Robust spin polarization of Yu-Shiba-Rusinov states in superconductor/ferromagnetic insulator heterostructures

A. Skurativska, J. Ortuzar, D. Bercioux, F. S. Bergeret, and M. A. Cazalilla

Phys. Rev. B 107, 224507 – Published 15 June 2023

Abstract

Yu-Shiba-Rusinov (YSR) states arise as subgap excitations of a magnetic impurity in a superconducting host. Taking into account the quantum nature of the impurity spin in a single-site approximation, we study the spectral properties of the YSR excitations of a system of magnetic impurity in a spin-split superconductor, i.e., a superconductor in proximity to a ferromagnetic insulator at zero external magnetic fields. The YSR excitations of this system exhibit a robust spin polarization that is protected from fluctuations and environmental noise by the exchange field of the ferromagnetic insulator, which can be as large as a few Tesla. We compare the results of this quantum approach to the classical approach, which conventionally predicts fully polarized YSR excitations even in the absence of exchange and external magnetic field. Turning on a small magnetic field, we show the latter splits the YSR excitations in the regime where the impurity is strongly coupled to the superconductor, whilst the classical approach predicts no such splitting. The studied system can potentially be realized in a tunnel junction connected to a quantum dot in proximity to a spin-split superconductor.

Received 2 March 2023
Revised 9 May 2023
Accepted 11 May 2023

DOI:https://doi.org/10.1103/PhysRevB.107.224507

Physics Subject Headings (PhySH)

Impurities in superconductors Spin polarization

Tunnel junctions

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

A. Skurativska ^1,*, J. Ortuzar ², D. Bercioux^1,3, F. S. Bergeret^1,4,†, and M. A. Cazalilla ^1,3,‡

¹Donostia International Physics Center, 20018 Donostia–San Sebastián, Spain
²CIC nanoGUNE-BRTA, 20018 Donostia–San Sebastián, Spain
³IKERBASQUE, Basque Foundation for Science, Plaza Euskadi 5, 48009 Bilbao, Spain
⁴Centro de Física de Materiales (CFM-MPC), Centro Mixto CSIC-UPV/EHU, 20018 Donostia–San Sebastián, Spain

^*anastasiia.skurativska@dipc.org
^†fs.bergeret@csic.es
^‡miguel.cazalilla@dipc.org

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Vol. 107, Iss. 22 — 1 June 2023

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Images

Figure 1
Schematic picture of a possible realization of the studied system. It consists of a superconductor in proximity to a ferromagnetic insulator coupled to a quantum dot or a molecule that can be modeled as a spin- $S$ quantum impurity. The right normal metal is a ferromagnetic tunneling contact to probe the spin polarization. An external magnetic field $B$ is applied in different directions.
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Figure 2
Evolution of the many-body spectrum of the single-site model in Eq. (1) as the exchange field ( $h$ ), exchange coupling ( $J$ ), and external magnetic field ( $B$ ) are switched on sequentially. Their values are given in units of the strength of the superconducting pairing potential $Δ$ . The energies of the even and odd fermion-parity states are shown in blue and orange color, respectively. The expression for the odd-parity eigenstate $| o 〉$ is given in Eq. (4). The arrows indicate the subgap transitions corresponding to the YSR excitations with and without $B$ . In the rightmost panel, the system is in the strong coupling regime and the YSR excitations are split by $B$ .
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Figure 3
Spin polarization of the YSR excitations as a function of the energy $E$ and the exchange coupling $J$ in the single-site model. In the absence of the magnetic field, the system shows no splitting of the YSR excitations (a), while adding the magnetic field gives rise to the splitting of the YSR excitations in the strong coupling regime (b, c). The dashed line indicates the QPT. All the energies are given in units of $Δ$ . The values of the parameters used to generate the plots are $B = 0.1$ and $h = 0.3$ . Notice that the value of the $B$ field considered here is exaggerated in order to make the splitting visible on the scale of the plot.
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Figure 4
Polarization of the YSR excitations from the classical approach as a function of the dimensionless coupling parameter $α ≃ J S$ for two different impurity-spin $S$ orientations: parallel (a) and perpendicular (b) to the exchange field $h$ . In order to highlight the polarization of the YSR excitations here we plot $A_{↑} (ω) - A_{↓} (ω)$ normalized by the maximum value of the total density of states, that eliminates contribution from the continuum of states. The dashed line indicates the phase transition. The energies are in units of the superconducting pairing potential $Δ$ . In the two panels, we have set $h = 0.3$ .
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Figure 5
Polarization spectral density as a function of the energy $E$ and the angle of the external magnetic field $B = B (cos θ, sin θ)$ in the weak and strong coupling regime for the single-site (a, b) and classical (c, d) approaches. Energies are given in units of $Δ$ . The choice of system parameters is $B = 0.1, h = 0.3$ .
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Figure 6
Schematic representation of the low-energy spectrum of the single-site model as a function of exchange coupling $J$ for the case of zero (a) and nonzero (b) magnetic field $B$ . Arrows indicate possible transitions in the weak coupling ( $J < J_{c}$ ) and in the strong coupling ( $J < J_{c}$ ) regimes.
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