COMPRESIÓN DE VOZ PARA ROIP

All pSR data presented in this thesis are taken either in zero field or with field parallel to the initial muon polarisation (longitudinal). Figure 6.1 shows a schematic of a longitudinal muon spectrometer, with a ‘forward’ and a ‘backward’ detector. The difference between the signal from these two detectors gives the ‘asymmetry’ of the polarisation of the muons, and is derived from the difference

of the number of events observed in the forward detector Np(t) and the number of

events observed in the backward detector A^b(0- The depolarisation is thus

aG{t) = [Np(t) - ck/Vb(0]/[ A^f(0 + ûA^b(0] (6.3)

where a is an experimentally verified parameter related to the relative efficiencies

of the forward and backward detectors, a is the initial asymmetry of the muons

(see chapter 3) and G(t) is the depolarisation function.

Beam

Sample

Figure 6.1. A schematic view of a longitudinal pSR experimental arrangement, with a muon counter E and two decay positron counters EF and EB.

The muon data presented in this thesis derive from experiments at the Rutherford Appleton Laboratory in the UK (April 1998, September 1999, December 1999, January 2000 and June 2000) and at the Paul Scherrer Institut

(PSI) in Switzerland (August 1999). Table 6.1 shows a summary o f all the experiments performed. The difference between these two facilities is that RAL’s ISIS is a pulsed source, whereas PSI is a continuous source. The muons at RAL arrive in pulses o f 70 ns width, whereas the PSI muons arrive at a constant rate. Experimentally this difference presents itself in an initial self-imposed deadtime o f ISIS data, in which no muon signal can be observed. The pulse is finite and the uncertainty in the arrival time of individual muons with respect to the starting signal means that the time resolution o f a pulsed spectrometer is limited in order to avoid false counts from incoming muons. The maximum frequency that can be seen is the inverse o f the pulse width, thus for a pulse width o f 70 ns the maximum frequency is just above 14 MHz. For relatively slow relaxation phenomena like superparamagnetic relaxation, this is usually not a problem [Cox, 1987]. The pulsed source data do have some advantages compared to data obtained from a continuous source. For pulsed source data, it is very much simpler to obtain a baseline count rate, since muons are not arriving constantly during data collection. This extends the useable timescale from implantation compared to a continuous source, which is tremendously useful when studying slow relaxation phenomena.

Date Duration Facility (beamline) Samples studied

April 1998 3 days ISIS (EMU) FeoiAggg

Feo6Ag94 Fe26CUogAg66

July 1999 2 days PSI (DOLLY) Feo2Ag9g

Feo6Ag94 Fe26CUogAg66

September 1999 1 day ISIS (MuSR) Fe2oCui9Ag6i

Fe26CUogAg66

December 1999 2 days ISIS (ARGUS) Fe2oCui9Ag6i

Fe26CUogAg66

January 2000 3 days ISIS (MuSR) Fe2oCui9Ag6i

Fe2oCuo9Ag7i

June 2000 3 days ISIS (EMU) Fei2Cuo9Ag7i

Table 6.1. A summary o f all pSR experiments in this thesis.

(with the exception o f one) fitted to one or two exponentials, exp(-Ar), where X is

a relaxation parameter defined in more detail later, and t is time since muon

implantation.

Different methods for mounting the sample were tried. It is known that 4MeV muons have a stopping distance o f about 0.2g cm'^, so with sample densities measured to be around 5 g/cm^, a thickness o f about 1mm was required to ensure the muons stopped in the samples and did not go straight through it. The first method, used at ISIS, involved an aluminium sample holder (shown in figure 6.2) o f about 5 mm thickness with a 25 mm diameter by 2mm depth milled cavity for the sample. After the sample had been put within, a thin sheet o f Mylar was glued over the cavity. A silver mask was then added to prevent any muons from landing in the aluminium, and the entire assembly was then put in the beam.

25 mm Front view

Side view Figure 6.2. ISIS muon sample holder.

This set-up presented some problems for the samples studied here. Due to the high density o f Fe-Ag-Cu alloys, a comparatively large mass o f sample was required to fill the 0.5 cm^ cavity volume - an amount that was not always available. Also, because the samples were prepared with the cavity horizontal to the ground, and then placed vertically in the beam, gradual sagging against the Mylar sheet would occur, and the sample, as exposed to the beam, would change over time, sometimes exposing the aluminium behind the sample. This effect was particularly pronounced when using the closed-cycle refrigerator (CCR) instead of

a cryostat, due to the transmitted vibration of the CCR pump. In contrast to silver, aluminium does have a pSR depolarisation signal, which looks like a Gaussian, exp (-(f^ /2 ). This depolarisation component sometimes appeared and would confuse the analysis o f the data. Attempts were made to use the same set-up with

a shallower cavity (only 1mm) but the sagging problem persisted.

For the last few pSR experiments, a totally different set-up was used, consisting o f making a small envelope from silver foil with the sample inside, simply taped to a silver backing plate, thus eliminating the possibility o f any aluminium contamination signal altogether. With this method, some o f the best muon data were obtained.

