Electronic structure and magnetism of the Heusler alloy Mn2NiAl A ...

ARTICLE IN PRESSPhysica B 405 (2010) 3092–3095Contents lists available at ScienceDirectPhysica Bjournal homepage: www.elsevier.com/locate/physbElectronic structure and magnetism of the Heusler alloy Mn 2 NiAl: Atheoretical study of the shape–memory behaviorHongzhi Luo a,b,n , Guodong Liu a , Fanbin Meng a , Shijie Li a , Wei Zhu b ,Guangheng Wu b , Xiaoxi Zhu c , Chengbao Jiang ca School of Material Science and Engineering, Hebei University of Technology, Tianjin 300130, PR Chinab Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, PR Chinac School of Material Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100083, PR Chinaarticle infoArticle history:Received 9 April 2010Accepted 13 April 2010Keywords:Heusler alloyBand structureMartensitic transformationabstractThe electronic structure and magnetism of the Heusler alloy Mn 2 NiAl have been studied by firstprinciplescalculations. It is found that the phase transformation from the cubic to the tetragonalstructure lowers the total energy, indicating that the martensitic phase is more stable and that a phasetransition from austenite to martensite may happen at a lower temperature. Thus, ferromagnetic shapememory effect can be expected to occur in Mn 2 NiAl or in alloys of similar composition. Mn 2 NiAl is aferrimagnet in both the austenitic and martensitic phases. The total spin moments are 1.48 and 1.14 m B /f.u.for the austenite and martensite, respectively. Because the contribution of Ni to the total moment is small,the total moment is mainly determined by the antiparallel aligned Mn(A) and Mn(B) spin moments.& 2010 Elsevier B.V. All rights reserved.1. IntroductionIn recent years, Mn-based Heusler alloys have received muchattention because of their potential application as half-metallicmaterials, ferromagnetic shape–memory alloys (FSMAs) and otherfunctional materials. Half-metallic materials can act as a spinfilter providing a current with a high degree of spin polarization,which is of great importance in spin-dependent devices [1].Mn 2 VAl, Mn 3 Ga, and also Mn 2 CoZ (Z¼Al, Ga, Si, Sb) have beenpredicted to be half-metallic materials by theoretical andexperimental studies [2–5]. Meanwhile, new FSMAs have alsobeen discovered among Mn-based Heusler alloys [6–8]. FSMAs aremagnetic materials that exhibit a martensitic transformationtogether with large magnetic-field-induced strains. They canserve as magnetic actuator material.In studies of FSMA, it is found that most FSMAs among theHeusler alloys are Ni–Mn based alloys, which can be obtained bysubstitution of some main group elements for Ni or Mn inNi 50 Mn 50 alloys [9]. Besides experimental studies on the Ni–Mnsystem, theoretical calculations also play an important role inthe search for new FSMAs. Chakrabarti and Barman [10]have predicted by first-principles calculations the martensitictransformation behavior in the stoichiometric Heusler alloyn Corresponding author at: School of Material Science and Engineering, HebeiUniversity of Technology, Tianjin 300130, P R China. Tel.: +86 22 60204765;fax: +86 22 26564129.E-mail addresses: hongzhi_luo@yahoo.com.cn, luo_hongzhi@163.com (H. Luo).Mn 2 NiIn, in which the main group element In has beensubstituted for 50% of the Ni in NiMn. Accordingly, a martensitictransformation has been observed in Mn 50 Ni 40 In 10 ribbons atabout 200 K [7]. So, to synthesize new FSMAs, theoreticalcalculations may be of essential importance.In this paper, the electronic structure and magnetic propertiesof the Heusler alloy Mn 2 NiAl with bcc and with tetragonalstructure are studied by