Doppler-scanning tunneling microscopy current imaging in superconductor-ferromagnet hybrids

One of the remarkable properties of superconductivity is the emergence of persistent screening currents in the presence of applied magnetic field—the Meissner state. The shielding currents supporting the Meissner state penetrate into the superconductor at a distance on the order of the superconducting penetration length, λ. Similarly, when a magnetic flux quantum, an Abrikosov vortex, enters a type-II superconductor, its existence is supported by the supercurrents that are circulating around the vortex core within a distance on the order of λ. These persistent non-dissipative currents are generated by the bosonic Cooper pairs that form a superfluid condensate.

The superfluid velocity is directly proportional to the gradient of the phase of the order parameter, $∇φ$⁠. It modifies the quasiparticle excitation spectra in the superconductor to^1,2

Here, the Δ is the superconducting pair potential, $vF$ is the Fermi velocity, and $vs$ is the superfluid velocity. The second term in the equation is the Doppler energy. The Doppler term shifts the energy of the quasiparticles up or down depending on the relative direction between the velocities $vF$ and $vs$⁠. It should be noted that this equation is valid only when the Doppler term is small enough that it does not affect the order parameter. For example, it cannot be used to calculate density of states (DOS) near the vortex core where the Doppler term diverges and the quasiparticle density of states is dominated by the vanishing order parameter.

Scanning tunneling spectroscopy measures the spatial distribution of quasiparticle DOS and thus could be used to map the supercurrents in the superconductors with high spatial resolution, being limited by the superconducting coherence length ξ.³ 

The first observation of the effect of the superconducting current on the quasiparticle DOS was observed in planar junctions.⁴ The Doppler term effect was very well resolved although no spatial distribution could be obtained. The effect has been less pronounced in scanning tunneling microscopy (STM) experiment due to the nature of the probe. Lately, several groups have studied the superfluid velocity around Abrikosov vortex core using STM.^5–8 Theoretically, the effect of the Doppler term on quasiparticle DOS has been extended for the case of d-wave superconductors⁹ as well as multi-band s-wave superconductors, such as MgB₂.¹⁰ 

Here, in a superconductor/ferromagnet hybrid planar structure, we show that low temperature scanning tunneling microscopy can be used to image the intricate supercurrent pattern flowing in the superconductor regardless of the origin of the superconducting currents. When directly in contact, the electronic properties of superconductor/ferromagnet systems will be strongly dominated by proximity effects, which can lead to a number of exciting physical phenomena such as so-called long range triplet superconductivity.^11,12 On the other hand, if the two materials are electrically isolated, the resulting system's properties are governed only by the magnetic interactions.^13–16 In particular, the properties of the superconductor can be strongly altered due to the orbital interaction with the ferromagnet's stray field. This could lead to a variety of interesting opportunities such as the ability to guide the supercurrent by altering the magnetic domain structure in the ferromagnet,¹⁷ control vortex mobility,¹⁸ and induce the nucleation of filamentary superconductivity.^19–21 

The majority of experiments on planar magnetically coupled superconductor/ferromagnet heterostructures have so far been primarily focused on global measurements^13,22–25 with theoretical insights based on London formalism.^26,27 However, the increased use of local probes, such as the scanning tunneling microscopy^28,29 and magnetic force microscopy (MFM),^30,31 has begun to reveal a rich body of new physics on the mesoscopic scale. In this work, we examine the local DOS in a thin lead film magnetically coupled to a Co-Pd multilayer. The magnetic domain structure of the Co-Pd multilayer film induces a Meissner current pattern in the magnetically coupled lead superconducting film. Using Doppler-STM current imaging, we map the distribution of currents in the superconducting film, both in the Meissner state and in the presence of induced Abrikosov vortices. We show that STM could be used to measure superfluid velocity in the presence of arbitrary inhomogeneous magnetic field.

The multilayer ferromagnet Co-Pd film was grown by successive dc magnetron sputtering of 2 nm Co and 2 nm Pd for a total of 200 bilayers onto a Si(100) substrate in a vacuum system with a base pressure of 2 × 10⁻⁸ Torr. A small magnetic field of a few hundred Oersted was applied in-plane during the multilayer deposition because this has been shown to promote a more uniform stripe domain structure.³² To inhibit the proximity effect between the ferromagnet and superconducting lead film, a thin 10 nm film of Al₂O₃ was consequently deposited on top of the Co-Pd multilayer film by rf magnetron sputtering of aluminum in a partial pressure of oxygen (30 sccm Ar/10 sccm O₂). The resulting [2 nm Co/2 nm Pd]_N=200 has been characterized by superconducting quantum interference device (SQUID) magnetization measurements and room temperature MFM, as shown in Figure 1. The MFM measurements were performed prior to the deposition of the Pb film and after the STM measurements to confirm that the magnetic pattern remains unchanged after application of magnetic fields of up to 500 Oe. Ultrathin 30 nm Pb films were deposited at 100 K onto the Co-Pd/Al₂O₃ using e-beam evaporation at a rate of approximately 0.2 nm/min and allowed to gradually warm to room temperature; the deposition temperature and rate of annealing strongly influence the final morphology of the film. To avoid contamination of the Pb surface, the deposition was performed in situ in an ultrahigh vacuum deposition chamber directly connected to the STM with a base pressure better than 4 × 10⁻¹¹ Torr.

