Ab initio study on exchange integrals and magnetic anisotropy change of BaFe12-xScxO19 (x=0, 0.5, 1, 1.5, 2)

We investigate the exchange integrals and magnetic anisotropy change in Sc substituted barium hexaferrite BaFe12-xScxO19 (x = 0, 0.5, 1, 1.5, 2) by density functional theory (DFT) calculations. The general gradient approximation (GGA) with on-site coulomb repulsion U (GGA + U) method was used to improve the description of the strongly correlated 3d electrons of Fe. Our calculations reveal that Sc3+ preferentially replace Fe3+ at the 4f(2) and 2b sites successively. The total energies of 9 spin configurations are calculated to obtain 8 inter-sublattice exchange integrals for different values of x. Comparison of the exchange integrals between BaFe12O19 (BFO) and BaFe12-xScxO19 (x = 0.5, 1, 1.5, 2) (BFSO) shows that substituting Sc for Fe influences most interactions involving the 4f(2) sites. The f(1)-f(2) and f(2)-k interactions decreases as substitution increases, while the b-f(2) interaction fluctuates significantly as x changes. Magnetic anisotropy change of Sc substituted M-type barium hexaferrite (Ba-M hexaferrite) has been studied by using the force theorem method. The results show that Sc3+ in its preferred 4f(2) and 2b sites contribute to the decrease of the uniaxial magnetic crystal anisotropy. The magnetic anisotropy of BFSO transforms from uniaxial to planar with transition point in the range of 1 < x < 1.5.