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Robust evidence for the stabilization of the premartensite phase in Ni-Mn-In magnetic shape memory alloys by chemical pressure

The thermodynamic stability of the premartensite (PM) phase has been a topic of extensive investigation in shape memory alloys as it affects the main martensite phase transition and the related physical properties. In general, the PM phase is stable over a rather narrow temperature-composition range. We present here evidence for chemical pressure induced suppression of the main martensite transition and stabilization of the PM phase over a very wide temperature range from 300 K to around 5 K in a magnetic shape memory alloy (MSMA) Ni50Mn34In16 using magnetic susceptibility, synchrotron X-ray powder diffraction (SXRPD) studies and first-principles calculations. The ac-susceptibility studies show a highly skewed and smeared peak around 300 K without any further transition up to the lowest temperature of our measurement (5 K) for around 5% Al substitution. The temperature evolution of the SXRPD patterns confirms the appearance of the PM phase related satellite peaks at and below 300 K without any splitting of the main austenite (220) peak showing preserved cubic symmetry. This is in marked contrast to the temperature evolution of the SXRPD patterns of the martensite phase of the Al free as well as around 3% Al substituted compositions where the austenite (220) peak shows a clear splitting due to Bain distortion/symmetry breaking transition. Our theoretical calculations support the experimental findings and reveal that the substitution at the In site by a smaller size atom, like Al, can stabilize the PM phase with preserved cubic symmetry. Our results demonstrate that Al-substituted Ni-Mn-In MSMAs provide an ideal platform for investigating the physics of various phenomena related to the PM state.

main martensite transition and stabilization of the PM phase over a very wide temperature range from 300 K to ~5 K in a magnetic shape memory alloy (MSMA) Ni50Mn34In16 using magnetic susceptibility, synchrotron X-ray powder diffraction (SXRPD) studies and first-principles calculations. The ac-susceptibility studies show a highly skewed and smeared peak around 300 K without any further transition up to the lowest temperature of our measurement (5 K) for ~5% Al substitution. The temperature evolution of the SXRPD patterns confirms the appearance of the PM phase related satellite peaks at T ≤ 300 K without any splitting of the main austenite (220) peak showing preserved cubic symmetry. This is in marked contrast to the temperature evolution of the SXRPD patterns of the martensite phase of the Al free as well as ~3% Al substituted compositions where the austenite (220) peak shows a clear splitting due to Bain distortion/symmetry breaking transition. Our theoretical calculations support the experimental findings and reveal that the substitution at the In site by a smaller size atom, like Al, can stabilize the PM phase with preserved cubic symmetry. Our results demonstrate that Al-substituted Ni-Mn-In MSMAs provide an ideal platform for investigating the physics of various phenomena related to the PM state.

I. INTRODUCTION
Large shape change under the influence of external stress and its recovery on annealing above a characteristic temperature is the key property of a class of functional materials named shape memory alloys (SMAs) [1][2][3][4] . The origin of the large recoverable shape change (strain) in SMAs is intimately linked with a diffusionless martensite phase transition in which a higher symmetry cubic austenite phase transforms to a lower symmetry martensite phase with tetragonal/orthorhombic/monoclinic Bain distortion [5][6][7] . The martensite transition in SMAs is a reversible transition, unlike in the steels where it is irreversible 8 . An interesting precursor or premartensite (PM) transition has been reported to precede the martensite phase transition in some of the SMAs 3,9,10 . This phenomenon and its role on the structure-property correlations in various SMAs has since been extensively investigated 3,[10][11][12][13][14][15] . The precursor PM phase occurs at an intermediate temperature range between high temperature austenite and low temperature martensite phase with preserved cubic symmetry of the austenite phase 3, 10-15 .
