Total electron density distribution at (010) plane, the exact position of the slice is (0, 0.5, 0) in fractional coordinates. (a): La2SrAl2O7; (b): Gd2SrAl2O7.
Band structure of Ln2SrAl2O7 compounds, Ln = La, Nd, Sm, Eu, Gd, and Dy. The dashed line is the Fermi level.
Several possible magnetic structures of Ln2SrAl2O7 structures, for simplicity, only the sublattice of Ln3+ ions is shown. The arrows represent the spin directions, for instance, up for spin up electrons and down for spin down electrons. (a) Ferromagnetic state (FM); (b) Anti-ferromagnetic state-1 (AFM1); (c) AFM2; (d) AFM3.
Exchange coefficients in Heisenberg model for Ln3+ sublattice, J2 and J3 are the exchange interactions of the two square lattices, and J1 is the inter-layer exchange coefficient.
Calculated band gaps of 5s, 5p, and 4f orbitals between spin up and spin down channels due to the exchange splitting, respectively. Both LSDA and LSDA + U methods are applied. The unit is eV.
Spin magnetic moments of Ln3+ ions of Ln2SrAl2O7 structures in ferromagnetic (FM) and three anti-ferromagnetic (AFM) states, and ΔE represents the energy difference between FM and AFM states. The FM state is assumed to be the ground state. The magnetic moments of Ln3+ ions in the structures are also calculated using LSDA + U method for FM state only, and the results are listed in the table. The unit for energy difference is meV/cell, and for magnetic moment that is μB, one should note that for AFM structures, negative sign of magnetic moments merely refers to spin down direction.
Calculated magnetic properties of Ln2SrAl2O7 compounds in ferromagnetic state, including the ground state electronic configuration of Ln3+ ions, the spin angular momentum (S), orbital angular momentum (L), total angular momentum (L), Lander factor (g), and the magnetic moments of S, L and J, are shown. The spin magnetic moments are compared with LSDA and LSDA + U calculations, the unit of magnetic moment is Bohr magnetron (μB).
Article metrics loading...
Full text loading...