first-principles calculations. Thepossibility of martensitic transformation behavior in Mn 2 NiAl ispredicted.2. Computational methodsThe electronic structure has been calculated using thepseudopotential method with a plane-wave basis set based ondensity-functional theory [11,12]. The interactions between theatomic core and the valence electrons are described by theultrasoft pseudopotential [13]. The electronic exchange-correlationenergy has been treated under the local-density approximation(LDA) [14,15]. For all cases, a plane-wave basis set cut-off of500 eV was used and 182 k points were employed in theirreducible Brillouin zone. These parameters ensured goodconvergence of the total energy. The convergence tolerance inthe calculations was selected as 1 10 6 eV/atom. The calculationswere performed based on the theoretical equilibrium latticeparameters.0921-4526/$ - see front matter & 2010 Elsevier B.V. All rights reserved.doi:10.1016/j.physb.2010.04.022

ARTICLE IN PRESSH. Luo et al. / Physica B 405 (2010) 3092–3095 30933. Results and discussion-2703.9The Heusler alloy crystallizes in a highly-ordered bcc structureand has a stoichiometric composition X 2 YZ, where X and Y aretransition-metal elements, and Z is a main-group element.Generally, the Heusler-alloy structure can be looked upon as fourinterpenetrating fcc lattices, in which the transition-metal atomsoccupy the A(0, 0, 0), B 1 4 ,1 4 4 ,1 and C12 ,1 2 2 ,1 sites, respectively. Themain-group-element occupies the D 3 4 ,3 4 4 ,3 site. As an example,Fig. 1 presents the crystal structure of the Heusler alloy.According to previous studies, the site preference of the 3delements is determined by the number of their valence electrons.The elements with less d electrons prefer occupying the B siteswhereas elements with more electrons prefer the (A, C) sites [16].So,in the stable structure of Mn 2 NiAl, one Mn atom and one Ni atomoccupy the (A, C) sites and the other Mn enters the B site, leaving theD site to Al. This is called the Hg 2 CuTi-type of structure [16] as hasbeen reported for Mn 2 NiSn [17] or Mn 2 NiGa [6]. This structure isdifferent from the Cu 2 MnAl type of structure, which is usual forHeusler alloys. In the Cu 2 MnAl type of structure, the two Mn atomsoccupy the (A, C) sites equally and leave the B site to Ni.To determine the theoretical lattice parameter, and test the sitepreference in Mn 2 NiAl, we have performed calculations onMn 2 NiAl with the Hg 2 CuTi- and with the Cu 2 MnAl-type ofstructure in both the non-magnetic (PM) and the ferromagnetic(FM) states. The results are presented in Fig. 2. It can be seen that,in both structures, the FM states are lower on the energy scale andthus more stable. The energy difference between the Hg 2 CuTi- andthe Cu 2 MnAl-type of structure is 0.92 eV, confirming the sitepreference discussed above. The equilibrium lattice constant ofMn 2 NiAl is 5.636 Å, which is a bit smaller than that of Mn 2 NiGa [6],due to the smaller atomic radius of Al compared with that of Ga.Fig. 3 presents the calculated total and partial density of states(DOS) of Mn 2 NiAl in the austenitic phase. The total DOS ofMn 2 NiAl consists of a low-energy part (below 6 eV), which ismainly made up of the s-states of Al, and a high-energy part(above 5 eV), which mainly arises from the contributions of thed-states of Mn and Ni atoms, together with the p-states of Al.