At PSI, other problems were encountered. The two days o f beamtime there were on the DOLLY beamline (so called because it is an exact copy or ‘clone’ of another beamline, GPS) using the ‘Mango’ cryostat, which had been custom built by the low-Temperature group there. The procedure for using this cryostat was still in its infancy in August 1999, and it is now believed that the powder samples were not fully in the beam during data accumulation. This meant that some aluminium was in the beam, and that these depolarisation patterns are contaminated with an aluminium signal. The data obtained can, however, still indicate the amount o f depolarisation due to the magnetic clusters. At PSI, the existence o f a very fast relaxing component, hidden in the initial deadtime at ISIS, was revealed. The data obtained gives an impression o f the size o f the fast relaxing component, and this information has been useful in further analysis. Sample PSI depolarisation patterns, scaled to emphasise the fast relaxing component, are shown in figure 6.3. Interestingly the rapid depolarisation component becomes less significant as the temperature drops, which is consistent with later data.

Despite the experimental problems outlined above, much useful muon data have been accumulated during the course o f this project, enough for it to warrant a chapter o f its own. This is in part due to the complexities o f gaining understanding of how superparamagnetic effects manifest themselves in pSR, and in part due to the complexities o f the behaviour o f muons. While all other techniques mentioned

measurement time in |uSR is dependent on the field distributions within the sample and can vary from 10'"^ to 10'^^ seconds [Bewley et al., 1998]. It is believed for these samples that the muon measurement time is of the order of microseconds, but this is only an approximate figure.

Fe^Ag,^50K

Tim e (|is) Time (u s)

Fe^Ag,^300K Fe^Ag,^300K

T im e (u s) Time (u s)

Figure 6.3. Sample relaxation patterns from PSI, on the alloy FeoôAg9 4.

2. juSR and Superparamagnetism

How does superparamagnetic unblocking manifest itself in pSR? Muons landing in an environment with no applied field and randomly oriented internal magnetic moments should depolarise in a Gaussian Kubo-Toyabe relaxation [Uemura,

1985; Schenck and Gygax, 1995]:

where is the muon gyromagnetic ratio 13.6 x 2;rkHz/G and A is the width of the random fields. If the magnetic environment starts to change within the lifetime o f the muons, such as by superparamagnetic relaxation, the above relaxation becomes a dynamic Kubo-Toyabe, for which no exact analytical form exists [Schenck et al., 1995]. For low fluctuation frequencies, this resembles an exponential relation:

Gz (0 = V3 exp (-% vt). (6.5)

For higher fluctuation frequencies, one gets

Gz if) = exp ( - 2 t!v \ (6.6)

which is similar to the spin lattice fluctuation regime [Schenck and Gygax, 1995]. In our samples, for the static case, muons implanted in the sample (and not the mask or the sample holder) may be expected either to land inside the magnetic grains or in the matrix. Muons that land inside the clusters experience a strong local field of several kG [Ucko et al., 2001], and those in clusters not aligned in the detector direction (^/g on average) will as such depolarise due to precession about the moments before they can be seen at ISIS. The resultant signal will be an

offset o f VsfltFc, where Vc is the volume fraction o f clusters in the sample.

Muons landing outside the grains will experience a field that varies depending on the local field at the landing spot o f the muon. The muons will then depolarise at a rate dependent on the local field. For a system o f randomly oriented static spins one would normally expect a Gaussian Kubo-Toyabe-type

relaxation, but since the system in question consists o f magnetic clusters, the V3

“recovery” is not seen and the resultant signal is a fast exponential relaxation [Uemura et al., 1985]. An analytical expression has been derived for a system of equal clusters by Uemura et al, but for a system o f clusters with a distribution of sizes, no such expression can be obtained [Uemura et al., 1985].

In a continuous medium one would expect the distribution of

distance from the grain surface. However, in a nanoscale granular alloy the sample is not continuous (figure 6.4). Muons are known to diffuse in metals [Cox, 1987], and we believe the muons landing in a silver grain will diffuse to the grain boundaries before they decay. It is therefore likely that the probability distribution will be discontinuous, with divisions o f one or more silver grains’ separation from the magnetic grain. This assumption is borne out in the observations o f two relaxation exponentials rather than a continuum. For this reason we have adopted a 3-box histogram theory incorporating a fast relaxation component, a slow relaxation component and a non-relaxing component for muons very far from any magnetic grains. The final depolarisation equation is thus

Gz (0 = VsûtFc + fliexp(->^-iO + a2exp(-À2t) + (6.7)

where À\ and Z2 are the relaxation parameters, a is the initial asymmetry,

fli, « 2 and « 3 are the asymmetry contributions o f the three muon ‘scenarios’ in

which the muons do not land directly inside a cluster. The initial observed

asymmetry <20 (being what emerges from fitting) should thus be equation (6.7) at t

= 0, and the final asymmetry is the same equation when ^ ~ 2 0 jus.

Low-temperature depolarisation patterns fit best to a single, low A exponential. By comparing this A to the slow relaxation signal for the two- exponential depolarisation type, one can conclude that the depolarisation from the muons near the clusters is, at low temperatures, simply too fast to be observed when the fields are static. In Fe^CuogAgyg, for instance, data at the lowest temperature 5 K shows a depolarisation pattern consisting solely of one exponential, with a A approximately equal to that o f the second exponential in the 50 K pattern. For some samples the fast relaxing exponential could not be seen at any temperature, which is probably be due to the clusters being too few and too separated to yield an appreciable fast relaxation depolarisation that is significant enough to emerge in the analysis o f the data.