GASTRONOMÍA Platos típicos

Before presenting the results of the LEµSR study a short synopsis of the new electromagnetic proximity theory, and how it relates to the direct and inverse proximity effects, is included for reference. The development of this theory provides a recent example of how theory and experiment can work well together to discover an entirely new and hitherto unknown ef- fect. During the course of a single year a series of landmark theory papers have been published [40–42] in response to puzzling experimental results [39, 60, 82, 85]. The net result is a completely new understanding of S/F proximity systems which will prove to be crucial in further development of related technologies.

4.2.1 EM proximity phenomena within SF systems

When a superconductor is in direct contact with a ferromagnet, and elec- tronic transport occurs across the interface between the two, unconventional

superconducting states are generated. The mixing of the S and F orders involved in direct proximity is well understood and results in a number of interesting transport phenomena. These include, oscillations in critical temperature Tc (see for example [7–12]) and critical current (for example

[13–16]), π phase shifts [17–20], colossal Tc suppression [21] and long range

triplet supercurrents [22–29], and all rely on the conversion of some conven- tional singlet pairs into the odd-frequency s-wave triplet state. In addition to the direct proximity at the S/F interface the inverse proximity effect, which describes how through the transfer of spin polarised Cooper pairs across the interface the superconductor acquires a small net magnetisation, has been predicted [33–35] and until recently was thought to be the only mechanism through which a magnetisation could be transferred from the ferromagnet into the superconductor. This effect occurs over a lengthscale governed by the superconducting coherence length, ξs, which is typically

only of the order of 10 nm. In more recent times, a series of puzzling ex- perimental observations, made using neutron scattering [82, 85] and µSR [39, 60], as discussed within the previous chapter, have been published. These papers reported the long range transfer of a magnetisation to the su- perconductor which occurred over lengthscales far exceeding any coherence length phenomena and which therefore could not, at the time of publica- tion, be explained within the existing body of theory. These results have motivated the development of the new theory of electromagnetic proximity [40–42].

In essence, the electromagnetic (EM) proximity effect describes how the interaction of a superconductor with the vector potential of a ferromagnetic layer influences its screening response. In the initial theory work the au- thors consider a simple S/F bilayer system and show that coupled to the di- rect proximity effect there is an additional electromagnetic component [40]. Within such a system, whenever transfer of electrons from S to F is allowed there will immediately be, as described in section 1, electron pair correla- tions induced within the ferromagnet. Since the ferromagnetic layer has a vector potential associated with its magnetisation, a screening current must then be induced in response over a lengthscale λL into the superconductor.

This occurs as a consequence of the full system (superconducting layer and S/F interface) being described by a common superconducting wavefunction [40]. Since the lengthscale over which the condensate responds to this vector potential is governed by λL, where for a dirty system λL ξs, this picture

provides a natural framework in which to interpret the experimentally ob- served long range effects referenced previously. It is crucial to note that direct electronic contact between S and F is required to generate this ef- fect because there must be superconducting currents inside the ferromagnet which experience its vector potential and consequently induce the screening response.

The new electromagnetic proximity mechanism is thus responsible for a modification to the orbital screening profile across the superconductor even in zero field. The spatial form of the induced response within the super- conductor due to the EM proximity component is given by the expression shown in equation 4.1 [40]

Bz(x) =AEMexp ((x−dS)/λL) , (4.1)

where AEM is the strength of the EM proximity. The form given by equa-

tion 4.1 can be simply deduced using Maxwell’s equations and the London relation though a more proper microscopic treatment using the Usadel for- malism [136] has been shown to arrive at a consistent result [40, 41]. The EM amplitude, AEM, is proportional to both the magnetisation of the fer-

romagnetic layer and to how the thickness of that layer compares with the coherence length within it. It therefore follows naturally that these param- eters will determine both the sign and magnitude of the resultant effect and that consequently, depending on the material parameters of the system, the EM proximity amplitude may be paramagnetic or diamagnetic. A simple back-of-the-envelope estimate for a strong ferromagnet demonstrates that

AEM ≈(10−100) Oe which is easily comparable the anomalous screening

amplitudes discussed within section 3 [40].

Based on the discussion above it would be naively expected that in a spin valve structure, such as those studied experimentally in reference [39], the EM contribution would be maximised for a collinear arrangement of the ferromagnetic layers. This is in fact the opposite of what has been exper- imentally observed. In a detailed follow up work [41] the authors of the theory address the specific case of how the EM proximity manifests within these SFF spin valve structures and find, in fact, due to the appearance of additional equal spin triplet correlations the EM component to be max- imised in the case of the noncollinear arrangement which agrees with the experimental results presented here.

4.2.2 Testing EM proximity within SF thin films

The EM proximity effect describes the spread of a magnetisation out of the ferromagnet and into the superconductor as a consequence of the conden- sate feeling the vector potential at the S/F interface. The main predictions of the EM proximity theory regarding the resultant modification of the spa- tial flux profile across the sample are as follows:

1) There should be an amplitude, originating at the S/F interface, that represents a non-zero offset in the flux profile when compared with the standard Meissner screening which necessarily goes to zero at the S/F and vacuum interfaces.

2) This amplitude should decay away exponentially over a lengthscale of the London penetration depth, λL, which is typically much longer than

the superconducting coherence length, ξS.

3) The sign and magnitude of the EM amplitude should depend on the thickness of the ferromagnetic layer and the direction of its magnetisa- tion.

When one considers these consequences of EM proximity, it becomes clear that LEµSR, being sensitive to the local flux, is the ideal choice of technique with which to probe the theory and as previously demonstrated in chapter 3 has been used extensively to measure novel effects within these S/F thin film systems.