Abstract
The interfacial coupling of two materials with different ordered phases, such as a superconductor (S) and a ferromagnet (F), is driving new fundamental physics and innovative applications. For example, the creation of spinfilter Josephson junctions and the demonstration of triplet supercurrents have suggested the potential of a dissipationless version of spintronics based on unconventional superconductivity. Here we demonstrate evidence for active quantum applications of SFS junctions, through the observation of macroscopic quantum tunnelling in Josephson junctions with GdN ferromagnetic insulator barriers. We show a clear transition from thermal to quantum regime at a crossover temperature of about 100 mK at zero magnetic field in junctions, which present clear signatures of unconventional superconductivity. Following previous demonstration of passive SFS phase shifters in a phase qubit, our result paves the way to the active use of spin filter Josephson systems in quantum hybrid circuits.
Introduction
Superconductor (S)/Ferromagnet (F) interfaces are a special class of hybrid systems where different ordered phases meet and generate new nanoscale phenomena and new forms of global order^{1,2}. A ferromagnetic barrier in a Josephson junction (JJ) generates novel physics^{3,4} and represents a technological key for advances in weak superconductivity, spintronics and quantum computation^{5,6,7}. Recent interest in ultralowpower, highdensity cryogenic memories has spurred new efforts to simultaneously exploit superconducting and magnetic properties so as to create novel switching elements having these two competing orders^{8}. SFS junctions are expected to shed light on several aspects of unconventional superconductivity, including transport through spinaligned triplet Cooper pairs^{4,9,10,11,12,13,14}.
The NbNGdNNbN junctions investigated in these experiments are spin filter devices^{15} with an unconventional predominant second harmonic currentphase relation (CPR)^{16}. By changing the thickness of the GdN ferromagnetic insulator (FI) barrier it is possible to change its magnetic properties and hence the spin filter efficiency (SFE)^{16,17}. In this paper we report measurements on NbNGdNNbN junctions for very low and very high SFE values, from almost a few percent up to 90%, with an intermediate value of 60%. By increasing the thickness of GdN we also obtain junctions with lower values of the I_{c}R_{n} product, where I_{c} is the critical current and R_{n} the normal state resistance. Following the previous demonstration by Feofanov et al.^{18} of passive SFS phase shifters in a phase qubit, the experiment reported here demonstrates the active quantum potential of SFS JJs via the occurrence of macroscopic quantum tunnelling (MQT) in spin filter devices.
Results
Transport properties of spin filter JJs
The hallmark of the spin filter effect is the decrease in resistance in the R vs T curves below the ferromagnetic transition, as shown in Fig. 1a (T_{Curie}≃33 K for GdN). SFE is defined as the percentage difference in the tunnelling probability for up/down spin electrons owing to the difference in barrier heights of the up/down spin channel in the FI caused by exchange splitting, so that 100% SFE corresponds to pure tunnelling of one spin sign. See Methods for details concerning the calculation of SFE. Table 1 collects the parameters of the measured junctions. All the NbNGdNNbN JJs present hysteresis >90% in the current–voltage (IV) characteristics, in a wide range of Josephson coupling energies E_{J}=I_{c0}φ_{0}/2π (where I_{c0} is the critical current in the absence of thermal fluctuations and φ_{0}=h/2e is the quantum flux). For all the measured devices the junction area is about 7 μm × 7 μm≃50 μm^{2}.
In Fig. 1d, IV curves, measured as a function of temperature T for the junction with the highest SFE, are reported. The dependence of I_{c} as a function of H at T=4 K is reported in Fig. 1c. The blue curve is the first measurement of the magnetic pattern, after nominal zerofield cooling. I_{c}(H) has then been measured both in the downward direction of the magnetic field sweep and in the upward direction (black and red curves, respectively). The black and red curves show a distinctive shift of the absolute maximum of I_{c} from −1 mT to +1 mT, respectively, arising from the hysteretic reversal of the FI barrier^{19}. The period of I_{c}(H) in nonspin filter junctions for the same geometry is twice as large (3 mT), pointing to a largely predominant second harmonic in the CPR in spin filter JJs, as discussed in ref. 16.
