In a recent study Viskadourakis et al. discovered that extremely underdoped La_2CuO_(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 bi-quadratic magnetoelectric coupling can explain the experimentally observed polarization dependence on magnetic field. This coupling leads to several novel low-temperature effects including a feedback enhancement of the magnetization below the ferroelectric transition, and a predicted magnetocapacitive effect.
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