Anomalous spin exciton with a magnetoroton minimum in a quantum Hall ferromagnet at a filling factor $\nu =2$

In ZnO-based two-dimensional electron systems with strong Coulomb interaction, the anomalous spin-exciton branch is revealed. As probed by inelastic light scattering, in a ferromagnetic quantum-Hall state with the filling factor $\nu =2$, a spin exciton has a negative momentum dispersion with steepness dependent on the electron density. The negative dispersion of the spin exciton is associated with its interaction with higher-energy spin-flip modes that exist near $\nu =2$. Surprisingly, the anti-Stokes light scattering on spin excitons at ferromagnetic state $\nu =2$ is amplified by orders of magnitude, indicating the macroscopic accumulation of these excitations. The experimental findings are confirmed by the exact diagonalization method—these calculations show a magnetoroton minimum in the dispersion of spin excitons and also the attractive interaction between magnetoroton spin excitations.

Figure 1

(a) The schematic picture of the rotational stage, used for the Raman experiment with variable transferred momentum and in tilted magnetic field. (b) The cascade of Raman spectra of spin exciton at ferromagnetic $\nu =2$ and different values of the in-plane momentum (indicated next to curves). The flags are set on the centers of mass of the peaks. The calculated Zeeman energy position is shown by arrows. (c) The same sequence but for the paramagnetic state with $\nu =1.93$. Here the SE dispersion is negligible. (d) The processed momentum dispersion of SEs from panels (b) and (c). The single-particle Zeeman terms are subtracted from the energies. The dashed lines serve as a guide for the eyes. The inset shows a single-particle representation of SEs for FM and PM phases.

Figure 2

Plots of SE dispersions at the ferromagnetic phase of $\nu =2$ in the five studied samples. The energies are given minus the Zeeman term. The magnetic fields and tilt angles are indicated on the graphs. The abscissa is given in dimensionless wave vector $q{l}_B$ for corresponding normal magnetic fields. The lines are guides for the eyes.

Figure 3

(a) Left: The single-particle representation of the simplest spin-flip transitions at the ferromagnetic phase at $\nu =2$. Filled spin Landau levels are drawn by bold lines. Single-mode transitions (I–IV) are explicitly accounted in the HFA calculations below. Double-mode states V and VI with the same set of quantum numbers are examples of unaccounted terms. Right: The illustration of screening processes, caused by virtual inter-LL transitions, contributing to the RPA (random phase approximation) static dielectric function ${\varepsilon }_s\left(q\right)$ (see the text). (b) The comparison of SE momentum-dispersion at $\nu =2$ FM for the sample with $n_s=2.85\times {10}^{11}$ ${\mathrm{cm}}^{-2}$ obtained in experiment (solid symbols), exact diagonalization (open symbols) and screened HFA. (c) Dispersion curves of the two lowest SEs at $\nu =2$ FM for four different electron densities.

Figure 4

The plot of measured energies of the two interacting modes SE1 and SE2, probed by Raman scattering nearby ferromagnetic state at $\nu =2$. Note the increased magnetic field tilt angle $\mathrm{\Theta }={41}^{\circ }$ provides stable FM phase not just at $\nu =2$, but also in vicinity.

Figure 5

Calculated dispersion laws for the two lowest hybrid modes SE1 and SE2 and the dispersion of the twin-SE mode in the FM phase $\nu =2$. The diagram shows the double-exciton diagram of the twin-SE as the two clumped magnetoroton SEs with opposite momenta.

Figure 6

(a) The resonant Raman spectrum of the lowest SE mode, showing an anomalously strong signal of anti-Stokes component. The experimental details are given in the graph. (b) The log-log power-intensity dependence of both the Stokes and anti-Stokes components of SE. The fitted slope values are signed next to the data plots.