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Effect of compositional and antisite disorder on the electronic and magnetic properties of Ni–Mn–In Heusler alloy
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 J. Phys.: Condens. Matter 27 175502 (http://iopscience.iop.org/0953-8984/27/17/175502) View the table of contents for this issue, or go to the journal homepage for more
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Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 27 (2015) 175502 (10pp)
doi:10.1088/0953-8984/27/17/175502
Effect of compositional and antisite disorder on the electronic and magnetic properties of Ni–Mn–In Heusler alloy Parijat Borgohain and Munima B Sahariah Institute of Advanced Study in Science and Technology, Guwahati-35, India E-mail: [email protected] Received 22 December 2014, revised 26 February 2015 Accepted for publication 2 March 2015 Published 15 April 2015 Abstract
A systematic study has been done on the electronic and magnetic properties of metamagnetic Ni–Mn–In Heusler alloy with compositional and structural (anti-site) disorder at high temperature austenite phase. The electronic structure calculation shows an increasing Mn–Ni hybridization which occurs due to the decrease in Mn–Ni bond length as the system approaches martensite phase. The results obtained from magnetic moment calculations follow a similar trend to the previous experimental and theoretical results. The magnetic coupling parameters, Jij , obtained from the ab initio calculation explains the presence of competing ferromagnetic (FM) and antiferromagnetic (AFM) interactions in the system and the dominating AFM interactions nearer to the martensite phase. Keywords: electronic structure, Heusler alloy, exchange interaction (Some figures may appear in colour only in the online journal)
interactions towards the enhancement [12]. Chun-Mei Li et al [13] reported a major feature that particularly stands out for Ni–Mn–In system in its magnetic properties which show marked differences from those of other Ni–Mn-based Heusler alloys, i.e., the magnetization in the austenite phase increases with increase in Mn content in the system as a result of ferromagnetic (FM) coupling between Mn1 –Mn2 instead of antiferromagnetic (AFM) coupling as found in Ni2 Mn1+x Ga1−x and Ni2 Mn1+x Sn1−x . Again, the martensite of Ni2 Mn1+x In1−x possesses much smaller magnetic moment compared to its well defined FM parent phase and even to FM L21 -Ni2 MnIn. There have been reports about investigating the difference in concentration dependence of total magnetic moment per formula unit in Ni–Mn–Sn and Ni–Mn–In alloy [14–18]. In addition, similar to Ni–Mn– Sn and Ni–Mn–Sb systems, a large exchange bias (EB) has been experimentally found in the martensitic state of Ni49.5 Mn34.5 In16 bulk polycrystal indicating the coexistence of FM and AFM states and their coupling at the interfaces [6]. Sasioglu et al [19] and Entel et al [20] have reported the importance of magnetic exchange parameters in the physical properties of the disordered Heusler alloys and have explained the origin of the competing FM and AFM interactions
1. Introduction
Ferromagnetic shape memory materials have led to an area of intensive research over the last decade because of their multifunctional properties, rendering them useful in different domains from spintronics to magnetic cooling technologies [1– 3]. The non-stoichiometric Heusler alloys of type Ni–Mn–Z (Z = In, Sn, Sb) have many interesting properties, such as magnetic shape memory effect (MSME) [1], magnetic field induced strain (FIS) [4], magnetoresistance (MR) [5], exchange bias (EB) [6], magnetocaloric effect (MCE) [7–9] and metamagnetic behaviour [10], for which it has become a wide area of exploration. Unlike the prototype Ni–Mn–Ga, the family of Ni–Mn–Z (Z = In, Sn and Sb) alloys undergo martensitic phase transition (MPT) only in the offstoichiometric condition Ni2 Mn1+x Z1−x [11]. In particular, Ni–Mn–In has been of great interest because it shows a signature for both direct MCE (adiabatic temperature change Tad > 0) in the case of Ni-excess atoms and inverse MCE (Tad < 0) for excess Mn. Moreover, recent reports show the enhancement of MCE in Co doped Ni–Mn–In with adiabatic temperature change, Tad = −6 K in 2 T field, indicating the influence of the localized electronic orbital 0953-8984/15/175502+10$33.00
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E-EF (eV) Figure 1. Concentration dependence of the DOS for minority spin states as a function of energy, E–EF (eV) for compositions (a) Ni2 MnIn (b) Ni2 Mn1.06 In0.94 (c) Ni2 Mn1.10 In0.90 (d) Ni2 Mn1.14 In0.86 (e) Ni2 Mn1.20 In0.80 (f ) Ni2 Mn1.30 In0.70 (g) Ni2 Mn1.32 In0.68 (h) Ni2 Mn1.34 In0.66 with different degrees of disorders; black, red, green, blue, cyan and violet curves denote disorders of 0%, 10%, 20%, 30%, 40% and 50%. The inset shows the concentration dependent DOS as a function of E–EF (eV) for the corresponding compositions.
that emerges out from the magnetic exchange parameters, coupled with increasing valence electron concentration. The influence of configurational (antisite) order and disorder in Co2 MnGa alloy and a disorder in Ni–Mn–Ga alloy was discussed by Singh et al [21], Arroyave et al [22], Siewart et al [23] and Ghosh et al [24] using first-principles magnetic exchange parameter calculations. However, there are contradictory reports about the magnetic interactions in Ni–Mn–In martensite phase of being either paramagnetic or antiferromagnetic [25–27]. Recent study on spin-valve-like magnetoresistance in Mn2 NiGa [28], ab initio calculations of magnetic exchange parameters of Ni2 Mn1+x Sn1−x [14] and Monte Carlo simulations of Ni2 Mn1+x Z1−x (Z = In, Sn and Sb) [29], indicate that structural disorder in Mn site occupancy influences the magnetic properties of these compounds. Therefore, a systematic study on nonstoichiometric Ni2 Mn1+x In1−x alloy with different degrees of disorder would rather prove useful in order to have a deeper insight into the occurrence of different magnetic phases leading towards characteristic behaviour in the system. In this paper, we report ab initio calculations on electronic structure and magnetic exchange parameters of nonstoichiometric Ni2 Mn1+x In1−x alloy with cubic L21 structure in the composition range 0 x 0.34 (x = 0, 0.06, 0.10, 0.14, 0.20, 0.30, 0.32, 0.34), where different degrees of antisite
disorder are, 0%, 10%, 20%, 30%, 40%, 50%. The systematic study of the magnetic exchange parameters in this specified range has not been reported earlier. 2. Computational details
The spin-polarised Relativistic Korringa–Kohn–Rostoker (SPR-KKR) code based on Green’s function formalism is used for ab initio electronic structure and magnetic exchange parameter calculations. The calculations are carried out for high temperature austenite phase with L21 structure (space group Fm3m) for both ordered and disordered Ni2 Mn1+x In1−x Heusler alloy. In the case of disordered alloy, the effect of substitutional disorder is taken into account by using singlesite coherent potential approximation (CPA). The magnetic exchange parameters are calculated with the formulation of Liechtenstein et al [30–32]. The self-consistent field (SCF) calculations are performed to attain a self-consistent potential by using a maximum number of CPA iterations and CPA tolerance as 20 and 0.01 Ry, respectively. The experimental lattice parameters from reference [9] have been used in all the calculations. The exchange-correlation potential used in this calculation is Vosko–Wilk–Nusair (VWN) based on Broyden2 scheme that starts after first iteration [33]. 2
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Figure 2. Total density of states (states/eV) and projected density of states as a function of energy, E–EF (eV) for Ni2 Mn1−y Iny Mnx+y In1−x−y , where x is the increasing concentration of Mn atoms and y is the percentage of disorder(= 0%, 10%, 20%, 30%, 40%, 50%), (a) Ni2 Mn1.06 In0.94 (y = 0%); blue, magenta, orange, violet, green, dark green and cyan colours of the curve denotes: total DOS, atom resolved DOS of Ni, Mn1 , Mn2 and orbital resolved DOS of Ni(3d), Mn1 (3d) and Mn2 (3d) (b) Ni2 Mn1.32 In0.68 (y = 0%) (c) Ni2 Mn1.06 In0.94 (y = 50%) (d) Ni2 Mn1.32 In0.68 (y = 50%).
