Field induced superconductivity in a magnetically doped two-dimensional crystal

Magnetic field induced superconductivity is a rare property in nature due to the sensitivity of spin-singlet Cooper pairing to time-reversal symmetry breaking perturbations. However, in rare cases, an interplay between magnetic fields and ions can be engineered to bring about superconductivity at finite fields. Here we use ultra-thin LaSb$_2$ doped with dilute Ce paramagnetic impurities to demonstrate a magnetic field-induced superconducting dome in a two-dimensional crystal. The reduced dimensionality of the structure enables the use of an in-plane magnetic field to dynamically suppress spin fluctuations on the Ce-site, which leads to an anomalous enhancement of the critical temperature with increasing field. By modelling the spin scattering dynamics across the experimental parameter space, we reveal insight into the complex nature of paramagnetic impurities in magnetic fields at low temperature, and how their manipulation can result in the ability to tune between competing magnetic pair-breaking regimes. Realizing this physics in a two-dimensional crystalline setting invites the application of similar approaches to unconventional forms of superconductivity while also highlighting new experimental standards which should be employed when studying ultra-thin materials in general.

💡 Research Summary

The authors investigate a striking example of magnetic‑field‑induced superconductivity in an ultra‑thin, two‑dimensional crystal. They start from LaSb₂, a recently discovered 2D superconductor with a monoclinic structure that remains superconducting down to a thickness of 4.4 nm (≈5 quintuple layers). Angle‑dependent critical‑field measurements confirm its 2D nature and reveal an in‑plane critical field far exceeding the Pauli limit, indicating that orbital depairing is strongly suppressed in the parallel geometry.

To introduce a controllable source of time‑reversal‑symmetry breaking, the authors substitute a tiny fraction of La atoms with Ce ions, which act as paramagnetic impurities. By varying the Ce flux during molecular‑beam epitaxy they obtain a series of samples with Ce concentrations ranging from essentially zero to ≈0.025 at %. X‑ray diffraction shows that the crystal lattice stays intact, while secondary‑ion‑mass‑spectroscopy provides an estimate of the impurity concentration. As expected from Abrikosov‑Gor’kov (AG) theory, the zero‑field superconducting transition temperature Tc is progressively suppressed with increasing Ce content, and superconductivity disappears completely at a critical concentration of about 0.025 %.

The most remarkable observation occurs for a sample with an exchange‑scattering rate v_s ≈ 0.89 Tc₀ (corresponding to the critical Ce concentration). At zero magnetic field this sample is a weakly localized metal, but when a modest in‑plane magnetic field (μ₀H‖ ≈ 0.6 T) is applied, a full zero‑resistance state emerges, with a maximum Tc of ≈120 mK. Mapping Tc versus H‖ yields a dome‑shaped superconducting region that is absent at H‖ = 0. This constitutes a clear demonstration of field‑induced superconductivity in a crystalline 2D material.

To explain the dome, the authors employ the Kharitonov‑Feigelman (KF) theory, an extension of AG that incorporates the finite polarizability of impurity spins. In this framework the total pair‑breaking rate Γ contains three contributions: (i) exchange scattering from the Ce spins, which is reduced when the spins become polarized by the external field; (ii) the usual orbital depairing associated with the perpendicular component of the field; and (iii) the paramagnetic (Zeeman) depairing of the conduction electrons. The impurity polarization follows a Brillouin function of H‖/T, so Γ decreases from its unpolarized value v_s to a reduced value v_s J/(J + 1) as the spins become fully aligned (J = 5/2 for Ce³⁺). This reduction of Γ initially overcomes the orbital and Zeeman pair‑breaking, causing Tc to rise with H‖. At larger fields the orbital and Zeeman terms dominate again, producing the downturn on the high‑field side of the dome.

The authors further probe the interplay of pair‑breaking mechanisms by applying a small out‑of‑plane field H⊥ while keeping H‖ fixed at the dome maximum. H⊥ rapidly suppresses superconductivity via the orbital effect, yielding an out‑of‑plane critical field μ₀Hc2⊥ ≈ 7 mT. Fits to the Werthamer‑Helfand‑Hohenberg (WHH) model provide the coherence length ξ as a function of H‖. Intriguingly, points on the left and right sides of the dome that share the same Tc exhibit different ξ and London penetration depth λ values. This asymmetry is traced back to the different temperature dependence of Γ on the two sides of the dome: on the low‑field side Γ continues to fall with decreasing temperature, enhancing superconductivity, whereas on the high‑field side Γ is already near its minimum and shows only weak temperature variation.

Overall, the work demonstrates that in a truly two‑dimensional system an in‑plane magnetic field can be used as a dynamic knob to suppress spin‑flip scattering from dilute magnetic impurities, thereby turning a non‑superconducting film into a superconductor. The KF theory captures the essential physics with realistic parameters (antiferromagnetic exchange coupling, J = 5/2 for Ce³⁺) and provides a quantitative description of the entire H‖–T phase diagram.

The implications are broad. First, field‑induced superconductivity does not require exotic mechanisms such as Ising spin‑orbit locking, spin‑triplet pairing, or finite‑momentum (FFLO) states; it can arise simply from the competition between impurity‑induced exchange scattering and conventional orbital/paramagnetic depairing. Second, many 2D materials may unintentionally contain trace magnetic impurities, and their superconducting properties could be dramatically altered by modest in‑plane fields—an effect that might have been missed in previous studies that did not explore the parallel‑field regime. Third, the observed asymmetries in ξ and λ suggest new experimental diagnostics for the dynamical response of magnetic impurities in superconductors.

Finally, the authors propose that similar strategies—precise doping of paramagnetic ions combined with in‑plane magnetic fields—could be applied to a wide variety of layered superconductors, potentially uncovering hidden superconducting phases and offering a new route to engineer superconductivity on demand.