Large spin-phonon coupling and magnetically-induced phonon anisotropy in Sr$M$O${}_3$ perovskites ($M$=V,Cr,Mn,Fe,Co)

First-principles calculations reveal large zone-center spin-phonon coupling and magnetically-driven phonon anisotropy in cubic perovskites Sr$M$O${}_3$ ($M$=V,Cr,Mn,Fe,Co). In particular, the frequency and splitting of the polar Slater mode is found to depend strongly on magnetic ordering. The coupling is parameterized in a crystal-structure-dependent Heisenberg model and its main features seen to arise from the Goodenough-Kanamori rules. This coupling can be expected to produce distinct low-energy alternative phases, resulting in a rich variety of coupled magnetic, structural and electronic phase transitions driven by temperature, stress, electric field and cation substitution.