The iteration depth for Broyden algorithm is chosen as 40. The convergence criteria for the SCF mixing and maximum number of SCF iterations are set to 0.20 and 200, respectively. The scattering path operator is calculated by the Brillouin zone (BZ) integration [34] with special point method using a regular k-mesh grid of 22 × 22 × 22 with 834 k points for which the E mesh points is set to 30. The SCF calculations are done using the arc-like contour path in the complex energy plane. The upper energy value Emax is taken as EF (Fermi energy) and the real part of lowest energy value Emin is set to −0.2 Rydberg. The angular momentum expansion
(Nl) is based on the atomic properties of the atom types and for transition metals maximum l-value, i.e. lmax is 2 which has been used for all the calculations and the total energy convergence obtained for all calculations is 0.01 mRy. The self-consistent potential thus generated is used for the density of states (DOS) and magnetic exchange parameter (Jij ) calculations. For Jij and DOS calculations spin-polarized scalar-relativistic (SP-SREL) Dirac–Hamiltonian is used with lmax = 2 on a grid of 57 × 57 × 57, i.e. 4495 k points. The calculation of Jij is done with respect to the central site i of a cluster atoms with the radius of the sphere, Rclu = 3, 3
J. Phys.: Condens. Matter 27 (2015) 175502
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where, Rclu = max | Ri − Rj |. For all the calculations we have used coherent potential approximation (CPA), but CPA neglects short-range interactions. However, it has been shown in reference [35] that CPA works well on full Heusler alloys as the short-range interactions have minimal influence on the electronic structure.
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3. Results and discussion
To gain an insight into the origin of magnetic properties and to understand the occurrence of different magnetic phases leading towards characteristic changes in behaviour of Ni–Mn–In, we have investigated the electronic structure for different compositional and antisite disorders. The structure of Ni–Mn–In under study in the range, 0 x 0.34, is cubic L21 which belongs to the austenite phase and beyond this range the martensitic phase exists [25]. Figure 1 illustrates the DOS (states/eV) for minority spin states as a function of Mn excess atoms with different degrees of disorder (y = 0–50%) for Ni2 Mn1−y Iny Mnx+y In1−x−y (x = 0, 0.06, 0.10, 0.14, 0.20, 0.30, 0.32, 0.34). The antisite disorder of 10% in the system implies swapping of Mn–In atoms, i.e. 10% of Mn atoms are replaced by 10% of In atoms and 10% of In atoms are replaced by 10% of Mn atoms. We specify Mn1 as the Mn atom in the original Mn-site and Mn2 as the Mn atom in the In-site. The inset shows the variation of total density of states for majority and minority spin states with excess Mn atoms and increasing antisite disorder.
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show the nature of the DOS curves as well as the changes in the curves. For all the compositions considered in our case, the contribution towards the atom resolved DOS of any particular element is observed mainly due to the d-orbitals of that element. In figures 2(a)–(d) the 3d-orbitals of Ni, Mn1 , Mn2 atoms show dominant contribution towards the atom resolved DOS, whereas contribution from s and p orbital is negligible. The total DOS across the Fermi level for the minority spin states (figure 2(a)) shows noticeable changes with four broadened peaks, two from bonding states and two from antibonding states, as already mentioned in figure 1, and the contribution of the atom resolved DOS towards the nature of the peaks. For the peaks at −1.5 eV and −0.38 eV, the hybridization is due to Ni 3d, Mn1 and Mn2 3d orbitals. With increasing Mn atoms and antisite disorder the peak at 1.3 eV due to the hybridization between Mn1 3d orbitals with Ni 3d and Mn2 3d orbitals gets broadened and becomes flat showing changes in magnitude. Thus, some marked changes in the atom resolved DOS in figures 2(a)–(d), i.e., difference in DOS magnitude and broadening of peak for minority spin states of Mn1 3d orbitals above Fermi level and splitting of the peaks into two has been noticed. However, for Mn2 3d orbitals an opposite behaviour, i.e. two peaks turning into a single broad peak with gradual increase in magnitude has been noticed. This explains that with increasing antisite disorder the contribution of Mn1 3d orbitals towards the hybridization has been dominated by Mn2 3d orbitals and the corresponding changes in the behaviour of the DOS at EF can be well understood from figure 3. The density of states at Fermi level as a function of excess Mn atoms for minority spin states considering 0–50% Mn–In swap is illustrated in figure 3. In the composition range, x 0 0.32, the density of states increases with increasing Mn atoms showing a sudden rise for x = 0.34 with 0% disorder. A similar kind of behaviour, i.e. increase in DOS with increasing Mn atoms has been observed for the rest of the disorders. The DOS curves in figure 3 follow a similar trend for low percentage of Mn excess and lower percentage of Mn– In swap while the trend is reversed for higher percentage of
3.1. Electronic structure
The DOS for majority and minority states just below the Fermi level has two peaks each and is continuous across the Fermi level. For majority spin states the DOS across the Fermi level decreases exponentially and does not show many changes with different degrees of disorder. However, significant changes are observed in the case of minority spin states across the Fermi level. The major change for minority spin states is observed at 1 eV, as can be seen in figures 1(a)–(h) with different degrees of disorder. For stoichiometric composition (figure 1(a)), the peak observed at 1 eV above Fermi level gradually decreases with antisite disorder for 0% to 30% Mn–In swap and gets split into two for 40% and 50% swap. A similar kind of behaviour in the peaks, i.e. the splitting of the peak into two and the gradual decrease in magnitude as well as broadening of the peak with change in concentration and disorder has also been observed for the other compositions. For the minority spin states near the crossover of curves at 0.25 eV with different disorders a valley is formed at 0.5 eV which becomes flat with increasing Mn–In swap percentage. The reason behind these changes can be well attributed to the increasing concentration of Mn atoms in the In sites. However, the explanation for the changes can be clearer from figure 2. Figure 2 illustrates the total, atom- and orbital resolved (3d) density of states as a function of energy for the compositions (a) Ni2 Mn1.06 In0.94 for y = 0% (b) Ni2 Mn1.32 In0.68 for y = 0% (c) Ni2 Mn1.06 In0.94 for y = 50% (d) Ni2 Mn1.32 In0.68 for y = 50% which clearly 4
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swap and Mn concentration. The results obtained from the DOS calculations can be well reflected while explaining the magnetic properties.
