Anomalous Hall effect in IV-VI magnetic semiconductors

Abstract

Topological contribution to the anomalous Hall effect in IV-VI narrow-gap semiconductors with a nonzero spontaneous magnetization due to magnetic impurities is considered theoretically. The off-diagonal conductivity is calculated in the relativistic model of the IV-VI semiconductors. Spin-orbit interaction in these compounds is strong and cannot be treated perturbatively. Therefore, it is included in the Hamiltonian of a clean ͑defect-free͒ system. Geometrical interpretation of the topological contribution to the Hall conductivity is also briefly discussed.

Intrinsic spin Hall effect in silicene: transition from spin Hall to normal insulator

“…The density of spin current in the silicene plane can be written as where is the spin conductivity with being the n ‐th component of electron spin, and is the j ‐th component of the in‐plane electric field. The quantum‐mechanical operator of spin current density may be defined as where is the velocity operator Upon calculating spin current as the expectation value of the spin current operator in the linear response theory, one finds the zero‐frequency spin Hall conductivity is given by the formula 12, 13…”

“…Calculating the appropriate Green's functions and following the general procedure 13, one finds the spin Hall conductivity from Eq. (3).…”

Thermally induced spin polarization in a magnetized two-dimensional electron gas with Rashba spin-orbit interaction

“…( 17) for the spin polarization in the bare bubble approximation leads to their multiplication by a factor 1 + γ = 2/(1 − 2β). This renormalization factor is equal to that found in the case of the spin polarization induced by an external electric field 42 . Note, the parameter β in Eqs.…”

“…The key steps of the derivation of the above formula are described elsewhere 38,42 . Equation ( 6) is our starting expression for further considerations.…”

“…( 27) and ( 28) is equivalent to the parameter β introduced in Ref. 42. It is also worth noting that in Ref.42 the velocity vertex was renormalized, whereas here we renormalized the spin vertex.…”