Effect of a substrate on the magnetoelectric effect in rare-earth-doped bismuth iron garnet

The mechanism of relaxation of the electric polarization in thin films of rare-earth-doped bismuth iron garnet on glass and gallium gadolinium garnet substrates is determined in magnetic fields of 0 and 12 kOe in the temperature range of 80–380 K. The change in the sign of the residual electric polarization after switching off the electric field and the magnetic-field-induced shift of the hysteresis loop in the applied magnetic field are found. Linear and quadratic magnetoelectric effects with the tensor components depending on the substrate type are observed. The linear magnetoelectric effect is related to the spin-orbit coupling of electrons at the film-substrate interface, whereas the quadratic one is determined by the exchange-striction mechanism.