Effect of the temperature and magnetic field induced martensitic transformation in bulk Fe$_{45}$Mn$_{26}$Ga$_{29}$ alloy on its electronic structure and physical properties

TL;DR

This study investigates how temperature and magnetic fields induce martensitic transformations in Fe-Mn-Ga alloys, significantly altering their electronic structure and physical properties, with potential implications for magnetic and electronic applications.

Contribution

It provides detailed experimental and theoretical analysis of the electronic and physical property changes during martensitic transformation in Fe-Mn-Ga alloys, highlighting the effects of magnetic fields.

Findings

Martensitic transformation occurs between 194 K and 328 K with hysteresis.

Magnetic field shifts transformation temperatures to higher values.

Transformation causes increased magnetization and decreased resistivity.

Abstract

Effect of the temperature and magnetic field induced martensitic transformation (MT) on the electronic structure and some physical properties of bulk Fe$_{45.2}$Mn$_{25.9}$Ga$_{28.9}$ Heusler alloy has been investigated. {According to the experimental results of DSC, magnetic and transport measurements direct and reverse martensitic transformation without external magnetic field takes place within 194 $\leq T \leq$ 328 K temperature range with a hysteresis up to $\Delta T \approx$ 100 K defined as $\Delta T$ = $A_{f,s}$ - $M_{s,f}$, where $A_{f,s}$ and $M_{s,f}$ are the critical temperatures of direct and reverse martensitic transformation. External magnetic field of $\mu_{0}H$ = 5 T causes a high-temperature shift of MT temperatures.} MT from parent austenite L2$_{1}$ phase to martensitic tetragonally distorted L2$_{1}$ one (i. e. to L1$_{0}$) causes significant changes in the electronic structure of alloy, a drastic increase in alloy magnetization, a decrease in the alloy resistivity, and a reversal of the sign of the temperature coefficient of resistivity from negative to positive. At the same time experimentally determined optical properties of Fe$_{45.6}$Mn$_{25.9}$Ga$_{28.9}$ Heusler alloy in austenitic and martensitic states look visually rather similar being noticeable different in microscopic nature as can be concluded from first-principle calculations. Experimentally observed changes in the physical properties of the alloy are discussed in terms of the electronic structures of an austenite and martensite phases.

Equations

$$\Delta T=T_0(m_1{V}_1-m_2{V}_2)\Delta H/q,$$

$$\Delta T=T_0{m}_1{V}_1\Delta H/q,$$

Full text

††journal: Intermetallics

1 Introduction

Magnetic shape memory alloys (MSMAs) have found significant attention due to the possibility of rearrangement of martensite variants by external magnetic field. This property opens wide perspectives of their practical applications in medicine, robotics, active or passive damping [1]. Among MSMAs Ni-based Heusler alloys (HA) like Ni2MnGa, Ni2FeGa or Ni2MnAl probably are most investigated [2, 3, 4]. In Ni-based MSMA HAs direct martensitic transformation (MT) from ferromagnetic (FM) austenite phase to FM martensite one is accompanied with a small reduction in alloy magnetization and an increase in alloy resistivity.

Quite distinct changes in these properties induced by a direct MT have been found in off-stoichiometric Fe2MnGa alloys [5, 6, 7, 8]. The direct MT in these alloys is accompanied with a significant decrease in alloy resistivity and a transition from paramagnetic (PM) austenite to an FM martensite phase.

Phase equilibria upon phase transitions (like MT) are usually discussed in the framework of thermodynamics [9]. Effect of the electronic structures on such structural transformations was taken into account in a few reports [10, 11].

Among various experimental methods for studying of electronic structures of metals the optical spectroscopy (namely spectroscopic ellipsometry) is usually considered as such that manifests a higher compared to x-ray spectroscopy energy resolution ($\sim$ 0.01 eV) within $\pm$ 5 - 6 eV energy range near the Fermi level ($E_{F}$). Hence, spectroscopic ellipsometry was successfully employed for studying the solid-state reactions in multilayered films [12], structural transformations in bulk metals and alloys [13]. For example, Sasovskaya et al. have shown experimentally that austenite to martensite transformation in NiTi alloy is accompanied with the appearance of a new intense absorption band in a near infrared region of spectra for martensite state [14]. It was also theoretically predicted that MT in Ni2MnGa HA results from changes the electronic structure of alloy as well as its optical properties [15]. Furthermore, Gan’shina et al. have shown that the temperature induced martensitic transformation in Fe48Mn24Ga28 alloy causes visible changes in the equatorial Kerr effect spectra which reflect the changes in the electronic structure and magnetic properties of alloy [16]. In this work, we try to consider the effect of the temperature and magnetic field induced MT in Fe2MnGa alloy on its physical properties in close relation to the changes in the electronic structures of alloy studied theoretically and experimentally by employing the spectroscopic ellipsometry.

2 Experimental details

A slightly off-stoichiometric bulk polycrystalline Fe2MnGa 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 promote the volume homogeneity, the ingots were remelted five times. After ingot melting, the weight loss was about 3 $\%$.

The actual composition of the fabricated bulk Fe2MnGa HA sample was evaluated by using energy dispersive x-ray spectroscopy and found to be Fe45.2Mn25.9Ga28.9.

The structural characterization of the sample was carried out at room temperature (RT) employing x-ray diffraction (XRD) in ${\theta}-$2${\theta}$ geometry with Co-Kα (${\lambda}$=0.17902 nm).

An SC 404 F1 Pegasus differential scanning calorimeter (DSC) was used to determine the phase transformation temperatures.

Magnetic properties of the bulk Fe45.2Mn25.9Ga28.9 alloy were investigated over a temperature range $80\leq T\leq 370$ K by measuring the DC-magnetic susceptibility in a weak magnetic field of 5 Oe and by measuring the magnetization over a temperature range $4\leq T\leq 350$ K and a range of magnetic fields $0.5\leq H\leq 50$ kOe by using the PPMS-P7000 system.

Transport properties were measured by using the four-probe technique over a range of temperatures $80\leq T\leq 440$ K using the sample of $2.20\times 1.25\times 10.00$ mm3 in size.

A bulk sample for optical measurements of about 10 $\times$ 30 $\times$ 2 mm3 in size was cut from the ingot employing spark erosion technique followed by mechanical polishing with diamond pasts. To eliminate surface contaminations induced by mechanical polishing, the sample before optical measurements was annealed at $T$ = 573 K during 150 minutes at high vacuum conditions.

Optical properties [$Re({\sigma})=\omega\varepsilon_{2}/4\pi$ and $\varepsilon_{1}$, where $\sigma$ is the optical conductivity (OC), $\varepsilon_{1}$ and $\varepsilon_{2}$ are the real and imaginary parts of the diagonal components of the dielectric function $\widetilde{\varepsilon}=\varepsilon_{1}-i\varepsilon_{2}$] of the samples were measured by using a spectroscopic rotating-analyzer ellipsometer in a spectral range of 250 - 2500 nm (5.0 - 0.5 eV) at a fixed incidence angle of 73*∘* at $T$ = 173 and 373 K, respectively.

3 Results and discussion

3.1 Electronic structure

Figure 1 shows the spin-resolved energy dependencies of the density of electronic states [$N(E)$, DOS] for the stoichiometric Fe2MnGa alloy with L21 and tetragonally distorted L21 (i. e. L10) types of structure calculated for lattice constants obtained from volume optimization procedure (for the L21 phase) and from experiment (for tetragonal phase). Calculations details can be found elsewhere [17]. It is seen that $N(E)$ dependence for L21 phase is characterized by energy gap near Fermi level ($E_{F}$) for minority bands and deep minimum for majority bands making this phase even not half-metallic but almost semi-metallic. At the same time for tetragonal phase narrow and intense maximum of the $N(E)$ dependence is observed at $E_{F}$ for minority bands. It can be expected that such a drastic difference in DOS values at $E_{F}$ for L21 and L10 phases will lead to some difference in transport properties of alloy and stability of these phases. Calculated magnetic moments for L21 and L10 phases of Fe2MnGa alloy are ${\mu}=$ 2.01 and 6.35 $\mu_{B}/f.u.$, respectively.

