GHz non-reciprocal optical conductivity in hematite ($α$-$\text{Fe}_2\text{O}_3$)

We study the non-reciprocal properties of the iron oxide $α$-Fe$_2$O$_3$ (hematite) in the canted easy-plane antiferromagnetic phase, specifically in the GHz to THz frequency range. First, using the the microscopic spin Hamiltonian, we obtain the correct classical ground state where the canting is induced by the Dzyaloshinskii-Moriya interactions (DMI). The magnon spectrum is simulated using linear spin wave theory. We then compute the polarizability and the sub-gap optical conductivities using linear response. We find that the conductivity tensor contains frequency peaks at the zero momentum magnon gaps of order $0.1~$meV which can be tuned by the DMI and on-site anisotropic spin interactions. Furthermore, we show that the canting-induced net magnetic moment $\mathbf{m}$ represents a measure for the effective time-reversal-symmetry breaking and non-reciprocity of the system: a finite $\mathbf{m}$ results in a non-zero Hall conductivity. Finally, we discuss the prospective application of hematite in non-reciprocal circulator design, by computing the non-reciprocal circulator transmission amplitude using the conductivities as input.