Research articles Electronic structure, magnetic and optical properties of Co 2 TiZ (Z = B, Al, Ga, In) Heusler alloys Rakesh Jain a , N. Lakshmi a,⇑ , Vivek Kumar Jain a , Vishal Jain b , Aarti R. Chandra a , K. Venugopalan a a Department of Physics, Mohanlal Sukhadia University, Udaipur, Rajasthan 313001, India b Department of Physics, NIMS University Rajasthan, Jaipur 303121, India article info Article history: Received 21 January 2017 Received in revised form 19 May 2017 Accepted 13 June 2017 Available online 15 June 2017 Keywords: Heusler alloy Electronic structure properties Half metallicity Spintronics Magnetism Optical properties abstract Electronic structure, magnetic and optical properties of Co 2 TiZ (Z = B, Al, Ga, In) Heusler alloys have been computed by density functional theory implemented in WIEN2k within generalized gradient approxima- tion for exchange correlation functions. Lattices constants, bulk modulii, energy gaps, spin polarization and density of states have been calculated. Negative value of formation energy of these alloys evidences their stability. Spin polarization of Co 2 TiZ (Z = Al, B, Ga, In) are 100%, 99%, 97% and 80% respectively and Co 2 TiAl shows true half metallic ferromagnetism. Co 2 TiZ, for Z = B, Al, Ga, shows stable half metallically over a wide range of pressure making them suitable for fabricating thin films for spintronics applications. Optical parameters such as complex dielectric function, refractive index, reflectivity, absorption, extinc- tion coefficient, optical conductivity have also been calculated. Ó 2017 Elsevier B.V. All rights reserved. 1. Introduction In 1983, a new Heusler alloy, NiMnSb, was predicted by de Groot to be a half-metallic ferromagnetic [1]. Such materials, showing metallic behavior in one of the spin directions while semi- conducting behavior for the other in electron density of states (DOS) are called half metallic ferromagnetic (HMF). Properties such as tunneling magneto-resistance (TMR), giant magneto-resistance (GMR), capacity to be used as spin valves and for spin injection to semiconductors [2–7] make materials which show HMF proper- ties very attractive for fabrication of spintronics devices. Although Heusler alloys, with a formula X 2 YZ, having a face centered cubic structure, have been studied for substitution of elements at X, Y and Z atomic positions [8–16], large possibilities still remain to tai- lor the electronic structure properties by substituting different elements. Many alloys based on Co and Ti show HMF behavior. For exam- ple, Co 2 YZ (Y = Ti, V, Cr, Mn, Fe and Z = Al, Ga) are being studied by various researchers due to formation of an ordered, single phase along which they are also half-metallic [17–21]. Among these, Co 2 - TiZ (Z = Si, Ge and Sn), alloys with potential for 100% spin polariza- tion (SP) with half-metallicity and other properties such as enhanced Curie temperature, conductivity, saturation magnetiza- tion and Seebeck coefficient have attracted considerable attention [22]. Electronic structure calculations carried out using the self- consistent FPLAPW method by Dahmane for Ti 2 ZAl (Z = Co, Fe, Mn) show them to be HMF in nature with band gaps of 0.65, 0.58 and 0.39 eV respectively [23]. Mechanical properties and evolution of magnetic properties under pressure in Heusler alloys with Boron as sp element such as Ni 2 MnB, Co 2 NbB and Ti 2 CoB have been studied because of their high melting point, hardness and a high resistance to oxidation [24–26]. For actual realization of HM materials in spintronics based devices, these must be available in form of thin films or multilay- ers. However, depending on the substrate used, when these mate- rials are cast in the form of multilayers or thin films, a change in the lattice constant can occur because of strain. Inter-atomic dis- tances may be also changed by the application of pressure. In turn, these effects can be expected to modify the structural and mag- netic properties as has been reported by several workers [27–29]. In the present work we report results of studies of the ground state electronic structure, magnetic properties and effect of pressure on the half metallic properties of Co 2 TiZ (Z = B, Al, Ga, In) Heusler alloys using the full potential linearized augmented plane wave (FPLAPW) method in the WIEN2k code. 2. Computational details The electronic structures of Co 2 TiZ (Z = B, Al, Ga and In) were investigated by means of FP-LAPW method by using WIEN2k pack- age. The energy threshold between the core and the valence states http://dx.doi.org/10.1016/j.jmmm.2017.06.074 0304-8853/Ó 2017 Elsevier B.V. All rights reserved. ⇑ Corresponding author. E-mail address: nlakshmi@mlsu.ac.in (N. Lakshmi). Journal of Magnetism and Magnetic Materials 448 (2018) 278–286 Contents lists available at ScienceDirect Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm