Antiferromagnetic and ferromagnetic spintronics and the role of in-chain and inter-chain interaction on spin transport in the Heisenberg ferromagnet

Spin-transport and current-induced torques in ferromagnet heterostructures given by a ferromagnetic domain wall are investigated. Furthermore, the continuum spin conductivity is studied in a frustrated spin system given by the Heisenberg model with ferromagnetic in-chain interaction $$J_1<0$$ J 1 < 0 between nearest neighbors and antiferromagnetic next-nearest-neighbor in-chain interaction $$J_2>0$$ J 2 > 0 with aim to investigate the effect of the phase diagram of the critical ion single anisotropy $$D_c$$ D c as a function of $$J_2$$ J 2 on conductivity. We consider the model with the moderate strength of the frustrating parameter such that in-chain spin-spin correlations that are predominantly ferromagnetic. In addition, we consider two inter-chain couplings $$J_{\perp ,y}$$ J ⊥ , y and $$J_{\perp ,z}$$ J ⊥ , z , corresponding to the two axes perpendicular to chain where ferromagnetic as well as antiferromagnetic interactions are taken into account.