The theory of superconductivity developed by Bardeen, Cooper and Schrieffer (BCS) explains the stabilization of electron pairs into a spin-singlet, even frequency, state by the formation of an energy gap within which the density of states is zero. At a superconductor interface with an inhomogeneous ferromagnet, a gapless odd frequency superconducting state is predicted, in which the Cooper pairs are in a spin-triplet state. Although indirect evidence for such a state has been obtained, the gap structure and pairing symmetry have not so far been determined. Here we report scanning tunnelling spectroscopy of Nb superconducting films proximity coupled to epitaxial Ho. These measurements reveal pronounced changes to the Nb subgap superconducting density of states on driving the Ho through a metamagnetic transition from a helical antiferromagnetic to a homogeneous ferromagnetic state for which a BCS-like gap is recovered. The results prove odd frequency spin-triplet superconductivity at superconductor/inhomogeneous magnet interfaces.
In 1961, Ivar Giaever reported1 the energy gap in the excitation spectrum of the underlying metallic band structure of superconducting Al, which directly verified the theory of superconductivity developed by Bardeen, Cooper and Schrieffer2 (BCS). The superconducting density of states (DOS) is determined by the symmetry of the Cooper pair wavefunction in time, orbital and spin spaces. For BCS superconductors such as Al and Nb, the Cooper pairs are in a spin-singlet state in which their wavefunction is even with respect to exchange of time coordinates—this is so-called even-frequency superconductivity.
At a superconductor/ferromagnet (S/F) interface, in which the magnetization of the F layer is inhomogeneous, an additional odd frequency pairing symmetry is predicted in which the Cooper pairs are in a spin-triplet state with either zero (Sz=0) or a net spin projection3,4 (Sz=±1). For simplicity, we will hereafter refer to these different types of Cooper pairs as spin-zero and spin-one states. The classification odd frequency stems from the fact that the wavefunction of the Cooper pairs is odd with respect to an exchange of the time coordinates.
Indirect evidence for the generation of odd frequency triplet states has emerged from measurements of S/F/S Josephson junctions, which demonstrate a coherence length in F that is much longer than predicted for BCS (singlet) proximity effects5,6,7,8,9,10,11 or in junctions with ferromagnetic insulators with high spin-polarizations12. Odd frequency triplet pairing has also been inferred from critical temperature measurements of S/F/F spin valves13,14,15,16,17,18,19. The superconducting excitation spectrum for the odd frequency triplet state should be gapless, meaning the net subgap DOS should be enhanced rather than suppressed20,21 at certain energies (voltages). To date, tunnelling conductance measurements to detect odd frequency superconductivity have mainly focused on the F-side of metallic22,23,24 and oxide25,26,27 S/F interfaces for which a superconducting minigap appears in the DOS because of the superconductor proximity effect28, and which has been predicted to contain both even and odd frequency components and to disappear on a length scale of the ferromagnet singlet pair coherence length ξF,Singlet of 1–5 nm. However, discriminating between the odd and even frequency components in the DOS has proven to be controversial and so the results have so far been inconclusive. Eschrig and Löfwander theoretically demonstrated that a spin-active interface also enhances odd frequency pairing correlations on the S-side of an S/F interface29. Here the superconducting DOS should in principle be easier to detect because, unlike on the F-side, the DOS is not masked by the normal state background.
To isolate the odd frequency contributions with certainty, it is necessary to amplify them. This can be achieved by introducing a spin-active layer—a magnetic layer with a magnetization direction that is non-parallel to the F layer—at the S/F interface3. Such a layer can enhance the pairing amplitude of the spin-triplet state. The mechanism behind this effect first involves mixing the singlet pairs because of the spin-dependent phases picked up by electron scattering at the S/F interface, which then results in the emergence of a spin-zero triplet state. The presence of a spin-active layer then rotates the triplet pairs in spin-space and spin-aligned triplet pairs form.
