Negative refraction index in the magnetic semiconductorIn2−xCrxO3: Theoretical analysis

Abstract

Based on theoretical arguments, we have found that homogeneous indium oxide is a negative refractive index material if doped with Cr. In accordance with calculations, this magnetic semiconductor or ${\text{In}}_{2\ensuremath{-}x}{\text{Cr}}_{x}{\text{O}}_{3}$ in its polycrystalline form should possess a fully isotropic strongly pronounced negative refractive index at $\ensuremath{\sim}10.48\text{ }\text{THz}$. The effect is due to the coexistence of the spin-wave mode with the plasmonic mode, and both modes are activated by the electromagnetic field of the light with simultaneous permittivity and permeability responses within the frequency band close to the ferromagnetic resonance. The analytical and numerical calculations of the frequency-dependent refractive index, $n(\ensuremath{\omega})$, were conducted in the framework of the macroscopic theory of ferromagnets, the modified band theory, and the conduction electrons-mediated exchange integral formalism.