Summary

Chapter 2. Methodology

Chapter 3

Role of composition, site ordering

and magnetic structure for structural stability in Ni and Mn excess

off-stoichiometric Ni ₂ MnSb

3.1 Introduction

The most important feature driving the giant magnetocaloric effect in a mate- rial is the presence of first-order martensitic phase transition (MPT) accompanied with a significant change in magnetization. Unlike the prototype magnetic shape memory Ni-Mn-Ga family, Ni-Mn-Z (Z=In, Sn, Sb) Heusler alloys undergo MPT from high temperature L21 parent austenite phase to a low temperature tetragonal or orthorhombic martensite phase resulting in many exotic properties, only in off-stoichiometric compositions with substantial Z-deficiency [113, 238–241]. The off-stoichiometric Sb-deficient Ni-Mn-Sb systems exhibit giant magnetocaloric effect associated with the MPT near room temperature [130, 132] drawing special atten- tion. Extensive experimental investigations, as discussed in chapter 1, have revealed that MPT and associated properties in Ni-Mn-Sb alloys crucially depend on the concentration ratio of Ni, Mn and Sb. The martensitic transformation is observed in Ni2Mn1+xSb1−x alloys forx≥0.4 [242]. Complex magnetic structure with short- range correlations are also predicted. The observed decrease of magnetic moment with increasing electron-atom ratio e/a; a behaviour opposing the general trend in Heusler compounds, is attributed to the presence of these anti-ferromagnetic corre-

The contents of this chapter are published inPhysical Review B99, 064112 (2019)

Chapter 3. Role of composition, site ordering and magnetic structure for structural stability in Ni and Mn excess off-stoichiometric Ni₂MnSb

lations. Similar features are observed by Khanet al.[243]. Experiments on systems with low Sb concentration (between 0.44 and 0.48) with either Ni content being fixed [96, 132] or varying in a way to make the system Ni-deficient [146, 243], observed significant inverse magnetocaloric effect and exchange bias. All these experimental results pointed towards the presence of substantial anti-ferromagnetic inter- actions present due to excess amount of Mn occupying presumably the Sb sites. The experiments, though wonderfully established the potential multi-functional traits in Ni-Mn-Sb systems, certain fundamental questions remain to be answered. The systems investigated were always Sb-deficient and Mn-excess. This propels one to examine the role of composition on the properties, in particular the impact on the stabilities of the high-temperature austenite and the low-temperature martensite phases. Coupled with this is the question regarding the impact of site ordering in the system on its physical properties. Previous studies on off-stoichiometric Ni-Mn- Z (Z=Sn, Ga, In) showed that in the off-stoichiometric compositions, the excess atom does not always prefer to occupy the deficient atom site. The magnetic structure, as a consequence of this, also plays an important role in deciding the phase stability and the associated properties. For example, Hu et al. [244] showed that, for most of the off-stoichiometric Ni2MnGa, though the excess atoms of the rich component occupy the deficient atom sites, in cases of Ga-rich alloys, the excess Ga atoms always prefer the Mn sites irrespective of whether the system is Mn-deficient or not. For Ni-deficient Ga-excess Ni2MnGa systems, some of the Mn atoms move to the Ni sites and the excess Ga atoms occupy the Mn sites. For Ni2Mn1+xSn1−x, it was shown that the experimental phase diagram for Curie temperature can be verified only when an intermixing of Mn and Sn atoms is considered [223]. Li et al. [245] suggested a possibility of Mn-In ordering for Mn-excess off-stoichiometric Ni2Mn1+xIn1−x compositions. They showed that magnetic ordering in the system can affect the martensitic phase transition significantly. It was found that if there is ferromagnetic (FM) coupling between the Mn atoms at Mn and In sites then no MPT occurs whereas for anti-ferromagnetic (AFM) coupling, MPT occurs in the system. For Mn2Ni1+xSn1−x [246] also, an intricate relation between the site occupancy, magnetic ordering and the stability of the martensite phase was observed.

Thus a knowledge of the site-occupancy will be essential for Ni-Mn-Sb systems for investigation of its physical properties. Detailed and systematic investigation about the effects of site ordering and magnetic structure on phase stability for compositions beyond those considered in the experiments would help understand the fundamental physics of the system and help choose the composition ranges where practical

3.1 Introduction applications due to the presence of MPT are most suitable.

Since relative stabilities of phases is central towards other novel features of this system, finding a good predictor for martensitic transformation temperature (T_M) is important. The electron-atom ratio (e/a) has been identified to be a predictor of TM for systems undergoing martensitic transformations: a larger e/a indicates a higherTM [247–249]. However, such a connection is coarse grained and fails in some situations. For the samee/aratio, changes in atomic order (site occupancy) also can change the TM. For example, replacement of Ga by Al or In and variations in the long-range atomic order changed TM without altering thee/a ratio [250–253]. This is also true for Ni-Mn-Sb alloys. AlthoughTM varies ase/afor Ni2Mn1+xSb1−x [242] and for Ni_2−xMn_1.56+xSb_0.44[146], Khanet al.[254] concluded from their experiments on Ni_2+xMn_1.52−xSb_0.48 that rather than the e/a, the hybridization between Ni and excess Mn 3d states is responsible for variations in the TM. On the other hand, for some compounds undergoing MPT, TM is found to be closely related to elastic shear modulus C^′: the lower the shear modulus, calculated in the austenite phase, the higher theTM will be [255,256]. Various off-stoichiometric Ni2MnGa alloys also show this TM dependence onC^′ [244,257]. The total energy difference ∆E between the high temperature parent austenite phase and the low temperature tetragonal martensite phase is another quantity to correlate TM and C^′ with the composition of the compounds. A higher ∆E corresponds to a higher TM [258, 259]. It is therefore, of fundamental interest, to correlate the trend of variation in T_M for off- stoichiometric Ni-Mn-Sb compositions with these physical quantities and decide the best predictor of TM.

In this chapter, we present a systematic study over the entire composition range in Mn and Ni-excess off-stoichiometric Ni2MnSb systems to explore the importances of various physical factors affecting the phase stability. To this end, we have sys- tematically explored the importances of composition, atomic ordering and magnetic structure and the consequences on phase stability and various properties. The mi- croscopic origin of the observed features has been interpreted from the composition, site-ordering and magnetic ordering dependent electronic structures. We have tried to address the reasons behind choice of Sb-deficient systems in experiments, how critical the role of relative compositions of Ni and Mn are in effecting martensitic transformation, how site occupancy and magnetic structure are intricately related with one another to impact the phase stability and also provided a predictor for martensitic transformation temperature, one that is independent of the details of the off-stoichiometry.