Strong spin-orbit coupling in the noncentrosymmetric Kondo lattice

Editors' Suggestion

Strong spin-orbit coupling in the noncentrosymmetric Kondo lattice

A. Generalov, J. Falke, I. A. Nechaev, M. M. Otrokov, M. Güttler, A. Chikina, K. Kliemt, S. Seiro, K. Kummer, S. Danzenbächer, D. Usachov, T. K. Kim, P. Dudin, E. V. Chulkov, C. Laubschat, C. Geibel, C. Krellner, and D. V. Vyalikh

Phys. Rev. B 98, 115157 – Published 27 September 2018

Abstract

Strong spin-orbit coupling (SOC) in combination with a lack of inversion symmetry and exchange magnetic interaction proves to be a sophisticated instrument allowing efficient control of the spin orientation, energy and trajectories of two-dimensional (2D) electrons and holes trapped at surfaces or interfaces. Exploiting Kondo-related phenomena and crystal-electric-field effects at reduced dimensionalities opens new opportunities to handle their spin-dependent properties offering novel functionalities. We consider here a 2D Kondo lattice represented by a Si-Ir-Si-Yb (SISY) surface block of the heavy-fermion material ${YbIr}_{2} {Si}_{2}$ . We show that the Kondo interaction with $4 f$ moments allows finely tuning the group velocities of the strongly spin-polarized carriers in 2D itinerant states of this noncentrosymmetric system. To unveil the peculiarities of this interaction, we used angle-resolved photoemission measurements complemented by first-principles calculations. We established that the strong SOC of the Ir atoms induces spin polarization of the 2D states in SISY block, while the 2D lattice of Yb $4 f$ moments acts as a source for coherent $f - d$ interplay. The strong SOC and lack of inversion symmetry turn out to lead not only to the anticipated Rashba-like splitting of the 2D states, but also to spin splitting of the $4 f$ Kramers doublets. They couple temperature-dependently to the spin-polarized 2D states and thereby guide the properties of the latter.

Received 13 July 2018
Revised 7 September 2018

DOI:https://doi.org/10.1103/PhysRevB.98.115157

Physics Subject Headings (PhySH)

Kondo effect Spin-orbit coupling

Heavy-fermion systems

Angle-resolved photoemission spectroscopy Density functional calculations Kondo lattice model

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

A. Generalov¹, J. Falke², I. A. Nechaev³, M. M. Otrokov^3,4, M. Güttler², A. Chikina⁵, K. Kliemt⁶, S. Seiro⁷, K. Kummer⁸, S. Danzenbächer², D. Usachov⁹, T. K. Kim¹⁰, P. Dudin¹⁰, E. V. Chulkov^3,4,9,11,12, C. Laubschat², C. Geibel¹³, C. Krellner⁶, and D. V. Vyalikh^11,12,14,*

¹MAX IV Laboratory, Lund University, Box 118, 22100 Lund, Sweden
²Institut für Festkörper- und Materialphysik, Technische Universität Dresden, D-01062 Dresden, Germany
³Centro de Física de Materiales CFM-MPC and Centro Mixto CSIC-UPV/EHU, 20018 Donostia/San Sebastián, Basque Country, Spain
⁴Tomsk State University, Lenina Av., 36, 634050 Tomsk, Russia
⁵Swiss Light Source, Paul Scherrer Institute, CH-5232 Villigen-PSI, Switzerland
⁶Kristall- und Materiallabor, Physikalisches Institut, Goethe-Universität Frankfurt, Max-von-Laue Strasse 1, D-60438 Frankfurt am Main, Germany
⁷IFW Dresden, Helmholtzstr. 20, D-01069 Dresden, Germany
⁸European Synchrotron Radiation Facility, 71 Avenue des Martyrs, Grenoble, France
⁹Saint Petersburg State University, Saint Petersburg 198504, Russia
¹⁰Diamond Light Source, Harwell Campus, Didcot OX11 0DE, United Kingdom
¹¹Donostia International Physics Center (DIPC), 20080 Donostia/San Sebastián, Basque Country, Spain
¹²Departamento de Fisica de Materiales UPV/EHU, 20080 Donostia/San Sebastián, Basque Country, Spain
¹³Max-Planck-Institut für Chemische Physik fester Stoffe, D-01187 Dresden, Germany
¹⁴IKERBASQUE, Basque Foundation for Science, 48011 Bilbao, Spain