In this article we report scanning tunnelling DOS measurements on superconducting films of Au/Nb proximity coupled to an epitaxial film of Ho. These measurements reveal pronounced changes to the subgap DOS in Nb that sensitively depend on the magnetic phase of Ho; by controlling the magnetic structure of Ho we are able to distinguish between singlet and triplet pair correlations in the superconducting DOS of Nb, since through the magnetic phase of Ho we are able to amplify (suppress) the triplet (singlet) components.
To obtain discriminating evidence for the symmetry of the superconducting state at S/F interfaces and to correlate subgap structure to magnetism, we performed scanning tunnelling spectroscopy measurements on epitaxial Nb (20 nm)/Ho (9.5 nm)/Nb (6.5 nm) thin films capped with a 3-nm-thick protective layer of Au (see Fig. 1a and for supporting X-ray diffraction data see Supplementary Figs 1 and 2). The Au protects the structure from oxidation, while the 6.5-nm-thick non-superconducting base layer of Nb provides the correct seed for epitaxial growth30. The Nb (20 nm)/Ho (9.5 nm)/Nb (6.5 nm) multilayer had a superconducting transition of ∼6.6 K and without Ho of ∼8.6 K (see Supplementary Fig. 3).
In single crystal Ho a basal plane helical magnetic phase forms below 133 K (refs 31, 32), where the helix turn angle, the angle between magnetic moments in adjacent layers, is 30°. On application of a sufficiently large field parallel to the basal plane, a metamagnetic transition to a stable ferromagnetic (F) state takes place in which the moments are aligned in plane33. We show below and in ref. 30 that our Ho thin films behave in a similar way.
In Fig. 1b we have plotted the in-plane magnetization versus field loop M(H) for an epitaxial sample at 10 K. The initial magnetization curve shows a transition to a square F hysteresis loop, which is stable over subsequent field cycles. The fact that the initial magnetization curve goes outside the loop demonstrates a phase transition to an F state. The saturation magnetization (Ms) reaches ∼2,026 emu cm−3, which is close to the theoretical value of 10.34 μB per atom34 and shows that the Ho has near bulk properties.
In Fig. 1c we have plotted the zero-field magnetic phase diagram of our Ho. This was created by the following procedure. First, an in-plane magnetic field (which we call the ‘set field’ or HSET) was applied and the corresponding magnetization was measured (M(HSET)). This field was then switched off; therefore, the remanent magnetization Mr due to HSET can be measured. This procedure was repeated with successively larger values of HSET until saturation was achieved. Below HSET=200–250 mT, Mr and M(HSET) barely increase, which implies the helix phase in Ho is robust (region 1 of Fig. 1c), but beyond this field range, Mr and M(HSET) sharply increase indicating the onset of the metamagnetic transition in which the helix deforms and contains a significant F component (region 2 of Fig. 1c). Beyond approximately 500 mT, the Ho is F (region 3 of Fig. 1c).
Scanning tunnelling spectroscopy was performed at 290 mK with an IrPt tip (well below the superconducting transition temperature of the films investigated) mounted on a 3He cryostat in which in-plane magnetic fields of up to 500 mT could be applied35. The spatial distribution of the superconducting-related spectral features was investigated and, in addition to BCS gaps, two different subgap structures consistently appeared in the DOS in the as-cooled tunnelling conductance dI/dV versus bias voltage V as shown in Figs 2 and 3; dI/dV is normalized to the normal state conductance at high bias (5 mV). The most common non-BCS subgap structure consisted of a double peak in dI/dV at symmetrical values of bias voltage (which we name the double peak spectra; see Figs 2a and 3e). In other areas, a conductance peak at zero-bias voltage was obtained (which we name the zero peak spectra; see Figs 2b and 3f); however, this feature was far less common (in ∼10% of scans).
