Spin–orbit interaction in the magnetization of two‐dimensional electron systems

Abstract

This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.We review recent experimental and theoretical work on the quantum oscillations of the magnetization M, i.e., the de Haasvan Alphen (dHvA) effect, in two-dimensional electron systems (2DESs) with spin-orbit interaction (SOI). We focus first on a theoretical modeling by numerically solving the Hamiltonian including the Rashba (R) and Dresselhaus (D) SOI and the Zeeman term in an arbitrarily tilted magnetic field B. We second present experimental data on the SOI-modified quantum oscillations of M(B) in 2DESs formed in the InGaAs/InP and AlGaAs/GaAs material systems for different tilt angles between the 2DES normal and the direction of B. We find pronounced beating patterns in InGaAs/InP that are described quantitatively by assuming a dominant R-SOI except for a distinct frequency anomaly in M present in nearly perpendicular B. In AlGaAs/GaAs, beating patterns occur at large tilt angles. Here, anomalies in the dHvA wave form occur. The findings demonstrate that the understanding of the ground state energy of a 2DES is incomplete when SOI is present. Finally, we predict that the amplitude and anisotropy of specific dHvA oscillations with respect to the in-plane magnetic field component allow one to quantify the magnitude and relative signs of both R-SOI and D-SOI when simultaneously present.Calculated fan chart of Landau levels and oscillatory Fermi energy E F in a 2DES subject to SOI. The beating patterns in E F contain information on the SOI. They manifest itself in a variety of experimentally accessible observables. In this feature article, we focus on the magnetization M as a thermodynamic state variable. The inset sketches a micromechanical cantilever magnetometer used to measure M using the torque τ = M × B.

Integer effects in the entanglement and spin fluctuations of a quantum Hall system with Rashba interactions

“…The density of delocalized states thus remains sharp about the band centers, which causes several thermodynamic and transport quantities of the 2D electron gas to exhibit pronounced changes as the Fermi level jumps discontinuously between delocalized band gaps [20][21][22][23][24][25]. Indeed, experimental observations of the Shubnikov-de Haas effect and de Haas-van Alphen effect have been used to obtain the value of the Rashba parameter [21,24,[26][27][28][29][30][31][32][33][34][35]. The second objective of this work is to show that similar integer effects exist in the total spinorbit entanglement entropy originating from the Rashba interaction (section 3).…”

Micromechanical measurement of beating patterns in the quantum oscillatory chemical potential of InGaAs quantum wells due to spin-orbit coupling

“…The resonant excitation of mechanical modes of microcantilevers was reported to further enhance the sensitivity in M. [6][7][8] The quasistatically detected quantum oscillatory magnetization M(B), i.e., the de Haas-van Alphen (dHvA) effect, was shown to exhibit beating patterns when the 2DESs exhibited spin-orbit interaction (SOI). 9 However, in AlGaAs-based systems, it was possible to detect beatings only at high tilt angles of B, 10 and in asymmetric InGaAs quantum wells (QWs) only a single beat node was resolved at low tilt angles due to the inherently small sensitivity of torque magnetometry at small B. 11 The chemical potential l of a 2DES was detected in separate experiments using nanostructured single electron transistors, 12 or via magnetocapacitance measurements 13 and electrometry on bilayer 2DESs 14,15 that were formed in dedicated heterostructures.…”

Experimental determination of Rashba and Dresselhaus parameters andg*-factor anisotropy via Shubnikov-de Haas oscillations

“…The presence of R-SOI leads to beatings in the quantum oscillations in such a way that the peak-to-peak amplitudes of the jumps at even and odd integer ν interchange their signal strength (dashed lines in figure 1(a)). Neglecting level broadening and a finite temperature for the moment these amplitudes directly correspond to the energy gap between subsequent spinsplit Landau levels E n¢ [37][38][39].…”