Crystal tensor properties of magnetic materials with and without spin-orbit coupling. Application of spin point groups as approximate symmetries

Abstract

Spin space groups, formed by operations where the rotation of the spins is independent of the accompanying operation acting on the crystal structure, are appropriate groups to describe the symmetry of magnetic structures with null spin-orbit coupling. Their corresponding spin point groups are the symmetry groups to be considered for deriving the symmetry constraints on the form of the crystal tensor properties of such idealized structures. These groups can also be taken as approximate symmetries (with some restrictions) of real magnetic structures, where spin-orbit and magnetic anisotropy are however present. Here we formalize the invariance transformation properties that must satisfy the most important crystal tensors under a spin point group. This is done using modified Jahn symbols, which generalize those applicable to ordinary magnetic point groups [Gallego et al., Acta Cryst. (2019) A75, 438-447]. The analysis includes not only equilibrium tensors, but also transport, optical and non-linear optical susceptibility tensors. The constraints imposed by spin collinearity and coplanarity within the spin group formalism on a series of representative tensors are discussed and compiled. As illustrative examples, the defined tensor invariance equations have been applied to some known magnetic structures, showing the differences of the symmetry-adapted form of some relevant tensors, when considered under the constraints of its spin point group or its magnetic point group. This comparison, with the spin point group implying additional constraints in the tensor form, can allow one to distinguish those magnetic-related properties that can be solely attributed to spin-orbit coupling from those that are expected even when spin-orbit coupling is negligible.

41 pages, 7 figures

References in corpus (11)

• Anomalous Hall effect
• Giant momentum-dependent spin splitting in centrosymmetric low Z antiferromagnets
• Giant Anomalous Hall Effect in the Chiral Antiferromagnet Mn3Ge
• Spin-polarized current in non-collinear antiferromagnets
• Orbitronics: the Intrinsic Orbital Hall Effect in p-Doped Silicon
• Prediction of low-Z collinear and noncollinear antiferromagnetic compounds having momentum-dependent spin splitting even without spin-orbit coupling
• Symmetry-imposed shape of linear response tensors
• Spin Hall effect emerging from a chiral magnetic lattice without spin-orbit coupling
• Ground state magnetic structure of Mn${}_3$Ge
• Symmetry analysis with spin crystallographic groups: Disentangling effects free of spin-orbit coupling in emergent electromagnetism
• On the separation of Hall and Ohmic nonlinear responses

Cited by in corpus (4)

• Automatic calculation of symmetry-adapted tensors under spin-group symmetry. STENSOR, a new tool of the Bilbao Crystallographic Server
• Nonrelativistic Functional Properties in Collinear Antiferromagnets Based on Multipole Representation Theory
• Probing multipolar order in the candidate altermagnet MnF${}_2$ through the elastocaloric effect under strain
• Nonlinear opto-magnetic signature of d-wave altermagnets