Terahertz-frequency magnetoelectric effect in Ni-doped ${\mathrm{CaBaCo}}_4{\mathrm{O}}_7$

We present a study of the terahertz-frequency magnetoelectric effect in ferrimagnetic pyroelectric ${\mathrm{CaBaCo}}_4{\mathrm{O}}_7$ and its Ni-doped variants. The terahertz absorption spectrum of these materials consists of spin excitations and low-frequency infrared-active phonons. We studied the magnetic-field-induced changes in the terahertz refractive index and absorption in magnetic fields up to 17 T. We find that the magnetic field modulates the strength of infrared-active optical phonons near 1.2 and 1.6 THz. We use the Lorentz model of the dielectric function to analyze the measured magnetic-field dependence of the refractive index and absorption. We propose that most of the magnetoelectric effect is contributed by the optical phonons near 1.6 THz and higher frequency resonances. Our experimental results can be used to construct and validate more detailed theoretical descriptions of magnetoelectricity in ${\mathrm{CaBaCo}}_{4-x}{\mathrm{Ni}}_x{\mathrm{O}}_7$.

Figure 1

Magnetic structure of ${\mathrm{CaBaCo}}_4{\mathrm{O}}_7$. Triangular layers are formed by the Co1 ions. Kagome layers are formed by Co2, Co3, and Co4 ions.

Figure 2

Temperature dependence of dc magnetization (in logarithmic scale) [(a)–(c)] and magnetic hysteresis loops [(d)–(f)] in parent and Ni-doped CBCO. The insets in panels (a)–(c) show the ac magnetization for the parent and Ni-doped CBCO with $H_{ac}=1$ Oe and $f=973$ Hz.

Figure 3

THz absorption (a) and refractive index (b) of ${\mathrm{CaBaCo}}_4{\mathrm{O}}_7$ pellets with different Ni content.

Figure 4

THz pulses transmitted by a ${\mathrm{CaBaCo}}_4{\mathrm{O}}_7$ pellet with $x=0.05$ Ni content at different applied magnetic fields. THz pulses arrive earlier in higher magnetic fields, indicating a lower refractive index and dielectric constant. The induced change in the refractive index is even in the direction of the applied magnetic field, i.e., does not change sign when magnetic field is reversed.

Figure 5

(a) Solid lines with symbols plot the magnetic field induced change in refractive index $\mathrm{\Delta }n\left(\omega \right)=n(\omega ,B)-n(\omega ,0\mathrm{T})$ at frequency $\omega =0.4$ THz and in applied field $B=17$ T. Dashed lines plot the quantity $\mathrm{\Delta }{n}_1\left(\omega \right)$, Eq. (6). (b) Temperature dependence of refractive index $n\left(\omega \right)$ at frequency $\omega =0.4$ THz and in zero magnetic field. The vertical axis on the right-hand side indicates the real part of the dielectric function at 0.4 THz calculated from $n\left(\omega \right)=\sqrt{{\varepsilon }_1\left(\omega \right)}$.

Figure 6

Change in the refractive index $\mathrm{\Delta }n\left(\omega \right)$ (a) and absorption coefficient $\mathrm{\Delta }\alpha \left(\omega \right)$ (b) in applied magnetic field in CBCO with $x=0.05$ Ni content. Solid black line shows the fit to the Lorentz model and Eqs. (4) and (5). (c) The magnetic field dependence of $\mathrm{\Delta }n\left(\omega \right)$ at 0.4 THz.