The low-temperature STM measurements were performed using an ultra-high vacuum Unisoku ³He system capable of reaching temperatures as low as 320 mK in the presence of magnetic fields perpendicular to the sample plane of up to 9 T. Differential conductance spectra (dI/dV) have been acquired using the standard lock-in ac modulation technique with a frequency of 373 Hz and a modulation amplitude of 0.2 mV. The zero bias conductance (ZBC) maps were acquired simultaneously with topography by periodically stopping scanning, disabling the feedback, and acquiring the conductance value at zero bias using the lock-in technique. We have used normal Pt-Ir tips for all measurements.

To provide a better understanding of the stray magnetic field emanating from the underlying ferromagnetic layer, we have simulated the magnetic domain structure in Co-Pd multilayer using LLG Micromagnetic solver.³³ The parameters used in the simulation were extracted from the magnetization loops of the actual film. The simulated volume has 0.2 × 2.0 μm² in cross section and a 5 × 5 nm² cell size. The simulated domain structure shown in Figures 1(c) and 1(d) has domain widths of approximately 200 nm, which is in full agreement with the MFM measurements in Figure 1(a) and that of the same multilayer system in a previous work.³⁴ As shown, the Co-Pd multilayer film breaks up into alternating up (red) and down (blue) magnetic domains with out-of-plane magnetization. Between the oppositely polarized domains, i.e., at the domain walls, the magnetization vector continuously rotates resulting in additional in-plane modulation of the magnetization. From the simulations, we have extracted the perpendicular and parallel components of the stray magnetic fields at a distance of 60 nm above the ferromagnet's film surface (Figure 1(e)). Both the perpendicular and parallel stray fields take a sinusoidal form, with the maximum stray fields in the perpendicular and parallel directions centered above the center of the domain and the domain wall, respectively. We would also like to emphasize that the values for the perpendicular stray field found from this simulation agree well with the estimated values from STM measurements on similar systems.²⁰ 

In Figure 2(a), we show a large scale topographic STM image of the Pb surface of the film. The film is 30 nm thick with surface corrugation on the order of few Angstroms. The ZBC image acquired simultaneously to the STM topography is shown in Figure 2(b). For S/F systems which meet specific materials dependent and geometry dependent properties, it is possible to have Abrikosov vortices spontaneously generated in the superconducting film due to the stray fields of the underlying magnetic template even without applying external magnetic field.^26,31 In our system, the conditions for nucleation of spontaneous vortices are not fulfilled, so they are induced only when an external magnetic field is applied.

The low-temperature ZBC map acquired in the absence of any externally applied magnetic field reveals a clear spatial modulation of zero bias conductance values on the length scale congruent with that of the underlying ferromagnet domain structure having stripe periodicity of (w ≈ 150–200 nm). Representative differential conductance spectra (dI/dV) taken in two characteristic locations with respect to the bright and dark stripes in the ZBC map of Figure 2(b) are shown in 2(c). The variation of the normalized ZBC values across the stripes is relatively small, but well within our resolution. The ZBC values range between approximately 0.2 and 0.14 in the bright and dark regions at T = 1.5 K, respectively. We can attribute this spatial modulation to the pair-breaking effect of the Meissner currents, i.e., the Doppler term in Equation (1), partially shielding the field emanating from the magnetic stripe domains in Co-Pd layer. For reference, the direction of the Meissner currents is illustrated in Figure 3(a).

A series of temperature dependent tunneling conductance spectra were subsequently acquired along the white dashed line of Figure 2(b), and a plot of the resulting normalized ZBC values in Figure 2(d) shows that this spatial electronic modulation persists with the same periodicity up to the transition to the normal state. The fact that the Doppler-induced spatial modulation of the ZBC is visible even at T ∼ T_c is important for application of this imaging method on other systems. The complete temperature dependence of the superconducting gap Δ(T) in the locations (i) and (ii) shown in Figures 2(e) and 2(f) was determined by fitting the tunneling spectra using the equation for tunneling conductance

where f(E) is the Fermi-Dirac distribution and G_nn is the conductance value at high bias. The effect of supercurrents on the tunneling spectrum produces lower coherence peaks and higher zero bias conductance. However, this effect is small for a superconductor/insulator/normal metal tunnel junction,⁵ and it can be accounted for by using a smearing parameter. Therefore, we have used the Dynes modified BCS formula for the superconducting density of states

where T is the temperature, Δ(T) is the temperature dependent energy gap, and Γ(T) is a temperature dependent phenomenological broadening parameter used to account for the finite lifetime of the quasi-particles.³⁵ The variation of the effective superconducting transition temperatures found from the fittings is consistent with the expected behavior based on the map, with the highest transition temperature extrapolated to the lowest ZBC regions in the map of Figure 2(b). Therefore, the small difference in the local effective T_c is due to the pair-breaking effect of the current.

