Ruling out the effect of stray fields

It has been discussed in previous chapters that in the absence of ferromag- netism the nuclear moments are the main source of magnetic inhomogeneity in these systems. This leads to a constant nuclear depolarisation rate, λ, within each material layer. On the other hand, for any system in which a fer- romagnetic layer is present the spatial dependence ofλbecomes dominated by the effect of the stray field originating at the S/F interface. In these cases, an approximately exponential decay profile forλwhich is maximal at the surface of the ferromagnet and decays away over typical lengthscales of up to 20nm is found to describe the data very successfully. It is therefore possible, through a careful analysis of the data, to modelλ as a function of

dI and compare the depolarisation amplitudes, λ0, and decay lengthscales,

ξλ, across the different samples to see how random fluctuations in the local

field vary. This is achieved through imposing the profile given by equation 2.8 on all the measured data and the results are presented in figure 5.8.

2 3 4 5

0 2 4 6 8

average probing depth (nm) dAlOx(nm)

20 40 60 80 0 3 2 1 0 0=4.2MHz T=10K T=2.5K 0(8nm)=2.2MHz 0 (MHz) (MHz) 1 0 NS=0.6MHz a) b)

Figure 5.8: Results of modelling the depolarisation rate at the interface as a function of oxide thickness. a) depolarisation rate as a function of the aver- age probing depth for thedI = 8 nm sample. The solid lines show the best

fit model profiles and the open (closed) symbols show the corresponding av- erages measured at T= 10 K (T= 2.5K) in the normal (superconducting) state. The black dotted lines show the result of “predicting” the averages from the full spatial profile. The horizontal dashed line indicates the po- sition at which the amplitude, λ0, was extracted. b) the plotted points

show the depolarisation amplitude (λ0) as a function of the oxide barrier

thickness (dI). The solid line is a guide to the eye and the dashed lines

represent the maximum depolarisation amplitude which corresponds to the

Figure 5.8a) presents the results of modelling the depolarisation rate data for the Cu(40)/Nb(50)/Al2Ox(8)/Co(2.4) sample. The quality of the data

and the imposed fit profile are representative of all the measured samples within the set. The solid lines correspond to the best fit form of equation 2.8 and the open and closed symbols correspond to the results of the aver- ages analysis for the 10 K normal state and 2.5 K superconducting state measurements respectively. As would be expected there is an enhanced depolarisation rate below the superconducting Tc due to increased flux gra-

dients associated with screening. The black dashed lines represent the result of calculating the spatial averages directly from the optimised profile as de- scribed in section 2.1.7. There is an excellent correspondence between the measured average flux values and those determined from the best fit profile for the data taken both above and below Tc which validates the practical

use of this phenomenological model. The horizontal dashed line indicates the definition of λ0, the depolarisation amplitude at the SI interface, which

for this sample was found to be 2.2 M Hz. The same analysis was carried out for all other barrier thicknesses and the value of λ0 extracted for each.

The resultant plot of the depolarisation amplitudes as a function of the barrier thickness is shown in figure 5.8b) where the connecting line is just a guide to the eye. The dotted lines represent the maximum observed value, which corresponds to both the dI = 0 nm and dI = 2 nm samples, and the

NS bilayer result which is significantly lower than even the result for the

dI = 8 nm sample. Any increase in the barrier thickness from dI = 2 nm

results in a slight drop off of the value of λ0 but at no point does it come

close to approaching the bilayer value of≈0.6M Hz in the superconducting state. In addition, for all samples the decay lengthscale, ξλ, of the depolari-

sation amplitude was found to be within the rangeξλ = (12±1)nm. When

taken together this suggests the observed flux lowering attributed to EM proximity is not due to a stray field effect. Whilst there is some variation in λ0 it does not correlate to the behaviour of the extracted values of AEM

which settle back to the bilayer response for dI = 8nm, a lengthscale over

which the stray fields still significantly effect the depolarisation.

5.3

Discussion of the S-F coupling dependence of EM

proximity.

The modelling of the full spatial dependence of the LEµSR data is consis- tent with there being an additional source of vector potential at the SIF

interface which in turn generates an additional component to the orbital screening. These observations are in line with current thinking regarding the expected electromagnetic proximity effects that ought to take place wherever a ferromagnet comes into contact with a superconductor. Indeed the experimental observations that: the additional response requires the presence of the ferromagnet; depends unambiguously on the direct sam- pling of F by the superconducting condensate and has its spatial origins at the SIF interface, are direct predictions of the theory. The measurements themselves provide excellent evidence against stray fields being related to the measured effect since for thick oxide barriersAEM →0 and the bilayer

result is recovered whilst the stray fields are still significantly higher than the bilayer case. Furthermore, the modelling of the muon depolarisation rate has shown that the stray fields decay over a longer lengthscale than the barrier thickness required to quench the observed additional screening component. It is also important to note that the observed dependence of

AEM on the oxide thickness is not systematic with the observed variations

in ms/area displayed in table 5.1 so cannot simply be due to variations in

the magnetisation of the F layer. For thinner oxide barriers, dI ≤ 4 nm,

a constant value of AEM was observed. The origin of this is currently un-

known and is not explicitly explored within the existing theory. Naively

AEM ought to depend on both the superconducting gap and on the con-

tact term between the superconductivity and ferromagnetism. The latter gradually reduces as the thickness of the insulating barrier increases and the former correspondingly strengthens due to a diminished effect of pair break- ing. The interplay of these two effects is not currently explored within the theory and it is possible the result may be an approximately constant value ofAEM though this remains an open question. The observation does, how-

ever, suggest the possibility to design a device in which the electromagnetic component can be maximised whilst minimising the effects of pair breaking.

