NMR response of nuclear-spin helix in quantum wires with hyperfine and spin-orbit interaction

We calculate the nuclear magnetic resonance (NMR) response of a quantum wire where at low temperature a self-sustained electron-nuclear spin order is created. Our model includes the electron mediated Ruderman-Kittel-Kasuya-Yosida (RKKY) exchange, electron spin-orbit interactions, nuclear dipolar interactions, and the static and oscillating NMR fields, all of which play an essential role. The paramagnet to helimagnet transition in the nuclear system is reflected in an unusual response: it absorbs at a frequency given by the internal RKKY exchange field, rather than the external static field, whereas the latter leads to a splitting of the resonance peak.

Figure 1

Absorption signal characteristics. Main (black): Center of the absorption line as a function of temperature $T$. Plot of the the power-law dependence of the NMR resonance Eq. (20) in the regions far away (left) and close (right) to the critical temperature $T_c$, with $\alpha =2g-3$. Right inset: Absorption as a function of NMR frequency (line profile), for zero (single peak, red; with $\hslash \omega \approx -2I{J}_{2k_F}$) and finite (double peak, green; with $\Delta =|{\epsilon }_{2k_F^{so}}^{-}Isin\theta |$) external $B$ field. Left inset (blue): $T_c$ as function of the Luttinger liquid parameter $0<K_{\rho }\le 1$ ($\equiv \text{noninteracting}$ limit).