First-principles investigation of magnetic properties in hyperkagome Mn₃TSi (T = Co, Rh, Ir) lattice

Based on first-principles calculations, we systematically investigate the electronic structures and magnetic properties of the hyperkagome lattice Mn₃TSi. The Fermi surface topologies of Mn₃RhSi and Mn₃IrSi exhibit notable similarities to each other but differ significantly from that of Mn₃CoSi. Competing antiferromagnetic interactions stabilize a 120° non-collinear triangular antiferromagnetic order, with spins canting out of the triangle planes, which leads to strong magnetic frustration. Itinerant magnetism, characterized by significant longitudinal spin fluctuations, especially in Mn₃CoSi, is described using the Heisenberg–Landau Hamiltonian, resulting in an approximate 5% suppression of the Néel temperatures. Linear spin-wave theory reveals pronounced magnetic excitations at Q = 1.7 Å⁻¹ in polycrystalline powder spectra of Mn₃CoSi and Mn₃RhSi, showing excellent agreement with experimental observations. Spin wave excitations for single crystals of all the three compounds are further predicted, with excitation energies reaching up to around 140 meV. Our findings advance the understanding of frustrated magnetism in hyperkagome lattices.