Measurements of switching current distributions
We have studied the escape rate of the superconducting phase ϕ as a function of temperature and for different values of the magnetic field, through standard switching current distribution (SCD) measurements^{20,21,22,23}. SCDs have been performed for all the samples reported in Table 1. According to the Resistively and Capacitively Shunted Junction (RCSJ) model ^{24,25}, for a JJ with a conventional CPR the dynamics is equivalent to that of a particle of mass m_{ϕ} moving in a washboard potential U(ϕ)=−E_{J}(cosϕ+γϕ). The particle mass is given by m_{ϕ}=C(φ_{0}/2π)^{2} with C the capacitance of the junction. The normalized bias current γ=I/I_{c0} determines the tilt of the potential.
The second harmonic component in the CPR, I=I_{1}sinϕ+I_{2}sin2ϕ, leads to a modified washboard potential , E_{1}=I_{1}/2e, which may assume the form of a double well for values of g=I_{2}/I_{1} larger than 0.5 (refs 26, 27, 28, 29 (see Fig. 2a). The presence of two wells in the washboard potential may result in the observation of two critical currents in the IV characteristics, since when tilting back the washboard potential the phase particle may be retrapped in one of the potential wells with finite probability^{27}; the case of ‘ϕ JJs’ with g <−1/2 has been recently studied^{28,29}. Measurements of twowell distinguished critical currents constitute a very direct criterion to estimate the g factor^{27,28}. Although spin filter JJs have a strong second harmonic component in the CPR^{16} we have not found evidence of two critical currents, and hence the case of ϕ junction with negative values of g is not considered in this work.
The sin2ϕ term in the CPR on average lowers the barrier height of the washboard potential without significantly altering the asymptotic expression of the potential barrier for γ close to one. The height of the potential barrier is given by: , where , and the plasma frequency is given by: . In addition, the second harmonic component does not modify the power law of ΔU. As a consequence in the thermal regime the s.d. σ of the SCDs is expected to scale as T^{2/3}, as in the case of the standard CPR^{20,21}.
The motion of the particle is subject to damping given by Q^{−1}, where Q=ω_{p}RC is the quality factor and R is the resistance of the junction. When the bias current is ramped from γ =0 to γ <1, the junction is in the zero voltage state in absence of thermal and quantum fluctuations, corresponding to the particle being localized in a potential well. At finite temperature the junction may switch into the finite voltage state for a bias current γ <1. This corresponds to the particle escaping from the well either by thermally activated processes or by tunnelling through the barrier potential (see Fig. 2b). In the thermal activation regime, the escape rate for weak to moderate damping (Q>1) is determined by^{30} , where the thermal prefactor is (ref. 31). The escape rate will be dominated by MQT at low enough temperatures^{32}. For Q>1 and γ close to 1 the escape rate in the quantum regime is: , where . The crossover temperature between the thermal and quantum regimes is given by^{33}
The experimental probability density of switching is related to the escape rate through the following equation ^{34}:
where ΔI/Δt is the current ramp rate.
The measurements have been performed in a dilution refrigerator, which reaches a base temperature of 20 mK. A full description of the apparatus is given in detail in the Methods section. The bias current of the junction is ramped at a constant sweep rate ΔI/Δt=2 mA s^{−1} and at least 10^{4} switching events have been recorded using a standard technique^{35}.
Figure 3a shows a set of SCDs as a function of temperature for the highSFE JJ reported in Fig. 1. The thermal behaviour of the SCDs is typical of underdamped JJs and the s.d. σ, which is proportional to the width of the switching histograms, increasing with temperature as expected. Figure 3b shows the SCDs measured below 1 K (black circles). The dependence of the s.d. σ on temperature is reported in Fig. 4a (right axis), along with the thermal behaviour of the mean value of the SCDs, I_{mean}, below 0.5 K (left axis). When decreasing the temperature, I_{mean} increases while σ decreases and both saturate at a crossover temperature of about 100 mK. Below this crossover the histograms overlap and the escape process is no longer regulated by thermal fluctuations, indicating the transition to the MQT regime^{20,21}.