Subgap dependence on film surface and magnetic phase
To rule out the possibility of spurious effects from surface defects as an explanation of the subgap structure and to ensure that the subgap structure is related to the superconductor proximity effect, we measured the spatial dependence of the tunnelling DOS and searched for correlations between the spectral features and the surface topography (Fig. 3): as shown, the subgap structure is sensitive to the surface topography and no subgap structure was obtained in regions with a high concentration of defects, showing up in the topography map as increased noise or protrusions and as abundance of black areas in the spectral map (see, for example, around x=−20 nm and y=−40 nm in Fig. 3a and b). Around grain boundary-like regions we observed either BCS-like gaps (often shallow) or metallic structure, but on defects we only observed noisy metallic spectra. For further details on how the spectral map in Fig. 3b is obtained from the measured DOS spectra, see Supplementary Fig. 4 and Supplementary Note 1.
Conductance maps at different voltages (0, −0.35, −0.5 and −1.5 mV) were also determined from the 16 × 16 matrix of DOS spectra recorded on the sample area shown in Fig. 3 (see Supplementary Figs 5 and 6). These maps show a good reproducibility of the local spectral features (Fig. 3c–f), which is in agreement with the spectral map reported in Fig. 3b.
We attribute the BCS-like spectra to positions where the Ho magnetic structure is disturbed such that no pronounced noncollinearity of the magnetization is present. While we cannot confirm this, to be certain that the BCS gap structure is not related to discontinuities of Ho and therefore to the absence of a magnetic proximity effect, we performed transmission electron microscopy (TEM) on cross-sectional lamellae of the specimen prepared by focused ion beam (FIB); see Fig. 4 and Methods for further details. Low-magnification scanning transmission electron microscopy images (Fig. 4a,b) show that the Ho layer is continuous, which is further supported by energy-dispersed X-ray data (see Fig. 4c–e). High-resolution TEM (Fig. 4f–i) shows that the Nb and Ho layers are crystalline, with little evidence of interdiffusion. Note that during the fabrication of the TEM lamella the top half of the Nb layer and the entire Au layer are damaged and amorphized because of a combination of Ga+ ion implantation occurring during the FIB processing and the deposition of a Pt/C capping layer.
The metallic spectra (Fig. 3c) might indicate surface contamination that suppresses superconductivity locally or that disables proper phase locking of the lock-in measurement. Importantly, the subgap structures (Fig. 2) do not appear preferentially at defects, but are more pronounced in clean regions, which is consistent with the presence of a stronger superconductor proximity effect.
Finally, we also tested control samples of Au (3 nm) on epitaxial Nb (20 nm) without Ho. On these samples only BCS gaps or metallic structure were ever observed (see Supplementary Fig. 7), which confirms that the subgap structure observed in Figs 2 and 3 are related to an unconventional proximity effect due to Ho interacting with Nb.
The most striking evidence that the subgap structure is related to the interaction of Ho with Nb and therefore to an exotic proximity effect was obtained by monitoring the dependence of the subgap features to the magnetic structure of Ho by applying magnetic fields. We first focus on the effect that magnetic fields have on the double peak spectra (similar to that shown in Figs 2a and 3e). In Fig. 5 we have plotted such spectra in zero field and following the application of successively larger in-plane set fields HSET, which cover the metamagnetic transition of Ho (other fields were also measured but are not shown for clarity). The same field sequence as that used to acquire the magnetic phase diagram in Fig. 1c was applied: (1) spectra were measured with the in-plane field on (HSET); (2) the field was switched off and spectra in zero field were obtained; Steps 1 and 2 were repeated with successively larger values of HSET. Spectra with the field on or off show qualitatively similar behaviour: a disappearing subgap structure in the F phase (500 mT; Fig. 5f); a field-dependent subgap structure below 200 mT where the bulk helix hardly changes with applied field (see Fig. 1c); and the appearance of a zero peak near 150 mT.
This behaviour is clearest in Fig. 5g, where we have plotted the difference (ΔG) in the differential conductance obtained at double peak voltage values to the differential conductance obtained at zero voltage as a function of HSET. Positive values of ΔG indicate dominant double peaks, while negative values indicate a dominant zero peak. The trend of ΔG (HSET) can be correlated to the magnetic structure of Ho. For fields between 200 and 500 mT, the entire magnetic helix in Ho (including surface states) irreversibly deforms and so the degree of magnetic inhomogeneity must decrease causing rapid suppression of the odd frequency components3,4, meaning that the DOS should resemble a BCS gap, consistent with the spectra shown in Fig. 5f. The spectra between 0 and 250 mT are perhaps the most interesting since the subgap structure shows an inversion in the sign of ΔG, despite the fact that the bulk helix in Ho is largely unaffected by magnetic fields in this range (Fig. 1c).
