Employing first principles electronic structure calculations in conjunction with the frozen-magnon method we calculate exchange interactions, spin-wave dispersion, and spin-wave stiffness constants in inverse-Heusler-based spin gapless semiconductor
(SGS) compounds Mn$_2$CoAl, Ti$_2$MnAl, Cr$_2$ZnSi, Ti$_2$CoSi and Ti$_2$VAs. We find that their magnetic behavior is similar to the half-metallic ferromagnetic full-Heusler alloys, i.e., the intersublattice exchange interactions play an essential role in the formation of the magnetic ground state and in determining the Curie temperature, $T_mathrm{c}$. All compounds, except Ti$_2$CoSi possess a ferrimagnetic ground state. Due to the finite energy gap in one spin channel, the exchange interactions decay sharply with the distance, and hence magnetism of these SGSs can be described considering only nearest and next-nearest neighbor exchange interactions. The calculated spin-wave dispersion curves are typical for ferrimagnets and ferromagnets. The spin-wave stiffness constants turn out to be larger than those of the elementary 3$d$-ferromagnets. Calculated exchange parameters are used as input to determine the temperature dependence of the magnetization and $T_mathrm{c}$ of the SGSs. We find that the $T_mathrm{c}$ of all compounds is much above the room temperature. The calculated magnetization curve for Mn$_2$CoAl as well as the Curie temperature are in very good agreement with available experimental data. The present study is expected to pave the way for a deeper understanding of the magnetic properties of the inverse-Heusler-based SGSs and enhance the interest in these materials for application in spintronic and magnetoelectronic devices.
The present manuscript completes the study presented in two recent research articles [K. Koumpouras and I. Galanakis, textit{J. Magn. Magn. Mater.} 323, 2328 (2011); textit{ibid}, textit{J. Spintron. Magn. Nanomater.} 1, in press]. Preliminary first-
principles calculations using the QUANTUM-espresso package [P. Giannozzi et al textit{J. Phys.:Condens. Matter} 21, 395502 (2009)] on the magnetic behavior of ultra-thin epitaxial multilayers between the BiFeO$_3$ magnetoelectric compound and various types of spacers are presented. As spacer we have considered i) InP semiconductor, ii) Fe which is a ferromagnet, and iii) metallic V. In all cases under study the growth axis of the multilayer was the [001]. Our results indicate that the magnetic properties are seriously downgraded for the ultrathin BiFeO$_3$ multilayers independent of the nature of the spacer and in some cases under study magnetism even vanishes. More extensive calculations are needed to establish a more clear view of the physical properties of the interfaces involving the BiFeO$_3$ compound.
We expand our study on cubic BiFeO$_3$ alloys presented in [K. Koumpouras and I. Galanakis, textit{J. Magn. Magn. Mater} 323, 2328 (2011)] to include also the BiMnO$_3$ and Bi$_2$MnFeO$_6$ alloys. For the latter we considered three different cases of
distribution of the Fe-Mn atoms in the lattice and six possible magnetic configurations. We show that Fe and Mn atoms in all cases under study retain a large spin magnetic moment, the magnitude of which exceeds the 3 $mu_B$. Their electronic and magnetic properties are similar to the ones in the parent BiMnO$_3$ and BiFeO$_3$ compounds. Thus oxygen atoms which are the nearest-neighbors of Fe(Mn) atoms play a crucial role since they mediate the magnetic interactions between the transition metal atoms and screen any change in their environment. Finally, we study the effect of lattice contraction on the magnetic properties of Bi$_2$MnFeO$_6$.