3.2 Crystalline structure

DSC measurements on sample heating and cooling clearly show an existence of exo- and endothermic processes displaced in the temperature and concerned probably with direct and reverse martensitic transformations in the alloy (see Fig. 2) [5, 6]. Unfortunately, $M_{f}$ temperature using DSC plot is impossible to determine. Fine structures of DSC plots within temperature ranges of direct and reverse martensitic transformations indicate on the multiple-step-transformation process [i. e. a step-like process of increase (decrease) in a volume of martensitic phase] in alloy taking place at somewhat different temperatures due to probably compositional heterogeneousness. Obtained DSC data agree with the results of dilatometric measurements of bulk Fe45.2Mn25.9Ga28.9 alloy upon its cooling and heating (see Fig. 3). These results show that direct martensitic transformation is started much below RT at $M_{s}\approx$ 240 - 255 K, while the reverse martensitic transformation is finished above RT at $A_{f}\approx$ 318 - 327 K. Thus, corresponding heat treatments will allow us to fix at RT either austenite or martensitic phases.

Figure 4 presents RT experimental XRD patterns of preliminary heat treated Fe45.2Mn25.9Ga28.9 alloy sample. The comparison of the obtained experimental XRD patterns with the results of XRD modelling (see Fig. 5) allows us to conclude that after heating up to $T$=373 K Fe45.2Mn25.9Ga28.9 HA at RT contains mainly L21 phase with the lattice parameters of $a=b=c$ = 0.5829 nm [superstructure lines (111), (200), (311), (331) and (420) are clearly seen] with the small admixture of, probably, tetragonal phase (reflection at 2$\Theta$ = 49.77*∘). After cooling down to $T$ = 78 K at RT the Fe45.2Mn25.9Ga28.9* alloy sample contains two phases. These are mainly body-centered tetragonal (tetragonally distorted L21) phase with the lattice parameters of $a=b=0.5345$ nm, $c=0.716$ nm and some amount of L21 phase with $a=b=c=0.5885$ nm (see Fig. 5). Even though superstructure reflections for L21 phase at this pattern are hard to be seen it is unlikely that cooling down to $T=$ 78 K causes significant atomic disorder in this phase of alloy.

Conclusions on the sample structures based on the results of XRD measurements are supported also by RT optical image of the sample surface - martensitic variants dominate on the surface of the sample previously cooled down the liquid nitrogen temperature (see Fig. 6).

The obtained lattice parameters for cubic austenite and martensitic tetragonal phases nicely agree with the results obtained in the literature. Zhu et al. the marentsitic phase for Fe50Mn22.5Ga27.5 HA at $T$ = 90 K have been indexed as a body-centered tetragonal structure with the lattice parameters $a=b$ = 0.5328 nm and $c$ = 0.7113 nm and largest lattice distortion, $(c-a)/a=33.5{\%}$ among all the reported FSMAs [5]. The similar result has been obtained by Omori et al. for Fe44Mn28Ga28 HA - martensitic phase has been identified as non-modulated tetragonal one with the lattice parameters of $a=b$ = 0.5368 nm, $c$ = 0.7081 nm and the $c/a$ = 1.319, where the distorted L21 structure is taken as the unit cell of the non-modulated tetragonal martensite. The volume change due to the forward transformation $\Delta$V/V is +0.73 $\%$ [6].

In our case lattice distortion $(c-a)/a$ of the tetragonal phase is 34.5 ${\%}$. Forward MT induces the volume increase of $\Delta$V/V = 3.28 $\%$.

Abnormally intense (400) reflection for L21 phase indicates on the presence of some texture in polycrystalline Fe45.2Mn25.9Ga28.9 alloy sample.