In recent years, the appearance of the PM phase has received considerable attention in another class of SMAs, known as magnetic shape memory alloys (MSMAs) [16][17][18][19][20][21][22][23][24] . The advantage of the MSMAs over the SMAs is that the magnetic field-induced shape change is accompanied with much larger strain (MFIS) which can be recovered within the martensite phase itself without any annealing above the transition temperature 25,26 . Also, the response time associated with the occurrence of the magnetic field-induced strain and its recovery is much faster than that in the conventional SMAs 25 opening the possibility for the development of a new class of multifunctional sensors and actuators based on application/removal of magnetic field without any temperature variation 25 . Besides the large MFIS [26][27][28] , the MSMAs have received tremendous interest in recent past due to the observation of several other exciting phenomena like large magnetocaloric effect [29][30][31][32][33] , giant magnetoresistance [34][35][36][37] , anomalous thermal properties 38,39 , exchange bias effect 40,41 , spin glass 42 , giant Hall effect 43 and anomalous Nernst effect 44 , all of which have great potential for technological applications. The study of the precursor PM phase in the MSMAs is of crucial importance in relation to several exotic phenomena like strain glasses 45
Among the various MSMAs, the crystal structure, phase stability and the magnetisation behaviour of the PM phase has been extensively investigated in the Ni-Mn-Ga system 16,18,21,22,46,47 . For example, the temperature dependence of the dc magnetisation in some of these alloys shows a small dip/peak at the PM transition 18,19,22 temperature at which it changes by ~2% as compared to that of the austenite phase 22,23 . In contrast, the martensite phase transition is accompanied with a huge change (>40%) in magnetisation 22,23 due to large Bain distortion and therefore much higher magnetocrystalline anisotropy of the martensite phase 48 . The PM phase of the near stoichiometric Ni2MnGa is characterized by the appearance of very weak intensity satellite peaks in the diffraction pattern even as the cubic austenite phase peaks remain almost unaffected due to the absence of any discernible Bain distortion 21,22 . As a result, the PM phase has been regarded as a micro-modulated precursor state with preserved cubic symmetry 18 . This is in contrast to the martensite phase in which, besides the appearance of the new satellite peaks, cubic austenite peaks also split due to significant Bain distortion signaling a symmetry breaking transition 21,22 . Recently, we presented evidence for the thermodynamic stability of both the PM and the martensite phases using a detailed temperature dependent SXRPD study on Ni2MnGa 22 .
The intermediate PM phase has been a subject matter of investigation in a few Ga-free Ni-Mn-X (X = Sn and In) MSMAs 23,24,49 also. For example, in Co-doped Ni-Mn-Sn alloys, obtained after pressure annealing 50,51 , the appearance of the precursor PM phase has been attributed to enhanced magnetoelastic coupling 18,19,23,52 . Chemical pressure, generated by substitution with smaller size atom, like Al at the In site in the Ni-Mn-In alloy composition, has also been reported to stabilize the PM phase over a modest temperature range of about 40 K 23 . The stabilization of the PM phase has also been reported in the conventional shape memory alloys like NiTi after partial substitution of Ni with Fe 3 and in NixAl100-x for x < 60 10, 53 , by chemical pressure tuning.
The foregoing results highlight the importance of chemical pressure-tuning of the transition temperature leading to the stabilization of the precursor PM phase and destabilization of the martensite phase. However, all these studies are mainly based on bulk magnetic measurements without any temperature dependent structural studies. Since the laboratory source X-ray power diffraction data often fails to capture the signatures of the PM phase 54 , any structural confirmation of the chemical pressure-tuned PM phase in MSMAs requires high-resolution SXRPD data, which not only reveal the presence of characteristic weak satellite peaks due to its high signal to noise ratio but also its ability to capture the Bain distortion, if present, and hence the signature of the symmetry breaking transition, unambiguously due to the high peak to peak resolution 22,46,55 . In the present work, we have carried out a comprehensive study on the effect of the chemical pressure generated by Al substitution in place of In in Ni50Mn34In16 MSMA using bulk magnetic measurements, temperature dependent high-resolution SXRPD studies and first-principles calculations. Our magnetic susceptibility studies on these alloys suggest that Al substitution in place of In destabilizes the martensite phase and stabilizes the PM phase over a wider temperature range. Our temperature dependent high resolution SXRPD studies on these alloys reveal Bain distortion in the martensite phase and its absence in the PM phase. The bulk magnetic and structural studies show that Al free Ni50Mn35In15 MSMA exhibits only the martensite phase of 3M type in the monoclinic space group P2/m with significant Bain distortion 56 . However, in the ~3% Al substituted Ni50Mn34In15.5Al0.5 alloy, a PM phase, stable over a narrow temperature window of ~10 K below the ferromagnetic TC ~ 317 K, precedes the appearance of the martensite phase at lower temperatures. The PM to martensite phase transition is shown to be an isostructural phase transition as both the phases are of 3M type in the monoclinic P2/m space group and differ only in terms of the absence or otherwise of the Bain distortion. More significantly, we show that on increasing the Al content to ~5% (i.e., Ni50Mn34In15.2Al0.8), only the PM phase, without any Bain distortion, occurs over the entire temperature range (300 K to 5 K) below the PM transition temperature TPM ~ 300 K without any signature of the martensite phase transition either in the magnetic or the structural studies. We also show that the TPM decreases with increasing magnetic field and the satellite peaks of the PM phase disappear in the presence of external magnetic field confirming the magnetoelastic coupling in this alloy composition. Using first-principles calculations, we further investigate the energetics of alloys which provide atomistic insight into the stabilization of PM phase in Al substituted Ni-Mn-In MSMA. Our results demonstrate that Al substituted Ni-Mn-In MSMAs provide an ideal platform for investigating the physics of PM phase related phenomena in MSMAs.

