Frequency-dependent transport through a spin chain

Motivated by potential applications in spintronics, we study frequency-dependent spin transport in nonitinerant one-dimensional spin chains. We propose a system that behaves as a capacitor for the spin degree of freedom. It consists of a spin chain with two impurities a distance $d$ apart. We find that at low energy (frequency), the impurities flow to strong coupling, thereby effectively cutting the chain into three parts, with the middle island containing a discrete number of spin excitations. At finite frequency, spin transport through the system increases. We find a strong dependence of the finite-frequency characteristics both on the anisotropy of the spin chain and the applied magnetic field. We propose a method to measure the finite-frequency conductance in this system.

Figure 1

(a) Schematic view of the nonitinerant spin system. The one-dimensional spin chain of finite length $L$ is adiabatically connected (meaning that the length of the transition region $L_t\gg 4a$) to two spin reservoirs. (b) Illustration of the working principle behind the spin capacitor. Strong impurities pin the field $\phi \left(\vec{r}\right)$, thereby blocking the system for spin transport.

Figure 2

(top) Plot of ${\log }_{10}\left|G_{\mathrm{BS}}\left(\omega \right)\right|$ [in units of ${\left(g{\mu }_B\right)}^2/h$] as a function of ${\log }_{10}(\omega /{\omega }_c)$ for different values of the Luttinger liquid interaction parameter $K$ (increasing from top to bottom). Used parameters are $B_0=70$ mT, $J={10}^2$ K, $L={10}^{6}a$, $d={10}^{4}a$, $K_r=1$, and $\Delta =0.3$. The black dots denote the frequencies ${\omega }^{*}$ where $|G_0\left({\omega }^{*}\right)|=|G_{\mathrm{BS}}\left({\omega }^{*}\right)|$. Our perturbative results cannot be used for $\omega <{\omega }^{*}$. (bottom) Idem for different values of $B_0$ (decreasing from top to bottom). Used parameters are $K=0.7$, $J={10}^2$ K, $L={10}^{6}a$, $d={10}^{4}a$, $K_r=1$, and $\Delta =0.3$. The oscillatory behavior is explained in the caption of Fig. 3 and the associated part in the text.

Figure 3

Backscattering conductance $G_{\mathrm{BS}}\left(\omega \right)$ as a function of $\omega /{\omega }_c$ for different values of the impurity separation $d$ (in units of $a$). Used values are $B_0=1.4$ T, $J={10}^2$ K, $L={10}^{4}a$, $K=0.7$, $K_r=1$, and $\Delta =0.2$. It is seen that, independent of $d$, the conductance oscillates with period $2\pi {\omega }_L$ [we estimate $({\omega }_L/{\omega }_c)\approx a/L$ here, the values for the free system]. The values of $d$ only influence the shape of the oscillations, not the period.