Anomalous Hall effect driven by dipolar spin waves in uniform ferromagnets

An anomalous Hall effect is shown to arise from the exchange interaction of conduction electrons with dipolar spin waves in ferromagnets. This effect exists even in homogeneous ferromagnets without relativistic spin-orbit coupling. The leading contribution to the Hall conductivity is proportional to the chiral spin correlation of dynamical spin textures and is physically understood in terms of the skew scattering by dipolar magnons.

Figure 1

Chiral spin correlation ${\chi |}_{\mathrm{odd}}$. (a) As a function of ${\mathit{r}}_3=(x,y,0)$ for ${\mathit{r}}_1=(0,200,0), {\mathit{r}}_2=(0,-200,0)$, and ${\tau }_1={\tau }_2={\tau }_3$. The unit of length is Å. (b) As a function of $a=\left|{\mathit{r}}_1-{\mathit{r}}_2\right|$ at $(x,y)=(100,0)$, (100,400), and (400,400) plotted by red, blue, and green lines, respectively. As seen, ${\chi |}_{\mathrm{odd}}$ is odd in $x$ while oscillating in $x,y$, and $a$, consistent with the vanishing spatial average of ${\left(\mathit{a}\times \mathit{b}\right)}_z\chi$.

Figure 2

The diagrams contributing to ${\sigma }_{xy}$ at $J^3$. In terms of ${\mathcal{E}}_{xy}\left(1,2,3\right)$, there are only two configurations; those in the top row and those in the bottom. The three variations within each row occur due to the cyclic permutation of magnon arguments in Eq. (14). Electron-magnon vertices with one (two) wavy line(s) represent $x,y$ components ($z$ component) in $H_{sd}$.

Figure 3

(a) $(I_1-I_3)(I_1-2I_3)$ in Eq. (17) for $(k_t,k_z)=k_F(sin\theta ,cos\theta )$ as a function of $cos\theta$. Note that $k_{t}d\theta =-k_{F}d(cos\theta )$. (b) Hall conductivity evaluated by Monte Carlo integration (red dots) with a fit $|{\sigma }_{xy}|/{\sigma }_0=6.83\times {10}^{-8}\times T^{2.29}{e}^{-0.001/T}$ (blue line). Plain power-law fitting gives $\sim T^{2.48}$. The same parameter set as in Fig. 1 has been used along with $\mu =0.6\left[\mathrm{eV}\right]$.