Magnetocaloric effect in a Fe–Mn–Ga alloy Open Access

The Fe–Mn–Ga alloys are prospective functional materials, which crystallize into different structures depending on composition, parameters of fabrication, and postprocessing conditions.^1–3 There are several main types of crystalline structures observed in the Fe–Mn–Ga system. In the majority of Fe–Mn–Ga alloys studied until now, these structures coexisted. They include the γ-phase (L1₂ structure from Pm3m space group) characteristic of stoichiometric bulk and melt-spun Fe₂MnGa,⁴ L2₁ Heusler phase (Fm3 m) reducing to B2 type if partially disordered, and tetragonal L1₀ phase (I4/mmm).

In a certain range of off-stoichiometric compositions,³ Fe–Mn–Ga alloys undergo coupled martensitic transformation (MT) between the paramagnetic austenitic L2₁ (B2) phase and ferromagnetic martensitic L1₀ one. This transformation can be triggered by a magnetic field that assigns Fe–Mn–Ga to ferromagnetic shape memory alloys (FSMA). In contrast to Ni–Mn–X (X = In, Sb, and Sn) FSMA, Fe–Mn–Ga alloys demonstrate upward shift of transformation temperatures in the magnetic field, higher magnetic susceptibility, and lower electric resistivity in the martensitic phase. Although the magnetic field-induced strain reaches 0.6%⁵ at a field of 8 T as a part of full transformation strain of ∼3.6%,³ a broad thermal hysteresis of Fe–Mn–Ga requires high magnetic fields to employ these alloys for potential applications in actuator or magnetoresistance technologies.

Another area wherein Fe–Mn–Ga alloys can be used is caloric cooling. One of the recent works⁶ revealed the possibility to reduce brittleness of the Fe–Mn–Ga alloys by cold rolling allowed for achieving the compressive strength of 1000 MPa and a ductility of 75%. This opens prospects of further utilization of these materials for elastocaloric cooling.

Caloric effects in bulk materials are the subjects of intensive research in the last decades, and among them, the magnetocaloric effect (MCE) is preferable for implementation in cooling devices due to high COP and simpler design of magnetocaloric systems. The efforts to make them commercially attractive are mainly concentrated on the improvement of systems’ design, selection, and development of suitable materials. Although many materials including rare earth ones such as Gd,⁷ Tb and their alloys,⁸ Fe–Rh,⁹ or Ni–Mn-based Heusler alloys^10–13 have already demonstrated strong adiabatic and isothermal MCE, search for new magnetocaloric materials continues.

A giant magnetocaloric effect in FSMA is observed in alloys undergoing a significant change of magnetic entropy due to magnetic transition (second order transition) or (and) significant change of lattice entropy in the process of magnetic field-induced structural transition (first order transition). In Fe–Mn–Ga alloys, considerable changes of magnetization and volume (≈1.35%)⁵ and, hence, magnetic and lattice entropies accompanying the transition between paramagnetic austenite and ferromagnetic martensite indicate possibility of strong MCE. Although broad thermal hysteresis of MT in Fe–Mn–Ga alloys impedes their employment as magnetocaloric materials, the magnetic field could be combined with mechanical stress to overcome this issue.

Besides, these alloys also exhibit the ferromagnetic-to-antiferromagnetic (FM-AFM) transition of second order, which could provide magnetocaloric cooling with perfect reversibility. Recently, the large negative magnetic entropy change ΔS of about 60 J/kg K at 5 T associated with field-induced FM-AFM transition coupled with structural transformation was reported in the Fe₄₅Mn₂₆Ga₂₉ alloy¹⁴ within a narrow temperature interval. This result was obtained by an indirect Maxwell method using magnetization measurements.

Another estimation of MCE yielded much lower value of entropy change, only about ∼1.6 J/kg K in stoichiometric composition alloy¹⁵ with single γ-phase. However, until now, no direct measurements were reported on MCE of Fe–Mn–Ga alloys. This motivated us to perform an experimental study of adiabatic change of temperature in a Fe–Mn–Ga alloy under magnetic field to understand whether this compound can be used in magnetic refrigeration technologies and what MCE prevails in Fe–Mn–Ga, based on the FM-AFM transition or based on MT. Taking into account that room temperature is the most realistic start temperature for magnetocaloric cooling, the Fe_47.1Mn_26.1Ga_26.8 alloy with MT, which starts just below room temperature, was studied.