to increase in Mn2 atoms that interacts ferromagnetically with Mn1 atoms in Ni2 Mn1+x In1−x (0 x 0.32) alloy. A different magnetic behaviour, i.e. slight decrease in the total magnetic moment value for higher percentage of Mn–In swap with increasing Mn content throughout the entire range has been observed. This decrease in total magnetic moment can be pointed towards sudden decrease of the magnetic moment values of Mn-atoms at Mn and In sites, respectively, as shown in figures 4(b) and (c). A slight increase in the magnetic moment for Mn1 atoms is seen with additional Mn in the system, while the moment for Mn2 decreases with excess Mn. In the case of disorder, (0–50% Mn–In swap) an opposite behaviour is observed, i.e., Mn1 atoms show increasing magnetic moment with increasing Mn–In swap percentage but Mn2 atoms show decreasing trend. Again, the magnetic moment of Ni atoms in figure 4(d) has been observed to increase with Mn content and decrease with different Mn– In swap percentage as the system approaches the martensite phase. This peculiar behaviour observed in the case of individual magnetic moments of Mn1 , Mn2 and Ni atoms with increasing Mn atoms and for different swap percentage tends to increase the total magnetic moment of the system. Thus, as expected, it has been found that with the increase in Mn atom concentration in Ni2 Mn1+x In1−x (0 x 0.34) cubic phase,
3.2. Magnetic moment
The concentration dependence of the magnetic moment per formula unit for Ni2 Mn1+x In1−x (x = 0, 0.25, 0.5) was theoretically studied where FM state had been found to be more stable than antiferromagnetic state in the austenite phase and martensite phase was found to occur for x > 0.32 [11]. Figures 4(a)–(d) illustrate the dependence of total magnetic moment and the magnetic moments of Mn1 , Mn2 and Ni atoms with respect to Mn excess and different percentage of Mn–In swap from present study. As illustrated in figure 5(a), the contribution of Mn atoms towards the total magnetic moment of the compound is large compared to the Ni atoms while the contribution of In atoms can be considered negligible. Figure 5(b) gives a schematic representation of cubic Ni–Mn–In magnetic moments with 20% Mn–In swap (Ni2 Mn0.80 In0.20 Mn 0.20 In0.80 ) in the stoichiometric composition. The variation of total magnetic moment with Mn atom concentration and different percentage of Mn–In swap shows an increasing trend in figure 4(a) which can be attributed 5
J. Phys.: Condens. Matter 27 (2015) 175502
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(a)
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Figure 5. Structural representation of cubic Ni–Mn–In with the magnetic moments (a) Ni2 MnIn (b) Ni2 Mn0.80 In0.20 Mn0.20 In0.80 . The length of the arrows gives only a qualitative representation of the magnetic moments.
3.3. Magnetic exchange parameters
Bond length (Å) of Mn-In
The magnetic exchange parameters for various compositions of Ni–Mn–In are obtained from the ab initio calculations. The calculated results directly point towards the existence of competing ferromagnetic and antiferromagnetic interactions in the system and it also reflects the behaviour of individual magnetic moment of the atoms. In order to have a better understanding about the interactions, it seems worth calculating the exchange parameters considering different Mn–In swap percentage for various compositions. Figures 6(a) and (b) illustrate the variation of lattice parameters with Mn excess and the variation of Mn–In and Mn–Ni bond lengths with composition under study. The intra-sublattice and inter-sublattice magnetic exchange parameters, Jij , as a function of distance for the compositions in the austenite phase which are closer and away from martensite phase with different swap percentage are shown in figures 7 and 8. The plots of intra-sublattice interaction clearly show Ruderman–Kittel– Kasuya–Yoshida (RKKY) oscillatory behaviour (figure 8) for all compositions. The exchange parameter values between any two atoms within the first co-ordination sphere is seen to be large when compared to the other co-ordination spheres. Within the first co-ordination sphere Mn1 –Ni, Mn2 –Ni and Mn1 –Mn1 interactions, J1 ’s are positive, i.e., ferromagnetic, whereas Mn2 –Mn2 and Mn1 –Mn2 interactions are antiferromagnetic, with the latter bearing stronger magnitude, as observed in figures 7 and 8. The occurrence of the antiferromagnetic interaction is due to shortening of Mn1 –Mn2 distance which has also been observed in the case of B2 -type disordered Ni–Mn based Heusler alloys [28, 37]. With increase in Mn concentration and for 0% Mn–In swap in
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the total magnetic moment increases, which is in agreement with the experiments [16, 29]. However, in the case of Ni– Mn–Sn metamagnetic shape memory alloys, the decrease in magnetic moment per formula unit with increasing Mn content is attributed to the antiferromagnetic coupling between the Mn atoms at Mn and Sn sublattices [18, 36].
Figure 6. (a) Lattice parameters and (b) Bond lengths as a function of Mn excess.
figures 7(a) and (b) the value of Jij for Mn1 –Ni and Mn2 – Ni increases which also occurs for 50% Mn–In swap, as shown in figures 7(c) and (d), where the Jij value for Mn1 – Ni gets dominated by Mn2 –Ni with increasing Mn–In swap percentage. The increase of Mn–Ni exchange parameters with Mn excess can be explained from the variation of magnetic moments which slightly increases in the case of Mn1 atoms, decreases in the case of Mn2 atoms and increases in the case of Ni atoms, as shown in figure 4. As Mn–Ni distance is large and due to the coupling between Mn 3d–Ni 3d orbitals, direct 6
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exchange plays a key role which leads to large ferromagnetic Mn–Ni interactions in the system. The changes in the magnetic exchange parameters, J1 , within the first co-ordination sphere with increase in Mn–In swap percentage and excess Mn are shown in figures 9(a)–(d). Although the co-existence of ferromagnetic and antiferromagnetic interactions have been observed in figures 7 and 8, the ground state of the system satisfies ferromagnetic stability in the lattice parameter range 5.9–6.2 Å for Ni2 MnIn with 50% Mn–In swap. This is due to strong contribution from ferromagnetic Ni–Mn exchange interactions which plays a dominating role. Also, previous study reports that the inter-sublattice Mn– Co interaction of Heusler compounds contributes strongly to the stability of ferromagnetic state [38]. Figure 9 illustrates the magnetic exchange parameters, J1 , with different Mn–In swap percentage as a function of excess Mn atoms in Ni2 Mn1+x In1−x for Mn1 –Mn1 , Mn1 –Mn2 , Mn1 –Ni and Mn2 –Ni interactions. The magnetic exchange
parameters are greatly influenced by antisite disorder which shows a linear decrease in the Mn1 –Mn1 interactions, with concentration and disorder as shown in figure 9(a). In Mn1 –Mn1 interactions, it has been observed that for 40% Mn–In swap, the magnetic exchange parameters approach zero with increasing concentration of x and become negative for 50% swap in the range, 0.30 x 0.34, showing onset of AFM interactions. For a fixed antisite disorder, the antiferromagnetic Mn1 –Mn2 interaction decreases with increase in Mn concentration, as shown in figure 9(b). On the other hand, for low percentage of antisite disorder and lower Mn concentration, the Jij value for Mn1 –Mn2 interaction becomes less antiferromagnetic with increasing antisite disorder for a fixed Mn concentration. For higher antisite disorder and higher Mn concentration, the trend is reverse. It has been found from EXAFS study that with Mn excess, the Mn–Ni bond distance decreases resulting in a higher Mn–Ni exchange interaction [39, 40]. In the present 7
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Figure 8. Intra-sublattice magnetic exchange parameters as a function of Distance in a.u. for (a) Ni2 Mn1.06 In0.94 with 0% disorder (b) Ni2 Mn1.32 In0.68 with 0% disorder (c) Ni2 Mn1.06 In0.94 with 50% disorder and (d) Ni2 Mn1.32 In0.68 with 50% disorder.