3.3 Magnetic properties

Magnetic properties of bulk Fe45.2Mn25.9Ga28.9 polycrystalline alloy sample are presented on Figs. 7 and 8. The temperature dependence of magnetization $M(T)$ obtained at weak ($H=$ 500 Oe) magnetic field exhibits two definite drops upon sample heating from $T=$ 4 K. Reverse sample cooling from $T=$ 350 K causes an increase of magnetic moment also at two steps started at $T\approx$ 248 and 153 K. It is clearly seen that the low-temperature peculiarity does not depend on heat-treatment direction while the high temperature one does (see Figs. 7 and 8). Such a behavior of $M(T)$ and $dM/dT$ dependencies supports two-phase nature of the sample revealed by XRD data: low-temperature peculiarity at $T\approx$ 150 K can be definitely ascribe to the Curie temperature of the cubic L21 phase while high-temperature one is concerned with MT between tetragonal and cubic phases.

It can be concluded that the Curie temperature for tetragonally distorted L21 phase at least, not less than $T\approx$ 315 K. Thus, for 150 $\leq T\leq{329}$ K temperature range we have the deal with nonmagnetic (i. e. PM) L21 phase and FM tetragonal matrensitic one.

Increase in the external magnetic field up to 50 kOe drastically changes the $M(T)$ and $dM/dT$ dependencies for Fe45.2Mn25.9Ga28.9 alloy: low-temperature peculiarities concerned with the Curie temperature of L21 phase disappear, $A_{f}$ temperature increases up to about 329 K, the hysteresis between $M(T)$ plots obtained on the sample heating and cooling and determined as $A_{f}$ - $M_{s}$ converges from ${\Delta}T_{H=500Oe}{\approx}$ 70 K down to ${\Delta}T_{H=5kOe}{\approx}$ 63 K (see Figs. 7 and 8). It should be noted here that the saturation magnetization of Fe45.2Mn25.9Ga28.9 alloy at $T=$ 4 K and ${\mu}_{0}{}H$=5 T $M_{sat}$=79 emu/g (or 3.26 $\mu_{B}$/f.u.) is close to those reported in the literature: 71 emu/g for Fe44Mn28Ga28 alloy, 83 emu/g for Fe43Mn28Ga29 alloy, 93.8 emu/g for Fe50.0Mn22.5Ga27.5 alloy [5, 6, 7]. Recall that calculated magnetic moments for L21 and L10 phases are ${\mu}=$ 2.01 and 6.35 $\mu_{B}/f.u.$, respectively. Therefore, taking into account two-phase nature of Fe45.2Mn25.9Ga28.9 alloy, experimentally determined its saturation magnetization value looks reasonable.

According to the results of first-principle calculations the specific magnetic moments of the L21 and tetragonal phases differ more than three times. Concerning $M(T)$ dependence obtained at $H=$ 500 Oe field (see Fig. 7) the amount of L21 phase in Fe45.2Mn25.9Ga28.9 alloy at $T\approx$ 150 K is comparable with tetragonal one. Therefore, almost invisibleness of FM to PM transition related to L21 phase in the $M_{H=50kOe}(T)$ plot can be explained by complete L21 to tetragonal phase transition induced by strong magnetic field rather than smearing in temperature of FM to PM transition in L21 phase.

The high-temperature shift of the MT temperatures with magnetic field $H$ once again supports an assumption that the Curie temperature for a tetragonal phase is not less than $T\approx$ 329 K.

It is known that the magnetic field is the factor which can play an important role in thermodynamical processes. For example, the effect of a magnetic field on the temperatures of direct and reverse martensitic transformations was investigated for Ni2+xMn1-xGa alloys in a pioneering paper of Dikstein et al. [18]. The shift of the phase equilibrium temperature under the influence of magnetic field can be expressed by Krivoglaz-Sadovsky equation [19]:

[TABLE]

where $T_{0}$ is the temperature of phase transition without magnetic field, $m_{1,2}$ and $V_{1,2}$ are magnetic moments and volumes of initial (1) and final (2) phases, ${\Delta}H$ is the change of external magnetic field, $q$ is the specific heat of transition. For the case of reverse MT in Fe45.2Mn25.9Ga28.9 alloy transition from FM martensitic phase to PM austenite L21 phase (m_{2}=m_{L21}$${\approx} 0 for 150 ${\leq}T{\leq}$ 312 K temperature range) this equation can be written as:

[TABLE]

It is clear that for our case external magnetic field should induce a positive shift of phase transition temperature. Indeed, according to the results shown in Figs. 7 and 8 this shift can be evaluated as ${\Delta}T$ = $A_{f}(H=50kOe)$ - $A_{f}(H=500Oe){\approx}$ 14 K for reverse MT or ${\Delta}T$ = $M_{s}(H=50kOe)$ - $M_{s}(H=500Oe){\approx}$ 21 K for direct MT.

Magnetization hysteresis loops for Fe45.2Mn25.9Ga28.9 polycrystalline alloy sample indicate on its rather high coercivity $H_{c}\approx$ 200 Oe and magnetization saturation field $H_{s}\approx$ 2000 Oe (see inset in Fig. 7).

3.4 Transport properties

Figure 9 shows the temperature dependencies of resistance $R(T)$ and DC magnetic susceptibility ${\chi}(T)$ for bulk Fe45.2Mn25.9Ga28.9 alloy obtained at very weak measuring magnetic field. Increase in temperature from $T=$ 78 K causes a nearly linear growth of resistance with the positive temperature coefficient of resistivity (TCR). At $T\approx$ 175 K small break of the $R(T)$ plot can be seen, TCR value becomes a little bit smaller. At $T\approx$ 272 K resistance rapidly growths by about 13 $\%$ indicating start of reverse MT in an alloy. At $T\approx$ 299 K reverse MT is finished and resistance of alloy starts to decrease almost linearly with temperature. It should be noted here that the temperatures of the peculiarities on the ${\chi}(T)$ plot coincide with those on the $R(T)$ plot obtained on the sample heating. Taking into account the results of magnetic measurements (see Figs. 7 and 8) low-temperature break of the TCR value can be definitely ascribe to the FM to PM transition in L21 phase of an alloy. Indeed, electron-magnon (spin-disorder) scattering usually reaches its maximum near the Curie temperature; above $T_{C}$ the spin-disorder mechanism is independent of $T$. Therefore, for some ferromagnetic metals and alloys (including FM HA), a distinct change in the slope of the $\rho(T)$ dependence can be expected at $T_{C}$ [20, 21, 22, 23].

Upon sample cooling from $T=$ 425 K resistance follows the same as on the heating way up to $T\approx$ 299 K where some break of the negative TCR value can be seen. The rapid drop of resistance at $T\approx$ 195 K indicates on the start of the forward MT which is finished at $T\approx$ 169 K. Thus, MT in Fe45.2Mn25.9Ga28.9 alloy causes the significant changes of the resistance value and the change of the TCR sign. Such a behavior is the direct consequence of the differences in the electronic structures of these phases, namely DOS values at $E_{F}$ for L21 and tetragonal phases of Fe2MnGa alloy (see Fig. 1).

It should be mentioned here that the calculated value of resistivity of Fe45.2Mn25.9Ga28.9 alloy sample shows unreasonably high-value $\rho_{78K}=$3.08 m$\Omega$cm probably due to internal cracks induced by sample cutting and concerned with sample brittleness. Therefore, the values of the resistivity Fe2MnGa alloys should be treated with caution.

Temperature dependencies of resistivity for bulk Fe45.2Mn25.9Ga28.9 HA obtained on sample heating and cooling exhibit huge temperature hysteresis - ${\Delta}T_{R}\approx$100 K. This value is rather close to hysteresis of magnetization obtained at $H=$ 500 Oe - ${\Delta}T_{M}\approx$ 90 K. Such a huge value of thermal hysteresis of structure and physical properties is probably concerned with great friction between the boundaries of martensite and austenite phases due to large lattice distortion at MT.

