AbstractSpin-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.