II. RESULTS AND DISCUSSION
The details of sample preparation, measurements and analysis are given in the Supplemental Material 57 ; also see Refs. [58][59][60][61][62][63][64][65][66][67][68] . Al-free Ni50Mn35In15 (or Ni2Mn1.4In0.6) MSMA 56  We now proceed to correlate the two anomalies in ꭓ(T) of Ni50Mn34In15.5Al0.5 with premartensite and martensite phase transitions using structural studies. Fig. 2 Thus, the SXRPD studies on the Ni50Mn34In15.5Al0.5 alloy above 300 K reveals cubic austenite to monoclinic (space group P2/m) PM phase transition at TPM without any Bain distortion, as revealed by the absence of any splitting of the "cubic" peaks while the SXRPD and rotating anode based laboratory source data reveal an isostructural PM to martensite phase transition with significant Bain distortion, as revealed by the splitting of the "cubic" peaks in the martensite phase.
On increasing the Al content from ~3% to ~5% (i.e., Ni50Mn34In15.2Al0.8 MSMA), the phase transition behaviour changes drastically. Fig. 1(b) shows temperature dependence of the real part of ꭓ(T) for ~5% Al substituted alloy, Ni50Mn34In15.2Al0.8. For the FC protocol, the paramagnetic to FM transition occurs at TC ~ 317 K with a sharp increase in the ꭓ(T), comparable to the TC of the base alloy as can be seen from a comparison of Fig. 1(b) with the temperature dependence of dc magnetization of the base alloy in Ref. 56 . On decreasing the temperature further, the rate of increase of ꭓ(T) decreases before peaking at the PM transition temperature TPM ~ 300K, as can be seen from the inset of Fig. 1(b). This peak is highly skewed and smeared out on the lower temperature side down to ~5 K. The gradually decreasing trend of ꭓ(T) below TPM is in marked contrast to its sharp drop in dc magnetisation of the base alloy 56 which is usually attributed to a very large magnetocrystalline anisotropy of the martensite phase 48 . More significantly, there is no signature of the second anomaly, seen in Fig. 1(a) for Ni50Mn34In15.5Al0.5, corresponding to the martensite transition in Ni50Mn34In15.2Al0.8.
The absence of martensite transition and stabilization of the PM phase indicated by the ꭓ(T) plot in Fig. 1(b) was confirmed by SXRPD studies at selected temperatures in the 400 to 100 K range and laboratory source XRD patterns at several temperatures in the 300 to 13 K range. Fig. 3(a) compares the SXRPD patterns of Ni50Mn34In15.2Al0.8 alloy at 400, 220 and 100 K. The insets in panels (i), (ii) and (iii) depict a magnified view of the profiles in the 2θ range 5.38º to 5.84º around the most intense Bragg peak. The inset of (ii) reveals the presence of satellite peaks at 220 K whose intensity increases on lowering the temperature to 100 K (see inset of (iii)). These satellite peaks are absent at 400 K, as can be seen in the inset of (i). The evolution of the SXRPD profiles as a function of temperature is shown in Figs. 3(b) and (c) at close temperature interval using a magnified (vertically zoomed) view of the intensity profile around the most intense cubic (220) peak. The most intense satellite appears around 300 K as shown with an arrow in Fig. 3(d), in agreement with the transition temperature TPM corresponding to the austenite to PM transition in the ꭓ(T) plot shown in Fig. 1(b). The intensity of the three prominent satellite peaks around the (220) cubic peak keeps growing below 300 K, as can be seen from Figs. 3(b) and (c). Further, the FWHM of the satellite peaks decreases (see Fig. 3(c)) with decreasing temperature suggesting that the correlation length or the domain size of the PM phase keeps growing below 300 K after its nucleation around TPM=300 K. Moreover, the cubic (220) peak does not show any splitting down to the lowest temperature 100 K upto which we could collect the SXRPD patterns (see Fig. 3(e)).
