Generalized Stoner criterion and versatile spin ordering in two-dimensional spin-orbit coupled electron systems

Abstract

Spin-orbit coupling is a single-particle phenomenon known to generate topological order, and electron-electron interactions cause ordered many-body phases to exist. The rich interplay of these two mechanisms is present in a broad range of materials, and has been the subject of considerable ongoing research and controversy. Here we demonstrate that interacting two-dimensional electron systems with strong spin-orbit coupling exhibit a variety of time reversal symmetry breaking phases with unconventional spin alignment. We first prove that a Stoner-type criterion can be formulated for the spin polarization response to an electric field, which predicts that the spin polarization susceptibility diverges at a certain value of the electron-electron interaction strength. The divergence indicates the possibility of unconventional ferromagnetic phases even in the absence of any applied electric or magnetic field. This leads us, in the second part of this work, to study interacting Rashba spin-orbit coupled semiconductors in equilibrium in the Hartree-Fock approximation as a generic minimal model. Using classical Monte-Carlo simulations we construct the complete phase diagram of the system as a function of density and spin-orbit coupling strength. It includes both an outof-plane spin polarized phase and in-plane spin-polarized phases with shifted Fermi surfaces and rich spin textures, reminiscent of the Pomeranchuk instability, as well as two different Fermi-liquid phases having one and two Fermi surfaces, respectively, which are separated by a Lifshitz transition. We discuss possibilities for experimental observation and useful application of these novel phases, especially in the context of electric-field-controlled macroscopic spin polarizations.

Interplay of spin–orbit coupling and Coulomb interaction in ZnO-based electron system

“…The observed SOC effect in strong correlation regime of ZnObased 2DES reaches into the unprecedented domain of an interplay between spin-orbit and Coulomb interactions. It was suggested recently [2][3][4] that the interplay of SOC and Coulomb interaction forms a variety of unconventional equilibrium spin structures, collective excitations, and corresponding phase transitions. These theoretical predictions could be possibly realized with certain choices of the parameters characterizing the 2DES.…”

“…Yet, the interplay of two mechanisms for spin orientation is suggested to have diverse manifestations encompassing the emergence of topological phases, spin textures, etc. [2][3][4] . An experimental realization of a system that shows both strong interaction between electrons, e.g., in the form of a Fermi liquid, and spin-orbit coupling is challenging.…”

Van Hove scenario of anisotropic transport in a two-dimensional spin-orbit coupled electron gas in an in-plane magnetic field

“…This means that Eqs. (22) establish only a relation between A and B and an additional equation is required to determine both coefficients. It is clear that this equation should be obtained from the requirement of electroneutrality of the system, which is not violated under nonequilibrium conditions considered here.…”

“…Another aspect of the anisotropic transport in spinorbit coupled systems is related to anisotropic phases that are formed because of spontaneous breaking of spatial symmetry in strongly interacting electron systems with SOI [19][20][21][22][23]. Though an external magnetic field is absent the anisotropic state of the electron liquid is formed due to a self-consistent magnetic field that is oriented in the plane of the 2D system [19].…”

Magnetic stability for the Hartree-Fock ground state in two dimensional Rashba-Gauge electronic systems

“…Underlying Physics shall be understood from the local symmetry properties associated to the spin concept. A spin gauge field vector in this context comes from the space-time induced phase difference between two correlated electronic states, which might be calculated from the first order expansion on the SU(2) generators group, and whose components leads into an effective Rashba spin-orbit magnetic field in momentum space ∼ E jσ · (n × ∂ j n), with n = (−k y , k x , 0)/k as the unitary vector tangent to the magnetic texture on the XY plane, E j as the applied electric field andσ as the set of Pauli matrices [13][14][15][16][17][18]. Attempts for the calculation of the Hartree Fock ground state have been performed by different techniques in terms of the Wigner-Seitz radius r s ∼ 1/ √ n s , (n s as the particle density), predicting partial spin polarization due to the Coulomb exchangedriven on semiconducting structures [19,20].…”