3.5 Optical properties

Figure 10 presents calculated interband optical conductivity spectra for perfectly ordered stoichiometric Fe2MnGa alloy with L21 and L10 types of atomic order. Both spectra are characterized by the set of interband transitions which form interband absorption peak at 0 $\leq\hbar\omega\leq$ 5 eV energy range. However, this peak for L21 phase has a larger intensity and is manifested more definitely. This result looks as unexpected considering noticeable difference in energy dependencies of the DOS values for these phases (see Fig. 1).

Experimental optical conductivity spectra of bulk Fe45.2Mn25.9Ga28.9 HA at different temperatures (i. e. in different structural states) are shown on Fig. 11. In order to obtain confidently the austenitic and martensitic states in the alloy, the optical measurements were carried out at $T$ = 373 K and $T$ = 173 K on the sample preliminary heated and cooled up to 573 and down to 78 K, respectively. Such an approach allows us definitely to fix martensitic and austenite phases in alloy and to minimize the temperature effect on the optical properties of the alloy. Unlike theoretical predictions the optical conductivity spectra for austenitic and martensitic phases look rather similar and both are characterized by broad intense interband absorption band located at $\hbar\omega\approx$ 1.2 eV.

To the best of our knowledge, there are few publications devoted to the experimental study of the optical properties of Fe2MnGa alloys [24, 25]. Thus, Kr$\acute{a}$l investigated the optical properties of several electrolytically polished bulk Fe-Mn-Ga alloys near the stoichiometry 2:1:1. All the investigated by him alloys of different compositions (and probably different crystalline structures) demonstrate rather similar optical properties [25]. Furthermore, the optical conductivity spectrum for bulk Fe46.6Mn24.2Ga29.2 HA obtained by Kr$\acute{a}$l in the spectral shape and absolute value practically coincides with that for Fe45.2Mn25.9Ga28.9 HA studied in a present work and shown on Fig. 11.

Such a similarity of the experimental optical properties of bulk Fe45.2Mn25.9Ga28.9 HA in the martensitic and austenitic phases probably can be concerned party with two-phase nature this alloy sample, whose optical properties predicted to be rather similar. At the same time the two-phase nature of Fe45.2Mn25.9Ga28.9 alloy sample was not sufficient for a complete masking of the changes in its magnetic and transport properties induced by MT because of the properties of pure austenitic and martensitic phases differ drastically.

4 Summary

1. First-principle calculations revealed that the stoichiometric Fe2MnGa alloy with L21 and L10 types of the atomic order has noticeable different $N(E)$ dependencies (especially at $E_{F}$), exhibits three times different magnetic moments of the formula units and manifests qualitatively similar calculated interband optical conductivity spectra.

2. Temperature-induced direct martensitic transformation in Fe45.2Mn25.9Ga28.9 Heusler alloy causes a rapid decrease in its resistivity value, changes of the TCR sign from negative to positive and leads to the transition from PM to FM state.

3. Direct and reverse MT in Fe45.2Mn25.9Ga28.9 Heusler alloy demonstrate about \Delta$$T$$\approx 90 - 100 K hysteresis in critical temperatures manifested by temperature dependencies of resistance and magnetization.

4. External magnetic field of $H$ = 50 kOe causes the positive shift of the critical temperatures and reduces temperature hysteresis width.

5. Experimentally observed changes in the magnetic and transport properties of Fe45.2Mn25.9Ga28.9 alloy induced by MT nicely can be explained by the changes in the electronic structures of alloy upon transition from the austenitic to martensitic phase.

6. MT does not lead to visible changes in the experimental OC spectra of Fe45.2Mn25.9Ga28.9 alloy because of partly its two-phase nature and not very significant difference in calculated optical properties of these phases.

5 Acknowledgments

This work has been supported by the project “Marie Skłodowska-Curie Research and Innovation Staff Exchange (RISE)” Contract No. 644348 with the European Commission, as part of the Horizon2020 Programme. We are also grateful to V. K. Nosenko and E. O. Svistunov for assistance and critical discussions.