NMR Probing of the Spin Polarization of the $\nu =5/2$ Quantum Hall State

Resistively detected nuclear magnetic resonance is used to measure the Knight shift of the ${}^{75}\mathrm{As}$ nuclei and determine the electron spin polarization of the fractional quantum Hall states of the second Landau level. We show that the $5/2$ state is fully polarized within experimental error, thus confirming a fundamental assumption of the Moore-Read theory. We measure the electron heating under radio frequency excitation and show that we are able to detect NMR at electron temperatures down to 30 mK.

Figure 1

(a) The NMR excitation and detection protocol as described in the text. (b) $R_{xx}$ as a function of gate voltage showing the detection point. (c) $R_{xx}$ versus applied radio frequency with a power of $-5\mathrm{dBm}$; under excitation at $\nu =5/2$ and detection at $\nu =2.16$ (red line) and a scan at the detection point (blue line). All measurements in this Letter are performed at $B=5\mathrm{T}$. Note that we have a remanent field of $-27\mathrm{mT}$, which reduces the effective magnetic field to $4.973\mathrm{T}$ [23].

Figure 2

(a) Resistivity ${\rho }_{xx}$ at $B=5\mathrm{T}$ versus gate voltage $V_G$ for various rf powers: $+1$, $-2$, $-8$, $-11$, and $-14\mathrm{dBm}$. The green curve is ${\rho }_{xx}$ at $T=13.5\mathrm{mK}$ without rf power. (b) ${\rho }_{xx}$ at filling factor $\nu =5/2$ versus the electron temperature. The dotted red line is a fit to ${\rho }_{xx}={\rho }_0+{\rho }_1\exp [-\Delta /2T]$ giving $\Delta \simeq 300\mathrm{mK}$. (c) Electron temperature versus rf power. Below $-14\mathrm{dBm}$, the temperature is limited by the current $I=30\mathrm{nA}$. The red triangles correspond to $I=5\mathrm{nA}$.

Figure 3

Change of the longitudinal resistance $\Delta R$ as a function of radio frequency ($f-f_0$), where $f_0$ is the resonance frequency at $\nu =2$. The rf power is here $-11\mathrm{dBm}$. Inset: Knight shift as a function of the filling factor. The red dotted line corresponds to full electron polarization according to the shift obtained at $\nu =5/3$.

Figure 4

(a) NMR signal at $\nu =5/2$ for different rf powers. (b) Electron spin polarization at $\nu =5/2$ as a function of $T/\Delta$. To further reduce the heat load on the sample at the lowest rf powers, the current is reduced to $I=1\mathrm{nA}$ during the excitation phase. NMR signal (c) and the resistivity together with the electron spin polarization (d) in the vicinity of $\nu =5/2$ at rf power $-14\mathrm{dBm}$. Note the correspondence of the symbols in (a)–(b) and in (c)–(d).