Influence of the single-particle Zeeman energy on the quantum Hall ferromagnet at high filling factors

In a recent paper [B. A. Piot et al., Phys. Rev. B 72, 245325 (2005)], we have shown that the lifting of the electron spin degeneracy in the integer quantum Hall effect at high filling factors should be interpreted as a magnetic-field-induced Stoner transition. In this work, we extend the analysis to investigate the influence of the single-particle Zeeman energy on the quantum Hall ferromagnet at high filling factors. The single-particle Zeeman energy is tuned through the application of an additional in-plane magnetic field. Both the evolution of the spin polarization of the system and the critical magnetic field for spin splitting are well described as a function of the tilt angle of the sample in the magnetic field.

Figure 1

(Color online) $R_{xx}\left(B\right)$ measured at $T=50\mathrm{mK}$ for sample NRC0050. The experimentally determined $\delta \nu$ are also plotted (closed circles). The evolution of the spin polarization $m\left(B\right)$ calculated using Eq. (4) in the presence of a Zeeman energy $(g^{*}=-0.44)$ (dashed line), and without Zeeman energy $(g^{*}=0)$ (thick solid line) are also shown. The condition $\delta \nu =0.5$ used to estimate $B_{ss}$ is indicated by the dotted horizontal line.

Figure 2

(Color online) $R_{xx}\left(B_{\perp }\right)$ for sample LPN06 measured at $T=30\mathrm{mK}$ for different tilt angles $\left(\theta \right)$.

Figure 3

(Color online) Parameter $\delta \nu \left(B_{\perp }\right)$ for sample NU1783b, extracted from measured $R_{xx}\left(B\right)$ at $T=50\mathrm{mK}$ for different tilt angles (symbols). Spin polarization $m$ calculated using Eq. (6) (solid and broken lines).

Figure 4

(Color online) (a) $B_{ss}\left(\theta \right)∕B_{ss}\left(0\right)$ as a function of $\theta$ for three different samples at $T=50\mathrm{mK}$: F1200 (full circles), NU1783b (open squares) and LPN06 (open circles). Self-consistent solutions of Eq. (6), for the three samples, are also plotted (lines). (b) $B_{ss}\left(0\right)∕B_{ss}\left(\theta \right)$ as a function of $1∕\cos \left(\theta \right)$ for the three samples (symbols) together with the predictions of Eq. (6) (lines).