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Triple-gap superconductivity of MgB2 - (La,Sr)MnO3 composite. Which of the gaps is proximity induced?

Interplay of superconductivity and magnetism in a composite prepared of the ferromagnetic half-metallic La_0.67Sr_0.33MnO (LSMO) nanoparticles and the conventional s-wave superconductor MgB_2 has been studied. A few principal effects have been found in bulk samples. With an onset of the MgB_2 superconductivity, a spectacular drop of the sample resistance has been detected and superconductivity has been observed at temperature up to 20K. Point-contact (PC) spectroscopy has been used to measure directly the superconducting energy coupling. For small voltage, an excess current and doubling of the PC's normal state conductance have been found. Conductance peaks corresponding to three energy gaps are clearly observed. Two of these gaps we identified as enhanced \Delta_{\pi} and \Delta_{\sigma} gaps originating from the MgB_2; the third gap \Delta_{tr} is more than three times larger than the largest MgB_2 gap. The experimental results provide unambiguous evidences for a new type of proximity effect which follows the phase coherency scenario of proximity induced superconductivity. Specifically, at low temperature, the p-wave spin-triplet condensate with pairing energy \Delta_{tr} is essentially sustained in LSMO but is incapable to display long-range supercurrent response because of a phase-disordering state. The proximity coupling to MgB_2 restores the long-range phase coherency of the triplet superconducting state, which, in turn, enhances superconducting state of the MgB_2.

excess current and doubling of the PC's normal state conductance have been found. Conductance peaks corresponding to three energy gaps are clearly observed. Two of these gaps we identified as enhanced ∆ π and ∆ σ gaps originating from the MgB 2 ; the third gap ∆ tr is more than three times larger than the largest MgB 2 gap. The experimental results provide unambiguous evidences for a new type of proximity effect which follows the phase coherency scenario of proximity induced superconductivity. Specifically, at low temperature, the p-wave spin-triplet condensate with pairing energy ∆ tr is essentially sustained in LSMO but is incapable to display long-range supercurrent response because of a phase-disordering state. The proximity coupling to MgB 2 restores the long-range phase coherency of the triplet superconducting state, which, in turn, enhances superconducting state of the MgB 2 .
When an itinerant ferromagnet (F) is in contact with an s-wave superconductor (S), superconductivity is expected to decay rapidly (a few nanometers) inside the F owing to the incompatible nature of superconductivity and ferromagnetic order [1]. This expectation was indeed confirmed in various materials and geometries. On the other hand, a series of recent experiments [2][3][4][5][6][7] present clear evidences that a simple physical interpretation of the proximity effect, reading that the Cooper pairs are broken by a strong exchange field in the F layer, is in reality too simplistic, and an extension of the existing concepts of interplay between superconductivity and ferromagnetism is needed.
From the theoretical viewpoint, a case of an F with a uniform exchange field is well understood and the proximity effect may be described by taking into account the splitting of electronic bands of opposite spins [1]. The situation becomes more complicated if the magnetic structure is inhomogeneous, and only few works (see, e.g. [8]) have been devoted to the problem of superconducting proximity systems with non-collinear magnetic disorder correlated on length scales of an order or larger than the superconducting coherence length. On the other hand, being an experimentally accessible electronic system with tunable parameters, hetero-structures with inhomogeneous magnetism (e.g., superconducting nano-composites) offer a unique testing ground for studying superconducting proximity systems with an arbitrary length of magnetic disorder. However, to our knowledge, up to now no reports have been devoted to a superconductive composite of (nano)granular half-metal ferromagnet (hmF) and a conventional s-wave superconductor.
