Negative Refraction Observed in a Metallic Ferromagnet in the Gigahertz Frequency Range

It is generally believed that nature does not provide materials with negative refraction. Here we demonstrate experimentally that such materials do exist at least at GHz frequencies: ferromagnetic metals reveal a negative refraction index close to the frequency of the ferromagnetic resonance. The experimental realization utilizes a colossal magnetoresistance manganite ${\mathrm{La}}_{2/3}{\mathrm{Ca}}_{1/3}{\mathrm{MnO}}_3$ as an example. In this material the negative refractive index can be achieved even at room temperature using external magnetic fields.

Figure 1

Temperature dependence of the conductivity and magnetization of the LCMO film. Left scale: Magnetic moment of LCMO for different magnetic fields. Right scale: conductivity at $\nu =150\mathrm{GHz}$ without magnetic field (blue) and in an external field of ${\mu }_{0}H=5\mathrm{T}$ (green). Dashed line indicates the border between ferromagnetic metallic and paramagnetic semiconducting phases.

Figure 2

Complex transmittance of LCMO within two possible experimental geometries. (a) Amplitude of the transmission coefficient for magnetic ($\tilde{h}\perp {\mu }_{0}H$, black curve) and nonmagnetic ($\tilde{h}\parallel {\mu }_{0}H$, red curve) geometries. (b) Phase shift of the transmittance. The notations are the same as in (a). The inset represents the experimental geometries. Here the wave vector $\overrightarrow{k}$ gives the propagation direction, ${\mu }_{0}H$ is the external magnetic field, and $\tilde{e}$ and $\tilde{h}$ are the ac electric and magnetic fields of the electromagnetic wave, respectively.

Figure 3

Magnetic field-dependence of the dielectric permittivity (a) and magnetic permeability (b) of LCMO at $\nu =150\mathrm{GHz}$ and $T=210\mathrm{K}$. Green curves—real parts, blue curves—imaginary parts. The inset shows the magnetic permeability in the vicinity of the resonance field.

Figure 4

Magnetic field dependence of the refractive index (a) and absorption coefficient (b) of LCMO at $\nu =150\mathrm{GHz}$ and for different temperatures. Symbols—experiment, lines—fits to the Lorentz form of the ferromagnetic resonance. The inset presents the refractive index at $T=210\mathrm{K}$ on the complex scale.

Figure 5

(a) Lowest experimentally achieved value of the refractive index at two frequencies of the experiment. (b) Strength of the ferromagnetic mode obtained from the Lorentz fits. Symbols represent experimental data; lines are guides to the eye.