A further confirmation of the observation of MQT comes from measurements of SCDs in magnetic field. The behaviour of σ(T) at H=1.1 mT is shown in Fig. 4b. At this value of the magnetic field, which reduces I_{c} to half of the value measured at zero field (see the blue squares in Fig. 1c), lower values of σ have been measured and T_{cross} is reduced by a factor , down to about 70 mK, in agreement with MQT theory^{33}. In both cases of 0 and 1.1 mT, T_{cross} has been determined by the intersection of the T^{2/3} curve in the thermal activation regime (dashed green lines in Fig. 4b) and the mean value of σ in the MQT regime (black full lines in Fig. 4b). The measurements in presence of magnetic field prove that the flattening of σ at H=0 mT is a quantum effect and is not due to noise or heating in the measurement setup^{20,21,22,23}.
Discussion
In the literature there are no measurements of SCDs on junctions with a dominant second harmonic component in the CPR. Numerical simulations of the phase dynamics as a function of the damping parameter Q, the g factor and the temperature T give the conditions for which a doublewell potential effectively behaves in the escape process as a single well (for details see Supplementary Figs 1 and 2 and Supplementary Note 1). Namely, for values of Q≃10 SCDs with a single peak have been obtained for g ≤2 or in the limiting case of pure second harmonic CPR (I_{1}=0). In this case the washboard potential changes its periodicity but assumes the form of a singlewell potential. Instead, for g⩾2, two critical currents should be observed. In fact, the heights of the two barriers approach each other when increasing the g factor, and the phase may be retrapped in both the potential wells with a finite probability, resulting in a bimodal switching distribution when counting many escape events^{27,28,29} (see Supplementary Fig. 3 and Supplementary Discussion). As this is not observed, a pure second harmonic is the only possible explanation consistent with both measurements of magnetic field pattern^{16} (see Fig. 1c) and SCDs.
I_{c0} can be obtained by fitting the probability density of switching P(I) (red lines in Fig. 3b) in the thermal and quantum regime, I_{c0}=30.41±0.05 μA. A quite accurate value of the capacitance C can be obtained from the crossover temperature T_{cross}, which depends on Q, C and I_{c0}, see equation (1). By inserting the values of I_{c0} and Q in the expression for T_{cross} we get C=4.5±0.9 pF. These values lead to ω_{p}≈14 GHz. Nevertheless, as shown in Fig. 3c, the function a(g) in the equations for ΔU and ω_{p} is a slowly varying function for g>>1; thus, the junction parameters weakly depend on the g factor for high values of g.
We expect in future additional insights coming from a comparative analysis with samples with lower SFE. For junction crosssections of about 50 μm^{2} the I_{c} values for such junctions are too high to be in the conditions to observe unambiguously the transition from the thermal to the quantum regime as commonly occurring also in standard SInsulatorS junctions^{20,21,36,37,38,39}. Only further advances in fabrication able to insert SFIS junctions in cavities, and qubit architectures will give more refined feedback on the modes of the dissipative domains of the junction and on the triplet component. However, we can infer that the Q values of spin filter junctions are relatively higher than one would naively expect on the basis of the properties of the lowSFE samples, which are characterized by higher values of I_{c}. Concerning the Q values of spin filter JJs, the reduction in I_{c} is compensated by the increase of R_{n}, as reported in Table 1.
In conclusion, we have demonstrated the occurrence of MQT in NbNGdNNbN spin filter JJs. Spin filtering drives the SFS junction in the underdamped regime and in the appropriate window of junction parameters to observe MQT. The SCDs, together with the period of I_{c}(H) modulation, provide direct evidence for a pure second harmonic CPR in the junction where MQT was observed. This is clear evidence of unconventional superconductivity, and it is possible that transport occurs by means of a pair of spinaligned triplet Cooper pairs^{16}, which may suppress magnetic sources of decoherence^{40,41}. Demonstration of macroscopic quantum phenomena in spin filter devices gives promise for their application in quantum hybrid circuits^{18} and also possibly as quiet memories.
