Observation of Nonconventional Spin Waves in Composite-Fermion Ferromagnets

We find unexpected low energy excitations of fully spin-polarized composite-fermion ferromagnets in the fractional quantum Hall liquid, resulting from a complex interplay between a topological order manifesting through new energy levels and a magnetic order due to spin polarization. The lowest energy modes, which involve spin reversal, are remarkable in displaying unconventional negative dispersion at small momenta followed by a deep roton minimum at larger momenta. This behavior results from a nontrivial mixing of spin-wave and spin-flip modes creating a spin-flip excitonic state of composite-fermion particle-hole pairs. The striking properties of spin-flip excitons imply highly tunable mode couplings that enable fine control of topological states of itinerant two-dimensional ferromagnets.

Figure 1

Inelastic light scattering experiments. (a) Experimental setup. (b) Color plot of ILS intensities of spin-reversed excitations at $\nu =3/7$ as function of the exciting photon energy $E_L$. The tilt angle is $\theta =50°$ and $B_{\mathrm{tot}}=8\mathrm{T}$. The inset shows spectra of the SW mode at $E_Z$ and of sub-$E_Z$ excitations for $E_L=1.51997\mathrm{eV}$ (indicated as a dashed line).

Figure 2

Inelastic light scattering spectra in the energy range of lowest spin-reversed excitations. (a) Results for $1/3\le \nu \le 4/9$ ($1\le p\le 4$) at $\theta =50°$. The tail below $E_Z$ increases with increasing $\Lambda \mathrm{L}$ number $p$. At $\nu =1/3$ only a high energy tail is observable. (b) Spectra at $\nu =3/7$ for $\theta =30°$ (black squares). The black (blue) line is a fit with three individual Lorentzians shown in gray. The peak positions are marked with vertical lines.

Figure 3

Calculated wave vector dispersions. (a) The lowest spin-reversed excitation at $\nu =2/5$, $3/7$, and $4/9$ for electron density $n=5\times {10}^{10}{\mathrm{cm}}^2$ and QW width of 35 nm. Mode coupling is included as described in the text. The error bar at the end of each curve represents the typical statistical error in the energy determined from the Monte Carlo method. (b) Wave vector dispersion at $\nu =3/7$. The dash-dotted gray (red) curve is for the lowest SW excitations without coupling to SFE modes. The dash-dotted black (blue) line is the spin-flip exciton $2\uparrow \to 0\downarrow$ without coupling to SW modes. The black solid curve, same as in (a) for $3/7$, incorporates mode couplings as described in the text. An illustration of the SFE is shown. (c) $\Lambda \mathrm{L}$ scheme for fully spin-polarized QHE state at $p=3$ ($\nu =3/7,3/5$). SW transition from $2\uparrow \to 2\downarrow$ (center panel) and SFE transition from $2\uparrow \to 0\downarrow$ (right panel) are outlined.

Figure 4

Upper panel: Spectra at $\nu =4/9$ for $\theta =50°$ (solid squares) and $\theta =30°$ (solid circles) and at $\nu =4/7$ for $\theta =30°$ (open blue circles). The solid lines are calculated ILS intensities for $\nu =4/9$ at $\theta =50°$ and 30°. Lower panel: Calculated wave vector dispersion for $\nu =4/9$.