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

ARTICLE https://doi.org/10.1038/s41467-021-23483-4 OPEN Interplay of spin–orbit coupling and Coulomb interaction in ZnO-based electron system 1234567890():,; D. Maryenko 1 ✉, M. Kawamura 1, A. Ernst 2,3, V. K. Dugaev4, E. Ya. Sherman5,6, M. Kriener M. S. Bahramy 7,10, Y. Kozuka8,9 & M. Kawasaki1,7 1, Spin–orbit coupling (SOC) is pivotal for various fundamental spin-dependent phenomena in solids and their technological applications. In semiconductors, these phenomena have been so far studied in relatively weak electron–electron interaction regimes, where the single electron picture holds. However, SOC can profoundly compete against Coulomb interaction, which could lead to the emergence of unconventional electronic phases. Since SOC depends on the electric field in the crystal including contributions of itinerant electrons, electron–electron interactions can modify this coupling. Here we demonstrate the emergence of the SOC effect in a high-mobility two-dimensional electron system in a simple band structure MgZnO/ZnO semiconductor. This electron system also features strong electron–electron interaction effects. By changing the carrier density with Mg-content, we tune the SOC strength and achieve its interplay with electron–electron interaction. These systems pave a way to emergent spintronic phenomena in strong electron correlation regimes and to the formation of quasiparticles with the electron spin strongly coupled to the density. 1 RIKEN Center for Emergent Matter Science(CEMS), Wako, Japan. 2 Institute for Theoretical Physics, Johannes Kepler University, Linz, Austria. 3 Max Planck Institute of Microstructure Physics, Halle, Germany. 4 Department of Physics and Medical Engineering, Rzeszów University of Technology, Rzeszów, Poland. 5 Department of Physical Chemistry, University of the Basque Country UPV/EHU, Bilbao, Spain. 6 Ikerbasque, Basque Foundation for Science, Bilbao, Spain. 7 Department of Applied Physics and Quantum-Phase Electronics Center (QPEC), The University of Tokyo, Tokyo, Japan. 8 Research Center for Magnetic and Spintronic Materials, National Institute for Materials Science (NIMS), Tsukuba, Japan. 9 JST, PRESTO, Kawaguchi, Saitama, Japan. 10Present address: Department of Physics and Astronomy, The University of Manchester, Manchester, UK. ✉email: NATURE COMMUNICATIONS | (2021)12:3180 | https://doi.org/10.1038/s41467-021-23483-4 | www.nature.com/naturecommunications 1 NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-021-23483-4 Results Formation of electron system. We start with the discussion of the 2DES formation, since it is central for tuning the interplay between two interaction mechanisms. The 2DES is realized in the c-plane of wurtzite ZnO by interfacing it with MgxZn1−xO (Fig. 1a). Its formation is validated by our first-principles calculations, modeling the interface between two semi-infinite systems, ZnO and MgxZn1−xO (Fig. 1b). While Mg substitutes Zn stoichiometrically, its position is shifted from the original Zn atom position resulting in c-axis shrinking of the MgxZn1−xO layer. This and the different chemical environment brought in by Mg atoms lead to a polarization discontinuity at the MgxZn1−xO/ ZnO interface, which is compensated by accumulating electrons at the interface. Respectively, the electron density depends on the Mg-content5. Spin–orbit coupling. In such a wurtzite heterostructure the electrons are allowed to be polarized by the spin–orbit interaction, since both structural and crystal inversion symmetries are broken. The corresponding Hamiltonian for electrons in the cplane is: h i ð1Þ H SOC ¼ αR þ γðbhk2z i  k2k Þ ðσ x ky  σ y kx Þ; where αR and γ are the Rashba and Dresselhaus coefficients respectively6–8. Here kz = − i∂/∂z acting on the electron 2 a b ZnO 0.5 E-EF (eV) MgxZn1-xO MgxZn1-xO 0.0 CB -0.5 -1.0 VB -1.5 0 2 4 6 8 10 12 14 16 18 # unit cell 5.2 Å z x y Zn ZnO Mg 3.25 Å O 40 E-EF (meV) S pin–orbit coupling is a single particle relativistic effect producing in atomic physics a bilinear interaction between the electron spin and its orbital momentum. In solids the SOC is transformed into a symmetry-permitted coupling between the orientation of the electron spin and its crystal momentum. This coupling can lead to spin–momentum locking and establishes a spin-dependent band structure influenced by the crystal symmetry. Prominent examples here are the Rashba and Dresselhaus couplings, whose appearance requires the breaking of the structural and crystal inversion symmetries. By contrast, Coulomb interaction dictates collective electron behavior in solids, e.g., by establishing a Fermi liquid or a Mott insulator, and can also generate spin-polarized phases due to the Stoner instability1. Thus, SOC orients electron spin with respect to its momentum while the Coulomb interaction can counteract by aligning the spins in one direction, e.g., by producing a spin-depended exchange interaction. The usual single particle description of SOC-related effects in the presence of Coulomb interaction is poorly applicable, since the relativistic effect on quasiparticle excitations in strongly interacting systems is not known. Yet, the interplay of two mechanisms for spin orientation is suggested to have diverse manifestations encompassing the emergence of topological phases, spin textures, etc.2–4. 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. It requires a system with sufficiently strong relativistic effects to unfold the role of spin–orbit coupling and with a high mobility at a low carrier density to enhance the Coulomb interaction effect. Here we demonstrate a realization of such a regime in the twodimensional electron system (2DES) at the MgxZn1−xO/ZnO interface. The SOC effect is identified from the beatings of the Shubnikov-de Haas oscillations (SdH) in conductivity, which varies with the electron density N. Upon lowering N the system shows an enhancement of the electron effective mass, attributed to electron–electron interaction. Thus, we can tune the interplay between two interaction mechanisms and achieve an interaction regime for 2DESs, where the emergence of novel quantum states is anticipated. c-axis ARTICLE 20 0 2DES -20 -40 3 4 5 6 7 8 # unit cell 9 10 Fig. 1 Electronic structure of MgxZn1−xO/ZnO interface. a Schematic view of high mobility MgZnO/ZnO heterostructure. Both wurtzite crystal structure of ZnO and MgxZn1−xO/ZnO interface breaks the inversion symmetry. b The interface band structure is calculated using self consistent Green function method for semi-infinite systems considering x = 5%, a typical Mg content in the heterostructures. The conduction band (CB) of ZnO lowers at the interface forming the confinement potential for high mobility electrons. The size of the band gap in ZnO and MgxZn1−xO is underestimated due to the lack of the conventional densi (...truncated)