## Abstract

The local effects of isolated magnetic adatoms on the electronic properties of the surface of a superconductor were studied with a low-temperature scanning tunneling microscope. Tunneling spectra obtained near magnetic adsorbates reveal the presence of excitations within the superconductor's energy gap that can be detected over a few atomic diameters around the impurity at the surface. These excitations are locally asymmetric with respect to tunneling of electrons and holes. A model calculation based on the Bogoliubov-de Gennes equations can be used to understand the details of the local tunneling spectra.

Superconductivity and magnetism in solids occur because of dramatically different microscopic behaviors of electrons. In a superconductor, electrons form pairs with opposing spins, whereas to produce magnetism, electrons are required to have their spins aligned to form a net local magnetic moment. The competition between these effects manifests itself in the dramatic reduction of the superconducting transition temperature when magnetic impurities are introduced in a superconductor (1). Within the context of the pioneering theoretical work of Abrikosov and Gor'kov (2) and its extentions (3, 4), a magnetic perturbation reduces the superconducting order parameter and leads to the appearance of quasi-particle excitations within the superconducting gap. Macroscopic planar tunnel junctions doped with magnetic impurities have shown sub-gap features in the superconductor's tunneling density of states (5). No direct measurement, however, has yet been reported on the structure of a magnetically induced quasi-particle excitation on the atomic length scale around a single magnetic impurity.

We directly probed the local electronic properties of a superconductor in the vicinity of a single, isolated magnetic atom with a scanning tunneling microscope (STM). We found that, near magnetic adatoms on the surface of a conventional superconductor, localized quasi-particle excitations at energies less than the superconductor's energy gap are induced in the superconductor by the impurities. Previously, the STM has been used to obtain local information on the nature of the electronic excitations of a vortex in a type II superconductor (6) on length scales comparable with the superconducting coherence length ξ_{0}. In contrast, the excitations reported here are detected over a few atomic diameters near the impurity, at length scales far shorter than ξ_{0}. We can explain the main features of our data with a model calculation of the local electronic properties of a magnetically doped superconductor based on the Bogoliubov-de Gennes equations; however, some features of the data remain unexplained.

We performed our experiments using an ultrahigh vacuum STM, which operates at temperatures down to *T* = 3.8 K. We used a single-crystal Nb(110) sample (99.999% purity) that was cleaned by numerous cycles of ion sputtering and vacuum annealing. Niobium samples of similar quality have bulk transition temperature *T*_{c} ∼ 9.2 K, superconducting energy gap 2Δ ∼ 3.05 meV, and ξ_{0} ∼ 400 Å. STM images of the sample after it had been processed and cooled to low temperatures showed the sample surface to be well ordered, with terraces as large as 100 Å, and to have an acceptable terrace defect density for our experiments. The main surface impurity was oxygen, which images as a dip in STM topographs. The local tunneling density of states (LDOS) of the Nb surface was obtained from measurement of the differential conductance *dI*/*dV* (where *I* is the current) of the STM junction versus sample bias voltage *V* (with respect to the tip) performed under open feedback loop conditions with standard low-frequency ac lock-in detection techniques. The width of the tunneling barrier (the height of the tip above the surface) during the measurements was adjusted before opening the feedback loop by setting the junction impedance *R*_{j} at an eV >> Δ. We used a polycrystalline Au wire as our tip; however, the chemical identity of the last atom on the tip is unknown.

We first measured the tunneling density of states for the Nb surface without the magnetic impurities. The spectrum in Fig. 1A is highly reproducible at different locations on the Nb surface, such as near atomic step edges and in the vicinity of surface defects such as oxygen. This spectrum can be fitted very well with the thermally broadened Bardeen-Cooper-Schrieffer (BCS) density of states (Fig. 1A) with a value of 2.96 meV for 2Δ, which is consistent with that reported for Nb, and a sample temperature of 3.85 K (7).