Methods
Determination of SFE
SFE at a particular temperature is calculated from the R vs T curve. SFE at any temperature below the Curie temperature (T_{Curie}) of GdN and above the superconducting transition temperature (T_{c}) of NbN is calculated by defining SFE where σ↑, σ↓ are current densities of the up and down spin channels, respectively. By invoking WKB approximation, we can derive where R* is the measured value of resistance, and R is the value of resistance in the absence of spin filtering. R is estimated by fitting an exponential to the R vs T curve to temperatures above 50 K, and extrapolating the exponential to temperatures below the T_{Curie} of GdN. For calculating SFE below T_{c} of NbN, an exponential is fitted to the temperature dependence of SFE between T_{Curie} and T_{c}, and the fitted exponential is extrapolated to lower temperatures to obtain an estimate of SFE.
Setup for SCDs
The SCDs have been measured by thermally anchoring the samples to the mixing chamber of He^{3}/He^{4} Oxford dilution refrigerator. The bias current is ramped at a constant sweep rate ΔI/Δt of about 2 mA s^{−1}, the voltage is measured using a lownoise differential amplifier and is fed into a threshold detector, which is set to generate a pulse signal when the junction switches from the superconducting state to the finite voltage state. This signal is used to trigger a fast volt meter to record the value of the switching current. This procedure is repeated at least 10^{4} times at each temperature, which allows to compile a histogram of the switching currents. Filtering is guaranteed by a room temperature electromagnetic interference filter stage followed by lowpass RC filters with a cutoff frequency of 1.6 MHz anchored at 1.5 K, and by a combination of copper powder and twisted pair filters thermally anchored at the mixing chamber of the dilution refrigerator.
Additional information
How to cite this article: Massarotti, D. et al. Macroscopic quantum tunnelling in spin filter ferromagnetic Josephson junctions. Nat. Commun. 6:7376 doi: 10.1038/ncomms8376 (2015).
References
 1
Buzdin, A. I. Proximity effects in superconductorferromagnet heterostructures. Rev. Mod. Phys. 77, 935–976 (2005).
 2
Bergeret, F. S., Volkov, A. F. & Efetov, K. B. Odd triplet superconductivity and related phenomena in superconductorferromagnet structures. Rev. Mod. Phys. 77, 1321–1373 (2005).
 3
Ryazanov, V. V. et al. Coupling of two superconductors through a ferromagnet: Evidence for a π junction. Phys. Rev. Lett. 86, 2427–2430 (2001).
 4
Robinson, J. W. A., Witt, J. D. S. & Blamire, M. G. Controlled injection of spintriplet supercurrents into a strong ferromagnet. Science 329, 59–61 (2010).
 5
Golubov, A. A., Kupriyanov, M. & Il'Ichev, E. The currentphase relation in Josephson junctions. Rev. Mod. Phys. 76, 411–469 (2004).
 6
Buzdin, A. I. Peculiar properties of the Josephson junction at the transition from 0 to π state. Phys. Rev. B 72, 100501 (2005).
 7
Kawabata, S., Kashiwaya, S., Asano, Y., Tanaka, Y. & Golubov, A. A. Macroscopic quantum dynamics of π junctions with ferromagnetic insulators. Phys. Rev. B 74, 180502 (2006).
 8
Baek, B., Rippard, W. H., Benz, S. P., Russek, S. E. & Dresselhaus, P. D. Hybrid superconductingmagnetic memory device using competing order parameters. Nat. Commun. 5, 3888 (2014).
 9
Bergeret, F. S., Volkov, A. F. & Efetov, K. B. Longrange proximity effects in superconductorferromagnet structures. Phys. Rev. Lett. 86, 4096–4099 (2001).
