Large spin splitting in the conduction band of transition metal dichalcogenide monolayers

We study the conduction band spin splitting that arises in transition metal dichalcogenide (TMD) semiconductor monolayers such as MoS2, MoSe2, WS2, and WSe2 due to the combination of spin-orbit coupling and lack of inversion symmetry. Two types of calculation are done. First, density functional theory (DFT) calculations based on plane waves that yield large splittings, between 3 and 30 meV. Second, we derive a tight-binding model that permits to address the atomic origin of the splitting. The basis set of the model is provided by the maximally localized Wannier orbitals, obtained from the DFT calculation, and formed by 11 atomiclike orbitals corresponding to d and p orbitals of the transition metal (W, Mo) and chalcogenide (S, Se) atoms respectively. In the resulting Hamiltonian, we can independently change the atomic spin-orbit coupling constant of the two atomic species at the unit cell, which permits to analyze their contribution to the spin splitting at the high symmetry points. We find that—in contrast to the valence band—both atoms give comparable contributions to the conduction band splittings. Given that these materials are most often n-doped, our findings are important for developments in TMD spintronics.

Electronic properties of transition metal atoms on Cu2N/Cu(100)

We study the nature of spin excitations of individual transition metal atoms (Ti, V, Cr, Mn, Fe, Co, and Ni) deposited on a Cu2N/Cu(100) surface using both spin-polarized density functional theory (DFT) and exact diagonalization of an Anderson model derived from DFT. We use DFT to compare the structural, electronic, and magnetic properties of different transition metal adatoms on the surface. We find that the average occupation of the transition metal d shell, main contributor to the magnetic moment, is not quantized, in contrast with the quantized spin in the model Hamiltonians that successfully describe spin excitations in this system. In order to reconcile these two pictures, we build a zero bandwidth multi-orbital Anderson Hamiltonian for the d shell of the transition metal hybridized with the p orbitals of the adjacent nitrogen atoms, by means of maximally localized Wannier function representation of the DFT Hamiltonian. The exact solutions of this model have quantized total spin, without quantized charge at the d shell. We propose that the quantized spin of the models actually belongs to many-body states with two different charge configurations in the d shell, hybridized with the p orbital of the adjacent nitrogen atoms. This scenario implies that the measured spin excitations are not fully localized at the transition metal.

Derivation of the spin Hamiltonians for Fe in MgO

A method to calculate the effective spin Hamiltonian for a transition metal impurity in a non-magnetic insulating host is presented and applied to the paradigmatic case of Fe in MgO. In the first step we calculate the electronic structure employing standard density functional theory (DFT), based on generalized gradient approximation (GGA), using plane waves as a basis set. The corresponding basis of atomic-like maximally localized Wannier functions is derived and used to represent the DFT Hamiltonian, resulting in a tight-binding model for the atomic orbitals of the magnetic impurity. The third step is to solve, by exact numerical diagonalization, the N electron problem in the open shell of the magnetic atom, including both effects of spin–orbit and Coulomb repulsion. Finally, the low energy sector of this multi-electron Hamiltonian is mapped into effective spin models that, in addition to the spin matrices S, can also include the orbital angular momentum L when appropriate. We successfully apply the method to Fe in MgO, considering both the undistorted and Jahn–Teller (JT) distorted cases. Implications for the influence of Fe impurities on the performance of magnetic tunnel junctions based on MgO are discussed.