56 Å).   susceptible to the composition variation and T t gradually decreases as the increase of Ta content. It is noted that for the Hf 0.87 Ta 0.13 Fe 2 , Hf 0.86 Ta 0.14 Fe 2 and Hf 0.85 Ta 0.15 Fe 2 alloys, the M(T) branch on cooling is almost overlapped with that on heating, indicating the nature of second-order transition. Accordingly, the T t temperatures for these three alloys are determined to be 323 K (Hf 0.87 Ta 0.13 Fe 2 ), 302 K (Hf 0.86 Ta 0.14 Fe 2 ) and 277 K (Hf 0.85 Ta 0.15 Fe 2 ), respectively. On the other hand, for the Hf 0.84 Ta 0.16 Fe 2 alloy, a thermal hysteresis of~2 K between cooling and heating paths can be observed and the averaged T t is estimated to be 248 K, suggesting the nature of first-order transition. Nevertheless, such thermal hysteresis remains to be quite low, which is conducive to the reversibility of MCE. Based on the M(T) curves, it is inferred that the increase of Ta content allows a gradual evolution in the nature of magnetic transition from second-order to first-order.

Results
ization on cooling corresponds to the transition from high-temperature AFM phase to low-temperature FM phase. Apparently, the AFM to FM transition temperature (Tt) is susceptible to the composition variation and Tt gradually decreases as the increase of Ta content. It is noted that for the Hf0.87Ta0.13Fe2, Hf0.86Ta0.14Fe2 and Hf0.85Ta0.15Fe2 alloys, the M(T) branch on cooling is almost overlapped with that on heating, indicating the nature of second-order transition. Accordingly, the Tt temperatures for these three alloys are determined to be 323 K (Hf0.87Ta0.13Fe2), 302 K (Hf0.86Ta0.14Fe2) and 277 K (Hf0.85Ta0.15Fe2), respectively. On the other hand, for the Hf0.84Ta0.16Fe2 alloy, a thermal hysteresis of ~2 K between cooling and heating paths can be observed and the averaged Tt is estimated to be 248 K, suggesting the nature of first-order transition. Nevertheless, such thermal hysteresis remains to be quite low, which is conducive to the reversibility of MCE. Based on the M(T) curves, it is inferred that the increase of Ta content allows a gradual evolution in the nature of magnetic transition from second-order to first-order. Figure 2b compares the M(T) curves under the field of 0.005 T and 1.5 T for the Hf0.84Ta0.16Fe2 alloy. It is evidenced that the AFM to FM transition is accompanied by large magnetization jump. Owing to such magnetization difference, the AFM to FM transition is thus shifted to higher temperature region on increasing the magnetic field, since the magnetic field favors the phase with high magnetization. Under the field of 1.5 T, the AFM to FM transition temperature can be increased by 11 K, with the rate of 7.3 KT −1 .  It is evidenced that the AFM to FM transition is accompanied by large magnetization jump. Owing to such magnetization difference, the AFM to FM transition is thus shifted to higher temperature region on increasing the magnetic field, since the magnetic field favors the phase with high magnetization. Under the field of 1.5 T, the AFM to FM transition temperature can be increased by 11 K, with the rate of 7.3 K T −1 .
To acquire further insights into the magnetic transition for the Hf 1−x Ta x Fe 2 alloys, field-up and field-down isothermal magnetization (M(H)) curves across the AFM to FM transition were measured with the maximum field up to 5 T, as shown in Figure 3. The M(H) curves were measured in a discontinuous protocol. Prior to the measurements at each temperature, the sample was firstly zero field heated to a temperature well above the AFM to FM transition temperature, and then zero field cooled down to the measuring temperature. After that, the field-up and field-down M(H) curves were measured. For the Hf 0.87 Ta 0.13 Fe 2 alloy (Figure 3a), typical ferromagnetic behavior can be observed at the temperatures below T t (i.e., 323 K), where the magnitude of saturation magnetization gradually increases with decreasing the temperature. At the temperatures above 323 K, the field dependence of magnetization tends to exhibit a linear relation, showing the typical characteristic of antiferromagnetic state. It is noted that there is no obvious magnetic hysteresis between field-up and field-down M(H) curves. The M(H) curves for the Hf 0.86 Ta 0.14 Fe 2 alloy exhibit similar characteristics with those of Hf 0.87 Ta 0.13 Fe 2 alloy, as demonstrated in Figure 3b. magnetic state. It is noted that there is no obvious magnetic hysteresis between field-up and field-down M(H) curves. The M(H) curves for the Hf0.86Ta0.14Fe2 alloy exhibit similar characteristics with those of Hf0.87Ta0.13Fe2 alloy, as demonstrated in Figure 3b.