The experimentally determined behaviour of the direct proximity, pa- rameterised through ASF, as a function of the coupling strength makes

intuitive sense. The 15% reduction in the standard Meissner screening re- sponse observed in the absence of an insulating barrier, and the steady loss of this amplitude as the S-F coupling is reduced such that fordI ≥4nmthe

bilayer Meissner screening was recovered, was clearly anticipated. The novel piece of understanding to come out of this observation is really that, given

appropriate control samples, a full spatial analysis of the kind carried out here provides access to quantitative measures of how the proximity effects develop within these systems. Additionally, the relative strengths of the pair breaking and the EM proximity suggests the importance of accounting for these electromagnetic effects in both the interpretation of experimental results and in the design of new S/F devices. Indeed as discussed within chapter 4 this new model provides a framework in which to interpret a num- ber of previously published anomalous results within the field [39, 60, 82, 85]. It is important to note that whilst the suggested supply of additional vector potential is the local magnetisation of the ferromagnet this has not been unambiguously determined through these measurements. The asym- metric spatial profile of the additional screening, which originates from the SIF interface region and disappears once the ferromagnet becomes isolated, is highly consistent with the theoretical predictions. It is perfectly possi- ble, however, that there are additional contributions to the vector potential as discussed within section 4.4. It is likely that further theoretical develop- ments will steer new experimental efforts to identify and disentangle possible contributions.

5.4

Conclusions on the use of oxide barriers to manip-

ulate EM proximity

Within the present chapter, the influence of inserting insulating oxide bar- riers between superconducting and ferromagnetic layers on the direct and electromagnetic proximity effects has been studied. A full set of samples of the form NSI(dI)F were measured using LEµSR and the data analysed

within a model consistent both with pair breaking effects and the new EM proximity theory. A non monotonic dependence of the total flux expulsion as a function of the barrier thickness was observed. This could be decom- posed into two distinct and opposing contributions: the first, parameterised by ASF, arising from the anticipated pair breaking of the ferromagnetic

exchange field, and the second the EM proximity effect. The latter being of strength AEM was, for the combination of material parameters present

within these sample systems, persistently diamagnetic and substantially larger than the corresponding effect of pair breaking. Both of these ob- served contributions were ultimately suppressed, and the bilayer response

recovered, through insertion of a thick insulating oxide barrier at the S/F interface. This strongly suggests stray fields are not substantially contribut- ing to the physics. For all of the measured samples the imposed model was an excellent description of the spatial dependence and magnitude of the observed flux lowering. The use of an effective lambda (λef f) and an EM

proximity strength (AEM) provided the means to extract a quantitative

measure of both proximity effects without the need to model explicitly the full quasiclassical profiles. This type of systematic analysis could prove to be invaluable in the study of more complex devices which seek to exploit these proximity effects.

Whilst in general an excellent correspondence between theory and exper- iment was found there do remain some open questions. In particular, there are two points arising from this work which require further experimental and theoretical investigation to address. Firstly, the approximately con- stant value ofAEM for barrier thicknesses of dI ≤4nmcame as a surprise.

The origins of this dependence are currently unknown and are not easily accessible within the existing theory. Further calculations are required to determine explicitly how a stronger gap function, resulting from the decou- pling of the ferromagnetic layer from the superconductor, may effect the generation of the EM proximity amplitude. Secondly, these measurements still do not confirm for certain the source of the additional vector potential at the SIF interface. Whilst it seems likely to be the magnetisation of the ferromagnet further measurements, possibly conducted in zero applied field, are essential to test the details of the source of the large EM effect observed within these systems.

6

|

Platinum within N/S/F het-

erostructures

The work presented in this final experimental chapter marks somewhat of a departure from the themes of the previous studies contained within this thesis. Whereas the content of chapters 3, 4 and 5 was focused on under- standing new fundamental proximity effects within mesoscopic S/F hybrid thin films this chapter has been largely motivated by the interesting ma- terial properties of platinum. The work on platinum containing samples presented here can be broadly split into two parts. The first deals with the effect of inserting platinum spacer layers at both the S/F and N/S in- terfaces within the general Cu/Nb/Co sample structures studied previously. The second seeks to replace the copper normal metal layer with platinum to form NS and NSF bilayer and trilayer systems. These are found to behave very differently from the comparable gold and copper based systems.