 10
Fominov, Y. V., Golubov, A. A. & Kupriyanov, M. Y. Triplet proximity effects in FSF trilayers. JETP Lett. 77, 510–515 (2003).
 11
Halász, G. B., Blamire, M. G. & Robinson, J. W. A. Magneticcoupling dependent spintriplet supercurrents in helimagnet/ferromagnet Josephson junctions. Phys. Rev. B 84, 024517 (2011).
 12
Khaire, T. S., Khasawneh, M. A., Pratt, W. P. Jr. & Birge, N. O. Observation of spintriplet superconductivity in Cobased Josephson junctions. Phys. Rev. Lett. 104, 137002 (2010).
 13
Sprungmann, D., Westerholt, K., Zabel, H., Weides, M. & Kohlstedt, H. Evidence for triplet superconductivity in Josephson junctions with barriers of the ferromagnetic Heusler alloy Cu2MnAl. Phys. Rev. B 82, 060505 (2010).
 14
Anwar, M. S., Veldhorst, M., Brinkman, A. & Aarts, J. Long range supercurrents in ferromagnetic CrO2 using a multilayer contact structure. Appl. Phys. Lett. 100, 052602 (2012).
 15
Senapati, K., Blamire, M. G. & Barber, Z. H. Spinfilter Josephson junctions. Nat. Mater. 10, 849–852 (2011).
 16
Pal, A., Barber, Z. H., Robinson, J. W. A. & Blamire, M. G. Pure second harmonic currentphase relation in spinfilter Josephson junctions. Nat. Commun. 5, 3340 (2014).
 17
Pal, A., Senapati, K., Barber, Z. H. & Blamire, M. G. Electric field dependent spin polarization in GdN spin filter tunnel junctions. Adv. Mater. 25, 5581–5585 (2013).
 18
Feofanov, A. K. et al. Implementation of superconductor/ferromagnet/superconductor πshifters in superconducting digital and quantum circuits. Nat. Phys. 6, 593–597 (2010).
 19
Blamire, M. G., Smiet, C. B., Banerjee, N. & Robinson, J. W. A. Field modulation of the critical current in magnetic Josephson junctions. Supercond. Sci. Technol. 26, 055017 (2013).
 20
Devoret, M. H., Martinis, J. M. & Clarke, J. Measurements of macroscopic quantum tunneling out of the zerovoltage state of a currentbiased Josephson junction. Phys. Rev. Lett. 55, 1908–1911 (1985).
 21
Martinis, J. M., Devoret, M. H. & Clarke, J. Experimental tests for the quantum behavior of a macroscopic degree of freedom: the phase difference across a Josephson junction. Phys. Rev. B 35, 4682–4698 (1987).
 22
Bauch, T. et al. Macroscopic quantum tunneling in dwave YBaCuO Josephson junctions. Phys. Rev. Lett. 94, 087003 (2005).
 23
Longobardi, L. et al. Direct transition from quantum escape to a phase diffusion regime in YBaCuO biepitaxial Josephson junctions. Phys. Rev. Lett. 109, 050601 (2012).
 24
Barone, A. & Paternò, G. Physics and Applications of the Josephson Effect John Wiley and Sons (1982).
 25
Likharev, K. K. Superconducting weak links. Rev. Mod. Phys. 51, 101–159 (1979).
 26
Tzalenchuk, A. Y. et al. Mesoscopic Josephson junctions of highT c superconductors. Phys. Rev. B 68, 100501(R) (2003).
 27
Goldobin, E., Koelle, D., Kleiner, R. & Buzdin, A. I. Josephson junctions with second harmonic in the currentphase relation: Properties of ϕ junctions. Phys. Rev. B 76, 224523 (2007).
 28
Sickinger, H. et al. Experimental evidence of a ϕ Josephson junction. Phys. Rev. Lett. 109, 107002 (2012).
 29
Goldobin, E., Kleiner, R., Koelle, D. & Mints, R. G. Phase retrapping in a pointlike ϕ Josephson junction: the butterfly effect. Phys. Rev. Lett. 111, 057004 (2013).