^*Corresponding author: denis.vyalikh@dipc.org

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 98, Iss. 11 — 15 September 2018

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Tetragonal crystal structure of ${YbIr}_{2} {Si}_{2}$ . (a) Bulk unit cell. The Yb atomic layers are separated from each other by the tightly bonded Si-Ir-Si trilayer blocks thus the cleavage plane will be between Si and Yb layers. (b) Evolution of the Brillouin zone from bulk to surface symmetry. The black zone corresponds to $I 4 / m m m$ , grey to $P 4 / m m m$ , and red to $P 4 m m$ and $P 4 / n m m$ . (c) Si-terminated surface of ${YbIr}_{2} {Si}_{2}$ . The surface related Si-Ir-Si-Yb (SISY) block is surrounded by a dotted line.
Reuse & Permissions
Figure 2
Spectral pattern reflecting itinerant and $4 f$ electron bands. (a) ARPES data taken from a Si-terminated ${YbIr}_{2} {Si}_{2}$ crystal at a temperature of 1 K along the $\bar{M} - \bar{X}$ direction and superimposed with itinerant bands calculated by DFT. The spin polarization of the calculated bands is highlighted in red (in-plane positive $σ_{x}$ component) and blue (in-plane negative $σ_{x}$ component). The observable regions of the interplay between $f$ and $s p d$ states at $E_{F}$ are highlighted with red and blue patches. (b) Electron density distribution (integrated over the $a b$ plane) of the 2DESs residing in the surface SISY block as calculated near the $\bar{M}$ point (at the $k$ points $\approx 1 / 4 th$ of the $\bar{M} - \bar{X}$ distance for the $α$ and $β$ states and 1/16th of $\bar{M} - \bar{X}$ for the $δ$ states, respectively).
Reuse & Permissions
Figure 3
Close-up ARPES maps disclosing the interplay of spin-polarized 2D and $4 f$ states. Normalized raw data in (a) obtained at $T = 1 K$ and $h ν = 45 eV$ along the $\bar{X} - \bar{M}$ direction in the SBZ. Blue arrows indicate the “neck” of doughnut FS. (b) Second derivative applied along the energy distribution curves (EDC) of the map in (a). This allows to disclose the fine spectral details revealing a “looplike” splitting of a $4 f$ CEF Kramers doublet marked by the red circle. It helps also to better visualize the hybridization (avoided-crossing) gaps as the one marked by a red arrow.
Reuse & Permissions
Figure 4
Temperature-dependent properties of the $f - d$ interaction. ARPES-derived spectral pattern reflecting the topology of the hybrid $f - d$ states obtained at 8 (a) and 100 K (b). The MDC-normalized data magnified within the dashed green rectangle in the left panels in (a) and (b) are depicted in the middle panels together with the applied curvature procedure in the right panels. The derived dispersion for the $α$ bands near $E_{F}$ (marked by green triangles) experiencing renormalization due to spin-dependent interplay with the $4 f s$ is shown in (c) for 8 K and 100 K on both sides of the $\bar{X}$ point. (d) MDC curves at $E_{F}$ extracted for 8 and 100 K demonstrating the narrowing of the “neck” of the $4 f$ -derived doughnut FS at higher temperature.
Reuse & Permissions
Figure 5
All-itinerant DFT band structure and spin polarization of the Si-terminated surface of ${YbIr}_{2} {Si}_{2}$ . (a) The fat bands of the 19-layer slab show the localization of the states on the atomic layers within the SISY block. Green, blue, and orange fat bands correspond to the Si-, Ir-, and Yb-atomic layer, respectively. The shaded areas cover the surface-projected bulk states of ${YbIr}_{2} {Si}_{2}$ . The zero of the energy scale on the left side is the Fermi level within the DFT calculation. Best matching with experimental ARPES data would be achieved by shifting the Fermi level to the position marked on the right side with “PES $E_{F}$ .” (b) A magnified view of the BE range, where the $4 f$ bands interact with the 2DESs. (c) The spin polarization of the bands shown in the figure (b) with the enhanced contribution coming from the Ir and subsurface Yb atoms of the SISY block. The in-plane positive (negative) $σ_{x}$ component is highlighted in red (blue). The main features of the band dispersions related to the fine details of the ARPES spectral pattern are indicated by the arrow and the circle as in Fig. 3. The rectangle highlights the spin splitting of a $4 f$ band before it enters the bulk continuum.
Reuse & Permissions

Physical Review B

covering condensed matter and materials physics