In a recent study, Viskadourakis et al. (arXiv:1111.0050) discovered that extremely underdoped La${}_2$CuO${}_{4+x}$ is a relaxor ferroelectric and a magnetoelectric material at low temperatures. It is further observed that the magnetoelectric response is anisotropic for different directions of electric polarization and applied magnetic field. By constructing an appropriate Landau theory, we show that a biquadratic magnetoelectric coupling can explain the experimentally observed polarization dependence on magnetic field. This coupling leads to several interesting low-temperature effects, including a feedback enhancement of the magnetization within the ferroelectric phase, and a predicted magnetocapacitive effect.

• Received 17 February 2012

DOI:https://doi.org/10.1103/PhysRevB.85.140405