We verified the absence of splitting in this peak even below 100 K using the laboratory source Xray powder diffraction data (see inset of Fig. 3(e)). The absence of any splitting of the (220) cubic peak, shown in the inset of Fig. 3(e), down to 13 K is in marked contrast to that shown in Fig.   S2(b) (see Supplemental Material 57 ) Ni50Mn34In15.5Al0.5 alloy. This confirms the stability of the PM phase down to 13 K with preserved cubic symmetry without any discernible Bain distortion.
The absence of any splitting of the (220) austenite peak, the appearance of the satellite peaks at T ≤ TPM ~ 300 K and the absence of any peak in the ꭓ(T) plot in Fig. 1 The LeBail refinement using the SXRPD pattern at 400 K ( Fig.4(a)) for the Ni50Mn34In15.2Al0.8 alloy for the cubic austenite phase in the space group Fm3 ̅ m confirmed that all the peaks in the SXRPD pattern could be indexed very well. The results of this refinement are shown in Fig. 4(a) which reveals an excellent fit between the observed and calculated profiles for the refined unit cell parameter a = 6.0169 (1) Fig. 4(c). The enlarged view of Fig. 4(c) around the diffuse peak in the M(T) is shown in Fig. 4(d) where the peak temperatures are marked by arrows. The variation of the peak temperatures in M(T) with field, shown in Fig. 4(e), reveals that TPM shifts towards the lower temperature side linearly with increasing magnetic field. This has been attributed to magnetoelastic coupling 18,19,23,50 . We verified the magnetoelastic coupling in Ni50Mn34In15. which nevertheless accounts for the small energy difference between the austenite and the PM phases for this alloy composition. In order to unambiguously establish the role of Al in stabilizing the modulated PM phase, we calculated the total energies of both the phases for an alloy with only Al in place of In, i.e., Ni50Mn33.3Al16.7. The inset (i) of Fig. 5(b) shows that the total energy at 0 K for the PM phase around its equilibrium volume is lower than that of the austenite phase by more than 2 meV/atom for this In free alloy. The amplitudes of the atomic modulations in the PM phase are also substantially larger in this case, as shown in the inset (iii) of Fig. 5(b). All these suggest that the stability of the modulated PM phase increases with increasing Al content in place of In in Ni-Mn-In based MSMAs. It is important to mention that the temperature-dependent excitations, e.g., lattice vibrations, magnetic excitations etc., are likely to alter the relative stability of the austenite phase with respect to that of the PM phase at higher temperatures 83 . Nevertheless, at low temperatures, our calculations predict PM phase to be more stable than the austenite phase for Alsubstituted Ni-Mn-In based MSMAs.
Moreover, we note that the stability of the PM phase in Ni50Mn33.3Al16.7 is strongly dependent on

III. CONCLUSIONS
To conclude, we presented here evidence for chemical pressure induced suppression of the main martensite transition and stabilization of the PM phase over a very wide temperature range from 300 K to ~5 K in a magnetic shape memory alloy Ni50Mn34In16 using magnetic susceptibility,  profiles of the (220) cubic Bragg peak is depicted in the 400 to100 K range while its inset depicts the XRD profiles in the 300 to 13 K range recorded on a rotating anode-based diffractometer.  The Al atoms are behind the In atoms in the insets (ii) and (iii) of (a).

Supplemental Material
Robust evidence for the stabilization of the premartensite phase in Ni-Mn-In magnetic shape memory alloys by chemical pressure X-ray powder diffraction (XRD) data were collected using an 18-kW rotating Cu anode-based xray diffractometer (Rigaku) fitted with a curved graphite crystal monochromator in the diffraction beam. A closed-cycle He refrigerator-based low temperature attachment was used for XRD measurements in the 300 to 13 K range. In addition, high-resolution synchrotron x-ray powder diffraction (SXRPD) data were collected in the 400-100 K range at temperature interval of 10 K in the cooling cycle at a wavelength of λ ~ 0.207 Å at P02.1 beamline of Petra-III DESY, Germany.