A slightly off-stoichiometric bulk polycrystalline Fe_47.1Mn_26.1Ga_26.8 alloy was prepared by melting together pieces of Fe, Mn, and Ga of 99.99% purity in an arc furnace with a water-cooled Cu hearth under a 1.3 bar Ar atmosphere. The Ar gas in the furnace before melting was additionally purified by multiple remelting of a Ti₅₀Zr₅₀ alloy getter. To increase the volume homogeneity, the ingots were remelted five times. After ingot melting, the weight loss was about 3%.The chemical composition of the alloy was determined using a Bruker EDS detector.

Magnetization measurements were carried out using the commercial Quantum Design PPMS. Temperature dependence of the magnetization was being determined in the temperature range from 5 to 400 K at a rate of 1 K/min. The field dependence of magnetization was measured sequentially at 300 and 250 K on cooling and at 80 K on heating from 50 K. The measurements of adiabatic change of temperature ΔT(T) under a magnetic field were performed using the differential Cu-Constantan-Cu micro-thermocouples with 300 ms time steps. This system was designed to study the magnetocaloric effect in materials with first- and second-order transitions.¹⁶ Point-to-point measurements of ΔT in the magnetic field of 4 T were conducted on cooling from 380 K. Before the measurement, stabilization of temperature has been carried out at each temperature point for 1–2 h. Then, a sample was being hold in the magnetic field for 600–700 s to ensure data accuracy.

Electrical resistivity was measured by a four-terminal method. The martensitic temperatures were determined from resistivity vs temperature curves by the standard method of tangent lines as intersections of tangent lines touching hysteresis curves. The magnetically induced change of MT temperatures was estimated using the shift of inflection points in thermal hysteresis curves under the magnetic field. The inflection points were disclosed by the calculation of second derivative of magnetization as a function of temperature.

The x-ray diffraction study was performed on a commercial DRON diffractometer in the Bragg–Brentano geometry with CoK_α radiation. The bulk polycrystalline sample, which was studied in the experiment, had not been crushed into powder to avoid the introduction of additional mechanical stress. As a result, the crystallites in the sample were not oriented randomly but rather had pronounced preferential orientation, and the peak intensities could be described only with certain precision. This limitation did not allow us to determine the occupation of the atomic sites and fractions of different phases. Still, the characteristic peak positions 2Θ have provided the information to determine the space groups of the phases present in the sample.

The variation in electrical resistivity shows temperature hysteresis typical for alloys with MT (Fig. 1). MT in Fe–Mn–Ga alloys is known to occur only between the parent L2₁ (B2) phase and tetragonal martensite.⁵ In Fe_47.1Mn_26.1Ga_26.8 alloy, the electron concentration e/a ≈ 6.39 is just between the values characteristic of γ-phase (e/a > 6.39) and those (6.27 < e/a < 6.39) wherein MT is observed in the Fe–Mn–Ga system.¹ As follows from Fig. 1, the characteristic temperatures of the forward transformation are M_S = 281 ± 3 K and M_F = 247 ± 3 K, while the reverse transformation starts at A_S = 310 ± 3 K and finishes at A_F = 345 ± 3 K. The resistivity of the martensitic phase is lower than that of the austenitic one by 10% in accordance with the results of ab initio calculations, which show higher density of states near the Fermi energy for tetragonal martensite.¹⁷ The temperature coefficient of resistance in the martensitic phase has positive value reflecting metallic type conductivity. In austenitic phase, its sign remains positive, but the resistivity grows much more gradually with temperature. This contradicts its semiconductor-like behavior earlier observed in the high-temperature phase of Fe–Mn–Ga alloys, in which the structure is predominantly composed of L2₁ phase.^1,17–19 Therefore, growth of resistivity with temperature above A_F indicates the coexistence of the L2₁ structure with tetragonal martensite or (and) γ-phase, which demonstrate positive temperature coefficient of resistance.

In order to determine the phase content of the Fe_47.1Mn_26.1Ga_26.8 alloy at temperatures above MT ones, the x-ray diffraction pattern has been analyzed using the Rietveld method. The best agreement between the theoretical and experimental 2Θ values for the diffraction peaks was observed assuming the mixture of the ordered L2₁ (B2) and L1₂ structures. Figure 2 demonstrates that most of the peaks of the L1₂ structure including $( 111 ) L 1 2$⁠, $( 200 ) L 1 2$⁠, and $( 220 ) L 1 2$ are present in the diffraction spectra. Low intensity of the other peaks of this structure could be ascribed to the partial antisite disorder of Mn and Ga atoms and/or nonrandom orientation of the crystallites.

