Interlayer RKKY coupling in bulk Rashba semiconductors under topological phase transition

Abstract

The bulk Rashba semiconductors BiTeX (X=I, Cl and Br) with intrinsically enhanced Rashba spin-orbit coupling provide a new platform for investigation of spintronic and magnetic phenomena in materials. We theoretically investigate the interlayer exchange interaction between two ferromagnets deposited on opposite surfaces of a bulk Rashba semiconductor BiTeI in its trivial and topological insulator phases. In the trivial phase BiTeI, we find that for ferromagnets with a magnetization orthogonal to the interface, the exchange coupling is reminiscent of that of a conventional threedimensional metal. Remarkably, ferromagnets with a magnetization parallel to the interface display a magnetic exchange qualitatively different from that of conventional three-dimensional metal due to the spin-orbit coupling. In this case, the interlayer exchange interaction acquires two periods of oscillations and decays as the inverse of the thickness of the BiTeI layer. For topological BiTeI, the magnetic exchange interaction becomes mediated only by the helical surface states and acts between the one-dimensional spin chains at the edges of the sample. The surface state-mediated interlayer exchange interaction allows for the coupling of ferromagnets with non-collinear magnetization and displays a decay power different from that of trivial BiTeI, allowing the detection of the topological phase transition in this material. Our work provides insights into the magnetic properties of these newly discovered materials and their possible functionalization.

Floquet control of indirect exchange interaction in periodically driven two-dimensional electron systems

“…In the regime E F > Δ we can model the main contributing quasienergy band with the Hamiltonian H = 2 k 2 /2m * + Δ. To obtain the exchange interaction for k F R 1, we expand the analytic susceptibility of this model [4] around the KA and perform the one-dimensional integral with respect to q x [10]. This leads to I(R) ≈ −I μμ C sin(2πR/Λ + π/4)/R 3/2 where Λ is given in equation ( 9) and 2C −1 = ta 2 ΛE F /2.…”

“…The magnetic exchange coupling in these systems oscillates as a function of the non-magnetic spacer thickness with a period given by its Fermi level [4]. The envelope of these oscillations decays as a power law that depends on the dimensionality of the spacer material and the conduction electrons' properties [5][6][7][8][9][10]. Hence, the methods of control of the indirect magnetic exchange have relied on the variation of the metallic layer thickness [11][12][13][14][15][16], implementation of lower dimensional materials hosting exotic fermions [5][6][7][8][9][10] or excitons [17][18][19], and gate voltage variations [20][21][22][23].…”

Nonequilibrium RKKY interaction in irradiated graphene

“…and then sum over m to arrive at the exchange in the Floquet representation in Eq. (12). From the definitions of the real-space Green's functions [63], one can show that […”

“…As a function of the impurity separation, it oscillates between positive and negative values indicating ferromagnetic and antiferromagnetic spin couplings with a period determined by the host's Fermi level [4]. The envelope of these oscillations decays in a power law that depends on the dimensionality and the specific band structure of the host material [5][6][7][8][9][10][11][12]. For systems with parabolic bands, the envelope of the RKKY oscillations decays as R −3 in three dimensions and as R −2 in two dimensions [1][2][3].…”

“…Manipulation of the RKKY interaction is also possible through materials engineering of magnetic multilayers, where the interlayer interaction is predominantly due to RKKY coupling [25,26]. An applied static electric field [27][28][29][30][31] could also provide a means to control the RKKY interaction in materials and structures with considerable spin-orbit coupling [11,12,32,33].…”