The sample containing capillary was spinning continuously to minimize the texturing effect in the SXRPD data. Further, high-resolution SXRPD data were collected without and with magnetic field bias (0 Oe and 2500 Oe) at 294 K at a wavelength of λ ~ 0.495 Å on the Xpress beamline of Elettra,

Crystal structure of Ni-Mn-In-Al magnetic shape memory alloys (MSMAs):
Phase purity and crystal structures were confirmed by x-ray powder diffraction measurements. The average long-range ordered structure was confirmed by LeBail technique using the high-resolution synchrotron as well as laboratory source x-ray powder diffraction patterns. All the refinements were carried out using FULLPROF package 11 . For the Al ~ 3% composition with chemical formula Ni50Mn34In15.5Al0.5, the LeBail refinement using the SXRPD data confirms the cubic austenite phase structure in the Fm3 ̅ m space group at 400 K. The observed, calculated and difference profiles obtained after the refinement are shown in Fig. S1(a). The refined lattice parameter is found to be 6.01009(6) Å. The presence of (111) and (200) Bragg reflections (the inset (i) of Fig. S1(a)) confirms the L21 ordering in the cubic austenite phase 12 . The LeBail refinement using SXRPD data at 310 K reveals that all the peaks can be indexed using the 3M modulated monoclinic structure in the P2/m space group with a = 4.3869(7) Å, b = 5.6866(1) Å, c = 13.0028(2) Å and β = 93.695 (3) º as can be seen from the excellent fit between the observed and calculated profiles shown in Fig.   S1(b). The LeBail refinement using the SXRPD data at 110 K reveals that all the peaks can be indexed using 3M modulated monoclinic structure in the P2/m space group as can be seen from Fig. S1(c), which depicts the fit between the observed and calculated profiles. The LeBail refinement using the laboratory source XRD data also shows the 3M modulated monoclinic structure in the P2/m space group at 300 K (see Fig. S2(a)). The laboratory source XRD data at different temperatures (300 to 13 K) are shown in Fig. S2(b). The enlarged view around most intense Bragg peak, shown in the inset of Fig. S2(b), confirms the 3M modulated monoclinic martensite phase (P2/m space group) upto the lowest temperature (13 K) up to data was collected for Ni50Mn34In15.5Al0.5 MSMA.
For the second composition (Al ~ 5%) with the chemical formula Ni50Mn34In15.2Al0.8, the LeBail refinement using of laboratory source XRD data at 300 K confirms the cubic in Fm3 ̅ m space group symmetry of the austenite phase. The results of the refinements are shown in Fig. S3(a). The refined lattice parameter is found to be 6.0135(2) Å. The inset of Fig. S3(a) shows the presence of (111) and (200) Bragg reflections which confirms the L21 ordering in the austenite phase. The laboratory source XRD data at different temperatures from 300 K to 13 K are shown in Fig. S3(b).
The enlarged view around the most intense Bragg peak is shown in the inset of Fig. S3(b), which reveals the absence of any Bain distortion as the cubic peaks do not exhibit any splitting down to 13 K up to which the data was collected for Ni50Mn34In15.2Al0.8 MSMA.

Resistivity:
The resistivity of Ni50Mn34In15.2Al0.8 as a function of temperature measured during the warming cycle is shown in Fig. S6. It shows smooth monotonic behavior without any step or peak expected for a martensite transition. This feature confirms the absence of martensite transition in Ni50Mn34In15.2Al0.8. First-principles total energy calculations in the ferromagnetic state of Ni50Mn33.3Al16.7: The origin of the PM phase in Al substituted Ni-Mn-In alloy, investigated in the present manuscript, lies in the coupling between magnetism and crystal structure, i.e., magnetoelastic coupling. The effect of magnetism on the stability of the PM phase can be qualitatively understood from the total energies calculated at two different magnetic states, i.e., antiferromagnetic and ferromagnetic states. In order to highlight the effect of magnetism on the stability of the PM phase concretely, we have, in addition to the antiferromagnetic state discussed in the manuscript (inset (i) of Fig. 5(b) in the manuscript), chosen an artificial ferromagnetic state in Ni50Mn33.3Al16.7 with all Mn spins oriented in the same direction and calculated total energies of both austenite and PM phase. Our calculations in the ferromagnetic state with significantly higher magnetic moment per