In the low field regime (<250 mT), the helix remains intact at least in the bulk of the Ho (Fig. 1c); however, at the surface of Ho the interlayer antiferromagnetic nearest-neighbour exchange-coupling energy abruptly decreases, and the surface stabilizes ferromagnetically (in-plane) over several atomic planes36,37. From the Mr/Ms ratio of ∼0.08 at 250 mT, we estimate an F region of ∼0.5 nm per surface or approximately two atomic planes (the c axis parameter at low temperature is 0.564 nm). Such a surface is characteristic of a spin-active interface and indeed in this field regime a zero-energy peak appears in the DOS, which is the sought after signature of the odd frequency spin-one triplet component20,21.
We stress here that spectra similar to that shown in Fig. 3c,d were unaffected by magnetic field, which is consistent with the view that in those regions with pure BCS gaps or metallic structure the proximity coupling between Ho and Nb is weak. We performed additional tests to rule out artefacts because of magnetostrictive drifts. For instance, if a double-peak structure vanished by increasing the magnetic field, we scanned the surrounding area to check whether it appeared in a position nearby but none were observed. The double-peak subgap structure of Fig. 5 has been recorded in an area where no zero-bias peak is observed in the as-cooled DOS.
To understand further the behaviour of zero-energy peaks, we investigated the effect of a magnetic field where zero peaks dominate the as-cooled DOS. As shown in Fig. 6, the zero peak first increases with field before disappearing before the onset of the metamagnetic transition. This is consistent with our hypothesis that such zero-energy peaks are related to the F surface of Ho. This may also explain why zero peaks do not always appear in the as-cooled state as the magnetic noncolinearity at the surface of Ho is likely to spatially vary.
The fact that the zero-energy peak in Fig. 6 first increases with field before decreasing is broadly consistent with the zero peak behaviour observed in Fig. 5 (although the initial surface magnetic state of Ho must be different in Fig. 5 than in Fig. 6 as the zero field peak was absent in as-cooled state). The behaviour of the zero peaks in both Figs 5 and 6 suggests that the degree of noncollinearity between the surface F component and the helix initially increases with field until the field is sufficient to align the surface spins to the top spins of the helix and initiate the metamagnetic transition (>150 mT).
We also investigated the temperature dependence of a zero peak and the effect of out-of-plane magnetic fields to rule out Kondo as an explanation of their appearance. The zero peaks typically disappear below 1 K (Supplementary Fig. 8), although at higher temperatures the differential conductance becomes noisy since the tip–sample position is unstable. With an out-of-plane field, the magnitude of a zero peak is always found to decrease and none were observed to split with field (Supplementary Fig. 9), which is inconsistent with a Kondo effect. The zero peaks disappear below an out-of-plane field of 500 mT (Supplementary Fig. 9).
The existence of the subgap structure alone indicates unconventional superconductivity; however, to understand more fully the subgap structure and its relation to odd frequency correlations and that of the zero-energy peak to surface magnetism, we have numerically calculated the DOS using the quasiclassical theory of superconductivity in the diffusive limit and solved in a fully self-consistent way (see Supplementary Note 2). This includes both the suppression of superconductivity near the interface region and the induced odd frequency pairing in the superconducting region.
