Spiral exchange coupling in trilayer magnetic junction mediated by diluted-magnetic-semiconductor thin film

Abstract

Electron carrier concentration dependent magnetization and transport properties in ZnO:Co diluted magnetic semiconductor thin films Exchange coupling between two magnetic films separated by an antiferromagnetic spacer

Spatial trends of noncollinear exchange coupling mediated by itinerant carriers with different Fermi surfaces

“…The twocomponent spinors ⌿ † and ⌿ are the creation/annihilation operators for the itinerant carriers. After integrating out the itinerant carriers, 23,[25][26][27] the exchange coupling between the ferromagnetic layers is described by an effective Heisenberg Hamiltonian,…”

“…Within the linear-response theory, 28,29 the mediated exchange coupling J ij is proportional to the static spin susceptibility tensor, 23,[25][26][27] ij ͑r, ͒ = ΄ g 0 + g 2 cos 2 g 2 sin 2 g 1 cos…”

“…The twocomponent spinors Ψ † , Ψ are the creation/annihilation operators for the itinerant carriers. After integrating out the itinerant carriers 23,24,29,30 , the exchange coupling be-tween the ferromagnetic layers is described by an effective Heisenberg Hamiltonian, H eff = ij J ij S i L S j R . Within the linear response theory 31,32 , the mediated exchange coupling J ij is proportional to the static spin susceptibility tensor, 23,24,29,30…”