We deposited a low coverage (about 0.005 of a monolayer) of adatoms on the cooled surface from calibrated electron-beam evaporation sources and examined the effect on the superconductor's LDOS. We chose Mn and Gd impurity atoms because of evidence for their magnetic behavior in bulk Nb (8, 9); hence they were likely candidates as magnetic impurities at the surface. As a control, we also repeated the measurements with ostensibly nonmagnetic Ag adatoms. After dosing the surface with one kind of impurity, we imaged the surface to find isolated adatoms on the terraces. The adsorbates image as bumps with heights of 1.0 Å in the case of Mn, 1.8 Å for Gd, and 0.8 Å for Ag in the STM topograph measured at *R*_{j} = 10 megohm.

Far away from the impurities (>30 Å), local tunneling spectroscopy showed that the LDOS is similar to that of the bare Nb surface before adatom deposition. However, in the immediate vicinity of magnetic adatoms, the LDOS was modified significantly. Spectra for Mn measured with the tip centered over an isolated Mn adatom and over a bare Nb spot 16 Å away are shown in Fig. 1B. Near the Mn impurity, there is an enhancement of the density of the excitations at energies less than the Nb's energy gap (|*V*| < 1.5 mV) in an asymmetric fashion about the Fermi energy *E*_{F}. This asymmetric contribution within the gap is accompanied by a similarly asymmetric reduction of the state density for the states at the gap edge. As we describe below, the appearance of the low-lying bound excitations and the local asymmetry between the electron and hole excitations are distinctive signatures of the magnetism of the impurities.

The details of the impurity-induced changes of the LDOS can be seen more clearly by plotting the difference between the *dI*/*dV* spectra measured near the impurity and that measured far away from the impurity where we observed an LDOS described by BCS. Such difference spectra measured at different lateral distances relative to the center of the impurity adatom are shown in Fig. 2. The results for Mn and Gd impurities show clear peaks in the LDOS due to the bound excitations in the immediate vicinity of these impurities at energies less than the gap. The amplitude of the peaks and the sign of the asymmetry about *E*_{F} are distinct signatures of the adatom's perturbing potential, as demonstrated by the differences between the data on Mn and Gd. The Ag atoms, being nonmagnetic, appear not to modify the superconductor's LDOS near *E*_{F} in any significant way. For Mn, the largest contribution of the bound excitation to the spectra occurred when the tip was centered over the impurity site, whereas for Gd this contribution was maximum when the tip was displaced laterally by 6 Å from the center of the adatom. Despite the variation, however, the impurity-induced bound excitations for both Mn and Gd impurities could only be detected within 10 Å around the impurities. These spatial characteristics are easily imaged by measuring the ac *dI*/*dV* at a fixed voltage while scanning the tip in constant dc current mode. Such images are shown in Fig. 3 along with the constant-current images for Mn and Gd adatoms. The bound-state excitation for each of the magnetic impurities is localized to the dark regions in these gray-scale images.

To account for the spectroscopic characteristics and spatial structure of the magnetic impurity-induced bound excitations observed in our experiments, we describe a model calculation of the local tunneling spectra for a classical spin impurity embedded in a bulk superconductor. In our model, we ignore the dynamics of the spin and choose a spherical geometry that ignores any possible surface effects. Self-consistent calculations by Schlottmann (10) show evidence for local suppression of the superconducting order-parameter (pair potential) on a length scale comparable with the Fermi wavelength λ_{F} around a magnetic impurity. However, tunneling measurements do not measure the order-parameter directly; therefore, we calculated the variation of the LDOS caused by the local changes of the order-parameter and the bound excitations predicted in (3) around the impurity. We considered the impurity to create a spin-dependent exchange potential *J* and an ordinary scattering potential *U*, which are both finite over a region of atomic dimensions with radius *a* around the impurity. In our model, we assumed *J* to be ferromagnetic; however, an antiferromagnetic interaction would produce the same results but with a change in the sign of the bound excitation's spin. In view of Schlottmann's calculations, for simplicity we assumed that the magnetic impurity suppressed the order-parameter to zero locally, for *r* < *a* (where *r* is the radial distance from the impurity), whereas outside this region the order-parameter was taken to be constant and equal to that of pure Nb. The spatial variation of the superconductor's properties can be described with the Bogoliubov-de Gennes (BdG) equations, which are coupled Schrödinger-like equations for time-reversed pairs of states in the superconductor (11, 12). These pairs of states correspond to electron-like and hole-like states that describe, respectively, the local tunneling excitations at positive and negative sample bias. We solved the BdG equations, considering only the lowest (*l* = 0) angular momentum state to be affected by the impurity, and without requiring a self-consistency condition for the pair-potential.

