Nonlocal Polarization Feedback in a Fractional Quantum Hall Ferromagnet

In a quantum Hall ferromagnet, the spin polarization of the two-dimensional electron system can be dynamically transferred to nuclear spins in its vicinity through the hyperfine interaction. The resulting nuclear field typically acts back locally, modifying the local electronic Zeeman energy. Here we report a nonlocal effect arising from the interplay between nuclear polarization and the spatial structure of electronic domains in a $\nu =2/3$ fractional quantum Hall state. In our experiments, we use a quantum point contact to locally control and probe the domain structure of different spin configurations emerging at the spin phase transition. Feedback between nuclear and electronic degrees of freedom gives rise to memristive behavior, where electronic transport through the quantum point contact depends on the history of current flow. We propose a model for this effect which suggests a novel route to studying edge states in fractional quantum Hall systems and may account for so-far unexplained oscillatory electronic-transport features observed in previous studies.

Figure 1

(a) Schematic of the sample. Crosses represent Ohmic contacts, voltage probes are indicated by dotted lines. Top-gate-defined QPCs with gaps ranging from 800 nm to $2.8\mu \mathrm{m}$ in the central region, two are shown in the inset (SEM image). (b) Bulk Hall resistance and diagonal resistance measured across a QPC with 1800 nm lithographic gap at a bath temperature of 70 mK with $-0.75\mathrm{V}$ applied to the corresponding gates. Dashed lines indicate $B=6.71$ and $B=6.79\mathrm{T}$. (c) to (f) Time traces of the longitudinal differential resistance. The bias current and the magnetic field are indicated on the top of each graph. (g) The dc bias current is set to zero for 10 sec, at three different points in consecutive periods. The differential longitudinal resistance drops, and oscillations continue after the original bias is restored. (h) The dc bias is interrupted for 100 sec. (i) Interruption of the dc bias for 57 min, a time span of aperiodic fluctuations is subsequently observed.

Figure 2

Model for self-oscillations driven by DNP. (a) A spin-polarized electron domain resides in the constriction, with degree of polarization $\sigma$, resulting in different transmissions for quasiparticles with up- and down-spins. Spin filtering leads to spin accumulation outside the constriction region, which is transferred to nuclei with polarization $p$ and $-p$. Through nuclear spin diffusion, DNP ($q$) builds up in the constriction, destabilizing the polarized domain. When the domain shrinks the spin filtering effect stops; after the DNP diffuses away the domain reforms and oscillations result. (b) to (d) Time-dependent oscillations produced by the model system (1). Parameter values are given in the text.

Figure 3

Influence of asymmetric gate voltage configurations (indicated on top) on the differential longitudinal resistance measured across a QPC with 2000 nm gap at $B=6.1\mathrm{T}$ with a bias current of $-10\mathrm{nA}$.

Figure 4

(a) Top (red curve): Differential resistance across a QPC with 2400 nm gap measured while irradiating the sample with rf. The rf frequency is incremented at regular time intervals. Oscillations driven by a dc current of 9 nA are suppressed when the rf frequency is close to the resonance frequency of ${}^{75}\mathrm{As}$. Bottom (pink curve): Simultaneously measured differential resistance in the bulk of the sample. Note the different scale on the $y$ axis. (b) Response to short irradiation at resonance frequency of ${}^{75}\mathrm{As}$, ${}^{69}\mathrm{Ga}$, and ${}^{71}\mathrm{Ga}$ for 10 sec each during the time interval indicated by a green bar, coinciding with a transient nonlinearity in the current-voltage characteristics. Aperiodic fluctuations of $R_{\text{Diag}}$ are observed during the time highlighted in yellow. (c) and (d) Response to the same rf sequence as in (b) applied when dc and differential resistances evolve similarly.

Figure 5

Bias dependence of resistance oscillations in a QPC with 1800 nm gap at $B=6.745\mathrm{T}$. The absolute value of dc bias is indicated on the left. Each $y$ axis spans $3.5\mathrm{k}\mathrm{\Omega }$ and a single tick indicates the average resistance.