Tercer trimestre: La Edad Media

The final objective of this chapter is to address what happens to the Meiss- ner screening profile after the addition of a thin ferromagnetic layer is made to the underside of the bilayer section. It would be expected that, due to the presence of the ferromagnetic exchange field, the superconducting gap would be reduced within the region close to the SF interface, weaken- ing the superconductivity and reducing the total number of screening pairs present within the system. Additionally, the exchange field opens up the possibility of generating odd-frequency pairs which are known to produce a paramagnetic screening response. The net result would be a reduction in the overall flux expulsion with a bias to a loss in amplitude towards the ferromagnetic layer. These expectations are recovered by calculations, the results of which are shown alongside the NS(I) profiles in figure 3.8. Curve

5∗ represents the effect of adding the thin Co(2.4) layer to the underside of the bilayer sample corresponding to curve 5. Additional parameters are required to describe the cobalt layer. The exchange field, Jz, was taken to

be 321 meV (see for example [141]) and the coherence length within the ferromagnetξF =

q ¯ hDF

JZ = 1 nm(see for example [8]). A clear reduction in

the overall flux expulsion is visible and most pronounced within the niobium layer as reasoned above. As will become immediately obvious, however, the LEµSR measurements on NSF(I) and NSF(II) highlight a surprising discrep- ancy between the quasiclassical theory calculations and the extracted flux averages. Whereas the theory predicts a decisive reduction flux expulsion the measurements show a substantial increase approximately corresponding to a further 50% increase when compared with the corresponding bilayer sample.

The results of the LEµSR measurements on NSF(I) and NSF(II) are shown, with S(II) and NS(II) as grey lines for reference, in figure 3.9. The stopping profiles in the top panel of figure 3.9c) are largely consistent with those of the bilayer but where before sampling the substrate a fraction of muons forEµ≥20keV will stop within the Co layer. These muons will be

immediately depolarised but represent a relatively small fraction of the those stopping within the sample. More importantly, the stray fields generated by the ferromagnetic layer will cause an increase in the depolarisation rate which will extend across most of the bilayer section. The result being a more strongly damped total signal and larger error bars in the extracted field values especially for average depths close to the cobalt.

280 284 288 292 296 300 304 0 20 40 60 80 100 S(II) NS(II) NSF(I) NSF(II)

Average implantation depth (nm) 40 80

20 60

Average implantation depth (nm) 3 2.5 2 1.5 1 0.5 0 D e p o la ri s a ti o n r a te (M H z ) NL NR 0.3 0.2 -0.3 -0.1 -0.2 0.1 0 2 4 6 8 10 P o s it ro n c o u n ts Time (s) 0 a) b) c) <B > (G) 0 100 120 Co Cu Nb 20keV 14keV 8keV 4keV p(x) a.u . Co Si 2.5 K 10 K

Figure 3.9: LEµSR results on the CuNbCo trilayer samples. a) Example raw LE-µSR data. NL and NR are the left and right detector data respectively

and the grey lines are fits to the data. The spectra shown are for NSF(II) measured at Eµ = 4 keV and T = 2.5 K. b) Depolarisation rate as a

function ofhxiabove and belowTcfor NSF(II). The position of the Co layer

is marked in green. c) Top panel: muon stopping profiles for several selected implantation energies with the lines indicating the corresponding average sampling depth. Bottom panel: Average field as a function of average depth. Open (closed) data points correspond to normal (superconducting) state measurements taken at10K (2.5K). The lines are a guide to the eye. The best fit field profiles for S(II) and NS(II) are shown in grey for reference. Figure 3.9a) shows an example raw spectrum measured for NSF(II) at a muon energy ofEµ = 4keV and a temperature ofT = 2.5K. As before, the

two detector signals are plotted separately with their associated fits shown as solid grey lines. Whilst there is no clear difference in the damping rate visible in the raw data at this energy when compared with the bilayer data in figure 3.6a) this data corresponds to a probing energy that focuses far from the Co layer. The reader is referred to appendix C for a comparison of the raw signal for different probing energies. The effect of the stray field from the cobalt layer is clearly visible, however, in figure 3.9b) which presents how

