The first principle calculation for geometry optimization, elastic, electronic, magnetic, thermal, transport and lattice-dynamical properties of new spin gapless full heusler compound Zr₂MnGa were studied within Density Functional Theory approach (DFT). The material obeys Slater Pauling (SP) rule and exhibit spin gapless semiconducting behavior with fully compensated ferrimagnetism (FCF). To the best of our knowledge, various mechanical, thermal, transport and lattice dynamical properties like elastic constant, bulk modulus and Debye temperature are reported for the first time using density functional theory (DFT). The structure satisfies all stability criteria and is thus found stable at equilibrium value of lattice constant. Zr₂MnGa crystallizes in inverse heusler structure which is stable at ground state and have zero magnetic moment per unit cell, following Slater Pauling (SP) rule. The calculated results indicate that the material exhibits SGS character at its equilibrium lattice constant i.e. there is an indirect energy gap of about 0.31 eV between conduction band and valence band at EF level of minority or majority spin channel, while there is no gap between the majority electrons in valence band and minority electrons in conduction band. Higher value of ZT and Seebeck coefficient (S) increases the efficiency of thermoelectric devices with greater output current and voltage. Obtained results support strong candidature of Zr2MnGa compound as promising material in spintronics devices.
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