In our recent works anomalous superconductivity has been detected in point contacts (PCs) of half-metallic manganite, (La,Sr)MnO 3 and (La,Ca)MnO 3 , with an s-wave superconductor, Pb or MgB 2 , [9,10]. Particularly, for proximity affected PCs, the coherent multiple Andreev reflection (sub-harmonic gap resonances) has been observed, and it has been found that proximity induced superconducting gap of (La,Sr)MnO 3 or (La,Ca)MnO 3 is much larger than that of the Pb or MgB 2 . It was implied that, at low temperature, non-coherent superconducting fluctuations are essentially sustained in half-metallic manganites and, in proximity affected region, the singlet S establishes phase coherence of the p-wave spin-triplet superconducting state of the manganites [9,10]. To verify this phase-disordering scenario for anomalous superconductivity of proximity affected PCs, we prepared and systematically studied normal and superconducting properties of the MgB 2 -(nano) La 0.67 Sr 0.33 MnO 3 (MgB:LSMO) composite. The basic idea was to obtain such a composite, where proximity coupled hmF/S interfaces govern superconducting properties of the sample. Fortunately, the idea was successful, and in this report we present the results of investigating transport properties of such systems. Our key findings are: (i) the samples of MgB:LSMO (nano)composite demonstrate evidences for bulk (triplet) superconductivity with large, up to 20K, critical temperature, T C ; (ii) three superconducting gaps are clearly observed. We identified two of these gaps as enhanced MgB 2 gaps, the third quasiparticle gap, ∆ tr , is more than three times larger than the largest MgB 2 gap and could not be attributed to this superconductor. Also, we found that (iii) all the energy gaps vanish simultaneously as the temperature increases towards T C of MgB 2 .
The origin of the large quasiparticle ∆ tr gap and an enhancement of the MgB 2 gaps cannot be explained on the basis of the existing theoretical models. We believe the results obtained are the first observation of the new type of superconducting proximity effect. That is, MgB 2 enhances the internal superconducting order parameter phase stiffness in LSMO and, in turn, being in superconducting state, LSMO enhances superconducting characteristics of MgB 2 . Taking into account half-metallic properties of LSMO and the Curie temperature magnitude, we think that in the case of LSMO we deal with even frequency p-wave spintriplet superconducting pairing.
Experimental details. Stoichiometric MgB 2 has a transition temperature T C = 39 K, the highest among conventional superconductors [11]. MgB 2 , however, is by no means an ordinary, but the weakly interacting multiple bands superconductor (σ and π bands). It demonstrates distinct multiple superconducting energy gaps (the σ and π gaps) with energy ∆ π = 2.3 meV and ∆ σ = 7.1 meV at T = 4.2K [11]. The coherence length ξ is anisotropic with ξ ab (0) ≈ 8nm and ξ c (0) ≈ 2nm [11]. La 0.67 Sr 0.33 MnO 3 is a hmF with the T Curie = 320K (see, e.g., [12]). Composites containing submicron MgB 2 powder and LSMO particles (about 20nm in size) have been produced. Details of the LSMO nanoparticles preparation may be found in Ref. [13]. The powders with different weight ratios of LSMO and MgB 2 were mixed and pressed (under pressure up to 60 kbar) in stripes, and a number of samples of different composition have been obtained.
The obtained composites were analyzed by the method of X-ray energy-dispersive spectroscopy (EDX) using INCAPentaFETx3 spectrometer and JSM-6490LV scanning electron microscopy (SEM). Exemplarily, one of the sample's SEM micrograph is shown in Fig. 1.
Also, AC and DC magnetization measurements were used to study superconducting and   Fig. 4 (a) and Fig. 4 (b), respectively. As follows from the data for χ(T) in Fig 4 (a), with decreasing temperature, a transition into ferromagnetic state occurs with T Curie = 320 K and then, below 39K, a diamagnetic response is developed. The measured magnetization hysteresis loop [see Fig.4 (b)] provides the unambiguous evidence that our composite is a type-II superconductor with a strong vortex pinning. At low temperature, with increasing an applied field, a diamagnetic response is suppressed and above 3.3 kOe a ferromagnetic response is again restored due to flux penetration and magnetization of the sample.
(ii) Point-contact spectroscopy allows a direct measurement of the superconducting gap. Figure 5 shows representative spectra of In, Ag, Nb -sample 3:1 PCs measured at T = 4.2 K. We underline that the PCs' resistivity varied by order, but multiple gaps structure in the quasiparticle density of states of the composite, as well as the gap energy magnitudes were robust features of superconducting composites and were reproduced in all PCs we prepared.