Since the STM tunneling current does not couple directly to the local magnetic field, but rather indirectly through the DOS in lead film, we seek to verify that the stripes seen in ZBC maps indeed correspond to the location of magnetic domain walls in Co-Pd layer underneath the thin lead film. In our recent measurements,³⁴ we have shown that the verification could be achieved by applying external magnetic field $Ha≤Hstray⊥$ and mapping the locations of Abrikosov vortices. The vortices will be located above the domains with magnetization collinear with the $Ha$ since the $Hstray⊥$ will be maximum above that stripe. In Figure 3(a), we show the same conductance map of 2(b), where the white dashed lines have been added to indicate the region with the highest ZBC. Similar conductance maps in small magnetic fields (±200 and ±300 Oe) of the same area as Figure 3(a) are shown in Figures 3(c)–3(f). From the direction of the applied magnetic field and the location of vortex cores, one can unequivocally identify the polarity of the underlying magnetic domains. The conductance maps in applied magnetic field show the vortex cores as regions of higher zero bias conductance due to spatial variation of the superconducting pair potential Δ in the vortex core (on the order of $∼ ξ$⁠) and the supercurrents flowing around the vortex core at a distance on the order of $∼ λ$⁠. Since the increase in states is dominated by the divergent drop in the pair wavefunction within the vortex core, the resulting lateral size of the vortex in ZBC maps gives an accurate measurement of the coherence length, which for this system is around $ξGL$ (1.5 K) ≈ 50 nm; in agreement with other ultrathin Pb films in clean limit.^20,36 The maps in Figures 3(c)–3(f) clearly show that vortices arrange preferentially along stripes, with an increasing density for higher applied magnetic fields. For opposite polarities, vortices are located along previously unoccupied stripes (Figures 3(c)–3(f)). Evidently, the vortex configuration reflects the nature of the underlying stripe magnetic domains of the ferromagnet. When an external magnetic field is applied, the domains anti-parallel to the external field will be at least partially compensated, and as a result, the regions above these domains will experience a decrease in the effective stray field. On the other hand, the regions above domains parallel to the applied field will experience an increase in the effective magnetic stray field. This verifies our initial assumption of the location of the domain walls from the Doppler-STM maps of the Meissner currents in Figure 2(b).

Although the effect of the supercurrents flowing around the Abrikosov vortex is small on the overall ZBC spatial modulation near the vortex, we could nevertheless directly see its Doppler shift in our ZBC maps. It is important to note that the supercurrent around the Abrikosov vortex circulates in opposite direction to the Meissner shielding currents. In the presence of Abrikosov vortices and underlying stripe magnetic domain structure, the Doppler term in Equation (1) is a superposition of supercurrents due to Meissner shielding (above the domain walls) and paramagnetic vortex flux (around the vortex core). Since they circulate in opposite directions, as shown schematically in Figure 3, the appearance of vortices will significantly reduce the Doppler term in the regions when these two contributions meet, i.e., above the domain walls. This reduction in stripe intensity with the appearance of vortices can be seen in Figures 3(c), 3(d), and 3(f). This can be seen even more clearly in the ZBC image 3(e) in which the in right-most stripe the vortices did not manage to nucleate. What we see here is a very clear enhanced vertical stripe separating the right-most and middle domain regions (stripe B), and a completely suppressed stripe between the left-most and central domain (stripe A). The enhancement of the intensity of stripe B is due to increased magnetic field gradient between the two domains without vortices due to application of the external field. The enhanced field gradient directly translates to increased supercurrent density according to London equations, resulting in enhancement of the Doppler term in Eq. (1). On the other hand, the introduction of vortices above the left-most domain essentially causes annihilation of the supercurrents at the domain wall A and loss of Doppler term effect along line A. In Figures 3(b) and 3(e), the direction of the Meissner shielding currents and the vortex paramagnetic supercurrents have been inferred from the contrast change of the stripes when vortices are added into the system. A schematic of the current pattern is reported in Figure 4, in the absence (a) and in the presence of vortices (b), and it is consistent with the theoretical predictions based on Ginzburg-Landau calculations.³⁷ 

In summary, we have performed low-temperature scanning tunneling microscopy measurements on a magnetically coupled Pb/(Co-Pd) superconductor/ferromagnet system. Using the Doppler shift contribution to the quasiparticle excitation spectrum in the superconductor, we obtain direct imaging of the supercurrents in the superconductor using low temperature scanning tunneling microscopy. We demonstrate the technique at the example of superconductor/ferromagnet hybrid structure that produces intricate current pattern consisting of combination Meissner shielding currents and Abrikosov vortex currents. This method could prove invaluable for mapping the supercurrents in applications where maximization of the supercurrent is desired, like in superconducting microwave cavities.^38–40 

Work done at Temple University, where the STM measurements were performed, was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under Grant No. DE-SC0004556. Work at Argonne National Laboratory was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under Grant No. DE-AC02-06CH11357.