The Heusler L2₁ phase is featured by hardly visible $( 111 ) L 2 1$⁠, $( 331 ) L 2 1$ reflections. The stronger (420) reflection indicates the presence of B2 ordering because of the abovementioned partial antisite disorder of the L2₁ phase. The $( 400 ) L 2 1$ peak is fundamental and is not affected by chemical disorder in contrast to the superstructural ones. The Rietveld refinement yielded lattice parameters of 3.709 ± 0.003 Å for L1₂ and 5.864 ± 0.006 Å for L2₁ structures, which closely correspond to those obtained earlier.

As is seen in Fig. 3, the magnetization in the field of 0.05 T exhibits two-stage growth on cooling and corresponding drop on heating. These features are related to successive martensitic and magnetic transitions. The characteristic temperatures of MT closely correspond to those determined from ρ(T): M_S = 274 ± 1 K, M_F =245 ± 1 K, A_S = 310 ± 1 K, and A_F = 341 ± 1 K. Small discrepancy between the M_S temperatures may stem from the influence of the FM-AFM transition in the γ-phase on magnetization of the alloy near the onset of forward MT. The sharp change of magnetization featured at 150 K and not seen in the ρ(T) dependence represents the Curie temperature, where the transition between paramagnetic and ferromagnetic states of the L2₁(B2) phase occurs. This structure does not transform completely to tetragonal martensite at MT in Fe–Mn–Ga alloys and can be found at temperatures far below M_F.²⁰ The bump in the M(T) curve between 190 and 280 K on heating is most likely related to lower martensitic temperatures of small part of the specimen due to compositional non-homogeneity. As the field was increased, martensitic temperatures T_M also increased in line with the Clausius–Clapeiron law $d T M/dH=−ΔM/ΔS$⁠, reflecting the growth of magnetization and the drop of lattice entropy at forward martensitic transformation. dT_M/dH was about 2.5 K/T for forward MT and only about 1.6 K/T for reverse one that resulted in narrowing the temperature hysteresis in the magnetic field (Fig. 3).

The M(H) shows very narrow magnetic hysteresis at T = 300 K in the high temperature phase, while it broadens at lower temperatures, below those of forward MT (Fig. 4). This behavior is typical in the case of formation and growth of antiferromagnetic domains or clusters in the ferromagnetic matrix.^21,22 The magnetization of the Fe_47.1Mn_26.1Ga_26.8 alloy does not achieve saturation at 80 and 250 K but is almost saturated with a value of 61 emu/g (2.6 μ_B/f.u.) in a field of 5 T at 300 K. The latter stems from ferromagnetism of the γ-phase coexisting with the paramagnetic L2₁ phase.

The variation in adiabatic change of temperature ΔT(T) shown in Fig. 5 can be divided into two regions, within which MCE has opposite signs. The high temperature region, where ΔT is positive, coincides with the temperature interval of the austenitic phase, while at temperatures of the martensitic phase, inverse MCE with negative ΔT is observed. Its maximum magnitude reaches 0.4 K in a field of 4 T at temperatures below 100 K. The adiabatic change of temperature in the magnetic field is seen to be reversible in both regions (Fig. 5); although at temperatures of MT and above them, the large thermal hysteresis of MT and low dT_M/dH should have hindered reversibility of MCE if it would be caused by field-induced MT. However, such a behavior is not observed. Hence, MCE in the alloy studied is not the result of magnetic field-driven MT as it occurs in Ni–Mn-based FSMA,¹¹ and only magnetic contribution into MCE rather than lattice one is relevant here.

The negative ΔT implies positive dM/dT in integral form of the Maxwell relation $ΔT( T , H)=− ∫ 0 H C P , H Δ T T ( ∂ M ( T , H ) ∂ T ) HdH$ due to the FM-AFM transition in the low-temperature region. According to previous reports, antiferromagnetic ordering exists in the cubic γ-phase of Fe–Mn–Ga alloys with near-stoichiometric compositions. Appearance of an antiferromagnetic state in the γ-phase was attributed to the formation of antiferromagnetic clusters in the ferromagnetic phase^4,23 or antiferromagnetic coupling of Fe and Mn sublattices.¹⁵ 

In the Fe_47.1Mn_26.1Ga_26.8 alloy, the γ-phase was shown to coexist with the L2₁ (B2) austenite and with the L1₀ martensite as manifested in the abovementioned features of structural, magnetic, and electric properties. Antiferromagnetic coupling in the γ-phase obviously arises between 240 and 300 K and further enhances on cooling as follows from broadening of the magnetic hysteresis and slower approaching to magnetic saturation (Fig. 4). This temperature interval is close to that of the FM-AFM transition reported in previous works.^24–26 

The FM-AFM transition in the γ-phase is hardly seen in the temperature dependence of magnetization (Fig. 3) because of sharper magnetization change due to MT and the Curie transition in the L2₁ (B2) phase in the same temperature interval. Only below Curie temperature, smooth decreasing magnetization occurs in the field of 0.05 T indicating the FM-AFM transition.

