NMR probing of spin and charge order near odd-integer filling in the second Landau level

Studies of spin degrees of freedom near odd-integer filling $\nu =3$ in the second Landau level have engendered conflicting accounts of the spin properties in this regime. Using resistively detected NMR as a probe of local spin density, we explore the nature of the ground state in the quantum Hall regime near $\nu =3$. Our Knight shift measurements reveal anomalies in NMR spectral line shapes near $\nu =3$, which demonstrate the presence of solid phases formed from charged quasiparticles, with maximal spin polarization (i.e., no additional spin flips) at each $\nu$. The long nuclear spin relaxation times demonstrate the absence of Skyrmions, or spin textures, in this phase. On the basis of these observations, we attempt to reconcile conflicting reports on the quasiparticle properties and spin wave excitations at $\nu \sim 3$, which may engender new paradigms for the understanding of spin excitations in a collinear ferromagnet with broken translational symmetry.

Figure 1

(a) RD-NMR spectrum of ${}^{75}\mathrm{As}$ for $\nu =2$ and 3 at $B=5$ T. The thick solid line is a numerical fit to the $\nu =3$ spectrum. Inset shows the LL filling at each $\nu$. (b) Squared subband wave functions and quantum well potentials along the growth direction $z$ for filling factor $\nu \left(=3\right)$ of the probed state and that of the readout ${\nu }_{\mathrm{read}} \left(=0.61\right)$.

Figure 2

(a) RD-NMR spectra for several filling factors near $\nu =3$ at $B=5$ T and 50 mK. The vertical dashed line represents the bare resonance frequency. Solid (dashed) lines are fits (simulations) based on a uniform 2DES model using ${\alpha }_{\nu }$ as a parameter (assuming maximum ${\alpha }_{\nu }$ at each $\nu$). (b) $R_{xx}$ and $R_{xy}$ and (c) ${\alpha }_{\nu }$ extracted from the fits in (a). The shaded regions indicate the range where the uniform model fails. The line in (c) delimits the maximum ${\alpha }_{\nu }$ value for a uniform 2DES.

Figure 3

Measured and simulated RD-NMR spectra at $B=4$ T for (a) $\nu =3.1$ and $2.9$ and (b) other $\nu$. The vertical dashed line represents the bare resonance frequency. Dashed lines delimit simulations based on a uniform 2DES, while solid lines represent fits assuming a triangular lattice of quasiparticles, where $\sigma$ is used as a parameter. For comparison, simulated spectra for $\sigma ={\ell }_B$ are shown in (a) by dashed-dotted lines. (c) Top panel: Quasiparticle probability density ${\rho }_{\nu }(x,y)$ at $|{\nu }^{*}|=0.1$ for $\sigma =0$ and ${\ell }_B$. Bottom panel: Profiles of ${\rho }_{\nu }(x,y)$ and the local spin density $[=1-{\rho }_{\nu }(x,y)]$ along the lattice sites for $\sigma =0$ and ${\ell }_B$ (delimited by thin and thick lines, respectively). (d) $\sigma$ fit results.

Figure 4

Experimental and simulated RD-NMR spectra at varying temperatures at $B=5$ T for (a) $\nu =2.9$ and (b) $3.1$. The abscissa is the frequency shift from the bare resonance frequency, $f_0$. Dashed (solid) lines are simulations that assume a uniform 2DES (a Wigner crystal). The $\sigma /{\ell }_B$ values are 1.6, 1.4, 1.1 in both (a) and (b) for 300–100 mK, and 0.4 in (a) and 0.7 in (b) for 50 mK.

Figure 5

Nuclear spin relaxation time $T_1$ for several $\nu$ near $\nu =3$ ($B=5$ T) for $T=10$ and 300 mK.