Magnetic anisotropy in Li-phosphates and origin of magnetoelectricity in LiNiPO4

Li-based phosphates are paradigmatic materials for magnetoelectricity. By means of first-principles calculations, we elucidate the microscopic origin of spin anisotropy and of magnetoelectric effects in LiNiPO4. The comparison with LiCoPO4 reveals that Co-d7 and Ni-d8 electronic clouds show distinct orbital shapes, which in turn result in an opposite trend of the local spin anisotropy with respect to the surrounding O6 cages. Due to magnetic anisotropy, the Ni-based phosphate shows a peculiar "angled-cross" spin ground-state, which is responsible for magnetoelectricity. In this respect, we show that, under a magnetic field Hx, an electronic polarization Pz arises, with an estimated linear magneto-electric coefficient in good agreement with experiments.