First-principles approach to investigate toroidal property of magnetoelectric multiferroic GaFeO₃

A first-principles approach incorporating the concept of toroidal moments as a measure of the spin vortex is proposed and applied to simulate the toroidization of magnetoelectric multiferroic GaFeO₃. The nature of space-inversion and time-reversal violations of ferrotoroidics is reproduced in the simulated magnetic structure of GaFeO₃. For undoped GaFeO₃, a toroidal moment of −22.38 μ_B Å per unit cell was obtained, which is the best theoretical estimate till date. Guided by the spin vortex free-energy minimization perturbed by an externally applied field, it was discovered that the minority spin markedly biases the whole toroidization. In summary, this approach not only calculates the toroidal moment but provides a way to understand the toroidal nature of magnetoelectric multiferroics