Microwave Magnetochiral Dichroism in the Chiral-Lattice Magnet ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$

Through broadband microwave spectroscopy in Faraday geometry, we observe distinct absorption spectra accompanying magnetoelectric (ME) resonance for oppositely propagating microwaves, i.e., directional dichroism, in the multiferroic chiral-lattice magnet ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$. The magnitude of the directional dichroism critically depends on the magnetic-field direction. Such behavior is well accounted for by considering the relative direction of the oscillating electric polarizations induced via the ME effect with respect to microwave electric fields. Directional dichroism in a system with an arbitrary form of ME coupling can be also discussed in the same manner.

Figure 1

(a) Picture of the experimental setup. The sample is mounted on the coplanar waveguide (CPW) directly. The sample shape is highlighted by the red line for clarity. $S_{12(21)}$ is the transmission coefficient for the microwave propagating along the $+{\mathit{k}}^{\omega }(-{\mathit{k}}^{\omega })$ direction. (b) Schematic of the electromagnetic-field distribution ${\mathit{E}}^{\omega }$ and ${\mathit{H}}^{\omega }$ accompanying the microwave propagating along the CPW. (c) The absorption spectra associated with the magnetic resonance, $\mathrm{\Delta }{S}_{12}$, at various magnetic fields with the ${\mathit{k}}^{\omega }\parallel \mathit{H}\parallel [100]$ configuration at 7.6 K. Each spectrum is shifted vertically for clarity. Inset: the crystal structure of ${\mathrm{Cu}}_2{\mathrm{OSeO}}_3$.

Figure 2

(a) Measurement configuration and the instantaneous responses of ${\mathit{M}}^{\omega }$ and ${\mathit{P}}^{\omega }$ derived from the $d\text{−}p$ hybridization model for the case that $\mathit{M}\parallel [100]$ with ${\mathit{E}}^{\omega }\parallel [001]$ and ${\mathit{H}}^{\omega }\parallel [0\overline{1}0]$. ${\mathit{M}}^{\omega }$ and ${\mathit{P}}^{\omega }$ induced by ${\mathit{E}}^{\omega }$ are denoted as ${\mathit{M}}_E^{\omega }$ (open red arrows) and ${\mathit{P}}_E^{\omega }$ (open blue arrows), respectively, whereas ${\mathit{M}}^{\omega }$ and ${\mathit{P}}^{\omega }$ induced by ${\mathit{H}}^{\omega }$ are denoted as ${\mathit{M}}_H^{\omega }$ (filled red arrows) and ${\mathit{P}}_H^{\omega }$ (filled blue arrows), respectively. (b) The absorption spectra $\mathrm{\Delta }{S}_{12}$ and $\mathrm{\Delta }{S}_{21}$ under 2000 Oe for ${\mathit{k}}^{\omega }\parallel [100]$ and ${\mathit{k}}^{\omega }\parallel [\overline{1}00]$, respectively. (c) The directional-dichroism spectra $\mathrm{\Delta }{S}_{12}-\mathrm{\Delta }{S}_{21}$ under $\pm 2000\mathrm{Oe}$. The measurements were performed at 7.8 K.

Figure 3

(a)–(c) Schematics of the experimental configurations for (a) ${\mathit{k}}^{\omega }\parallel \mathit{H}\parallel [100],{\mathit{H}}^{\omega }\parallel [0\overline{1}0]$, and ${\mathit{E}}^{\omega }\parallel [001]$, (b) ${\mathit{k}}^{\omega }\parallel \mathit{H}\parallel [100],{\mathit{H}}^{\omega }\parallel [001]$, and ${\mathit{E}}^{\omega }\parallel [010]$, and (c) ${\mathit{k}}^{\omega }\parallel \mathit{H}\parallel [111],{\mathit{H}}^{\omega }\parallel [11\overline{2}]$, and ${\mathit{E}}^{\omega }\parallel [1\overline{1}0]$. (d)–(f) The absorption spectra $\mathrm{\Delta }{S}_{12}$ at 2000 Oe under the microwave configuration of (a)–(c), respectively. (g)–(i) The directional dichroism spectra $\mathrm{\Delta }{S}_{12}-\mathrm{\Delta }{S}_{21}$ at $\pm 2000\mathrm{Oe}$ under the microwave configuration of (a)–(c), respectively. The measurements were performed at 7.6 K.

Figure 4

Magnetic-field (a) and temperature (b) dependence of the magnitude of the directional dichroism measured under the $\mathit{k}\parallel \mathit{H}\parallel [100]$ configuration at 7.6 K (closed circles). The variation of $P_{[001],H\parallel [110]}/M$ is also presented for comparison, in which $P_{[001],H\parallel [110]}$ and $M$ are measured under $\mathit{H}\parallel [110]$ and $\mathit{H}\parallel [001]$, respectively, at 5 K. The temperature dependences in (b) are measured at $H=2000\mathrm{Oe}$.