In the case of Hf0.85Ta0.15Fe2 alloy (Figure 3c), the M(H) curves exhibit the typical characteristic of ferromagnetism with no obvious magnetic hysteresis at the temperatures below Tt (i.e., 277 K). Above 277 K, step-like magnetization behavior can be observed, where a sudden jump in the slope followed by a rapid increase in magnetization at a certain critical field μ0Hcr takes place. This phenomenon is an indication of magnetic field-induced metamagnetic transition from AFM state to FM state. It is noted that magnetic field-induced AFM to FM transition is fully reversible, with very low magnetic hysteresis (e.g., ~0.1 T at 278 K) between the field-up and field-down isothermal magnetization curves. In addition, the critical field μ0Hcr to drive the AFM to FM transition is gradually elevated as the increase of temperature. As for the M(H) curves of Hf0.84Ta0.16Fe2 alloy demonstrated in Figure 3d, sharp step-like magnetization behaviors can be observed above Tt, indicating the occurrence of metamagnetic transition. Even though the magnetic hysteresis is widened when compared to that of Hf0.85Ta0.15Fe2 alloy, it remains in a relatively low level, e.g., ~0.2 T at 252 K.  In the case of Hf 0.85 Ta 0.15 Fe 2 alloy (Figure 3c), the M(H) curves exhibit the typical characteristic of ferromagnetism with no obvious magnetic hysteresis at the temperatures below T t (i.e., 277 K). Above 277 K, step-like magnetization behavior can be observed, where a sudden jump in the slope followed by a rapid increase in magnetization at a certain critical field µ 0 H cr takes place. This phenomenon is an indication of magnetic fieldinduced metamagnetic transition from AFM state to FM state. It is noted that magnetic field-induced AFM to FM transition is fully reversible, with very low magnetic hysteresis (e.g.,~0.1 T at 278 K) between the field-up and field-down isothermal magnetization curves. In addition, the critical field µ 0 H cr to drive the AFM to FM transition is gradually elevated as the increase of temperature. As for the M(H) curves of Hf 0.84 Ta 0.16 Fe 2 alloy demonstrated in Figure 3d, sharp step-like magnetization behaviors can be observed above T t , indicating the occurrence of metamagnetic transition. Even though the magnetic hysteresis is widened when compared to that of Hf 0.85 Ta 0.15 Fe 2 alloy, it remains in a relatively low level, e.g.,~0.2 T at 252 K.
In order to verify the nature of magnetic transition for the Hf 1−x Ta x Fe 2 alloys, the Arrott plots were calculated by using the field-up isothermal magnetization curves [27],  Figure 4. Since there is no negative slope for the Arrott plots in Figure 4a,b, the magnetic transition for the Hf 0.87 Ta 0.13 Fe 2 alloy and the Hf 0.86 Ta 0.14 Fe 2 alloy can be confirmed to be second-order. In contrast, the typical S-shape of Arrott plots manifests the first-order nature of magnetic transition for the Hf 0.85 Ta 0.15 Fe 2 alloy (Figure 4c) and the Hf 0.84 Ta 0.16 Fe 2 alloy (Figure 4d). Thus, the change of second-order transition to first-order transition appears at a tricritical point, which should lay somewhere at the composition x = 0.14-0.15. In order to verify the nature of magnetic transition for the Hf1-xTaxFe2 alloys, the Arrott plots were calculated by using the field-up isothermal magnetization curves [27], as shown in Figure 4. Since there is no negative slope for the Arrott plots in Figure 4a,b, the magnetic transition for the Hf0.87Ta0.13Fe2 alloy and the Hf0.86Ta0.14Fe2 alloy can be confirmed to be second-order. In contrast, the typical S-shape of Arrott plots manifests the first-order nature of magnetic transition for the Hf0.85Ta0.15Fe2 alloy (Figure 4c) and the Hf0.84Ta0.16Fe2 alloy (Figure 4d). Thus, the change of second-order transition to first-order transition appears at a tricritical point, which should lay somewhere at the composition x = 0.14-0.15. As the Hf0.84Ta0.16Fe2 alloy exhibits a sharp first-order magnetoelastic transition, temperature dependent XRD measurements were performed in order to acquire deep insights into the crystal structure evolution concomitant with the magnetoelastic transition. Figure  5a shows the temperature dependent XRD patterns for the Hf0.84Ta0.16Fe2 alloy across the first-order AFM-FM transition. It is seen that the hexagonal symmetry for the