A magnet can point up or down in a magnetic field. In magnetic materials, information is stored digitally by using two such "states" to represent ones and zeros. A proposal to store information in high-density "racetrack" memories has focussed attention on how electric currents in a magnetic material are affected by twisting of the magnetism in between regions - "domains" - where the magnetism is either all "up" or all "down". By performing extensive quantum mechanical calculations on a supercomputer, we find that a twist in the magnetism - a "domain wall" (Fig.1) - makes a finite contribution to the resistance of a material no matter how slowly the twisting occurs, when a relativistic effect, the spin-orbit coupling, is taken into account. Our finding for domain walls in the technologically important Ni_{80}Fe_{20} magnetic alloy, Permalloy, contradicts received wisdom for disordered materials and suggests that it should be possible to detect the number of domain walls in a nanowire with just electrical transport measurements.

In this work, we investigated diffusive transport through a number of domain wall (DW) profiles (Fig.1) of 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 discovered 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.

- Z. Yuan, Y. Liu, A.A. Starikov, P.J. Kelly and A. Brataas,
*Spin-Orbit-Coupling-Induced Domain-Wall Resistance in Diffusive Ferromagnets,*Phys. Rev. Lett. 1**09**, 267201 (2012)

**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 Ni_{80}Fe_{20} substitutional alloy is sandwiched between semiinfinite copper leads and alloy disorder is modelled using a lateral supercell periodically repeated in the x-y plane. Transport is in the z direction.