-2704.2-2704.5-2704.8-2705.1Mn 2 NiAlaustenite5.3 5.4 5.5 5.6 5.7 5.8 5.9Lattice constant (Å)Fig. 2. Calculated total energy for Mn 2 NiAl as a function of the lattice parametersfor both the Cu 2 MnAl- and the Hg 2 CuTi-type of structure in the non-magnetic(PM) and ferrimagnetic (FM) state.8 Mn 2 NiAlTotal0-8Austenite4 Mn (A)0-44 Mn (B)0-4Ni-2 02 2Al0-2-8 -6 -4 -2 0 2 4Energy (eV)Fig. 3. Calculated spin-projected total and partial DOS of Mn 2 NiAl in the austeniticphase.The general properties of the total DOS are dominated by Ni andMn 3d states in the bonding and antibonding region.In both the majority- and minority-spin directions, the totalDOS is separated into bonding and antibonding states by anenergy gap below the Fermi level (E F ). The majority-spin statesshow a three-peak structure, which arises from the contributionsof the spin-up bonding and antibonding states of both the Mn andthe Ni atoms. In the minority DOS, the states below the energygap are mainly composed of the bonding peaks of Mn (A) and Niand the states above the gap come from the antibonding peak ofMn (B). In the majority-spin states, the energy gap is locatedaround 0.33 eV, while in the minority-spin states, the gap isshifted to 0.65 eV due to the magnetic splitting.It should be noted that, in the total DOS of austenitic Mn 2 NiAl, E F islocated at the shoulder of a DOS peak in both spin directions, resultingin a relatively high N(E F ). It has been reported that a high N(E F ) willdecrease the structure stability while low N(E F )hastheoppositeeffect[18,19]. So, this may result in the possibility of a structuraltransformation with lowering temperatures. The electronic structureof the martensitic phase will be discussed in the next section.In Fig. 3, the PDOS of Mn(B) shows a two-peak structure (bondingFig. 1. Crystal structure of Heusler alloys. The unit cell has four crystal sites as the and antibonding peak) due to the crystal-field effect, which results basis: Að0,0,0Þ,B 1 in a large local spin moment at the Mn(B) site. It may be noted that,4 ,1 4 4 ,1 ,C 12 ,1 2 ,1 2 , and D 34 ,3 4 ,3 4 in Wyckoff coordinates.Energy (eV)DOS (electrons / eV)Hg 2 CuTi-type FMHg 2 CuTi-type PMCu 2 MnAl-type FMCu 2 MnAl-type PM

ARTICLE IN PRESS3094H. Luo et al. / Physica B 405 (2010) 3092–3095for Mn 2 NiAl, the structure of the PDOS of Mn(A) and Mn(B) isopposite to each other. In the majority states of Mn (B), the twopeaks are basically below the Fermi level and occupied and, in theminority PDOS, the antibonding peak is high above E F . In contrast,the partial DOS of Mn(A) lies mainly below E F in the minority-spinstates and, above E F , in the majority-spin states. Therefore, thecontributions to the total DOS from Mn(A) and Mn(B) are opposite toeach other, indicating an antiparallel configuration of their spinmoments [4]. This agrees well with reported results on Mn 2 NiGa[10]. InMn 2 NiAl, the two Mn atoms are nearest neighbors with adistance of 1.991 Å. The small distance may cause strong direct Mn–Mn interaction and result in the antiparallel orientation of Mn (A)and Mn (B) spin moments [20].The PDOS of Ni in Fig. 3 lies basically below the Fermi level andis quite symmetric in the majority- and minority-spin direction.The contribution of Ni to the total spin moment is small. The pstates of Al also hybridize with the 3d states of Mn and Ni. Thishybridization will induce a small spin moment at the Al site. Thedetails can be explained from the feature of covalent magnetism,as introduced in Ref. [21].Experimental lattice constants of martensitic Mn 2 NiAl are stillunavailable. We perform a structural optimization for it first. Inthe optimization of the martensitic phase, for convenience sake,we assume that there is no volume difference between theaustenitic and martensitic phases. That is also the case in manyother FSMAs such as Mn 2 NiGa, Mn 2 NiIn or Ni 2 MnGa [10,20,22].For