Proximity Band Structure and Spin Textures on Both Sides of Topological-Insulator/Ferromagnetic-Metal Interface and Their Charge Transport Probes

Abstract

The control of recently observed spintronic effects in topological-insulator/ferromagnetic-metal (TI/FM) heterostructures is thwarted by the lack of understanding of band structure and spin texture around their interfaces. Here we combine density functional theory with Green's function techniques to obtain the spectral function at any plane passing through atoms of Bi2Se3 and Co or Cu layers comprising the interface. In contrast to widely assumed but thinly tested Dirac cone gapped by the proximity exchange field, we find that the Rashba ferromagnetic model describes the spectral function on the surface of Bi2Se3 in contact with Co near the Fermi level E 0 F , where circular and snowflake-like constant energy contours coexist around which spin locks to momentum. The remnant of the Dirac cone is hybridized with evanescent wave functions injected by metallic layers and pushed, due to charge transfer from Co or Cu layers, few tenths of eV below E 0 F for both Bi2Se3/Co and Bi2Se3/Cu interfaces while hosting distorted helical spin texture wounding around a single circle. These features explain recent observation [K. Kondou et al., Nat. Phys. 12, 1027] of sensitivity of spin-to-charge conversion signal at TI/Cu interface to tuning of E 0 F . Interestingly, three monolayers of Co adjacent to Bi2Se3 host spectral functions very different from the bulk metal, as well as in-plane spin textures signifying the spin-orbit proximity effect. We predict that out-of-plane tunneling anisotropic magnetoresistance in vertical heterostructure Cu/Bi2Se3/Co, where current flowing perpendicular to its interfaces is modulated by rotating magnetization from parallel to orthogonal to current flow, can serve as a sensitive probe of spin texture residing at E 0 F .The recent experiments on spin-orbit torque (SOT) [1, 2] and spin-to-charge conversion [3,4] in topologicalinsulator/ferromagnetic-metal (TI/FM) heterostructures have ignited the field of topological spintronics. In these devices, giant non-equilibrium spin densities [5][6][7][8] are expected to be generated due to strong spin-orbit coupling (SOC) on metallic surfaces of three-dimensional (3D) TIs and the corresponding (nearly [9]) helical spinmomentum locking along a single Fermi circle for Dirac electrons hosted by those surfaces [10]. Such strong interfacial SOC-driven phenomena are also envisaged to underlie a plethora of novel spintronic technologies [11].These effects have been interpreted almost exclusively using simplistic models, such as the Dirac Hamiltonian for the TI surface with an additional Zeeman term describing coupling of magnetization of the FM layer to the surface state spins [10],Ĥ Dirac = v F (σ ×p) z − ∆m ·σ, wherep is the momentum operator,σ is the vector of the Pauli matrices, m is the magnetization unit vector and v F is the Fermi velocity. Thus, the only effect of FM layer captured byĤ Dirac is proximity effect-induced exchange coupling ∆ which opens a gap in the Dirac cone energymomentum dispersion [10], thereby making Dirac electrons massive. On the ...

Current-induced spin-orbit torques in ferromagnetic and antiferromagnetic systems

“…First, orbital hybridization between the transition metal and the topological insulator substantially alters the surface states at Fermi energy. The presence of magnetic adatoms shifts the Dirac cone downward in energy (Honolka et al, 2012;Scholz et al, 2012;Ye et al, 2012), and favor the presence of additional metallic bands with Rashba-like character across the Fermi level (Marmolejo-Tejada et al, 2017;Zhang et al, 2016a).…”

First-Principles Quantum Transport Modeling of Spin-Transfer and Spin-Orbit Torques in Magnetic Multilayers

“…On the other hand, SOT-MRAM has a disadvantage of being a three-terminal device. [50], and panels (c) and (g) are adapted from Ref. [49].…”

“…9(g). This points out at a knob that can be exploited to enhance SOT by searching for optimal combination of materials capable to generate penetration of SOC over long distances within the FM layer [50]. In fact, in the case of FM/TI and FM/monolayer-TMD heterostructures, proximity SOC coupling within the FM layer is crucial for SOT efficiency [23] where it has been considered [20] that applied current will be shunted through the metallic FM layer and, therefore, not contribute to nonequilibrium spin density generation at the interface where SOC and thereby induced in-plane spin textures are naively assumed to reside.…”

Proximity Spin–Orbit Torque on a Two-Dimensional Magnet within van der Waals Heterostructure: Current-Driven Antiferromagnet-to-Ferromagnet Reversible Nonequilibrium Phase Transition in Bilayer CrI3

“…This is due to the proximity effect where evanescent wavefunctions from TaSe 2 penetrate [Figs. 2 and 5] up to the first monolayer of CrI 3 to make it a current carrier, while also bringing [36] SOC from TaSe 2 to ensure that S CD (r) is not collinear to B XC (r). The giant SOC hosted by TaSe 2 itself due to inversion symmetry breaking in ultrathin layers of transition metal dichalcogenides (TMDs) [37,38] is confirmed by large S CD (r) within the spatial region of TaSe 2 monolayer in Fig.…”