High-Temperature Terahertz Optical Diode Effect without Magnetic Order in Polar ${\mathrm{FeZnMo}}_3{\mathrm{O}}_8$

We present a terahertz spectroscopic study of polar ferrimagnet ${\mathrm{FeZnMo}}_3{\mathrm{O}}_8$. Our main finding is a giant high-temperature optical diode effect, or nonreciprocal directional dichroism, where the transmitted light intensity in one direction is over 100 times lower than intensity transmitted in the opposite direction. The effect takes place in the paramagnetic phase with no long-range magnetic order in the crystal, which contrasts sharply with all existing reports of the terahertz optical diode effect in other magnetoelectric materials, where the long-range magnetic ordering is a necessary prerequisite. In ${\mathrm{FeZnMo}}_3{\mathrm{O}}_8$, the effect occurs resonantly with a strong magnetic dipole active transition centered at 1.27 THz and assigned as electron spin resonance between the eigenstates of the single-ion anisotropy Hamiltonian. We propose that the optical diode effect in paramagnetic ${\mathrm{FeZnMo}}_3{\mathrm{O}}_8$ is driven by single-ion terms in magnetoelectric free energy.

Figure 1

(a), (b) Absorption and refractive index in zero applied magnetic field ($\mathit{H}=0$) for different polarizations of the incident THz wave. (c) Temperature dependence of absorption.

Figure 2

Magnetic field dependence of transmitted intensity at $T=4\mathrm{K}$. (a) Magnetic field $\mathit{H}$ applied along the $c$ axis in Faraday measurement geometry. (b) Magnetic field $\mathit{H}$ applied perpendicular to the $c$ axis in Voigt measurement geometry.

Figure 3

Magnetic field dependence of resonance frequencies at $T=4\mathrm{K}$.

Figure 4

(a) Transmitted intensity for positive and negative magnetic field $\mathit{H}$. Solid lines show the transmitted intensity for positive magnetic field. Open circles of the same color show the transmitted intensity for negative magnetic field. (b) Absorption coefficient for positive (solid lines) and negative (open circles) magnetic field. (c) Temperature dependence of the optical diode effect.