Conductance peaks corresponding to three superconducting gaps with energies ∆ 1 (π) = 2.0 Here we will adopt abbreviation ∆ 1 (π) and ∆ 2 (σ) for gaps which originate (most probably) from the ∆ π and ∆ σ gaps of MgB 2 , respectively, and ∆ tr which we attribute (see discussion below) to the superconductivity of LSMO. It is worth underlining here that magnitude of ∆ tr is the same as those earlier detected in PCs of (La,Sr)MnO 3 and (La,Ca)MnO 3 with Pb or MgB 2 [9,10]. In Fig. 6, the energy gap ∆ tr temperature dependence is shown. From the BCS relation ∆(0) = 1.76k B T C , the ∆ tr (0) gap would lead to a S with T C ≈ 120 K.
The classic BCS gap temperature behavior is shown in the figure too. As is evident, the experimental data does not follow the BCS dependence.
Thus, principal features which arise from the data obtained in all PCs are (i) a triple-gap structure of the PCs spectra; (ii) the enhanced MgB 2 gaps. (Note , to avoid confusion, that within the accuracy of our measurements, the magnitude of the ∆ 1 (π) gap still remains in range of a bulk MgB 2 ∆ π gap [11].) Also, (iii) proximity induced quasiparticle gap ∆ tr is more than three times larger than the conventional ∆ σ gap of MgB 2 .
Discussion. Here we will concentrate on temperature region T < T C and superconducting state of the 3:1 and 4:1 samples. As already mentioned, an origin of the large quasiparticle ∆ tr gap and an enhancement of the largest MgB 2 gap, ∆ σ , cannot be conventionally explained on the basis of the existing theoretical models of proximity effect. Theoretically, the proximity effect in normal metal -multi-band (MgB 2 ) hybrid structures has been considered by Brinkman et al., [14]. A phenomenon was predicted, where the superconductivity in a two-band superconductor is enhanced by the proximity to a superconductor with a lower transition temperature (S'). The physics of this effect is explained by the coupling between S' and the π-band: S' superconductor enhances the superconductivity in the π-band, whereas the π −σ interband coupling causes an enhancement of the superconductivity in the σ-band.
However, for MgB:LSMO composite we found three quasiparticle gaps, the largest of which, ∆ tr , could not be attributed to MgB 2 . Also, a substantial increase in the magnitude of the largest of MgB 2 gap, ∆ σ , has been detected. Thus, a question arises as to which of these gaps is proximity induced?
Before giving a qualitative explanation of the observations, we summarize the physics of proximity effect at spin-active hmF/S interface which looks as follows (see, e.g., [15] and references therein). The conversion process between the singlet and equal-spin triplet supercurrents is believed to be governed by two important phenomena taking place in the half metal at the interface: (i) a spin mixing and (ii) a spin-rotation symmetry breaking.
Spin mixing is the result of different scattering phase shifts that electrons with opposite spin acquire when scattered (reflected or transmitted) from an interface. It results from either a spin-polarization of the interface potential, or differences in the wave-vector mismatches for spin up and spin down particles at either side of the interface, or both. It is a robust and ubiquitous feature for interfaces involving strongly spin-polarized ferromagnets.
Broken spin-rotation symmetry leads to spin-flip processes at the interfaces. Its origin depends on microscopic magnetic state at the hmF/sS interface, character of local magnetic moments coupling with itinerant electrons, etc., and even varies from sample-to-sample.
However, the exact microscopic origin of spin-flip processes at the interface is important only for the effective interface scattering matrix [15] and not for superconducting phenomena, since Cooper pairs are of the size of the coherence length ξ which is much larger than the atomic scale. Note, that for odd-frequency s-wave spin-triplet pairing [16] the static gap is zero. We observe nonzero gaps magnitudes, and thus this scenario of proximity effect is not related to our case.