λ changes as a function of the average probing depth for NSF(II). In the average values found both in the normal (red points) and superconducting (blue points) states the value ofλrises as the probing depth approaches the

Co layer (marked in green). This can be modelled, using an exponential profile as discussed in section 2.1.6, the result of which is plotted in each case as the solid line of corresponding colour. A good correspondence can be seen, particularly for the normal state data, between the model profile and the results of the average fitting. The extracted fit parameters of the model profile, an amplitude (λ0) and decay length (ξλ), are shown in table 3.4

for both NSF(I) and NSF(II). The values of both λ0 and ξλ are consistent

across the two sample sets which would be expected since the procedure of cobalt growth was the same for each sample series. The decay length of around15nmsuggests that the effects of the stray field are largely confined to a region of the niobium within20 nm of the cobalt layer.

Table 3.4: Table of extracted depolarisation amplitudes and decay lengths for NSF(I) and NSF(II)

sample λ0 ±∆λ0 ξλ ±∆ξλ

M Hz M Hz nm nm

NSF(I) 3.2 0.1 13 1.5

NSF(II) 3.4 0.1 14 2.0

The flux averages extracted using the conventional approach to the muon data analysis are presented in the bottom panel of figure 3.9c). As always the normal state measurements have simply recovered the applied field. Upon cooling to below the superconducting transition a flux lowering is once again observed across all measured energies. Surprisingly this is in fact enhanced when compared with the screening amplitude of the respec- tive bilayer. This rather interestingly is in direct opposition to the theoret- ical calculations presented in figure 3.8.

A crude comparison of the data for NS(II) and NSF(II) is presented in figure 3.10. This plot simply shows the point-by-point difference in the Meissner screening amplitudes as a function of the average probing depth. These amplitudes are calculated for each sample by taking the difference be- tween the corresponding normal and superconducting state measurements presented in figure 3.9. The results presented in figure 3.10 clearly show the difference is largest within the region close to the SF interface and tapers off with distance towards the surface.

Average implantation depth (nm) 20keV p (x ) (A U ) Nb Cu Y (<dB NS > - <dB NSF >) (G) -10 -5 0 0 20 40 60 80 100 14keV 8keV 4keV

Figure 3.10: The data points represent the point-by-point difference in the average flux lowering between NS(II) and NSF(II) plotted as a function of the average probing depth. Here Y represents either Si or Co(2.4)/Nb(3)/Si depending on the sample. The vertical dashed line represents the interface and the dashed profile is a guide to the eye indicating how the additional amplitude might role off spatially.

At the very highest probing energy,Eµ= 23keV, care needs to be taken not

to over-interpret the slight uptick in the data. This is because the stopping profile for the NSF structure begins to appreciably probe the cobalt layer which will effect the validity of taking a direct difference in amplitude to the NS sample. The top panel of figure 3.10 presents the stopping profiles for reference. At an energy of Eµ= 20keV there is only a small tail extending

beyond the bilayer section but for higher energies this fraction will increase and may begin to substantially effect the simple comparison being made since the spatial information is no longer the same.

Whilst highly simplified this method of comparison is nevertheless useful in providing some information as to the origin of the observed discrepancy between theory and experiment. Whatever the underlying effect, it appears to have its origins at the SF interface and extends across the sample decay- ing in amplitude as it goes. The lengthscale over which the additional com- ponent decays is much greater than the superconducting coherence length which suggests that the measured response cannot be associated with the inverse proximity effect due to spin polarised pairs existing close to the S/F

interface. In addition, whilst the stray fields originating from the cobalt layer extend across the full NS section there is no evidence for any asso- ciated influence on the behaviour of the sample in the normal state. This strongly suggests that stray field does not play a role in generating the additional component to the screening.34