Hf0.84Ta0.16Fe2 alloy remains unchanged upon the magnetic transition, confirming the characteristic of a magnetoelastic transition. Figure 5b plots the change of lattice parameters a and c as a function of temperature. On decreasing the temperature, the lattice constant c exhibits a gradual decrease in the measured temperature region, i.e., positive thermal expansion. In contrast, a sharp increase in the lattice constant a can be observed upon the occurrence of AFM-FM transition, with the ratio ∆a/a of 0.26%, showing the characteristic of negative thermal expansion. It is noted that the obvious discontinuity in the lattice parameter a is a reflection of first-order magnetoelastic transition. Figure 5c shows the temperature dependence of unit cell volume. It is evidenced that the magnetoelastic transition is accompanied by the increase in the unit cell volume and the volume change ∆V/V is estimated to be 0.51%. Such negative thermal expansion should be attributed to the large discontinuity in the lattice parameter a. As the Hf 0.84 Ta 0.16 Fe 2 alloy exhibits a sharp first-order magnetoelastic transition, temperature dependent XRD measurements were performed in order to acquire deep insights into the crystal structure evolution concomitant with the magnetoelastic transition. Figure 5a shows the temperature dependent XRD patterns for the Hf 0.84 Ta 0.16 Fe 2 alloy across the first-order AFM-FM transition. It is seen that the hexagonal symmetry for the Hf 0.84 Ta 0.16 Fe 2 alloy remains unchanged upon the magnetic transition, confirming the characteristic of a magnetoelastic transition. Figure 5b plots the change of lattice parameters a and c as a function of temperature. On decreasing the temperature, the lattice constant c exhibits a gradual decrease in the measured temperature region, i.e., positive thermal expansion. In contrast, a sharp increase in the lattice constant a can be observed upon the occurrence of AFM-FM transition, with the ratio ∆a/a of 0.26%, showing the characteristic of negative thermal expansion. It is noted that the obvious discontinuity in the lattice parameter a is a reflection of first-order magnetoelastic transition. Figure 5c shows the temperature dependence of unit cell volume. It is evidenced that the magnetoelastic transition is accompanied by the increase in the unit cell volume and the volume change ∆V/V is estimated to be 0.51%. Such negative thermal expansion should be attributed to the large discontinuity in the lattice parameter a. It has been reported that the order of magnetic transition can also be quantitatively analyzed by calculating the power law exponent n based on the ΔSM values [17], i.e., n = dln|ΔSM|/dlnH. In the temperature range of magnetic transition, n > 2 represents the firstorder transition, whereas n < 2 indicates the second-order transition. The temperature dependence of the exponent n for the present alloys under the field of 1.5 T was also calculated and presented in Figure 6. For the Hf0.87Ta0.13Fe2 and Hf0.86Ta0.14Fe2 alloys, the exponent n exhibits a trend of 1→minimum→2, evidencing the second-order transition [17]. For the Hf0.85Ta0.15Fe2 and Hf0.84Ta0.16Fe2 alloys, the magnitude of exponent n higher than 2 clearly demonstrates the first-order transition [17]. The determination of magnetic transition order by the exponent n is consistent with the results obtained by the Arrott plots. It has been reported that the order of magnetic transition can also be quantitatively analyzed by calculating the power law exponent n based on the ∆S M values [17], i.e., n = dln|∆S M |/dlnH. In the temperature range of magnetic transition, n > 2 represents the first-order transition, whereas n < 2 indicates the second-order transition. The temperature dependence of the exponent n for the present alloys under the field of 1.5 T was also calculated and presented in Figure 6. For the Hf 0.87 Ta 0.13 Fe 2 and Hf 0.86 Ta 0.14 Fe 2 alloys, the exponent n exhibits a trend of 1→minimum→2, evidencing the second-order transition [17]. For the Hf 0.85 Ta 0.15 Fe 2 and Hf 0.84 Ta 0.16 Fe 2 alloys, the magnitude of exponent n higher than 2 clearly demonstrates the first-order transition [17]. The determination of magnetic transition order by the exponent n is consistent with the results obtained by the Arrott plots.
