The Dzyaloshinskii-Moriya interaction (DMI) in magnetic materials plays an important role in spintronics, giving rise to chiral spin textures such as the nucleation and propagation of domain walls and skyrmions. The necessary ingredient for the emergence of the DMI is the lack of inversion symmetry combined with elements with strong spin-orbit coupling. We report on a first-principles investigation of generalized DMIs in bulk centrosymmetric crystals with noncentrosymmetric local sublattices, where we consider a prototype family of $\mathcal{PT}$-symmetric antiferromagnets, including, ${\mathrm{Mn}}_2\mathrm{Au}$, ${\mathrm{MnPd}}_2$ and MnCuAs in the tetragonal and orthorhombic phases. We employ a Green's function approach to calculate the interatomic relativistic exchange coupling which can, in turn, determine the sublattice elements of the generalized fifth-order DMI tensor $D_{\alpha \beta ,\gamma }^{s{s}^{\prime }}$. We demonstrate that the breaking of the local mirror symmetry and the resulting local Rashba-type spin-momentum locking yield local DMIs with opposite signs on the two antiparallel sublattices. We present numerical results and provide analytical expressions for the magnon dispersion in the presence of the sublattice DMI and show that the intra- (inter-) sublattice DMIs result in identical (opposite) contributions to the nonreciprocal components of the two low-frequency antiferromagnetic magnon modes.

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• Dzyaloshinskii-Moriya interaction
• Magnons
• Spintronics
• Antiferromagnets
• Density functional theory