Theoretical Study of the Magnetoelectric Effect in Tb ₂ (MoO ₄ )O ₃

We present, for the first time, a microscopic model describing the magnetoelectric effect in Tb 2 (MoO 4 )O 3 . By employing the Green’s function theory, we calculate the temperature and magnetic field dependencies of the magnetization, polarization, and dielectric constant. The results reveal a strong magnetic anisotropy in both the magnetization M c and the polarization P c . Furthermore, we demonstrate the magnetic field control of P c at 420 K for different orientations of the magnetic field h . This result may lead to the design of multiferroics at high temperatures. Due to the magnetoelectric coupling, the temperature dependence of the polarization P c ( T ) exhibits a weak anomaly at the Neel temperature T N , which disappears upon applying a magnetic field h b . At the Curie temperature T C , the dielectric constant displays a sharp peak that becomes broader and reduced in magnitude in the presence of h b .