Spin-orbital effects in magnetized quantum wires and spin chains

We present analysis of the interacting quantum wire problem in the presence of magnetic field and spin-orbital interaction. We show that an interesting interplay of Zeeman and spin-orbit terms, facilitated by the electron-electron interaction, results in the spin-density wave (SDW) state when the magnetic-field and spin-orbit axes are orthogonal. We show that this instability is enhanced in a closely related problem of Heisenberg spin chain with asymmetric uniform Dzyaloshinskii-Moriya (DM) interaction. Magnetic field in the direction perpendicular to the DM anisotropy axis results in staggered long-range magnetic order along the orthogonal to the applied field direction. We explore consequences of the uniform DM interaction for the electron-spin-resonance (ESR) measurements, and point out that they provide way to probe right- and left-moving excitations of the spin chain separately.

Figure 1

(Color online) Occupied subbands ${ϵ}_{\pm }$ of Eq. (4). Arrows illustrate spin polarization in different subbands. Dashed (dotted) lines indicate exchange (direct) Cooper scattering processes.

Figure 2

(Color online) Asymmetric back-scattering processes.

Figure 3

RG flow of Eq. (49).

Figure 4

(Color online) Occupied subbands ${ϵ}_{\pm }$ for the case of nonorthogonal spin-orbital and magnetic-field axes. Arrows illustrate spin polarization, as in Fig. 1. Filled dots indicate location of the center-of-mass for $(+)$ (red) and $(-)$ (blue) subbands. Dashed lines show $(\pm )$ subbands of Fig. 1, corresponding to the orthogonal orientation, $\beta =0$, for comparison.

Figure 5

(Color online) Band structure in the absence of magnetic field. Note the absence of the gap between the subbands at $k=0$.