Martin Wood Complex, Department of Physics, University of Oxford, Parks Road, Oxford, OX1 3PU
Professor Paolo Radaelli, Department of Physics, University of Oxford
Prof Amalia Coldea
Abstract
In the past two decades, there has been a resurgence of interest in compounds having electronic bands with lifted spin degeneracy, partly motivated by the requirement of new materials for spintronics. In addition to spin polarisation in ferromagnets, it is well known that spin degeneracy can be lifted even in non-magnetic materials by the famous Rashba- Dresselhaus (R-D) effect, which requires spin-orbit coupling (SOC) and is therefore largest in the presence of heavy elements. The R-D effect also requires the absence of inversion symmetry, due either to the bulk crystal structure being acentric or to symmetry breaking at interfaces. More recently, several groups came to the surprising realisation that spin degeneracy can also be lifted in some fully compensated antiferromagnets (AFM), including collinear AFM. In some cases, this splitting persists in the absence of spin-orbit coupling (SOC), due to the interaction between electron spins and the ‘effective Zeeman field’ (largely of magnetic exchange origin) produced by ordered magnetic moments – a phenomenon that has been named ‘altermagnetism’. I will present a general approach to construct a multipolar tensor expansion of k/ − k-symmetric, time-reversal-odd spin textures [1,2]. I will demonstrate that these spin textures decompose in an ‘altermagnetic’ (SOC-independent) component, which is invariant by rotation in spin space and is described by the spin-group or colour-group formalisms, and a SOC-dependent component that depends on spin orientation, described by the more familiar magnetic point groups that also determine macroscopic properties. I will also outline an extension of this procedure to deal with k/ − k-antisymmetric, time-reversal-even spin textures (including so-called p-wave textures). Finally, I will discuss experimental/computational approaches and future practical applications of ‘altermagnetism’.
References
[1] Radaelli, P. G. Tensorial approach to altermagnetism. Phys. Rev. B 110, 214428 (2024).
[2] Radaelli, P. G. & Gurung, G. Colour symmetry and non-collinear altermagnetism. arXiv:2501.02947 (2025).