We now proceed to our system. Within the double-exchange interaction model for holedoped manganites (see, e.g., [12]), the itinerant charge carriers provide both the magnetic interaction between magnetic moments of the nearest Mn 3+ -Mn 4+ ions and the system's electrical conductivity. Due to the short mean free path, that is typically the distance of about a lattice parameter, the charge carrier probes the magnetization on a very short length scale. At the interfaces with the superconductor, the local moments are expected to show a certain degree of disorder and it is reasonable to expect that the interface ferromagnetic manganites-wave S is a spin-active one. (Note also that local magnetic structure at the hmF/sS interface can be easily affected by an external influence that leads to hysteretic behavior of the equilibrium properties as we indeed observe in some cases.) Following to Refs. [9,10], we suggest that, at low temperature, non-coherent p-wave even-frequency spin-triplet superconducting condensate already exists in half-metallic manganites. Being In worthy to note here that in mean field BCS-Eliashberg theories, the temperatures of electron-pairing, T ∆ , and the long-range phase coherency, T ϕ , coincide and yield the critical temperature, T C . This means that the global phase coherency and energy gap appear/vanish at the same temperature, mainly due to the opening/disappearing of the gap with temperature (i.e., the relation T ϕ > T ∆ is a typical case). However, it has been shown [17] (see also [18]) that for systems with low conductivity and small super-fluid density (bad metals), the temperature of the global phase coherency T ϕ is reduced significantly and becomes comparable to or even smaller than the pairing temperature T ∆ . In this case, the critical temperature T C is determined by the global phase coherency, whereas the pair condensate could exist well above T C . The experimental results shown in Fig. 6 support the picture where the metastable superconducting islands of nonzero order parameter are frozen, while the long-range coherence associated with a bulk superconducting state is prevented by marked fluctuations in the phase. (The loss of long-range phase stiffness, rather than the vanishing of the pair condensate well above T C , is at present actively discussed in relation to several families of hole-doped cuprates; see, e.g. [19,20] and references therein.) The important consequence of the presence of the Cooper pair fluctuation above T C is an appearance of the so-called pseudo-gap [17,21,22], i.e., decreasing of the one-electron density of state near the Fermi level. A large pseudo-gap is indeed detected in numerous experiments on manganites [12] and it may be suggested that at least a portion of the observed pseudo-gap is due to pairing without global phase coherency. Diamagnetic response above T C provides additional arguments for survival of the pair condensate well above T C in cuprates [19] as well as in disordered MgB 2 [23] and oxy-pnictides [24]. However, for manganites this kind of response will be strongly suppressed by ferromagnetic order of the localized moments and spin-triplet state of the condensate.
Summary. We produced and studied magnetic and superconducting properties of MgB 2 -(nano) La 0.67 Sr 0.33 MnO 3 composite. Unconventional superconductivity of samples MgB:LSMO with 3:1 and 4:1 weight ratio with T C = 20 K has been observed. Three distinct quasiparticle energy gaps ∆ 1 (π), ∆ 2 (σ), and ∆ tr are clearly revealed. Two of these gaps were identified as gaps originating from the MgB 2 . The third gap ∆ tr , which is a few times larger than the largest MgB 2 gap, could not be attributed to this s-wave superconductor. In our opinion, the results obtained testify in favor of the induced long-range phase coherency of p-wave even frequency spin triplet superconductivity of half-metallic La 0.67 Sr 0.33 MnO 3 .
Specifically, in a ferromagnetic state of La 0.67 Sr 0.33 MnO 3 , a condensate lost phase stiffness and is incapable to display long-range supercurrent response, even though the gap amplitude is large. Nonetheless, reduced local phase rigidity survives. Being proximity coupled to MgB 2 , the long-range coherency is restored. An inverse effect of the proximity induced superconducting state with large gap is an enhancement of the MgB 2 superconducting state.
I.e., here we deal with some kind of "mutual" proximity effect.
The authors acknowledge I. A. Danilenko for the LSMO nanoparticles preparation. We also are grateful to M. Kupriyanov, Ya. Fominov for useful discussions, and M. Belogolovskii for helpful comments on the manuscript.