calculation also, due to decrease in Mn–Ni bond lengths as shown in figure 6, higher Mn–Ni exchange interaction takes place. As far as antisite disorder is concerned, Jij decreases linearly with increasing disorder for Mn1 –Ni, whereas for Mn2 –Ni, Jij increases. This reduction is due to the difference in behaviour which is observed from the magnetic moment of Mn1 , Mn2 and Ni atoms in figure 4. It also indicates that antiferromagnetic (AFM) interactions have become prominent with decrease in Mn1 –Mn2 bond distance. The magnitudes of Jij for different Mn2 –Ni interactions are comparatively less than Mn1 –Ni interactions with the exception for 40% and 50% Mn–In swap. A similar kind of behaviour to that in figure 7(b) for 40% and 50% swap has been observed in figure 9(b), which emphasizes the changes occurring due to excess Mn atoms and antisite disorder. These changes are due to the increase in Ni 3d–Mn 3d hybridization with decrease in Mn–In, Ni–Mn and Mn–Mn bond lengths which points towards the presence of AFM super exchange as the system approaches the martensitic
phase [11, 22, 41]. Thus, the exchange parameter calculations in the austenite phase explain the existence of competing ferro- and antiferromagnetic interactions in the system and the presence of dominating AFM interactions nearer to the martensite phase which agrees with the previous results. 4. Conclusions
We have performed the ab initio calculations for the electronic structure and the magnetic exchange parameters of Ni2 Mn1+x In1−x in the composition range, x = 0, 0.06, 0.10, 0.14, 0.20, 0.30, 0.32, 0.34, by varying the concentration of Mn atom and the degrees of antisite disorder from 0% to 50%. From the DOS calculation, significant changes have been observed in the minority spin states across the Fermi level with respect to compositional change and variation in disorder which has been well attributed to the increasing concentration of Mn atoms in the In-site. The atom- and 8
J. Phys.: Condens. Matter 27 (2015) 175502
P Borgohain and M B Sahariah
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Figure 9. Magnetic exchange parameters as a function of excess Mn atoms in Ni2 Mn1+x In1−x for (a) Mn1 –Mn1 and (b) Mn1 –Mn2
(c) Mn1 –Ni and (d) Mn2 –Ni interaction with 0–50% Mn–In swap.
dominating AFM interactions towards the martensite phase. The effects of antisite disorder and increasing valence electron concentration showing corresponding changes in the magnetic exchange parameters can be tuned by doping a transition metal into Ni–Mn–In alloy. Also, the addition of an anti- or nonferromagnetic element into the host alloy would lead to the reduction of the exchange parameters value predicting the material to behave as a good candidate for magnetic cooling technology.
orbital-resolved DOS explain that with high antisite disorder and Mn concentration the contribution of Mn atoms towards the hybridization has been dominated by Mn2 –Ni 3d orbitals. However, with low percentage of disorder and low Mn content Mn1 3d orbitals show more dominating behaviour towards hybridization with Ni 3d orbitals. For the compositions, Ni2 Mn1.32 In0.68 and Ni2 Mn1.34 In0.66 , with high Mn content and for 40–50% Mn–In swap, the abrupt change that is observed in the DOS and exchange interactions hints that the system is approaching the martensite phase. The calculations of the total magnetic moment and the magnetic moment of individual atoms explain that, as expected, the magnitude of the total magnetic moment increases with increasing concentration of Mn atoms for the range under study that agrees well with experiments and previous theoretical results. The results obtained from the magnetic exchange parameter calculations is due to the increase in Ni 3d–Mn 3d hybridization with decrease in Mn–In, Mn–Ni and Mn– Mn bond lengths which points towards the presence of AFM super exchange as the system approaches the martensite phase. Thus, the exchange parameter calculations in the austenite phase explain the presence of competing ferroand antiferromagnetic interactions in the system and the
Acknowledgments
This work was supported by Department of Science and Technology (DST), Govt. of India through project SR/FTP/PS-031/2012. PB acknowledges helpful feedback from Satyananda Chabungbam. References [1] Sutou Y, Imano Y, Koeda N, Omori T, Kainuma R, Ishida K and Oikawa K 2004 Appl. Phys. Lett. 85 4358 [2] Moya X, Manosa L, Planes A, Krenke T, Acet M and Wassermann E F 2006 Mater. Sci. Eng. A 438–440 911 9
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[22] Arroyave R, Junkaew A, Chivukula A, Bajaj S, Yao C and Garay A 2010 Acta Mater. 58 5220 [23] Siewert M, Gruner M E, Danneberg A, Hucht A, Shapiro S M, Xu G, Schlagel D L and Lograsso T A 2010 Phys. Rev. B 82 064420 [24] Ghosh S and Sanyal B 2010 J. Phys.: Condens. Matter 22 346001 [25] Bhobe P A, Priolkar K R and Nigam A K 2008 J. Phys. D: Appl. Phys. 41 235006 [26] Khovaylo V V, Kanomata T, Tanaka T, Nakashima M, Amako Y, Kainuma R, Umetsu R Y, Morito H and Miki H 2009 Phys. Rev. B 80 144409 [27] Aksoy S, Acet M, Deen P P, Manosa L and Planes A 2009 Phys. Rev. B 79 21401 [28] Priolkar K R, Bhobe P, Lobo D N, DSouza S W, Barman S R, Chakrabarti A and Emura S 2013 Phys. Rev. B 87 144412 [29] Buchelnikov V D, Entel P, Taskaev S V, Sokolovsky V V, Hucht A, Ogura M, Akai H, Gruner M E and Nayak S K 2008 Phys. Rev. B 78 184427 [30] Ebert H, Kodderitzsch D and Minar J 2011 Rep. Prog. Phys. 74 096501 [31] Liechtenstein A I, Katsnelson M I, Antropov V P and Gubanov V 1987 J. Magn. Magn. Mater. 67 65 [32] Turek I, Kudrnovsky J, Drchal V and Bruno P 2006 Phil. Mag. 86 1713 [33] Krenke T, Acet M, Wassermann E F, Moya X, Manosa L and Planeset A 2006 Phys. Rev. B 73 174413 [34] Monkhorst H J 1976 Phys. Rev. B 13 5188 [35] Ozdogan K, Sasioglu E and Galanakis I 2008 J. Appl. Phys. 103 023503 [36] Sokolovskiy V, Buchelnikov V, Khovaylo V, Taskaev S and Entel P 2014 Int. J. Refrigeration 37 273 [37] Galanakis I and Sasioglu E 2011 Appl. Phys. Lett. 98 102514 [38] Kurtulus Y, Dronskowski R, Samolyuk G D and Antropov V P 2005 Phys. Rev. B 71 014425 [39] Sasioglu E, Sandratskii L M and Bruno P 2008 Phys. Rev. B 77 064417 [40] Priolkar K R, Lobo D N, Bhobe P A, Emura S and Nigam A K 2011 Europhys. Lett. 94 38006 [41] Lobo D N, Priolkar K R, Bhobe P A, Krishnamurthy D and Emura S 2010 Appl. Phys. Lett. 96 232508
