Spin-orbit coupling induced splitting of Yu-Shiba-Rusinov states in antiferromagnetic dimers

Abstract

Magnetic atoms coupled to the Cooper pairs of a superconductor induce Yu-Shiba-Rusinov states (in short Shiba states). In the presence of sufficiently strong spin-orbit coupling, the bands formed by hybridization of the Shiba states in ensembles of such atoms can support low-dimensional topological superconductivity with Majorana bound states localized on the ensembles’ edges. Yet, the role of spin-orbit coupling for the hybridization of Shiba states in dimers of magnetic atoms, the building blocks for such systems, is largely unexplored. Here, we reveal the evolution of hybridized multi-orbital Shiba states from a single Mn adatom to artificially constructed ferromagnetically and antiferromagnetically coupled Mn dimers placed on a Nb(110) surface. Upon dimer formation, the atomic Shiba orbitals split for both types of magnetic alignment. Our theoretical calculations attribute the unexpected splitting in antiferromagnetic dimers to spin-orbit coupling and broken inversion symmetry at the surface. Our observations point out the relevance of previously unconsidered factors on the formation of Shiba bands and their topological classification.

Electronic and Magnetic Properties of Building Blocks of Mn and Fe Atomic Chains on Nb(110)

“…These values are given as ϑ AD in the table, and agree with the numerically calculated values ϑ SD within 0.1 • accuracy. The AFM ground states of the Mn u-1NN and Mn y-2NN dimers agree well with scanning tunneling spectroscopy experiments [7], but the Mn x-1NN dimer exhibits experimentally a FM ground state contrary to the AFM state obtained from our calculations. This may be caused by the limitations of the simulation techniques, e.g., the angular momentum cut-off, or additional structural relaxations that are not taken into account in the KKR calculations.…”

“…ϑ SD is the ground state angle based on spin dynamics simulations, and ϑ AD is the approximate ground state spin angle calculated using the spin model parameters (see Appendix A). The ϑ SD angles of the Mn u-1NN, Mn x-1NN, and Mn y-2NN dimers were reported in [7]. The ground state spin angle between the spin moments of the dimer atoms was determined by spin dynamics simulations, listed as ϑ SD in Table 1.…”

“…Beside significant advances in molecular metallic chains, so-called single chain magnets [1][2][3], this area has recently extended towards the investigation of magnetic-superconducting heterostructures, which may find applications in quantum computing. The presence of magnetic impurities on a superconducting surface leads to the emergence of so-called Yu-Shiba-Rusinov (YSR) states [4][5][6][7][8][9], due to the coupling of the localized magnetic moment to the Cooper pairs. In atomic chains, hybridized YSR states develop into bands [10,11], that can give rise to topological superconductivity and consequently to the appearance of Majorana bound states [12][13][14][15][16].…”

“…In atomic chains, hybridized YSR states develop into bands [10,11], that can give rise to topological superconductivity and consequently to the appearance of Majorana bound states [12][13][14][15][16]. In a recent study by Beck et al [7], an Mn adatom and Mn dimers on Nb(110) were investigated in the superconducting state. The experimental results supported by tight-binding model calculations based on density functional theory (DFT) data demonstrated that the YSR states hybridize not only for ferromagnetic but also for antiferromagnetic dimers, as a consequence of the spin-orbit coupling (SOC) present in the system.…”

“…In the present paper, we investigate the magnetic properties of Mn and Fe adatoms, dimers, and monatomic chains on Nb(110) along different crystallographic directions. Mn and Fe adatoms, Mn dimers, and Mn chains have already been studied on Nb(110) [7,8,14,28], the magnetic properties of which are now systematically investigated from the theoretical side. Determining the magnetic properties of atomic chains from first principles is a long-standing challenge [25,[29][30][31][32].…”