Consistent with the results in (3), we found that a finite value of *J* breaks the time-reversal symmetry between the electron-like and the hole-like states, and the BdG equations show that there is one bound excitation with energy *E*_{B} < Δ. This state, which is a mixture of both electron and hole excitations in the superconductor, contributes to the *dI*/*dV* spectra at eV = ±*E*_{B}. The spatial characteristics of these contributions are governed by the wave function of the bound excitation's electron and hole components, which oscillate with period of order λ_{F}, and decay with distance *r* from the impurity as (1/*r*^{2})*exp* (−2*r*/ξ), where ξ = ξ_{0}(Δ/). As shown in Fig. 4, for small *r*, the square of the electron and the hole components behave as 1/*r*^{2}, and they are ultimately cut off for *r* ≳ λ_{F}/2 (2.7 Å for Nb). This behavior is consistent with our observation that the bound excitation contribution to the LDOS decays rapidly within a few lattice constants near the impurity (13).

In our model, the presence of the magnetic potential that creates the bound excitation also causes a phase shift between its electron and hole components. An explicit example of this behavior is shown in Fig. 4, which displays the radial dependence of the electron and hole components for a particular value of *J*. A direct consequence of this phase shift is a local asymmetry in the spectra measured at positive and negative bias. The electron-hole asymmetry is largest at the impurity site and absent if the spectrum is spatially averaged over the whole system, as it is in the planar tunnel-junction experiments (5, 14). More specifically, for small |*J*|, the model shows that the bound excitation has a spin that is aligned with respect to the impurity, and the electron-like excitations are slightly favored at the impurity site. Increasing |*J*|, however, results in a monotonic increase of the phase shift (see inset of Fig. 4) and of the local asymmetry, accompanied by a shift of *E*_{B} toward the center of the gap. At a critical value of |*J*| = *J*_{c}, with *E*_{B} = 0 (at *E*_{F}) and the phase shift at π/2, there is a dramatic change in the nature of the bound excitation. For |*J*| ≥ *J*_{c}, the bound excitation's spin becomes anti-aligned with that of the impurity, whereas at the same time the local asymmetry between the electron and the hole components switches and heavily favors the hole-like excitations (the case of Fig. 4). In this regime, a further increase in |*J*| moves *E*_{B} back toward the gap edge. The dramatic behavior at *J*_{c} in our model and that of Shiba's in (3) are linked with the changes in the superconductor's ground state, previously investigated by Sakurai (15), in the limit of a strong magnetic impurity. In this regime, it is energetically favorable for the superconductor to add an unpaired spin with a favorable orientation at the impurity site. Our calculations show that this change in the ground state of the superconductor is reflected in the large local asymmetry of the bound excitation probed by tunneling. The local asymmetry in our model is fundamentally caused by the potential *J*; however, the spin-independent potential *U* can alter its strength.

Our model calculation can account for the detailed electron-hole asymmetry observed in local *dI*/*dV* measurements. This can be seen in Fig. 5, which shows a fit to the *dI*/*dV* difference spectra measured with the tip centered over the Mn adatom. To compute the fit, we calculated the wave function of not only the bound but also the extended excitations (*E* > Δ) in the superconductor at the impurity site and have thermally broadened the results for *T* = 3.8 K. We used *J* = 4 eV and *a* = 2.50 Å (16). These parameters show that Mn adatoms act as a strong magnetic impurity on the Nb surface, a fact that seems likely considering the strong overlap of the Mn *d* levels with those of the Nb surface. Our model, however, does not capture the detailed spatial dependence of the spectra in the case of Gd. A more through theoretical treatment would require a calculation that is self-consistent and accounts for the electronic structure of the surface.

During preparation of this manuscript, we have become aware of other recent theoretical work on the local electronic properties of a superconductor with magnetic impurities relevant to our experiments (17, 18).