Adiabatic temperature change (∆T ad ), as an important performance index of MCE, allows a straightforward assessment on the magnetocaloric properties [1]. Here, the ∆T ad values for the studied Hf 1−x Ta x Fe 2 alloys under a low field change of 1.5 T were directly measured under the discontinuous protocol. Figure 7a shows the temperature dependence of ∆T ad values on cooling for the studied Hf 1−x Ta x Fe 2 alloys on applying the magnetic field of 1.5 T. For the Hf 0.87 Ta 0.13 Fe 2 and Hf 0.86 Ta 0.14 Fe 2 alloys with the second-order magnetic transition, the temperature evolution of ∆T ad values is moderate and gradual, covering a wide temperature range. Under the field change µ 0 ∆H of 1.5 T, the maximum ∆T ad values of 1.4 K and 1.7 K can be obtained around the AFM-FM transition for the Hf 0.87 Ta 0.13 Fe 2 and Hf 0.86 Ta 0.14 Fe 2 alloys, respectively. The temperature dependence of ∆T ad values for the Hf 0.85 Ta 0.15 Fe 2 and Hf 0.84 Ta 0.16 Fe 2 alloys with the first-order magnetic transition is sharp and abrupt, appearing in a relatively narrow temperature range. Accordingly, the maximum ∆T ad values up to 2.7 K and 3.4 K can be achieved in the Hf 0.85 Ta 0.15 Fe 2 and Hf 0.84 Ta 0.16 Fe 2 alloys, respectively. It is shown that the height and width of the ∆T ad curves for the Hf 1−x Ta x Fe 2 alloys are in agreement with the first-order and second-order nature of the magnetic transitions. With the change of magnetic transition from second-order to first-order, the maximum ∆T ad values are also gradually enhanced, in line with the evolution of ∆S M values. It should be mentioned that although the ∆S M values obtained in the present alloys are not very remarkable, the ∆T ad values are quite impressive, especially for the alloys with the first-order magnetic transition. This effect could be due to the relatively low specific heat capacity C p for the Hf 1−x Ta x Fe 2 alloys (e.g., C p =~300 J kg −1 K −1 for the Hf 0.84 Ta 0.16 Fe 2 alloy, as shown in inset of Figure 7a), according to the relation ∆T ad ≈ −T∆S M /C p . By using the C p and the ∆S M value at 252 K (i.e., −5.21 J kg −1 K −1 ) for the Hf 0.84 Ta 0.16 Fe 2 alloy, the maximum ∆T ad value can be estimated to be 4.4 K under a magnetic field change µ 0 ∆H of 1.5 T, being relatively higher than that obtained by direct measurements. Adiabatic temperature change (ΔTad), as an important performance index of MCE allows a straightforward assessment on the magnetocaloric properties [1]. Here, the ΔTad values for the studied Hf1-xTaxFe2 alloys under a low field change of 1.5 T were directly measured under the discontinuous protocol. Figure 7a shows the temperature dependence of ΔTad values on cooling for the studied Hf1-xTaxFe2 alloys on applying the magnetic field of 1.5 T. For the Hf0.87Ta0.13Fe2 and Hf0.86Ta0.14Fe2 alloys with the second-order magnetic transition, the temperature evolution of ΔTad values is moderate and gradual, covering a wide temperature range. Under the field change μ0ΔH of 1.5 T, the maximum ΔTad values of 1.4 K and 1.7 K can be obtained around the AFM-FM transition for the Hf0.87Ta0.13Fe2 and Hf0.86Ta0.14Fe2 alloys, respectively. The temperature dependence of ΔTad values for the Hf0.85Ta0.15Fe2 and Hf0.84Ta0.16Fe2 alloys with the first-order magnetic transition is sharp and abrupt, appearing in a relatively narrow temperature range. Accordingly, the maximum ΔTad values up to 2.7 K and 3.4 K can be achieved in the Hf0.85Ta0.15Fe2 and Hf0.84Ta0.16Fe2 alloys, respectively. It is shown that the height and width of the ΔTad curves for the Hf1-xTaxFe2 alloys are in agreement with the first-order and second-order nature of the magnetic transitions. With the change of magnetic transition from secondorder to first-order, the maximum ΔTad values are also gradually enhanced, in line with the evolution