[3] Planes A, Manosa L and Acet M 2009 J. Phys.: Condens. Matter 21 233201 [4] Ullakko K, Huang J K, Kantner C, OHandley R C and Kokorin V V 1996 Appl. Phys. Lett. 69 1966 [5] Wang B M, Wang L, Liu Y, Zhao B C, Zhao Y, Yang Y and Zhang H 2009 J. Appl. Phys. 106 063909 [6] Wang B M, Liu Y, Wang L, Huang S L, Zhao Y, Yang Y and Zhang H 2008 J. Appl. Phys. 104 043916 [7] Bhobe P, Priolkar K and Nigam A 2007 Appl. Phys. Lett. 91 242503 [8] Sharma V K, Chattopadhyay M K, Kumar R, Ganguli T, Tiwari P and Roy S B 2007 J. Phys.: Condens. Matter 19 496207 [9] Li B, Ren W J, Zhang Q, Lv X K, Liu X G, Meng H, Li J, Li D and Zhang Z D 2009 Appl. Phys. Lett. 95 172506 [10] Kainuma R, Oikawa K, Ito W, Sutou Y, Kanomata T and Ishida K 2008 J. Mater. Chem. 18 1837 [11] Buchelnikov V and Sokolovskiy V 2011 Phys. Met. Metallogr. 112 633 [12] Comtesse D et al 2014 Phys. Rev. B 89 184403 [13] Li C M, Luo H B, Hu Q M, Yang R, Johansson B and Vitos L 2012 Phys. Rev. B 86 214205 [14] Sokolovskiy V V, Buchelnikov V D, Zagrebin M A, Entel P, Sahoo S and Ogura M 2012 Phys. Rev. B 86 134418 [15] Tan C L, Huang Y W, Tian X H, Jiang J X and Cai W 2012 Appl. Phys. Lett. 100 132402 [16] Kainuma R, Ito K, Ito W, Umetsu R, Kanomata T and Ishida K 2010 Mater. Sci. Forum 635 23 [17] Yasuda T, Sasaki S, Nishihara H, Kainuma R, Itoh W, Oikawa K, Ishida K, Neumann K U and Ziebeck K R A 2009 J. Magn. Magn. Mater. 321 773 [18] kanomata T, Fukushima K, Nishihara H, Kainuma R, Itoh W, Oikawa K, Ishida K, Neumann K U and Ziebeck K R A 2008 Mater. Sci. Forum 583 119 [19] Sasioglu E, Sandratskii L M, Bruno P and Galanakis I 2005 Phys. Rev. B 72 184415 [20] Entel P, Dannenberg A, Siewert M, Herper H C, Gruner M E, Buchelnikov V D and Chernenko V A 2011 Mater. Sci. Forum 684 1 [21] Singh N, Dogan E, Karaman I and Arroyave R 2011 Phys. Rev. B 84 184201
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Effect of compositional and antisite disorder on the electronic and magnetic properties of Ni–Mn–In Heusler alloy
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Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 27 (2015) 175502 (10pp)
doi:10.1088/0953-8984/27/17/175502
Effect of compositional and antisite disorder on the electronic and magnetic properties of Ni–Mn–In Heusler alloy Parijat Borgohain and Munima B Sahariah Institute of Advanced Study in Science and Technology, Guwahati-35, India E-mail: [email protected] Received 22 December 2014, revised 26 February 2015 Accepted for publication 2 March 2015 Published 15 April 2015 Abstract
A systematic study has been done on the electronic and magnetic properties of metamagnetic Ni–Mn–In Heusler alloy with compositional and structural (anti-site) disorder at high temperature austenite phase. The electronic structure calculation shows an increasing Mn–Ni hybridization which occurs due to the decrease in Mn–Ni bond length as the system approaches martensite phase. The results obtained from magnetic moment calculations follow a similar trend to the previous experimental and theoretical results. The magnetic coupling parameters, Jij , obtained from the ab initio calculation explains the presence of competing ferromagnetic (FM) and antiferromagnetic (AFM) interactions in the system and the dominating AFM interactions nearer to the martensite phase. Keywords: electronic structure, Heusler alloy, exchange interaction (Some figures may appear in colour only in the online journal)
interactions towards the enhancement [12]. Chun-Mei Li et al [13] reported a major feature that particularly stands out for Ni–Mn–In system in its magnetic properties which show marked differences from those of other Ni–Mn-based Heusler alloys, i.e., the magnetization in the austenite phase increases with increase in Mn content in the system as a result of ferromagnetic (FM) coupling between Mn1 –Mn2 instead of antiferromagnetic (AFM) coupling as found in Ni2 Mn1+x Ga1−x and Ni2 Mn1+x Sn1−x . Again, the martensite of Ni2 Mn1+x In1−x possesses much smaller magnetic moment compared to its well defined FM parent phase and even to FM L21 -Ni2 MnIn. There have been reports about investigating the difference in concentration dependence of total magnetic moment per formula unit in Ni–Mn–Sn and Ni–Mn–In alloy [14–18]. In addition, similar to Ni–Mn– Sn and Ni–Mn–Sb systems, a large exchange bias (EB) has been experimentally found in the martensitic state of Ni49.5 Mn34.5 In16 bulk polycrystal indicating the coexistence of FM and AFM states and their coupling at the interfaces [6]. Sasioglu et al [19] and Entel et al [20] have reported the importance of magnetic exchange parameters in the physical properties of the disordered Heusler alloys and have explained the origin of the competing FM and AFM interactions
1. Introduction
Ferromagnetic shape memory materials have led to an area of intensive research over the last decade because of their multifunctional properties, rendering them useful in different domains from spintronics to magnetic cooling technologies [1– 3]. The non-stoichiometric Heusler alloys of type Ni–Mn–Z (Z = In, Sn, Sb) have many interesting properties, such as magnetic shape memory effect (MSME) [1], magnetic field induced strain (FIS) [4], magnetoresistance (MR) [5], exchange bias (EB) [6], magnetocaloric effect (MCE) [7–9] and metamagnetic behaviour [10], for which it has become a wide area of exploration. Unlike the prototype Ni–Mn–Ga, the family of Ni–Mn–Z (Z = In, Sn and Sb) alloys undergo martensitic phase transition (MPT) only in the offstoichiometric condition Ni2 Mn1+x Z1−x [11]. In particular, Ni–Mn–In has been of great interest because it shows a signature for both direct MCE (adiabatic temperature change Tad > 0) in the case of Ni-excess atoms and inverse MCE (Tad < 0) for excess Mn. Moreover, recent reports show the enhancement of MCE in Co doped Ni–Mn–In with adiabatic temperature change, Tad = −6 K in 2 T field, indicating the influence of the localized electronic orbital 0953-8984/15/175502+10$33.00
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J. Phys.: Condens. Matter 27 (2015) 175502
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P Borgohain and M B Sahariah
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E-EF (eV) Figure 1. Concentration dependence of the DOS for minority spin states as a function of energy, E–EF (eV) for compositions (a) Ni2 MnIn (b) Ni2 Mn1.06 In0.94 (c) Ni2 Mn1.10 In0.90 (d) Ni2 Mn1.14 In0.86 (e) Ni2 Mn1.20 In0.80 (f ) Ni2 Mn1.30 In0.70 (g) Ni2 Mn1.32 In0.68 (h) Ni2 Mn1.34 In0.66 with different degrees of disorders; black, red, green, blue, cyan and violet curves denote disorders of 0%, 10%, 20%, 30%, 40% and 50%. The inset shows the concentration dependent DOS as a function of E–EF (eV) for the corresponding compositions.