Figure 7 shows the obtained DOS in the superconducting region near the Au/Nb interface using the following realistic material parameters: RB/RS=2, RS=RF, ξS=15 nm, h/Δ=3, λ=3.4 nm, τF,ϕ=1.3, τS,ϕ=0.4, dS=20 nm, dF=9.5 nm, DF/Ds=0.65, where RB is the resistance of the barrier between Nb and Ho, RS(F) is the bulk resistance of the Nb (Ho) region, DF(S) is the diffusion coefficient of the Ho (Nb) layer, ξS is the superconducting coherence length, h is the exchange field of Ho, Δ is the superconducting energy gap in Nb, λ is the period of the bulk helix in Ho, dS is the thickness of the Nb layer, dF is the thickness of Ho and τS(F),ϕ describe the spin-dependent interface scattering on the S (F) side of the interface.
In the as-cooled state, we assume that a magnetic helix forms in Ho and we model the effect of surface noncollinearity via spin-active boundary conditions (see Supplementary Note 2). In Fig. 7a there is no misalignment between the surface component and the helix and the double-peak structure dominates, while in Fig. 7b,c the surface component is misaligned (45° and 90°) with respect to the helix in the basal plane, in which case a dominant zero-energy peak is observed. In the fully F state, the subgap structure disappears (Fig. 7d).
The experimental features are qualitatively well described by this model, as noncollinearity between the surface F component and the helix dictates whether the double-peak or zero-energy peak structures arise. This model also provides an indirect explanation for why it is more likely to observe the double peaks than a zero peak in the as-cooled DOS. First, the exact magnetic configuration of Ho is likely to vary across the surface of Ho, and, second, that the likelihood of magnetic noncollinearity at the surface is low since ferromagnetic coupling will always prefer a more collinear surface state that favours the double peak structure.
In the model, the subgap structure arises because of odd frequency pairing correlations. The crossover from double peaks to a zero peak occurs in the model as the degree of noncollinearity increases between the surface F component and the helix. This effect could be related to going from dominant spin-zero odd frequency components in the collinear alignment to a scenario where all triplets, including the spin-one component (relative to the interface moment), contribute for the case with strong misalignment. Spin-split peaks inside the subgap region of the superconductor have been shown theoretically to occur in an S/F bilayer when only the spin-zero, odd frequency component is present38. This occurs because of spin-dependent scattering at the interface even in the absence of any magnetic inhomogeneity, which induces an effective exchange splitting in the superconductor. On the other hand, the generation of the spin-one odd frequency component is more efficient for the noncollinear alignment between the surface F component and the helix. In this case the zero-energy DOS becomes enhanced because of the gapless nature of odd frequency pairing and the fact that, unlike the spin-zero odd frequency component, the electrons in the spin-one pairs are aligned and affected equally by an effective exchange field induced by the spin-active interface so that they should not give rise to any spin-split structure in the DOS. We note that the triplet state observed here is different from that observed in Sr2RuO4, which is odd parity but even frequency and requires extreme sample purity39.
In conclusion, we have observed a magnetic-phase-dependent superconducting subgap DOS in Nb proximity coupled to Ho. The results demonstrate a profound modification of the superconducting state because of the presence of odd frequency spin-triplet pair correlations. The existence of triplet states in a superconductor is profoundly interesting in its own right. Such available states mean that within the energy gap of a superconductor a finite net spin polarization exists in the absence of dissipation. One intriguing possibility is that the spin-one triplet states could accommodate a spin accumulation, meaning that in a nonequilibrium S/F device, the S layer could serve as a spin sink or channel for transmitting spin in spintronics40.
Epitaxial thin-film growth
Au/Nb/Ho/Nb samples were grown by direct current magnetron sputtering on heated a-plane (110) sapphire substrates. The deposition chamber was continuously cooled via a liquid nitrogen jacket, giving a base pressure of ∼10−8 Pa with the water partial pressure below 10−9 Pa as confirmed by an in situ residual gas analyser. A base layer of 6.5-nm-thick, non-superconducting Nb (110) was first grown at a substrate temperature of 880 °C using a deposition rate of 0.035 nm s−1. This layer was essential to avoid oxidation of Ho and to initiate epitaxial growth. A 9.5-nm-thick layer of epitaxial Ho (002) was then grown on the Nb at 650 °C at a rate of 0.035 nm s−1. A 20-nm-thick layer of superconducting Nb (110) was then grown on Ho. Finally, substrates were allowed to cool to room temperature in 1.5 Pa of Ar and finally were capped with a 3-nm-thick layer of polycrystalline Au. While Au protects the underlying structure from oxidation, it also wets well to Nb and forms a highly stable intermetallic compound with Nb (and therefore at the Nb/Au interface in our experiment).
