A Tensorial Approach to 'Altermagnetism'

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 discuss a tensorial approach to the description of k/ − k-symmetric, time-reversal-odd splitting of electronic bands in magnetic materials, showing that tensors provide a general framework to discuss magnetic symmetry in both collinear and non-collinear altermagnets. [1] In general, one finds that spin textures decompose in an ‘altermagnetic’, (SOC-independent) component, which is invariant by rotation in spin space and is described by the spin-group/colour-group formalism, and a component that depends on spin orientation, described by the more familiar magnetic point groups. This approach also clarifies the connection between altermagnetism and well-known bulk properties, establishing that the vast majority of altermagnetic materials must also be piezomagnetic and MOKE-active.

[1] P.G. Radaelli, "A Tensorial Approach to 'Altermagnetism'", Physical Review B in press, arXiv:2407.13548