that emerges out from the magnetic exchange parameters, coupled with increasing valence electron concentration. The influence of configurational (antisite) order and disorder in Co2 MnGa alloy and a disorder in Ni–Mn–Ga alloy was discussed by Singh et al [21], Arroyave et al [22], Siewart et al [23] and Ghosh et al [24] using first-principles magnetic exchange parameter calculations. However, there are contradictory reports about the magnetic interactions in Ni–Mn–In martensite phase of being either paramagnetic or antiferromagnetic [25–27]. Recent study on spin-valve-like magnetoresistance in Mn2 NiGa [28], ab initio calculations of magnetic exchange parameters of Ni2 Mn1+x Sn1−x [14] and Monte Carlo simulations of Ni2 Mn1+x Z1−x (Z = In, Sn and Sb) [29], indicate that structural disorder in Mn site occupancy influences the magnetic properties of these compounds. Therefore, a systematic study on nonstoichiometric Ni2 Mn1+x In1−x alloy with different degrees of disorder would rather prove useful in order to have a deeper insight into the occurrence of different magnetic phases leading towards characteristic behaviour in the system. In this paper, we report ab initio calculations on electronic structure and magnetic exchange parameters of nonstoichiometric Ni2 Mn1+x In1−x alloy with cubic L21 structure in the composition range 0 x 0.34 (x = 0, 0.06, 0.10, 0.14, 0.20, 0.30, 0.32, 0.34), where different degrees of antisite
disorder are, 0%, 10%, 20%, 30%, 40%, 50%. The systematic study of the magnetic exchange parameters in this specified range has not been reported earlier. 2. Computational details
The spin-polarised Relativistic Korringa–Kohn–Rostoker (SPR-KKR) code based on Green’s function formalism is used for ab initio electronic structure and magnetic exchange parameter calculations. The calculations are carried out for high temperature austenite phase with L21 structure (space group Fm3m) for both ordered and disordered Ni2 Mn1+x In1−x Heusler alloy. In the case of disordered alloy, the effect of substitutional disorder is taken into account by using singlesite coherent potential approximation (CPA). The magnetic exchange parameters are calculated with the formulation of Liechtenstein et al [30–32]. The self-consistent field (SCF) calculations are performed to attain a self-consistent potential by using a maximum number of CPA iterations and CPA tolerance as 20 and 0.01 Ry, respectively. The experimental lattice parameters from reference [9] have been used in all the calculations. The exchange-correlation potential used in this calculation is Vosko–Wilk–Nusair (VWN) based on Broyden2 scheme that starts after first iteration [33]. 2
J. Phys.: Condens. Matter 27 (2015) 175502
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Figure 2. Total density of states (states/eV) and projected density of states as a function of energy, E–EF (eV) for Ni2 Mn1−y Iny Mnx+y In1−x−y , where x is the increasing concentration of Mn atoms and y is the percentage of disorder(= 0%, 10%, 20%, 30%, 40%, 50%), (a) Ni2 Mn1.06 In0.94 (y = 0%); blue, magenta, orange, violet, green, dark green and cyan colours of the curve denotes: total DOS, atom resolved DOS of Ni, Mn1 , Mn2 and orbital resolved DOS of Ni(3d), Mn1 (3d) and Mn2 (3d) (b) Ni2 Mn1.32 In0.68 (y = 0%) (c) Ni2 Mn1.06 In0.94 (y = 50%) (d) Ni2 Mn1.32 In0.68 (y = 50%).
The iteration depth for Broyden algorithm is chosen as 40. The convergence criteria for the SCF mixing and maximum number of SCF iterations are set to 0.20 and 200, respectively. The scattering path operator is calculated by the Brillouin zone (BZ) integration [34] with special point method using a regular k-mesh grid of 22 × 22 × 22 with 834 k points for which the E mesh points is set to 30. The SCF calculations are done using the arc-like contour path in the complex energy plane. The upper energy value Emax is taken as EF (Fermi energy) and the real part of lowest energy value Emin is set to −0.2 Rydberg. The angular momentum expansion
(Nl) is based on the atomic properties of the atom types and for transition metals maximum l-value, i.e. lmax is 2 which has been used for all the calculations and the total energy convergence obtained for all calculations is 0.01 mRy. The self-consistent potential thus generated is used for the density of states (DOS) and magnetic exchange parameter (Jij ) calculations. For Jij and DOS calculations spin-polarized scalar-relativistic (SP-SREL) Dirac–Hamiltonian is used with lmax = 2 on a grid of 57 × 57 × 57, i.e. 4495 k points. The calculation of Jij is done with respect to the central site i of a cluster atoms with the radius of the sphere, Rclu = 3, 3
J. Phys.: Condens. Matter 27 (2015) 175502
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where, Rclu = max | Ri − Rj |. For all the calculations we have used coherent potential approximation (CPA), but CPA neglects short-range interactions. However, it has been shown in reference [35] that CPA works well on full Heusler alloys as the short-range interactions have minimal influence on the electronic structure.
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3. Results and discussion
To gain an insight into the origin of magnetic properties and to understand the occurrence of different magnetic phases leading towards characteristic changes in behaviour of Ni–Mn–In, we have investigated the electronic structure for different compositional and antisite disorders. The structure of Ni–Mn–In under study in the range, 0 x 0.34, is cubic L21 which belongs to the austenite phase and beyond this range the martensitic phase exists [25]. Figure 1 illustrates the DOS (states/eV) for minority spin states as a function of Mn excess atoms with different degrees of disorder (y = 0–50%) for Ni2 Mn1−y Iny Mnx+y In1−x−y (x = 0, 0.06, 0.10, 0.14, 0.20, 0.30, 0.32, 0.34). The antisite disorder of 10% in the system implies swapping of Mn–In atoms, i.e. 10% of Mn atoms are replaced by 10% of In atoms and 10% of In atoms are replaced by 10% of Mn atoms. We specify Mn1 as the Mn atom in the original Mn-site and Mn2 as the Mn atom in the In-site. The inset shows the variation of total density of states for majority and minority spin states with excess Mn atoms and increasing antisite disorder.
