Rectification of spin currents in spin chains

We study spin transport in nonitinerant one-dimensional quantum spin chains. Motivated by possible applications in spintronics, we consider rectification effects in both ferromagnetic and antiferromagnetic systems. We find that the crucial ingredients in designing a system that displays a nonzero rectification current are an anisotropy in the exchange interaction of the spin chain combined with an offset magnetic field. For both ferromagnetic and antiferromagnetic systems we can exploit the gap in the excitation spectrum that is created by a bulk anisotropy to obtain a measurable rectification effect at realistic magnetic fields. For antiferromagnetic systems we also find that we can achieve a similar effect by introducing a magnetic impurity, obtained by altering two neighboring bonds in the spin Hamiltonian.

Figure 1

(a) Schematic view of the nonitinerant spin system. The 1D spin chain is adiabatically connected (see text) to two spin reservoirs. (b) A magnetic-field gradient $\Delta B$ gives rise to transport of magnetization through the spin chain, e.g., via spin waves. Depending on the exchange interaction ${\Delta }_i$ in the spin chain [see Eq. (1)], part of the spin current can be reflected. In a rectifying system, the magnitude of the spin current through the system depends on the sign of $\Delta B$.

Figure 2

Schematic view of the system under consideration (bottom) and the band structure for the ferromagnetic exchange interaction (top). The colored areas on the left and right in the top picture depict the filled states in the reservoirs. The position of the bottom of the band in the left reservoir depends on $\Delta B$. The striped area in the middle denotes the band of allowed states in the spin chain. It is seen that spin transport through the spin chain can be large for $\Delta B<0$, but only small for $\Delta B>0.$

Figure 3

Spin current as function of applied magnetic field for the parameters $J=10k_B$ J, $s=1$, $g=2$, $B_0=0.1$ $\text{T}$, $T=100$ $\text{mK}$, and $a=10$ $\text{nm}$. The spin currents for different anisotropies all saturate at the same positive value; this is the point where all the magnons incoming from the left reservoir are transmitted. This maximum current is on the order of ${10}^9$ magnons per second. Since the typical magnon velocity $\mathrm{v̄}={\mathit{Ja}}^2{k}_0/\hslash$ is on the order of ${10}^3$ $\text{m}$ ${\text{s}}^{-1}$, and assuming length $L\approx 1$ $\mu \text{m}$ for the spin chain, this is indeed within the single magnon regime.

Figure 4

Normalized rectification current $I_{\mathrm{r}}/\left|I_0\right|$ (main figure) and backscattering current $I_{\mathrm{BS}}/\left|I_0\right|$ (inset) as a function of the applied magnetic-field difference $\Delta B$ for different values of the exchange interaction $J$. Parameters are $K=0.63$, $B_0=750$ mT, and ${\Delta }^{\prime }=0.5$. The black dots in the main figure denote the values $\Delta B^{*}$ for which $\text{max}[|I_{\mathrm{BS}}(\Delta B^{*})|,|I_{\mathrm{BS}}(-\Delta B^{*})|]=|I_0(\Delta B^{*})|$. As explained in the text, our perturbative results are not valid for $\left|\Delta B\right|<\left|\Delta B^{*}\right|$.

Figure 5

$I_{\mathrm{BS}}/\left|I_0\right|$ as a function of the applied magnetic-field difference $\Delta B$ for different values of $K$. Parameters are $B_0=750$ mT, $J=100$ K, and ${\Delta }^{\prime }=0.5$. See the caption of Fig. 4 for the explanation of the black dots.

Figure 6

$I_{\mathrm{BS}}/\left|I_0\right|$ as a function of the applied magnetic-field difference $\Delta B$ for different values of $B_0$. Parameters are $K=0.63$, $J=100$ K, and ${\Delta }^{\prime }=0.5$. See the caption of Fig. 4 for the explanation of the black dots.