Controlling the magnetic anisotropy of Ru_mIr_n (m + n = 3) clusters using the MgO(001) substrate

Abstract

The large perpendicular magnetic anisotropy energy (MAE) and flexible regulation of the magnitude and direction of MAE have great potential in information storage devices. Here, utilizing the first-principles calculations, we...

Enhanced magnetic anisotropy of iridium dimers on antisite defects of two-dimensional transition-metal dichalcogenides

“…According to eqn (2), the MAE of Ir 2 @TMD nanosheets was determined by the matrix elements of the spin-orbital interaction for the d electrons between occupied and unoccupied states. Because of the rotational symmetry of Ir 2 , the 5d orbits of Ir element are split into groups d xy/x 2 Ày 2, d xy/yz , and d z 2, of which the non-zero matrix elements of the L z and L x operators 29,51,52 are…”

“…According to eqn (2), the MAE of Ir 2 @TMD nanosheets was determined by the matrix elements of the spin–orbital interaction for the d electrons between occupied and unoccupied states. Because of the rotational symmetry of Ir 2 , the 5d orbits of Ir element are split into groups d xy / x 2 − y 2 , d xy / yz , and d z 2 , of which the non-zero matrix elements of the L z and L x operators 29,51,52 are xz | L z | yz = 1, x 2 − y 2 | L z | xz = 2, xy | L x | xz = 1, x 2 − y 2 | L x | yz = 1 and , in units of ℏ. Then, the MAE can be obtained by analyzing the PDOS in a set energy range close to the Fermi energy, and can be expressed by the following formula:where MAE uu , MAE dd , and MAE ud refer to the contributions provided by each pair of orbitals to the MAE in the main spin (uu), minority spin (dd), and cross-spin (ud) states, respectively.…”