2 1.9 0% 10% 20% 30% 40% 50%
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show the nature of the DOS curves as well as the changes in the curves. For all the compositions considered in our case, the contribution towards the atom resolved DOS of any particular element is observed mainly due to the d-orbitals of that element. In figures 2(a)–(d) the 3d-orbitals of Ni, Mn1 , Mn2 atoms show dominant contribution towards the atom resolved DOS, whereas contribution from s and p orbital is negligible. The total DOS across the Fermi level for the minority spin states (figure 2(a)) shows noticeable changes with four broadened peaks, two from bonding states and two from antibonding states, as already mentioned in figure 1, and the contribution of the atom resolved DOS towards the nature of the peaks. For the peaks at −1.5 eV and −0.38 eV, the hybridization is due to Ni 3d, Mn1 and Mn2 3d orbitals. With increasing Mn atoms and antisite disorder the peak at 1.3 eV due to the hybridization between Mn1 3d orbitals with Ni 3d and Mn2 3d orbitals gets broadened and becomes flat showing changes in magnitude. Thus, some marked changes in the atom resolved DOS in figures 2(a)–(d), i.e., difference in DOS magnitude and broadening of peak for minority spin states of Mn1 3d orbitals above Fermi level and splitting of the peaks into two has been noticed. However, for Mn2 3d orbitals an opposite behaviour, i.e. two peaks turning into a single broad peak with gradual increase in magnitude has been noticed. This explains that with increasing antisite disorder the contribution of Mn1 3d orbitals towards the hybridization has been dominated by Mn2 3d orbitals and the corresponding changes in the behaviour of the DOS at EF can be well understood from figure 3. The density of states at Fermi level as a function of excess Mn atoms for minority spin states considering 0–50% Mn–In swap is illustrated in figure 3. In the composition range, x 0 0.32, the density of states increases with increasing Mn atoms showing a sudden rise for x = 0.34 with 0% disorder. A similar kind of behaviour, i.e. increase in DOS with increasing Mn atoms has been observed for the rest of the disorders. The DOS curves in figure 3 follow a similar trend for low percentage of Mn excess and lower percentage of Mn– In swap while the trend is reversed for higher percentage of
3.1. Electronic structure
The DOS for majority and minority states just below the Fermi level has two peaks each and is continuous across the Fermi level. For majority spin states the DOS across the Fermi level decreases exponentially and does not show many changes with different degrees of disorder. However, significant changes are observed in the case of minority spin states across the Fermi level. The major change for minority spin states is observed at 1 eV, as can be seen in figures 1(a)–(h) with different degrees of disorder. For stoichiometric composition (figure 1(a)), the peak observed at 1 eV above Fermi level gradually decreases with antisite disorder for 0% to 30% Mn–In swap and gets split into two for 40% and 50% swap. A similar kind of behaviour in the peaks, i.e. the splitting of the peak into two and the gradual decrease in magnitude as well as broadening of the peak with change in concentration and disorder has also been observed for the other compositions. For the minority spin states near the crossover of curves at 0.25 eV with different disorders a valley is formed at 0.5 eV which becomes flat with increasing Mn–In swap percentage. The reason behind these changes can be well attributed to the increasing concentration of Mn atoms in the In sites. However, the explanation for the changes can be clearer from figure 2. Figure 2 illustrates the total, atom- and orbital resolved (3d) density of states as a function of energy for the compositions (a) Ni2 Mn1.06 In0.94 for y = 0% (b) Ni2 Mn1.32 In0.68 for y = 0% (c) Ni2 Mn1.06 In0.94 for y = 50% (d) Ni2 Mn1.32 In0.68 for y = 50% which clearly 4
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Figure 4. (a) Dependence of total magnetic moment on x (excess Mn) and magnetic moments of (b) Mn1 (c) Mn2 and (d) Ni as a function of x (excess Mn) for 0–50% Mn–In swap.
swap and Mn concentration. The results obtained from the DOS calculations can be well reflected while explaining the magnetic properties.
to increase in Mn2 atoms that interacts ferromagnetically with Mn1 atoms in Ni2 Mn1+x In1−x (0 x 0.32) alloy. A different magnetic behaviour, i.e. slight decrease in the total magnetic moment value for higher percentage of Mn–In swap with increasing Mn content throughout the entire range has been observed. This decrease in total magnetic moment can be pointed towards sudden decrease of the magnetic moment values of Mn-atoms at Mn and In sites, respectively, as shown in figures 4(b) and (c). A slight increase in the magnetic moment for Mn1 atoms is seen with additional Mn in the system, while the moment for Mn2 decreases with excess Mn. In the case of disorder, (0–50% Mn–In swap) an opposite behaviour is observed, i.e., Mn1 atoms show increasing magnetic moment with increasing Mn–In swap percentage but Mn2 atoms show decreasing trend. Again, the magnetic moment of Ni atoms in figure 4(d) has been observed to increase with Mn content and decrease with different Mn– In swap percentage as the system approaches the martensite phase. This peculiar behaviour observed in the case of individual magnetic moments of Mn1 , Mn2 and Ni atoms with increasing Mn atoms and for different swap percentage tends to increase the total magnetic moment of the system. Thus, as expected, it has been found that with the increase in Mn atom concentration in Ni2 Mn1+x In1−x (0 x 0.34) cubic phase,
3.2. Magnetic moment
The concentration dependence of the magnetic moment per formula unit for Ni2 Mn1+x In1−x (x = 0, 0.25, 0.5) was theoretically studied where FM state had been found to be more stable than antiferromagnetic state in the austenite phase and martensite phase was found to occur for x > 0.32 [11]. Figures 4(a)–(d) illustrate the dependence of total magnetic moment and the magnetic moments of Mn1 , Mn2 and Ni atoms with respect to Mn excess and different percentage of Mn–In swap from present study. As illustrated in figure 5(a), the contribution of Mn atoms towards the total magnetic moment of the compound is large compared to the Ni atoms while the contribution of In atoms can be considered negligible. Figure 5(b) gives a schematic representation of cubic Ni–Mn–In magnetic moments with 20% Mn–In swap (Ni2 Mn0.80 In0.20 Mn 0.20 In0.80 ) in the stoichiometric composition. The variation of total magnetic moment with Mn atom concentration and different percentage of Mn–In swap shows an increasing trend in figure 4(a) which can be attributed 5
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(a)
(b)
Figure 5. Structural representation of cubic Ni–Mn–In with the magnetic moments (a) Ni2 MnIn (b) Ni2 Mn0.80 In0.20 Mn0.20 In0.80 . The length of the arrows gives only a qualitative representation of the magnetic moments.
3.3. Magnetic exchange parameters
Bond length (Å) of Mn-In
The magnetic exchange parameters for various compositions of Ni–Mn–In are obtained from the ab initio calculations. The calculated results directly point towards the existence of competing ferromagnetic and antiferromagnetic interactions in the system and it also reflects the behaviour of individual magnetic moment of the atoms. In order to have a better understanding about the interactions, it seems worth calculating the exchange parameters considering different Mn–In swap percentage for various compositions. Figures 6(a) and (b) illustrate the variation of lattice parameters with Mn excess and the variation of Mn–In and Mn–Ni bond lengths with composition under study. The intra-sublattice and inter-sublattice magnetic exchange parameters, Jij , as a function of distance for the compositions in the austenite phase which are closer and away from martensite phase with different swap percentage are shown in figures 7 and 8. The plots of intra-sublattice interaction clearly show Ruderman–Kittel– Kasuya–Yoshida (RKKY) oscillatory behaviour (figure 8) for all compositions. The exchange parameter values between any two atoms within the first co-ordination sphere is seen to be large when compared to the other co-ordination spheres. Within the first co-ordination sphere Mn1 –Ni, Mn2 –Ni and Mn1 –Mn1 interactions, J1 ’s are positive, i.e., ferromagnetic, whereas Mn2 –Mn2 and Mn1 –Mn2 interactions are antiferromagnetic, with the latter bearing stronger magnitude, as observed in figures 7 and 8. The occurrence of the antiferromagnetic interaction is due to shortening of Mn1 –Mn2 distance which has also been observed in the case of B2 -type disordered Ni–Mn based Heusler alloys [28, 37]. With increase in Mn concentration and for 0% Mn–In swap in
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the total magnetic moment increases, which is in agreement with the experiments [16, 29]. However, in the case of Ni– Mn–Sn metamagnetic shape memory alloys, the decrease in magnetic moment per formula unit with increasing Mn content is attributed to the antiferromagnetic coupling between the Mn atoms at Mn and Sn sublattices [18, 36].