of ΔSM values. It should be mentioned that although the ΔSM values obtained in the present alloys are not very remarkable, the ΔTad values are quite impressive, especially for the alloys with the first-order magnetic transition. This effect could be due to the The reversibility of ∆T ad for the magnetocaloric materials is of great importance for the potential applications. Considering the characteristic of zero hysteresis for the second-order magnetic transition, ∆T ad values for the Hf 0.87 Ta 0.13 Fe 2 and Hf 0.86 Ta 0.14 Fe 2 alloys are fully reversible. For the Hf 0.85 Ta 0.15 Fe 2 and Hf 0.84 Ta 0.16 Fe 2 alloys with the first-order magnetic transition, they also present very good reversibility in the ∆T ad values during the cyclic magnetization/demagnetization measurements. Figure 7b, 16 Fe 2 alloy can be achieved during the cyclic magnetization/demagnetization measurements. Such good reversibility should be attributed to that the rather low thermal hysteresis upon the magnetic transition, since these two alloys lay at the borderline of the first-order transition and the second-order transition. Table 1 compares the present reversible ∆T ad values with those for some typical magnetocaloric materials. The present reversible ∆T ad values are superior to those obtained in some alloys with magnetostructural transition.
havior of ΔTad values for the Hf0.85Ta0.15Fe2 at 275 K and the Hf0.84Ta0.16Fe2 alloys at 253 K under the field change of 1.5 T, respectively. The Hf1-xTaxFe2 alloys exhibit conventional MCE due to the transition from AFM state to FM state on cooling. Thus, the sample warms on magnetization and cools on demagnetization. Stable reversible ΔTad value of 2.7 K for the Hf0.85Ta0.15Fe2 alloy and 3.4 K for the Hf0.84Ta0.16Fe2 alloy can be achieved during the cyclic magnetization/demagnetization measurements. Such good reversibility should be attributed to that the rather low thermal hysteresis upon the magnetic transition, since these two alloys lay at the borderline of the first-order transition and the second-order transition. Table 1 compares the present reversible ΔTad values with those for some typical magnetocaloric materials. The present reversible ΔTad values are superior to those obtained in some alloys with magnetostructural transition.

Conclusions
In summary, the magnetoelastic transition and the related magnetocaloric effect in Laves phase Hf 1−x Ta x Fe 2 (x = 0.13, 0.14, 0.15, 0.16) alloys were investigated. It is shown that the increase of Ta content enables the gradual decrease of the AFM to FM transition temperature and also the conversion from the second-order transition to the first-order transition. Owing to the magnetization difference associated with such AFM to FM transition, the MCE is observed in these compounds in the temperature range from 325 K to 245 K. Under a low magnetic field change of 1.5 T, large ∆S M values of −3.04 J kg −1 K −1 and −5.21 J kg −1 K −1 are obtained in the Hf 0.85 Ta 0.15 Fe 2 and Hf 0.84 Ta 0.16 Fe 2 alloys with the first-order magnetic transition. Moreover, large reversible ∆T ad values up 2.7 K and 3.4 K are also achieved under a low magnetic field change of 1.5 T in the Hf 0.85 Ta 0.15 Fe 2 and Hf 0.84 Ta 0.16 Fe 2 alloys, respectively, being much higher than those obtained in some alloys with magnetostructural transition. Such remarkable magnetocaloric properties should be attributed to the rather low thermal hysteresis of first-order magnetic transition in the Hf 0.85 Ta 0.15 Fe 2 and Hf 0.84 Ta 0.16 Fe 2 alloys, as they lay at the borderline of the first-order and the second-order magnetic transition. Furthermore, the effect of doping elements will be explored in the following work towards tuning the magnetization difference across the magnetic transition and the resultant magnetocaloric properties.