Topological properties of the Zeeman splitting in altermagnets

Abstract: The fundamental properties of a magnetic state depend on which symmetries of the lattice leave the state unchanged when combined with flipping all the magnetic moments. In a ferromagnet, no such symmetry exists, resulting in a nonzero magnetization and a uniform Zeeman splitting of the spin-up and spin-down bands. In contrast, this type of symmetry is present in any collinear and commensurate antiferromagnet, since a lattice translation “undoes” the flipping of the spins, leading to degenerate spin-up and spin-down bands with no Zeeman splitting. Between these two types of magnetic states, however, lies a broad range of systems for which the symmetry that relates configurations of flipped spins is a rotation or a reflection. Called altermagnets, these states have no magnetization, like an antiferromagnet, but their bands display Zeeman splitting, like a ferromagnet. In this talk, I will discuss the various connections between altermagnets and phenomena of interest in correlated electronic systems, such as multipolar order and Pomeranchuk instabilities. I will then show that the Zeeman splitting of an altermagnet has symmetry-protected nodal lines that reside on the mirror planes of the crystal. A direct consequence of the coupling to the underlying crystalline environment, these nodal lines give rise to Fermi-surface pinch points that behave as Weyl nodes. Interestingly, magnetic fields applied along high-symmetry directions cannot immediately destroy the nodal lines. Instead, they become shrinking nodal loops that only disappear beyond a threshold value of the magnetic field, signaling a topological altermagnetic-to-ferromagnetic transition.  I will also present altermagnetic material candidates, focusing on a wide class of magnetic perovskites, and will discuss possible ways to manipulate and probe altermagnetic states experimentally by exploiting their unusual dynamic coupling to phonons.