Abstract
A superexchange mechanism between Eu${}^{2+}$ 4$f$ spins via the 3$d$ states of nonmagnetic Ti${}^{4+}$ ions is proposed through first-principles calculations based on a hybrid Hartree-Fock density functional approach to explain $G$-type antiferromagnetism in EuTiO${}_{3}$. This mechanism is supported by systematic calculations for related Eu${}^{2+}$-based perovskite oxides. In EuTiO${}_{3}$, the competition between the antiferromagnetic superexchange and an indirect ferromagnetic exchange via the Eu 5$d$ states leads to a delicate balance between antiferromagnetic and ferromagnetic phases. The superexchange mechanism involving the Ti 3$d$ states hints at the microscopic origin of the strong spin-lattice coupling in EuTiO${}_{3}$.
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