example, in Mn 2 NiGa, the experimental volume differencebetween the two phases is only 0.6% [6]. The minimum of thetotal energy E tot was obtained by varying c/a as a function of avolume-fixed tetragonal lattice. The results are presented in Fig. 4.It can be seen that there are two local energy minima in the E tot –c/a curve. The shallow one is at c/a¼0.97 and the deeper one atc/a¼1.222. This is quite similar to the case of Ni 2 MnGa [22]. Theminimum at c/a¼1.222 is lower on the energy scale, indicatingthat the martensite with c-axis lattice expansion and a, b-axislattice contraction is more stable. The equilibrium latticeconstants are a¼b¼5.43 Å and c¼6.88 Å and the c/a ratio is1.222, similar to the experimental result of 1.214 for Mn 2 NiGa [6].Fig. 5 presents the calculated total and partial DOS for martensiticMn 2 NiAl. It is seen that tetragonal distortion does not affect thegeneral shape of the total DOS. A main change is that the majorityDOS peak in the austenitic phase at 1.0eVsplitsintotwopeaksinthe martensitic phase at 1.26 and 0.69 eV, respectively.Meanwhile, an interesting difference in the total DOS around E F isobserved: the energy gap moves to the high-energy end in theEnergy (eV)-2705.20-2705.25-2705.30-2705.350.9c / aMn 2 NiAlmartensite1.0 1.1 1.2 1.3Fig. 4. Total energy as a function of the c/a ratio for Mn 2 NiAl in the martensiticphase.DOS (electrons / eV)840-4Mn 2 NiAlMartenitetotal2 Mn (A)0-24Mn (B)02 Ni0-20-2-8-6 -4 -2 0 2 4Energy (eV)Fig. 5. Calculated spin-projected total and partial DOS of Mn 2 NiAl in themartensitic phase.Table 1Calculated total and partial spin moments of Mn 2 NiAl with austenitic andmartensitic structure.Structure M total (m B /f.u.) M Mn(A) (m B ) M Mn(B) (m B ) M Ni (m B ) M Al (m B )Austenite 1.48 1.48 2.74 0.22 0.02Martensite 1.14 1.66 2.58 0.24 0.02martensitic DOS. In the austenitic phase, E F is located at the shoulderof the antibonding peak, but in the martensitic phase, E F moves tothe bottom of the energy gap, which reduces the value of N(E F )effectively. The total energy difference between the martensitic andthe austenitic phase is 0.07 eV/unit. This indicates that thetetragonal phase is more stable and that a martensitic transformationmay occur at lowering temperature. Similar results have alsobeen observed in Ni 2 MnGa and are known as the Jahn–Teller effect,in which the DOS peak at E F in the austenitic phase is divided intotwo peaks below and above E F with tetragonal distortion, resultingin a lowering of the total energy and causing the martensitictransformation [23].With the martensitic transformation, the majority antibondingpeak at 0.25 eV in the austenitic phase is shifted to 0.6 eV. Thevariation of the total DOS indicates a charge transfer from theoccupied to the unoccupied states. This transfer will introducemore d-holes in the majority states and make the total spinmoment of the martensite smaller than that of the austenite.The martensitic transformation does not change the configurationbetween the PDOS of Mn(A) and Mn(B). As a result, theirspin moments are also antiparallel like in the austenite. Thecalculated total and partial spin moments of Mn 2 NiAl are listed inTable 1. The total spin moments are 1.48 and 1.14 m B /f.u. for theaustenite and martensite, respectively. The variation of the totalmoment is mainly due to the change of the Mn spin moments. TheMn(A) moment is 1.48 m B in the austentic phase and 1.66 m Bin the martensitic phase, while the Mn(B) moment decreases from2.72 to 2.58 m B in the martensitic phase. All this leads to adecrease of the total spin moment. In both the austenitic andthe martensitic phase, the Ni moment is small (0.22 m B in theaustenitic phase and 0.24 m B in the martensitic phase) andcontributes little to the total spin moment. These results agreequite well with earlier discussions on Mn 2 NiGa and Mn 2 NiIn[10,20]. In these compounds, there is a ferrimagnetic couplingbetween the Mn(A) and the Ni or Mn(B) moment.Al

