Polarization-dependent Landau level crossing in a two-dimensional electron system in a MgZnO/ZnO heterostructure

We report electrical transport measurements in a tilted magnetic field on a high-mobility two-dimensional electron system (2DES) confined at the MgZnO/ZnO heterointerface. The observation of multiple crossing events of spin-resolved Landau levels (LLs) enables the mapping of the sequence of electronic states. We further measure the renormalization of electron spin susceptibility at zero field and the susceptibility dependence on the electron spin polarization. The latter manifests the deviation from the Pauli spin susceptibility. As a result, the crossing of spin-resolved LLs shifts to smaller tilt angles and the first Landau level coincidence event is absent even when the magnetic field has only a component perpendicular to the 2DES plane.

Figure 1

(a) Color rendition plot of $R_{xx}$ as a function of $B_{\perp }$ and $1/cos\left(\theta \right)$. Indicated are the electron states $(N,\uparrow$ or $\downarrow )$ at the chemical potential. (b) Scheme of LL crossings in a magnetic field assuming a fixed $B_{\perp }$ (left panel). $j$ indicates the index of LL crossings. $R_{xx}$ traces are shown for $\nu =5$ and 6 as functions of $1/cos\left(\theta \right)$. (c) Schematic of the sample. The sample is tilted in $B_{\mathrm{total}}$ so that the direction of the in-plane field is collinear with the current direction.

Figure 2

Estimation of spin susceptibility at several $\nu$'s. The inset equation describes the linear dependence with $g^{*}{m}^{*}=2.0$ for $j\le 3$. The gray shaded area indicates a range of $g^{*}{m}^{*}$ of 1.8 (upper edge) to 2.2 (lower edge).

Figure 3

Positions of LL crossings (closed symbols) at integer $\nu$ and angles $\theta$ extracted from Fig. 1. The spin polarization value $P$ is given at each crossing point. The solid lines are guides to the eye. A dashed red line emphasizes a systematic shift of coincidence events to smaller $1/cos\left(\theta \right)$. The open circle is one of the $j=1$ crossings obtained by extrapolating experimental data points. It lies at $1/cos\left(\theta \right)<1$ and emphasizes that the first crossing event has occurred in a purely perpendicular magnetic field.

Figure 4

(a) Spin polarization (estimated from Fig. 3) vs total magnetic field. The nonlinearity indicates a polarization-dependent spin susceptibility. The experimental points are bounded by (dashed) lines of constant $\chi$ corresponding to $P=0$ and $P=1$, respectively. (b) Analysis of in-plane field effect on LL crossing yields the subband separation ${\Delta }_{10}=5$ meV and the electron wave function extension 13 nm.