Spin-Orbit-Coupling-Induced Domain-Wall Resistance in Diffusive Ferromagnets

We investigate diffusive transport through a number of domain wall (DW) profiles of the important magnetic alloy Permalloy taking into account simultaneously noncollinearity, alloy disorder, and spin-orbit-coupling fully quantum mechanically, from first principles. In addition to observing the known effects of magnetization mistracking and anisotropic magnetoresistance, we discover a not-previously identified contribution to the resistance of a DW that comes from spin-orbit-coupling-mediated spin-flip scattering in a textured diffusive ferromagnet. This adiabatic DW resistance, which should exist in all diffusive DWs, can be observed by varying the DW width in a systematic fashion in suitably designed nanowires.

Figure 1

Schematic illustration of the magnetic configurations of (a) Bloch, (b) rotated Néel, and (c) Néel DWs. (d) Sketch of the scattering geometry used in the calculations in which a finite thickness of ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ substitutional alloy is sandwiched between semiinfinite copper leads and alloy disorder is modelled using a lateral supercell periodically repeated in the $x\mathrm{\text{−}}y$ plane. Transport is in the $z$ direction.

Figure 2

DWR of ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ Bloch DWs with Walker (a) and Linear (b) profiles as a function of the respective width parameters. For each length, we typically consider 10 different disorder configurations and the error bars are a measure of the spread of the results. Insets: DWR replotted as a function of $1/{\lambda }_{\mathrm{W}(\mathrm{L})}$.

Figure 3

(a) Difference between the resistivities of spin-spiral ($\rho$) and collinear (${\rho }_0$) Py. The solid line is a linear fit to the data with SOC, yielding a slope $0.102\pm 0.011\mathrm{f}\Omega {\mathrm{m}}^2$ in good agreement with the saturated DWR in Fig. 2. (b) Calculated saturation value of the DWR for Py Walker Bloch DWs as a function of the SOC strength. The solid line shows a quadratic fitting. The vertical dashed line indicates the true SOC strength.

Figure 4

DWRs of ${\mathrm{Ni}}_{80}{\mathrm{Fe}}_{20}$ Néel ($R_{\mathrm{DW}}^{\mathrm{N}}$) and rotated Néel ($R_{\mathrm{DW}}^{\mathrm{RN}}$) DWs with the Walker profile as a function of the width ${\lambda }_{\mathrm{W}}$. The dash-dotted lines show the DWRs after subtracting the AMR contributions described by Eq. (2). Inset: difference between the DWRs for Néel and rotated Néel walls. The thick line shows the analytical form $4{\lambda }_{\mathrm{W}}({\rho }_{\parallel }-{\rho }_{\perp })$ with ${\rho }_{\parallel (\perp )}$ taken from independent calculations for collinear Py [16].