Rapid Collapse of Spin Waves in Nonuniform Phases of the Second Landau Level

The spin degree of freedom in quantum phases of the second Landau level is probed by resonant light scattering. The long wavelength spin wave, which monitors the degree of spin polarization, is at the Zeeman energy in the fully spin-polarized state at $\nu =3$. At lower filling factors, the intensity of the Zeeman mode collapses, indicating loss of polarization. A novel continuum of low-lying excitations emerges that dominates near $\nu =8/3$ and $\nu =5/2$. Resonant Rayleigh scattering reveals that quantum fluids for $\nu <3$ break up into robust domain structures. While the state at $\nu =5/2$ is considered to be fully polarized, these results reveal unprecedented roles for spin degrees of freedom.

Figure 1

Evidence of loss of spin polarization away from $\nu =3$. (a) Color plot of resonant inelastic light scattering spectra with varying magnetic field shows the SW at the Zeeman energy $E_Z$. The intensity of the SW attenuates away from $\nu =3$ ($B_T=5.32\mathrm{T}$). The top inset shows the light scattering geometry. The bottom inset exhibits a spectrum at $\nu =3.01$. (b) $N=1$ optical emission involved in resonance enhancement of light scattering ($B_T=5.3\mathrm{T}$, $\theta =20°$, $T=40\mathrm{mK}$). The left inset shows the two step inelastic light scattering process for the SW. The right inset is the energy level diagram for optical emission from the $N=1,\uparrow$ LL.

Figure 2

Coexistence of novel quantum phases with the ferromagnetic SW. (a) Tuning ${\omega }_L$ for excitations at a filling factor slightly away from $\nu =3$ ($\nu =2.9$, $B_T=5.5\mathrm{T}$, $T=40\mathrm{mK}$) induces the collapse of the SW and the emergence of a continuum of low-lying energy excitations. The SW resonance is at higher ${\omega }_L$ than that of the continuum. (b) We monitor the behavior of the continuum while tuning the filling factor [30]. We track two distinct modes below $\nu =3$—the SW and continuum. The insets show the SW collapse, while the main panel shows the emergence of the continuum. The continuum is resonant at slightly lower laser energy ${\omega }_L(B)$ than the SW.

Figure 3

Temperature dependence measurements at various filling factors of low-lying modes. The continuum (black lines) melts at elevated temperature. The SW (red lines) reemerges at elevated temperature for $\nu \simeq 8/3$ ($B_T=6.0\mathrm{T}$) and $5/2$ ($B_T=6.42\mathrm{T}$; in the red spectrum at 2 K, there is a glitch at $E_Z$ not visible on the scale shown). The dashed line in the lower left panel is a guide to the eye.

Figure 4

RRS resonance profiles for $\nu =3.01$, 2.9, 2.66, and 2.49. No resonance enhancement is seen for the ferromagnetic state at $\nu =3$. At $\nu =2.9$, some structure in the resonance profile develops. At $\nu =2.66$ and $\nu =2.49$, a resonance is seen at $E_{1,\uparrow }$. Black dashed lines represent optical emission, while colored peaks represent elastically scattered light intensity. Diamonds (stars) represent the spectra in which the SW (continuum) has a maximum resonance.

Figure 5

Temperature dependence of the RRS profile for $\nu \sim 5/2$. Optical emission spectra (continuous lines) along with the laser peak heights (scatter plots) of RRS intensity are displayed. A peak in the resonance enhancement of the elastically scattered light coincides with the maximum intensity of the continuum and is attenuated at elevated temperatures. The inset shows the relationship between $I_{\mathrm{RRS}}$ and temperature. The solid line is a fit to the data using the Langmuir isotherm [24].