Figure 6. (a) Lattice parameters and (b) Bond lengths as a function of Mn excess.
figures 7(a) and (b) the value of Jij for Mn1 –Ni and Mn2 – Ni increases which also occurs for 50% Mn–In swap, as shown in figures 7(c) and (d), where the Jij value for Mn1 – Ni gets dominated by Mn2 –Ni with increasing Mn–In swap percentage. The increase of Mn–Ni exchange parameters with Mn excess can be explained from the variation of magnetic moments which slightly increases in the case of Mn1 atoms, decreases in the case of Mn2 atoms and increases in the case of Ni atoms, as shown in figure 4. As Mn–Ni distance is large and due to the coupling between Mn 3d–Ni 3d orbitals, direct 6
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Figure 7. Inter-sublattice magnetic exchange parameters as a function of distance in a.u. for (a) Ni2 Mn1.06 In0.94 with 0% disorder (b) Ni2 Mn1.32 In0.68 with 0% disorder (c) Ni2 Mn1.06 In0.94 with 50% disorder and (d) Ni2 Mn1.32 In0.68 with 50% disorder.
exchange plays a key role which leads to large ferromagnetic Mn–Ni interactions in the system. The changes in the magnetic exchange parameters, J1 , within the first co-ordination sphere with increase in Mn–In swap percentage and excess Mn are shown in figures 9(a)–(d). Although the co-existence of ferromagnetic and antiferromagnetic interactions have been observed in figures 7 and 8, the ground state of the system satisfies ferromagnetic stability in the lattice parameter range 5.9–6.2 Å for Ni2 MnIn with 50% Mn–In swap. This is due to strong contribution from ferromagnetic Ni–Mn exchange interactions which plays a dominating role. Also, previous study reports that the inter-sublattice Mn– Co interaction of Heusler compounds contributes strongly to the stability of ferromagnetic state [38]. Figure 9 illustrates the magnetic exchange parameters, J1 , with different Mn–In swap percentage as a function of excess Mn atoms in Ni2 Mn1+x In1−x for Mn1 –Mn1 , Mn1 –Mn2 , Mn1 –Ni and Mn2 –Ni interactions. The magnetic exchange
parameters are greatly influenced by antisite disorder which shows a linear decrease in the Mn1 –Mn1 interactions, with concentration and disorder as shown in figure 9(a). In Mn1 –Mn1 interactions, it has been observed that for 40% Mn–In swap, the magnetic exchange parameters approach zero with increasing concentration of x and become negative for 50% swap in the range, 0.30 x 0.34, showing onset of AFM interactions. For a fixed antisite disorder, the antiferromagnetic Mn1 –Mn2 interaction decreases with increase in Mn concentration, as shown in figure 9(b). On the other hand, for low percentage of antisite disorder and lower Mn concentration, the Jij value for Mn1 –Mn2 interaction becomes less antiferromagnetic with increasing antisite disorder for a fixed Mn concentration. For higher antisite disorder and higher Mn concentration, the trend is reverse. It has been found from EXAFS study that with Mn excess, the Mn–Ni bond distance decreases resulting in a higher Mn–Ni exchange interaction [39, 40]. In the present 7
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Figure 8. Intra-sublattice magnetic exchange parameters as a function of Distance in a.u. for (a) Ni2 Mn1.06 In0.94 with 0% disorder (b) Ni2 Mn1.32 In0.68 with 0% disorder (c) Ni2 Mn1.06 In0.94 with 50% disorder and (d) Ni2 Mn1.32 In0.68 with 50% disorder.
calculation also, due to decrease in Mn–Ni bond lengths as shown in figure 6, higher Mn–Ni exchange interaction takes place. As far as antisite disorder is concerned, Jij decreases linearly with increasing disorder for Mn1 –Ni, whereas for Mn2 –Ni, Jij increases. This reduction is due to the difference in behaviour which is observed from the magnetic moment of Mn1 , Mn2 and Ni atoms in figure 4. It also indicates that antiferromagnetic (AFM) interactions have become prominent with decrease in Mn1 –Mn2 bond distance. The magnitudes of Jij for different Mn2 –Ni interactions are comparatively less than Mn1 –Ni interactions with the exception for 40% and 50% Mn–In swap. A similar kind of behaviour to that in figure 7(b) for 40% and 50% swap has been observed in figure 9(b), which emphasizes the changes occurring due to excess Mn atoms and antisite disorder. These changes are due to the increase in Ni 3d–Mn 3d hybridization with decrease in Mn–In, Ni–Mn and Mn–Mn bond lengths which points towards the presence of AFM super exchange as the system approaches the martensitic
phase [11, 22, 41]. Thus, the exchange parameter calculations in the austenite phase explain the existence of competing ferro- and antiferromagnetic interactions in the system and the presence of dominating AFM interactions nearer to the martensite phase which agrees with the previous results. 4. Conclusions
We have performed the ab initio calculations for the electronic structure and the magnetic exchange parameters of Ni2 Mn1+x In1−x in the composition range, x = 0, 0.06, 0.10, 0.14, 0.20, 0.30, 0.32, 0.34, by varying the concentration of Mn atom and the degrees of antisite disorder from 0% to 50%. From the DOS calculation, significant changes have been observed in the minority spin states across the Fermi level with respect to compositional change and variation in disorder which has been well attributed to the increasing concentration of Mn atoms in the In-site. The atom- and 8
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(c) Mn1 –Ni and (d) Mn2 –Ni interaction with 0–50% Mn–In swap.
dominating AFM interactions towards the martensite phase. The effects of antisite disorder and increasing valence electron concentration showing corresponding changes in the magnetic exchange parameters can be tuned by doping a transition metal into Ni–Mn–In alloy. Also, the addition of an anti- or nonferromagnetic element into the host alloy would lead to the reduction of the exchange parameters value predicting the material to behave as a good candidate for magnetic cooling technology.
orbital-resolved DOS explain that with high antisite disorder and Mn concentration the contribution of Mn atoms towards the hybridization has been dominated by Mn2 –Ni 3d orbitals. However, with low percentage of disorder and low Mn content Mn1 3d orbitals show more dominating behaviour towards hybridization with Ni 3d orbitals. For the compositions, Ni2 Mn1.32 In0.68 and Ni2 Mn1.34 In0.66 , with high Mn content and for 40–50% Mn–In swap, the abrupt change that is observed in the DOS and exchange interactions hints that the system is approaching the martensite phase. The calculations of the total magnetic moment and the magnetic moment of individual atoms explain that, as expected, the magnitude of the total magnetic moment increases with increasing concentration of Mn atoms for the range under study that agrees well with experiments and previous theoretical results. The results obtained from the magnetic exchange parameter calculations is due to the increase in Ni 3d–Mn 3d hybridization with decrease in Mn–In, Mn–Ni and Mn– Mn bond lengths which points towards the presence of AFM super exchange as the system approaches the martensite phase. Thus, the exchange parameter calculations in the austenite phase explain the presence of competing ferroand antiferromagnetic interactions in the system and the
Acknowledgments
This work was supported by Department of Science and Technology (DST), Govt. of India through project SR/FTP/PS-031/2012. PB acknowledges helpful feedback from Satyananda Chabungbam. References [1] Sutou Y, Imano Y, Koeda N, Omori T, Kainuma R, Ishida K and Oikawa K 2004 Appl. Phys. Lett. 85 4358 [2] Moya X, Manosa L, Planes A, Krenke T, Acet M and Wassermann E F 2006 Mater. Sci. Eng. A 438–440 911 9
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