Electronic origin of spin phonon coupling effect in transition-metal perovskite materials

Spin-phonon couping in transition metal ABO$_3$ perovskites can be identified by the softening of the low-lying phonon modes including the polar ones, when the spin configuration is changed from being antiferromagnetic (AFM) to being ferromagnetic (FM). We studied the spin-phonon coupling effect by computing the changes of the superexchange energies as functions of typical soft modes' amplitudes in SrMnO$_3$ as an example. The superexchange interactions are computed by a recently developed extended Kugel-Khomskii model based on maximally localized Wannier functions. The spin-phonon coupling effect in SrMnO$_3$ is generally attributed to the suppressed superexchange interaction by all the soft modes under investigation. However, the spin-phonon coupling strength varies significantly among all the different soft modes. The individual superexchange interaction involves the hopping process between the $d$-like state of neighboring metal ions with strong hybridized oxygen $p$ character. As a result, the phonon modes, such as Slater and antiferrodistortive mode which modify the relative position of metal ion and oxygen octahedral cage, are found to be more effectively important in spin-phonon coupling effect. Furthermore, the electronic configuration also plays a crucial role.