For comparison, the FM-AFM transition signature is not present in the plot of temperature-dependent magnetization of Fe–Mn–Ga alloy,¹ which is composed of ≈40 vol. % of the γ-phase and ≈60 vol. % of the L2₁ (B2) phase. The growth of magnetization due to approaching the Curie point of L2₁ (B2) phase on cooling overlapped its decrease due to the FM-AFM transition in the γ-phase. However, in the M(T) plot of stoichiometric Fe–Mn–Ga alloy²⁶ comprising much smaller amount of the γ-phase, features of the FM-AFM transition are clearly seen in a field of 0.01 T since other magnetic or structural transitions within or near temperature interval of this transition are absent.

Here, despite minor influence of the formation of AFM ordering on the temperature dependencies of electric resistance and magnetization, it demonstrates the dominant effect on MCE of the Fe_47.1Mn_26.1Ga_26.8 alloy in the temperature interval of martensitic phase.

In order to compare MCE of Fe_47.1Mn_26.1Ga_26.8 measured in this work with the result earlier obtained by the Maxwell approach on another Fe–Mn–Ga alloy,¹⁵ we assessed the change of entropy corresponding to ΔT = −0.4 K. The change of entropy ΔS due to MCE can be expressed as ΔS = −C_pΔT/T, where C_p, ΔT, and T are the specific heat, the change of temperature owing to adiabatic MCE, and temperature of measurement, respectively. The substitution of C_p = 400 J/kg K^1,25 gives ΔS within the range of 0.6 ÷ 1.6 J/kg K at temperatures from 200 K to 100 K. Although ΔT would be somewhat higher if merely a single γ-phase exists, this estimation closely coincides with the magnitude of MCE reported in the alloy with single γ-phase.¹⁵ 

As follows from prior works, the FM-AFM transition is smeared out over a large range of temperatures^1,21 or conversely occurs in a relatively small temperature interval.^4,15,24 Here, the inverse MCE is observed in a broad temperature range at least from 80 to 240 K. Narrowing an interval of the FM-AFM transition could enhance the inverse MCE by modification of dM/dT entering into the Maxwell relation. The determination of MCE in Fe–Mn–Ga alloys with single γ-phase and high dM/dT of the FM-AFM transition is required to finally resolve whether these materials are suitable for magnetocaloric refrigeration.

Temperature dependence of MCE for the first time was directly measured in the Fe–Mn–Ga compound. The conventional MCE is observed at temperatures above M_S on cooling, while inverse MCE occurs within the temperature interval of the martensitic phase of the Fe_47.1Mn_26.1Ga_26.8 alloy. The adiabatic change of temperature yields its peak values of ∼ −0.4 K in the magnetic field of 4 T at temperatures below 100 K. The reversibility of MCE in the high-temperature phase reveals extremely low contribution of the field-driven MT into MCE. The negative sign of ΔT is associated with the change of magnetization due to the formation of antiferromagnetic ordering in the γ-phase below 240 K. The contribution into MCE from the γ-phase was dominant over the whole temperature interval of the study. The low magnitude of MCE may be caused by the coexistence of different crystalline structures in the alloy and weakly pronounced change of magnetization with temperature.

The authors acknowledge financial support of their experimental work in MGML within the program of Czech Research Infrastructures (Project No. LM2023065) and Professor Y. V. Kudryavtsev for valuable discussion.

The authors have no conflicts to disclose.

J. Kastil: Data curation (equal); Investigation (equal); Methodology (equal). J. Kamarad: Data curation (equal); Investigation (equal); Methodology (equal). A. V. Kolomiets: Data curation (equal); Validation (lead); Writing – review & editing (lead). S. M. Konoplyuk: Conceptualization (lead); Formal analysis (lead); Investigation (equal); Writing – original draft (lead). L. E. Kozlova: Resources (lead). A. O. Perekos: Data curation (equal); Investigation (equal). E. Dzevin: Methodology (equal).

The data that support the findings of this study are available within the article.