Assessing the atomic moment picture of spin dynamics with <i>ab initio</i> magnon wavefunctions

Our understanding of collective spin fluctuation in materials relies largely on Heisenberg-type spin Hamiltonians. Implicit in these spin models is the atomic moment picture wherein, transverse spin dynamics, the magnetization around an atom undergoes precessional motion as a rigid moment, which has been challenged by recent theoretical and experimental advances. To assess the validity of the atomic moment picture in spin dynamics, however, necessitates magnon wavefunctions from ab initio methods without a priori spin models. To this end, we develop an efficient model-free ab initio method for computing magnon spectrum and wavefunctions. Niu-Kleinman's adiabatic spin-wave dynamics is reformulated using linear perturbation theory into a generalized eigenvalue problem, which can be solved to produce magnon spectrum and wavefunctions without assuming atomic moments. We have implemented this method in the framework of density functional perturbation theory (DFPT). A dynamical extension of the Niu-Kleinman equation of motion is proposed to improve inaccurately predicted magnon energies owing to imperfect adiabaticity at higher energies. Based on the obtained ab initio magnon wavefunctions, we find that while the atomic moment picture is observed in typical $3d$ transition metal magnets, magnets with less localized $4d$ and $5d$ orbitals show deviations in varying degrees from this paradigm. In particular, in the so-called molecular orbital crystals, such as ${\mathrm{Na}}_{2}{\mathrm{IrO}}_{3}$ and ${\mathrm{SrRu}}_{2}{\mathrm{O}}_{6}$, the atomic moment picture becomes invalid because of orbital locking via interatomic hopping. Our results suggest that the usual spin Hamiltonian approach should be employed with extra caution. Possible experimental ramifications of the breakdown of the atomic moment picture in magnon excitation are also discussed.