Spin-transport and current-induced torques in ferromagnet heterostruc-tures given by a ferromagnetic domain wall are investigated. Furthermore , the continuum spin conductivity is studied in a frustrated spin system given by the two-dimensional Heisenberg model with ferromagnetic in-chain interaction J 1 < 0 between nearest neighbors and antiferromagnetic next-nearest-neighbor in-chain interaction J 2 > 0 with aim to investigate the effect of the phase diagram of the critical ion single anisotropy D c as a function of 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 ⊥,y and J ⊥,z , corresponding to the two axes perpendicular to chain where ferromagnetic as well as antiferromagnetic interactions are taken into account.