Electromagnon with Sensitive Terahertz Magnetochromism in a Room-Temperature Magnetoelectric Hexaferrite

An electromagnon in the magnetoelectric (ME) hexaferrite ${\mathrm{Ba}}_{0.5}{\mathrm{Sr}}_{2.5}{\mathrm{Co}}_2{\mathrm{Fe}}_{24}{\mathrm{O}}_{41}$ (${\mathrm{Co}}_2\mathrm{Z}$-type) single crystal is identified by time-domain terahertz (THz) spectroscopy. The associated THz resonance is active on the electric field ($E^{\omega }$) of the THz light parallel to the $c$ axis ($\parallel [001]$), whose spectral weight develops at a markedly high temperature, coinciding with a transverse conical magnetic order below 410 K. The resonance frequency of 1.03 THz at 20 K changes $-8.7\%$ and $+5.8\%$ under external magnetic field ($H$) of 2 kOe along [001] and [120], respectively. A model Hamiltonian describing the conical magnetic order elucidates that the dynamical ME effect arises from antiphase motion of spins which are coupled with modulating electric dipoles through the exchange striction mechanism. Moreover, the calculated frequency shift points to the key role of the Dzyaloshinskii-Moriya interaction that is altered by static electric polarization change under different $H$.

Figure 1

(a) Crystal structure of ${\mathrm{Ba}}_{0.5}{\mathrm{Sr}}_{2.5}{\mathrm{Co}}_2{\mathrm{Fe}}_{24}{\mathrm{O}}_{41}$ representing stacking of magnetic $S$ (blue) and $L$ (red) blocks. (b) Schematic illustration of transverse conical order (dotted lines) composed of ${\overrightarrow{\mu }}_S$ (blue arrow) and ${\overrightarrow{\mu }}_L$ (red arrow). Blue and red ellipsoids represent trajectories of the moment modulations. $\theta$ and $\varphi$ refer to the angles of ${\overrightarrow{\mu }}_S$ from [001] and ${\overrightarrow{\mu }}_L$ from [120], respectively.

Figure 2

Spectra of real (a) and imaginary (b) parts of complex dielectric constant for various $E^{\omega }\&H^{\omega }$ configurations at 20 K. (c) Temperature dependence of the ${ϵ}_2$ spectra for $E_{[001]}^{\omega }{H}_{[120]}^{\omega }$. (d) Temperature evolution of $\mathrm{\Delta }SW$ (left axis) and the static $P\parallel [100]$ (right axis) in a single ME domain state at $H=2\mathrm{kOe}\parallel [120]$ (Ref. [26]). $T_{\mathrm{con}}$ refers to transition temperature of the transverse conical state.

Figure 3

${ϵ}_2$ spectra for $E_{[001]}^{\omega }{H}_{[120]}^{\omega }$ under $H=2\mathrm{kOe}\parallel [120]$ (blue), $\parallel [001]$ (red), and 0 kOe (black). Solid (dashed) curves correspond to the data at 20 K (410 K). Inset shows $H$ directions applied to the sample. (b) Temperature dependence of the resonance frequencies upon the $H$ directions.

Figure 4

(a) Trajectories of the high-lying magnon mode. Red (blue) ellipsoid represents the modulation $\delta {\overrightarrow{\mu }}_L(\delta {\overrightarrow{\mu }}_S)$. Summary of $x$, $y$, and $z$ components of (b) the static moments and (c) their modulations. (d) Magnetization ($M_x$) vs external magnetic field $(H_x^{\mathrm{ext}})\parallel [120]$ relations at 20 K. The sphere denotes the experimental data. (e) Calculated frequencies of the high-lying mode under $H_x^{\mathrm{ext}}$ for various DM interaction strengths. Solid symbols denote the observed electromagnon resonance frequencies.