Quantifying the quantum nature of high spin YSR excitations in transverse magnetic field

Excitations of individual and coupled spins on superconductors provide a platform to study quantum spin impurity models as well as a pathway toward realizing topological quantum computing. Here, we characterize, using ultra-low temperature scanning tunneling microscopy/spectroscopy, the Yu-Shiba-Rusinov (YSR) states of individual manganese phthalocyanine molecules with high spin character on the surface of an ultra-thin lead film in variable transverse magnetic field. We observe two types of YSR excitations, depending on the adsorption geometry of the molecule. Using a zero-bandwidth model, we detail the role of the magnetic anisotropy, spin-spin exchange, and Kondo exchange. We illustrate that one molecular type can be treated as an individual spin akin to an isolated spin on the metal center, whereas the other molecular type invokes a coupled spin system represented by a spin on the center and the ligand. Using the field-dependent evolution of the YSR excitations and comparisons to modeling, we describe the quantum phase of each of the molecules. These results provide an insight into the quantum nature of YSR excitations in magnetic field, and a platform to study spin impurity models on superconductors in magnetic field.

💡 Research Summary

In this work the authors employ ultra‑low‑temperature scanning tunneling microscopy and spectroscopy (STM/STS) to investigate Yu‑Shiba‑Rusinov (YSR) bound states of individual manganese phthalocyanine (MnPc) molecules deposited on an ultra‑thin Pb(111) film. Two distinct adsorption geometries are identified, labelled MnPc1 (ligand axis parallel to a high‑symmetry direction of the Pb lattice) and MnPc2 (ligand axis bisecting a high‑symmetry direction). Because the Pb film is only a few monolayers thick, its in‑plane upper critical field exceeds 4 T, allowing the authors to apply a transverse magnetic field (B⊥) up to 4 T without destroying superconductivity.

For MnPc1 the zero‑field spectrum shows a single pair of YSR peaks, with stronger intensity at positive bias. Upon increasing B⊥ the peak first remains essentially unchanged up to ~0.5 T, then splits asymmetrically: the higher‑intensity branch moves non‑linearly toward the gap centre, displays an inflection point, and finally bends back toward the gap edge, while the lower‑intensity branch evolves almost linearly and loses intensity near the gap edge. No crossing of the gap centre occurs. The authors model this behavior with a zero‑bandwidth (ZBW) Hamiltonian containing a single S = 1 spin, axial (D) and transverse (E) anisotropy, Kondo exchange J_K, and a Zeeman term. The calculation reproduces the observed non‑linear splitting and the inflection point, indicating a partially screened ground state (a bound quasiparticle) that aligns with the field once Zeeman energy exceeds the anisotropy.

MnPc2 exhibits a richer spectrum: at zero field three pairs of YSR peaks are observed, with stronger intensity at negative bias. Two molecular orientations are examined (α = 15° and α = 45° relative to B⊥). In both cases the magnetic‑field evolution is highly non‑monotonic. For α = 15°, a new peak appears around 0.5 T, leading to five observable YSR excitations; as B⊥ increases further, several branches merge, reducing the count back to three by ~2 T. One branch of the outermost peak crosses the superconducting coherence peak around 2.5 T and persists outside the gap with diminishing intensity. For α = 45°, the inner peaks shift nearly linearly with slightly different slopes, while the outermost peak remains almost field‑independent up to 0.5 T, then splits; its lower branch merges with the inner peaks around 2.5 T, and its upper branch also crosses the coherence peak.

To capture these observations the authors extend the ZBW model to include two coupled spins: a central Mn spin S = 1 and a ligand spin S = ½ coupled antiferromagnetically (J_ex < 0). Different sets of anisotropy parameters (D, E), exchange couplings (J_K, J_ex), and g‑factors are used for the two orientations. The model reproduces the three‑peak zero‑field spectrum, the field‑induced splitting of the ligand‑derived Kramer’s doublet, and the appearance/disappearance of peaks as the Zeeman energy competes with anisotropy and inter‑spin exchange. The calculated energy‑level diagrams show that some excitations correspond to transitions within the S = 1 manifold (split by D and E), while others involve the S = ½ ligand, leading to a total of three observable YSR peaks at zero field. As B⊥ grows, the S = 1 levels shift non‑linearly, causing the number of accessible transitions to change (3 → 4 → 3), which the authors interpret as magnetic‑field‑driven quantum phase transitions (QPTs). These QPTs can be parity‑preserving (changing the spin projection of the ground state) or parity‑changing (adding or removing a bound quasiparticle).

Overall, the study demonstrates that high‑spin YSR systems in a transverse magnetic field cannot be described by a simple S = ½ picture. Instead, magnetic anisotropy, multi‑spin exchange, and Kondo coupling jointly dictate a complex, non‑linear evolution of the bound‑state energies and the number of observable excitations. While the zero‑bandwidth approach captures the main trends, discrepancies such as the gradual loss of intensity, the lack of abrupt spectral changes when peaks cross the coherence edge, and the sensitivity to molecular orientation suggest that additional effects—multi‑channel Kondo physics, realistic superconducting density of states, and non‑equilibrium transport—must be incorporated. The authors therefore call for more sophisticated theoretical treatments (e.g., numerical renormalization group, quantum Monte‑Carlo, or Keldysh non‑equilibrium Green’s function methods) to fully understand YSR physics in magnetic fields. This work provides a valuable experimental platform for testing spin‑impurity models on superconductors and for exploring quantum phase transitions relevant to topological quantum computing architectures.