Persistent Charge and Spin Currents in a Ferromagnetic Hatano-Nelson Ring

TL;DR

This paper studies persistent charge and spin currents in a ferromagnetic Hatano–Nelson ring with anti-Hermitian intradimer hopping, where non-reciprocity induces a synthetic flux $\Phi = N\phi$ and a non-Hermitian Aharonov–Bohm effect. A tight-binding model with dimerization and ferromagnetic exchange is analyzed, deriving the dispersion $E_{s,\alpha}(k+\phi)=\epsilon + s\mathpzc{h} + \alpha \sqrt{t_2^2 - |t_1|^2 + 2 i |t_1| t_2 \sin(k+\phi)}$ and computing persistent currents via a biorthogonal current operator framework. The results reveal a spin-split real spectrum while the imaginary spectrum remains spin-degenerate, flux-driven oscillations of both real and imaginary currents across topological regimes, and disorder-induced amplification of spin currents explained through the imaginary part of the biorthogonal spin-bond overlap. The study provides a framework for controlling spin transport in non-Hermitian topological systems and suggests avenues for non-Hermitian spintronics experiments.

Abstract

We investigate persistent charge and spin currents in a ferromagnetic Hatano-Nelson ring with anti-Hermitian intradimer hopping, where non-reciprocal hopping generates a synthetic magnetic flux and drives a non-Hermitian Aharonov-Bohm effect. The system supports both real and imaginary persistent currents, with ferromagnetic spin splitting enabling all three spin-current components, dictated by the orientation of magnetic moments. The currents are computed using the current operator method within a biorthogonal basis. In parallel, the complex band structure is analyzed to uncover the spectral characteristics. We emphasize how the currents evolve across different topological regimes, and how they are influenced by chemical potential, ferromagnetic ordering, finite size, and disorder. Strikingly, disorder can even amplify spin currents, opening powerful new routes for manipulating spin transport in non-Hermitian systems.

Figures (15)

• Figure 1: (Color online.) Schematic representation of the magnetic Hatano-Nelson ring. The yellow and cyan colored balls correspond to the $A$ and $B$ sublattices, respectively. The red arrows on each site indicate the orientation of the local magnetic moments, which are tilted with respect to the $z$-quantization axis. The intradimer hopping amplitudes are denoted by $t_c$ (clockwise, green) and $t_a$ (counterclockwise, blue), while the interdimer hopping amplitude is represented by $t_2$.
• Figure 2: (Color online.) Complex band structure as a function of $t_1$. Bands are computed using Eq. \ref{['dispers']}. (a) Real and (b) imaginary parts of $E(k)$ with $\mathpzc{h}=0$. (c) Real and (d) imaginary parts of $E(k)$ with $\mathpzc{h}=0.5$. The colors represent different spin states: red for $E_\downarrow^+$, blue for $E_\downarrow^-$ green for $E_\uparrow^+$, and orange for $E_\uparrow^-$.
• Figure 3: (Color online.) Complex energy spectra $E(k)$ in momentum space for three representative values of the intradimer hopping amplitude $t_1$, with fixed interdimer hopping $t_2 = 1$ and spin-dependent scattering parameter $\mathpzc{h} = 0$. Panels (a-b), (c-d), and (e-f) correspond to $\lvert t_1 \rvert = 0.75$, $1.0$, and $1.25$, respectively. Left column (a, c, e): real part of the spectrum $\mathrm{Re}[E(k)]$; right column (b, d, f): imaginary part $\mathrm{Im}[E(k)]$. The color codes for the bands are identical to those in Fig. \ref{['t1var']}.
• Figure 4: (Color online.) Complex energy spectra $E(k)$ in momentum space for three representative values of the intradimer hopping amplitude $t_1$, with fixed interdimer hopping $t_2 = 1$ and spin-dependent scattering parameter $\mathpzc{h} = 0.5$. Panels (a-b), (c-d), and (e-f) correspond to $\lvert t_1 \rvert = 0.75$, $1.0$, and $1.25$, respectively. Left column (a, c, e): real part of the spectrum $\mathrm{Re}[E(k)]$; right column (b, d, f): imaginary part $\mathrm{Im}[E(k)]$. The color codes for the bands are identical to those in Fig. \ref{['t1var']}.
• Figure 5: (Color online.) Real and imaginary energy eigenspectra as a function of the normalized magnetic flux $\Phi/\pi$. The first, second, and third columns correspond to $t_1 = 0.75$, $1$, and $1.25$, respectively. The number of unit cells is $N = 8$ and the interdimer hopping strength is $t_2 = 1$, with $\mathpzc{h} = 0.5$. Red and cyan colors denote the up- and down-spin sectors, respectively.