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We present a study of terahertz frequency magnetoelectric effect inferrimagnetic pyroelectric CaBaCo$_4$O$_7$ and its Ni-doped variants. Theterahertz absorption spectrum of these materials consists of spin excitationsand low-frequency infrared-active phonons. We studied themagnetic-field-induced changes in the terahertz refractive index and absorptionin magnetic fields up to 17 T. We find that the magnetic field modulates thestrength of infrared-active optical phonons near 1.2 and 1.6 THz. We use theLorentz model of the dielectric function to analyze the measured magnetic-fielddependence of the refractive index and absorption. We propose that most of themagnetoelectric effect is contributed by the optical phonons near 1.6 THz andhigher-frequency resonances. Our experimental results can be used to constructand validate more detailed theoretical descriptions of magnetoelectricity inCaBaCo$_{4-x}$Ni$_x$O$_7$.

Terahertz frequency magnetoelectric effect in Ni doped CaBaCo$_4$O$_7$