Topological altermagnetic to ferromagnetic transition promoted by spin-orbit coupling

The defining property of an altermagnetic state is that the symmetry that leaves the state unchanged when combined with flipping the magnetic moments is a rotation, which can be proper or improper. Because of this symmetry, the band structure of altermagnets displays a Zeeman splitting that vanishes in certain regions of momentum space. In this talk, we will discuss the impact of spin-orbit coupling on the properties of altermagnets. We will show that the magnetic moments in an altermagnetic state become intrinsically non-collinear, and that the Zeeman splitting acquires nodal lines protected by mirror symmetries of the lattice. This symmetry protection ensures that the nodal lines are stable against magnetic fields applied perpendicular to such mirrors. Consequently, a critical magnetic field needs to be applied for the nodal loops to collapse, resulting in a topological transition between a state with nodal Zeeman splitting, which is characteristic of an altermagnet, and a state with nodeless Zeeman splitting, which is charactertistic of a ferromagnet.