 30
Kramers, H. A. Brownian motion in a field of force and the diffusion model of chemical reactions. Physica 7, 284–304 (1940).
 31
Büttiker, M., Harris, E. P. & Landauer, R. Thermal activation in extremely underdamped Josephsonjunction circuits. Phys. Rev. B. 28, 1268–1275 (1983).
 32
Caldeira, A. O. & Leggett, A. J. Influence of dissipation on quantum tunneling in macroscopic systems. Phys. Rev. Lett. 46, 211–214 (1981).
 33
Grabert, H. & Weiss, U. Crossover from thermal hopping to quantum tunneling. Phys. Rev. Lett. 53, 1787–1790 (1984).
 34
Fulton, T. A. & Dunkleberger, L. N. Lifetime of the zerovoltage state in Josephson tunnel junctions. Phys. Rev. B 9, 4760–4768 (1974).
 35
Longobardi, L. et al. Thermal hopping and retrapping of a Brownian particle in the tilted periodic potential of a NbN/MgO/NbN Josephson junction. Phys. Rev. B 84, 184504 (2011).
 36
Washburn, S., Webb, R. A., Voss, R. F. & Farris, S. M. Effects of dissipation and temperature on macroscopic quantum tunneling. Phys. Rev. Lett. 54, 2712–2715 (1985).
 37
Li, S. X. et al. Quantitative study of macroscopic quantum tunneling in a dc SQUID: a system with two degrees of freedom. Phys. Rev. Lett. 89, 098301 (2002).
 38
Martinis, J. M., Nam, S., Aumentado, J. & Urbina, C. Rabi oscillations in a large Josephsonjunction qubit. Phys. Rev. Lett. 89, 117901 (2002).
 39
Berkley, A. J. et al. Entangled macroscopic quantum states in two superconducting qubits. Science 300, 1548–1550 (2003).
 40
Richard, C., Houzet, M. & Meyer, J. S. Superharmonic longrange triplet current in a diffusive Josephson junction. Phys. Rev. Lett. 110, 217004 (2013).
 41
Trifunovic, L. Longrange superharmonic Josephson current. Phys. Rev. Lett. 107, 047001 (2011).
Acknowledgements
We acknowledge financial support from COST Action MP1201 [NanoSC COST], by Progetto FIRB HybridNanoDev RBFR1236VV001 and by Regione Campania through POR Campania FSE 2007/2013, progetto MASTRI CUP B25B09000010007.
Author information
Affiliations
Contributions
D.M., A.P., L.L., M.G.B. and F.T. conceived the experiments, A.P. and M.G.B. designed and realized the junctions; D.M. carried out the measurements; D.M., G.R. and F.T. worked on the theoretical modelling and data analysis; D.M., M.G.B. and F.T. cowrote the paper. All authors discussed the results and commented on the manuscript.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing financial interests.
Supplementary information
Supplementary Information
Supplementary Figures 13, Supplementary Note 1, Supplementary Discussion and Supplementary References (PDF 502 kb)
Rights and permissions
This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/
About this article
Cite this article
Massarotti, D., Pal, A., Rotoli, G. et al. Macroscopic quantum tunnelling in spin filter ferromagnetic Josephson junctions. Nat Commun 6, 7376 (2015). https://doi.org/10.1038/ncomms8376
Received:
Accepted:
Published:
Further reading

Introduction: the Josephson Effect and Its Role in Physics
Journal of Superconductivity and Novel Magnetism (2021)

Electrodynamics of Highly SpinPolarized Tunnel Josephson Junctions
Physical Review Applied (2020)

Critical Current Suppression in SpinFilter Josephson Junctions
Journal of Superconductivity and Novel Magnetism (2020)

Fabrication of deepsubmicrometer NbN/AlN/NbN epitaxial junctions on a Sisubstrate
Applied Physics Express (2020)

Low temperature characterization of high efficiency spinfilter Josephson junctions
EPJ Web of Conferences (2020)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.