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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    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$J_1<0$$\end{document}J  1   <  0between nearest neighbors and antiferromagnetic next-nearest-neighbor in-chain interaction    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$J_2>0$$\end{document}J  2   >  0with aim to investigate the effect of the phase diagram of the critical ion single anisotropy    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$D_c$$\end{document}    D  cas a function of    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$J_2$$\end{document}    J  2on 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    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$J_{\perp ,y}$$\end{document}    J   ⊥  ,  yand    \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$J_{\perp ,z}$$\end{document}    J   ⊥  ,  z, corresponding to the two axes perpendicular to chain where ferromagnetic as well as antiferromagnetic interactions are taken into account.

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