Spin Orientation of Two-Dimensional Electrons Driven by Temperature-Tunable Competition of Spin–Orbit and Exchange–Magnetic Interactions

Abstract

Finding ways to create and control the spin-dependent properties of two-dimensional electron states (2DESs) is a major challenge for the elaboration of novel spin-based devices. Spin-orbit and exchange-magnetic interactions (SOI and EMI) are two fundamental mechanisms that enable access to the tunability of spin-dependent properties of carriers. The silicon surface of HoRhSi appears to be a unique model system, where concurrent SOI and EMI can be visualized and controlled by varying the temperature. The beauty and simplicity of this system lie in the 4f moments, which act as a multiple tuning instrument on the 2DESs, as the 4f projections parallel and perpendicular to the surface order at essentially different temperatures. Here we show that the SOI locks the spins of the 2DESs exclusively in the surface plane when the 4f moments are disordered: the Rashba-Bychkov effect. When the temperature is gradually lowered and the system experiences magnetic order, the rising EMI progressively competes with the SOI leading to a fundamental change in the spin-dependent properties of the 2DESs. The spins rotate and reorient toward the out-of-plane Ho 4f moments. Our findings show that the direction of the spins and the spin-splitting of the two-dimensional electrons at the surface can be manipulated in a controlled way by using only one parameter: the temperature.

Relativistic splitting of surface states at Si-terminated surfaces of the layered intermetallic compoundsRT2Si2(R=rare earth;TNechaev1, Krasovskii2 2018Phys. Rev. B140280View full textAdd to dashboardCite

“…We then consider the surface states of our model as a prototype of those of a paramagnetic phase of an RT 2 Si 2 compound and tune the relative strength of the competing spin-orbit and exchange interactions in order to illustrate how the surface states at the Si-terminated surface are influenced by the ferromagnetically ordered 4f moments of the subsurface rare-earth layer in a magnetic phase of this compound. The modification of the surface electronic structure suggested by the model is in full accord with the experimental ARPES (angle-resolved photoemission spectroscopy) observations and the corresponding ab initio calculations for magnetic phases of the RT 2 Si 2 compounds [11,12,21].…”

“…Recently, the RT 2 Si 2 intermetallic compounds have been suggested to be a promising candidate for applications in spinbased devices [10][11][12][13][14]. Here R stands for a rare-earth element (Sm, Eu, Gd, Ho, or Yb) and T for a transition metal (TM) element (Ir or Rh).…”

“…These compounds have a layered ThCr 2 Si 2 type structure [15], with the rare-earth layers separated by Si-T-Si trilayers. In the magnetic phase, the rare-earth 4f magnetic moments are ferromagnetically ordered within the layer and antiferromagnetically aligned with the nearestneighbor rare-earth layers [11,12,16,17]. The Si-T-Si-R four layer of the Si-terminated (001) surfaces of these ternary compounds gives rise to fascinating surface phenomena brought about by the competition between the Rashba effect and magnetic exchange interaction, where the former causes a momentum-dependent spin-orbit splitting of surface states and the latter introduces a Zeeman-like splitting of states with the opposite spin.…”

Weak magnetic anisotropy in GdRh2Si2 studied by magnetic resonance

“…hard direction 100 : Figure 3 shows the results of Eqns. (3,4) by using the experimental temperature dependent H res . The anisotropy field H A1 has to be distinguished from the internal exchange fields which lead to magnetic order.…”

“…online) Temperature dependence of resonance field Hres (closed triangles) and anisotropy field (open triangles, Eqns 3,4). for the data at 9.4 and 34 GHz.…”