Within the first section, measurements on both N/Pt(10)/S/X and N/S/ Pt(2)/F systems, with X=(Si,F), N=Cu(40), S=Nb(50) and F=Co(2.4), demonstrate that even a thin layer of platinum can have a profound effect on the measured response of the sample to an applied field. By simply placing a

2nmthick platinum spacer layer between the niobium and cobalt layers not only does the usual EM proximity contribution associated with the Co(2.4) layer get partially suppressed, or indeed cancelled out, but the temperature dependence of the signal is also greatly altered. Instead of immediately be- ginning to build up a diamagnetic screening response to the applied field, the sample demonstrates first a small paramagnetic uptick in the average flux before, at approximately2K belowTc, a bilayer-like screening response

begins to develop. This is in contrast to a similar NSnF sample structure, where a Cu(2) spacer layer is used instead, as discussed in appendix G. If instead the platinum spacer layer is placed at the N/S interface then the

standard normal metal proximity enhancement to the screening is largely destroyed despite clear evidence from STM measurements that there is a superconducting gap present at the sample surface. In addition, through comparison of results on NnS and NnSF sample structures, where n is a thin normal metal spacer, a reduced EM proximity amplitude appears to be present at the S/F interface within these systems. This provides further evidence that AEM appears to scale with the Meissner screening current

running along the S/F interface.

In the latter half of the chapter, results on systems where the normal metal has been completely replaced by platinum are presented. In both the measured bilayer and trilayer systems the normal metal - superconductor proximity effect behaves very differently. Most strikingly, in the case of the bilayer samples, it is not simply that the platinum layer does not exhibit a screening response but rather that the usual screening response of the niobium is completely absent, or more likely cancelled out by a paramag- netic feature, over a lengthscale of around 40 nm into the niobium layer. Moreover, comparable measurements on a platinum trilayer sample hint at a paramagnetic response at the Pt/Nb interface region and a diamagnetic screening within the niobium layer. Whilst the origin of these observa- tions cannot be concluded for certain they only occur in systems containing platinum which suggests material specific physics, such as strong spin-orbit interaction or Stoner enhanced paramagnetism, may be at play.

6.1

Introduction to platinum in S/F hybrid systems

The work presented in experimental chapters 3-5 presents new and intrigu- ing physics occurring at interfaces within mesoscopic superconducting sys- tems. These are due, in large part, to fundamental proximity effects occur- ring at interfaces between materials widely utilised in more complex devices [1–3, 46, 72, 146]. Platinum is an interesting addition to these structures owing to its substantial set of unusual material properties all of which have the potential to influence any conventional and unconventional supercon- ducting states found therein. It is interesting to pose the question of how known proximity effects: direct electronic, electromagnetic and inverse, will react to the presence of a high spin-orbit, short spin coherence length Stoner enhanced metal. Within this chapter LEµSR measurements are utilised in attempt to map out changes to the flux profile prompted by platinum.

Initial motivation for the presented work stemmed from the theory of weak and half-metallic ferromagnetism [69] as a means to generate uncon- ventional superconducting states in S/F hybrid systems. Since within these systems the exchange field is weaker, the resultant damage to the pair ampli- tude is greatly reduced and the lengthscale over which induced correlations can propagate is increased [3, 46]. A number of experimental results have in fact reported the successful generation and manipulation of supercurrents over long lengthscales through these materials (for example [21, 73, 147]). Given that platinum is a Stoner enhanced metal [148, 149], meaning it has a high density of states at the Fermi level and consequently an extremely large magnetic susceptibility, one might expect that in the presence of an applied field platinum may induce phase shifts within Cooper pairs that are ordinarily associated with ferromagnetism. In such a system the exchange field would become tunable within applied field and temperature space both of which are highly accessible experimental parameters. In some ways the expected response is reminiscent of the properties of weak and half metal- lic ferromagnets within these systems but without the growth difficulties. There are potential downsides to platinum, however, its short spin diffusion length, for example, means it could be highly disruptive to the transmission of spin correlations generated through S/F interactions [150]. In addition, the coherence length of pairs within platinum is likely to be shorter given its shorter mean free path when compared with gold and copper [151]. This will likely effect the readiness with which proximity induced superconductivity penetrates platinum layers.

Finally and perhaps most interestingly, platinum is a heavy metal and hosts a high spin-orbit interaction. This makes it an attractive material within the conventional spintronic community where platinum is often used in conjunction with ferromagnetic and insulating thin films to generate strong Rashba fields. These are typically used as a means to manipulate spin polarised currents through various device architectures [152, 153]. The properties of platinum within superconducting spintronic devices are, how- ever, comparatively little explored. It is intriguing to wonder how spin-orbit interactions may mesh with neighbouring superconducting layers in a hy- brid system. The topic has indeed been the focus of a number of theoretical works [61, 62, 154, 155] which predict a whole host of unconventional effects somewhat akin to those predicted, and measured, within S/F systems (see

for example [3]). In addition, the present focus on electromagnetic proxim- ity within S/F hybrid systems provides a timely link between the two fields and initial experiments on mesoscopic superconductors interfaced with plat- inum suggest a wealth of rich physics waiting to be uncovered [156–163].

In light of the potential physics at play within platinum containing S/F thin films a number of sample systems have been designed and measured using LEµSR. These fall into two groups. The first seeks to investigate the