Analysis of measured transport properties of domain walls in magnetic nanowires and films

Existing data for soft magnetic materials of critical current for domain-wall motion, wall speed driven by a magnetic field, and wall electrical resistance show that all three observable properties are related through a single parameter: the wall mobility $\mu$. The reciprocal of $\mu$ represents the strength of viscous friction between domain wall and conduction-electron gas. And $\mu$ is a function of the wall width, which depends in turn on the aspect ratio $t∕w$, where $t$ and $w$ are the thickness and width of the sample. Over four orders of magnitude of $\mu$, the data for nanowires show $\mu \propto {(t∕w)}^{-2.2}$. This dependence is in approximate agreement with the prediction of the 1984 Berger theory based on $s\text{−}d$ exchange. On the other hand, it is inconsistent with the prediction of the 2004 Tatara and Kohno theory, and of the 2004 Zhang and Li theory.

Figure 1

Wall mobility $\mu$ versus aspect ratio $t∕w$ of cross section of sample. Plain circles represent $\mu$ values from measurements of critical current density $j_c$. Circles with a tail to the left represent $\mu$ values from measurements of domain-wall resistance $R_{dw}$, and those with a tail to the right represent direct measurements of $\mu$. The numbers in the circles indicate the references from which the data come. The dashed straight line is fitted to the nanowire data, and has a slope of $-2.2$. The solid curve is the prediction of the 1984 Berger theory [see Eqs. (7, 8, 9)]. The two dotted curves are the predictions of the Tatara and Kohno theory and of the Zhang and Li theory.