$P$-wave Orbital Magnetism

Abstract: Realization of unconventional odd-parity magnets usually requires noncollinear spin textures of the underlying lattice. We propose a different concept of $p$-wave magnetism that originates from an orbital texture induced by loop currents. The resulting $p$-wave orbital magnetism is protected by the combined translation and time-reversal symmetry, with even-parity components arising when the symmetry is broken. Our proposal is exemplified by a two-dimensional (2D) lattice model whose energy spectrum contains Dirac points and which is characterized by a nontrivial topology controlled by the magnitude of the loop currents. Since the odd-parity magnetism precludes macroscopic magnetization, we suggest measuring it via orbital Hall conductivity. Our work establishes orbital degrees of freedom as an additional platform for unconventional $p$-wave magnetism beyond noncollinear spin textures, as well as makes a step forward to bridging odd-parity magnetism and topology.