Scanning tunnelling microscopy
The DOS spectra were acquired using a custom-built scanning tunnelling microscope (STM) in the spectroscopy mode with an IrPt tip, mounted on a 3He cryostat. The STM consists of one-segmented piezo tube for scanning and coarse approach, using slip and stick motion. In situ superconducting magnets can apply in plane and out-of-plane magnetic fields up to 500 mT and 1 Tesla, respectively. The electronic system has a voltage resolution of roughly 20 μV at base temperature (240 mK). In-depth instrument details are described in ref. 35, and its suitability for studying superconducting proximity effects has been demonstrated in ref. 41.
The topography maps were recorded by slowly scanning in the x direction. The images contain 256 × 256 data points. For recording the differential conductance dI/dV spectra the scan was stopped, and the feedback loop was switched off at a current of 300 pA and a voltage of 3 mV. The spectral map Fig. 3b contains 16 × 16 spectra. The spectra were acquired using a lock-in amplifier. The direct-current-bias voltage was modulated with an a.c. voltage, with root-mean-square amplitude of 14 μV and frequency of 733 Hz. The dI/dV was measured using a current-to-voltage converter with a gain of 1 V nA−1 and the measuring time per spectrum was typically ∼1–2 min. All spectra were acquired at a tunnelling resistance of 10 MΩ where the signal-to-noise ratio was optimal while avoiding distortions of the spectrum due to the presence of the counterelectrode. This tunnelling resistance is the value that we routinely adopt to perform STM measurements with our set-up.
For higher temperature measurements, the STM was allowed to stabilize for at least 5 min at each new temperature before spectra were acquired. All spectra are normalized with respect to the ohmic conductance measured at 5 mV and so well beyond the superconducting gap edge and voltage offsets were subtracted using the symmetry of the spectra. To ensure reproducibility of the observed superconducting-related spectral features and minimize noise contribution, each differential conductance spectrum is the average of three scans performed on the same sample spot.
Lamellae for TEM analysis were prepared using a FEI Helios Nanolab focused ion beam/scanning electron microscope (FIB/SEM). A 2-μm-thick capping layer was deposited to protect the film. Scanning transmission electron microscopy-High-Angle Annular Dark Field images and energy-dispersed X-ray maps were acquired on a FEI Osiris (200 kV acceleration voltage) equipped with a high-brightness field emission gun (X-FEG) and a Bruker Super-X detector.
How to cite this article: Di Bernardo, A. et al. Signature of magnetic-dependent gapless odd frequency states at superconductor/ferromagnet interfaces. Nat. Commun. 6:8053 doi: 10.1038/ncomms9053 (2015).
The work was funded by the Royal Society through a University Research Fellowship held by J.W.A.R., the Leverhulme Trust (J.W.A.R., E.S. and M.G.B.) through an International Network Grant (IN-2013-033), and the EPSRC through NanoDTC EP/G037221/1 (A.D.B. and J.W.A.R.). Further support was received from ERC AiG ‘Superspin’ (M.G.B.). Y.G. acknowledges financial support from King's College, Cambridge. A.D.B. acknowledges additional financial support from the Schiff Foundation and Cost Action MP1201. J.L. was supported by the ‘Outstanding Academic Fellows’ programme at NTNU and the Norwegian Research Council grants 205591 and 216700. Useful discussion with K. Halterman and F. S. Bergeret are acknowledged. G.D. and C.D. acknowledge funding from the ERC under grant number 259619 PHOTO-EM. C.D. acknowledges financial support from the EU under grant number 312483 ESTEEM2.
Supplementary Figures 1-9, Supplementary Note 1-2 and Supplementary References