Direct ab initio calculation of magnons in altermagnets: Method, spin-space symmetry aspects, and application to MnTe

We suggest the first method for direct ab initio calculation of adiabatic magnons in complex collinear magnets. The method is based on the density-functional-theory (DFT) calculation under two different constraints: one constraint governs the change of the magnetization with respect to the ground state, and the other is the symmetry constraint responsible for the value of the magnon wave vector. The advantages of the suggested method with respect to the usual approach of mapping of the electron system on the Heisenberg Hamiltonian of interacting magnetic moments are discussed. The performance of the method is demonstrated by the application to an altermagnet MnTe. The altermagnetism introduced as a concept in 2022 is at present an area of highly intensive research. The characteristic feature of altermagnets is the spin splitting of the electron states in reciprocal k space. Among the discovered properties of the altermagnets is the chirality splitting of the magnons in wave vector q space. We suggest an appoach to the study of the symmetry aspects of magnon chirality splitting. We show that both the chirality splitting of the magnons and the altermagnetic spin splitting of the electron states, though very different in their physical nature, have identical patterns in the corresponding wave vector spaces. Since the altermagnetism of MnTe is the consequence of the presence of the Te atoms, adequate attention is devoted to the symmetry analysis and calculation results for the Te moments induced in the magnon states. In the calculations, each magnon is characterized by its own electron band structure. We investigate the transformation of the electron structure in the transition of the material from the collinear ground state to noncollinear magnon states. We show the connection between the properties of magnon band structures and the chirality properties of magnons. In the investigation of the chirality splitting as well as in both the formulation and the application of our method, an important role play the aspects of generalized symmetry based on the application of the spin-space groups. The symmetry framework connects in one coherent picture different parts of the consideration: (i) the generalized translational symmetry of the magnons as a crucial condition for their efficient ab initio calculation, (ii) altermagnetic spin splitting of the electron states in the ground state, and (iii) chirality splitting and band structures of the magnon excitations.