ARTICLE IN PRESSH. Luo et al. / Physica B 405 (2010) 3092–3095 30954. ConclusionsThe electronic structure and magnetic properties of theHeusler alloy Mn 2 NiAl have been studied by first-principlescalculations. It is found that the phase transformation from cubicto tetragonal structure lowers the total energy effectively,indicating the possibility of a martensitic phase transition atlow temperatures. After the martensitic phase transformation, theFermi level is shifted from the shoulder of the antibonding peak inthe austenitic phase to the bottom of an energy gap, whichreduces the value of N(E F ) and increases the phase stability of themartensite. Thus, ferromagnetic shape memory effect may bediscovered in Mn 2 NiAl or in alloys with some adjustment of thecomposition. Mn 2 NiAl is a ferrimagnet in both the austeniticand the martensitic phases. The total spin moments are 1.48 and1.14 m B /f.u. for the austenite and the martensite, respectively. Thetotal moment is mainly determined by the antiparallel alignedMn(A) and Mn(B) spin moments because the contribution of Ni tothe total moment is small.AcknowledgementsThis work is supported by National Natural Science Foundationof China in Grant no. 50901028 and Natural Science Foundation ofTianjin Grant no. 08JCYBJC09700.References[1] H. Ohno, Science 281 (1998) 951.[2] R. Weht, W.E. Pickett, Phys. Rev. B 60 (1999) 13006.[3] I. Galanakis, K. Özdoğan, E. S-as-ıoğlu, B. Aktas-, Phys. Rev. B 75 (2007) 092407.[4] S. Wurmehl, H.C. Kandpal, G.H. Fecher, C. Felser, J. Phys.: Condens. Matter 18(2006) 6171.[5] G.D. Liu, X.F. Dai, H.Y. Liu, J.L. Chen, Y.X. Li, G. Xiao, G.H. Wu, Phys. Rev. B 77(2008) 014424.[6] G.D. Liu, J.L. Chen, Z.H. Liu, X.F. Dai, G.H. Wu, B. Zhang, X.X. Zhang, Appl. Phys.Lett. 87 (2005) 262504.[7] J.L. Sánchez Llamazares, T. Sanchez, J.D. Santos, M.J. Pérez, M.L. Sanchez,B. Hernando, Ll. Escoda, J.J. Suñol, R. Varga, Appl. Phys. Lett. 92 (2008) 012513.[8] H.Z. Luo, F.B. Meng, Z.Q. Feng, Y.X. Li, W. Zhu, G.H. Wu, X.X. Zhu, C.B. Jiang,H.B. Xu, J. Appl. Phys. 107 (2010) 013905.[9] T. Krenke, X. Moya, S. Aksoy, M. Acet, P. Entel, Ll. Mañosa, A. Planes,Y. Elerman, A. Yü cel, E.F. Wassermann, J. Magn. Magn. Mater. 310 (2007) 2788.[10] A. Chakrabarti, S.R. Barman, Appl. Phys. Lett. 94 (2009) 161908.[11] M.C. Payne, M.P. Teter, D.C. Allan, T.A. Arias, J.D. Joannopoulos, Rev. Mod.Phys. 64 (1992) 1045.[12] M.D. Segall, P.L.D. Lindan, M.J. Probert, C.J. Pickard, P.J. Hasnip, S.J. Clark,M.C. Payne, J. Phys.: Condens. Matter 14 (2002) 2717.[13] D. Vanderbilt, Phys. Rev. B 41 (1990) 7892.[14] S.H. Vosko, L. Wilk, M. Nusair, Can. J. Phys. 58 (1980) 1200.[15] J.P. Perdew, A. Zunger, Phys. Rev. B 23 (1981) 5048.[16] H.C. Kandpal, G.H. Fecher, C. Felser, J. Phys. D: Appl. Phys. 40 (2007) 1507.[17] R.B. Helmholdt, K.H.J. Buschow, J. Less-Common Metals 128 (1987) 167.[18] J.H. Xu, T. Oguchi, A.J. Freeman, Phys. Rev. B 36 (1987) 4186.[19] J. Tobola, J. Pierre, J. Alloys Compd. 296 (2000) 243.[20] S.R. Barman, A. Chakrabarti, Phys. Rev. B 77 (2008) 176401.[21] A.R. Williams, V.L. Moruzzi, C.D. Gelatt Jr., J. Kübler, K. Schwarz, J. Appl. Phys.53 (1982) 2019.[22] S. Özdemir Kart, M. Uludoğan, I. Karaman, T. C- ağın, Phys. Status Solidi (a) 205(2008) 1026.[23] S. Fujii, S. Ishida, S. Asano, J. Phys. Soc. Jpn. 58 (1989) 3657.