Nuclear spin relaxation in the SU(4) spin-pseudospin intertwined skyrmion regime in the $\nu =1$ bilayer quantum Hall state

We investigate the electron spin degree of freedom in imbalanced density $\nu =1$ bilayer quantum Hall states using the resistively detected nuclear-spin–lattice relaxation rate $1/T_1$. The values of $1/T_1$ in imbalanced states increase rapidly in the vicinity of $\nu =1$, similar to the phenomenon that is observed in the region in which skyrmion crystals are formed. Furthermore, the value of $1/T_1$ in the back layer (the layer from which electrons are transferred to the front layer) also increases in the intermediate imbalanced state. These results indicate that the low-energy electron-spin mode, similar to the mode observed in skyrmion crystals, exists across the two layers. We suggest that such a mode arises in spin-pseudospin intertwined SU(4) skyrmions.

Figure 1

$1/T_1$ measurement procedure using nuclear-spin polarization and relaxation in the monolayer $\nu =2/3$ QHS. (a) Typical example of time evolution of $R_{xx}$. Inset: Expanded view of the trace at which the magnitude of resistance changes is measured [open circle in the main figure] after nuclear-spin relaxation for $\tau$ seconds. (b) Plot of $\Delta R_{xx}$ as a function of $\tau$. The curve is the result of fitting.

Figure 2

Image plot of $R_{xx}$ as a function of the front and back gate voltages, $V_f$ and $V_b$, at $B=6.0$ T.

Figure 3

$1/T_1$ as a function of $\nu$ around the $\nu =1$ QHS for various values of $\sigma$, from 0 to 1.

Figure 4

Data set for $1/T_1$ as a function of $\sigma$ for the front and back layers at $\nu =0.9$ and $\nu =1.0$.