Sample preparation

Iron and silver are almost totally immiscible, and will not even alloy when melted together. In the study o f immiscible or partially miscible metal alloys, sample preparation presents a problem. An alloy o f these recalcitrant constituents can.

however, often be created by arc melting [Bewley and Cywinski, 1998], melt spinning [Lopez et al., 1998], sputtering [Jackson et al., 2000] or mechanical alloying [Schultz and Eckert, 1994], just to name a few techniques.

In this project, the majority o f samples were created by mechanical alloying in a high-energy ball mill. The workings o f a high-energy planetary ball mill can be seen in figure 3.1. The Fritsch Pulverisette 7 high-energy ball mill used here consists o f a turntable with attachments for two milling pots o f Cr-Ni steel or Syalon, a compound consisting o f Si3N4 and some dopant containing

aluminium. Because syalon has a lower density than Cr-Ni steel, it is thought that the syalon ball mill will have lower milling energy than the Cr-Ni steel one.

M illing bowl

Turntable

M illing bowl

Figure 3.1. A sketch o f the workings o f a planetary ball mill.

These milling pots each contain 6-7 balls o f the same material as the pot. When the turntable turns, the pots rotate as shown in the figure, which causes collisions that result in cold welding and fracturing o f crystallites. This initially produces layered powder particles on a microscopic scale, but further milling breaks down these layers into an increasingly refined microstructure that can

create a metastable alloy [Schultz and Eckert, 1994]. If the constituents are sufficiently miscible, an amorphous alloy will be the result.

Elemental powders with micron scale crystallites were weighed to achieve the correct stochiometry and mixed in a pot. The pot was sealed inside a Saffron glove box under an argon atmosphere in order to prevent oxidation. The results of the milling depend on the ratios of initial components and their miscibility. For

instance, FezoCugo, when milled for 60 hours, alloys completely, whereas Fe2oAggo

milled for the same time yields a nanoscale polycrystalline granular mixture. To prevent over-heating, the samples were only milled for two hours continuously (heating the pots to 40-50°C), after which a cooling period o f one hour would follow before the next two-hour milling period. As such, a 70 hour milling would

take approximately AYz days to complete.

One sample presented in this thesis was prepared by arc melting. The arc furnace used was an Edmund Bühler Arc-Melting apparatus. The electrode was made of tungsten and water-cooled. The electrode had a maximum possible current o f 400 A, and the generator could generate 18kW. The tungsten tip was brought near a water-cooled copper trough. The atmosphere inside the chamber was 0.5 bar Argon. The tungsten electrode was first “fired” onto a piece of zirconium (which melts under the beam) to clear the atmosphere o f impurities. The zirconium absorbs oxygen particularly well, as well as other impurities. Zr melts at 2128 K, but the actual temperature the arc could induce was proportional to the electrical resistance. Silver, for example, is a very good conductor and does thus not attain such high temperatures.

Because the trough was water-cooled, the cooling time o f the samples was short. The alloy composition after melting varied with gas pressure. In addition, the actual composition o f the sample can vary due to mass loss while under the arc beam. In the case o f the FeAg samples, a small loss o f silver through the arc- melting process was expected, thus leaving a higher ratio o f iron to silver. By moving the arc in a rolling motion, the melt could be mixed in a way that ensured homogeneity.

In following the procedure detailed above, it was seen that the FeAg mixture was slow to heat and turned into separate lumps under the arc. It is as yet

unclear what caused this; perhaps studying the effect o f melting pure silver would give an answer. It is unlikely that this is an effect o f the iron in the mixture.

2. Magnetic measurement techniques

In this project, being in the main an examination o f magnetic relaxation effects, a thorough investigation o f the magnetic properties can only be realised by investigating the relaxation behaviour through a variety o f measurement timescales (see chapter 2). Apart from the more traditional techniques o f DC Magnetisation and Mossbauer Spectroscopy, pSR has also been used in an attempt to explore an intermediate timescale.

i. VSM - Tm = 1-10 s

The Vibrating Sample Magnetometer, usually abbreviated as VSM, works by moving a magnetic sample rapidly up and down between the poles o f a magnet. The magnetisation is detected by induction coils placed between the poles and around the sample. This has a measurement timescale on the order o f 1-10 seconds. A VSM is, simply put, a gradiometer that measures the difference in induction in a space with and without a sample present. This leads to a direct

measurement o f the bulk magnetisation M. Important considerations when using a

VSM are the packing o f the sample for powder samples, the alignment o f the sample, and demagnetisation effects. As the space between the poles is only a few centimetres, the samples cannot easily be made large enough to wholly eliminate demagnetisation effects. Within the context o f this project, the VSM has been used to obtain magnetisation curves and hysteresis loops. Some of these have later been analysed via a Langevin function (see chapters 2 and 4).

The sample is mounted on a rod between the poles o f a magnet, where also a small pick-up coil is placed, as shown in figure 3.2. The sample vibrates sinusoidally at a fixed frequency o f 66 Hz in order to minimise interference from the mains frequency (50 Hz). An e.m.f. is generated in the pick-up coils that is proportional to the sample magnetisation. As the sample vibrates, a voltage is induced in the coils.

The VSM has a measurement sensitivity o f lO'"^ emu. In order to obtain an absolute value for the sample magnetisation it is necessary to calibrate the apparatus against a standard material, in this case a nickel foil, which has a known magnetic moment.

Pick-up coils

Sample

Magnet _{Magnet Magnet}

Side view

Front view Sample rod

Figure 3.2. The Vibrating Sample Magnetometer (VSM) magnet and pick-up coil arrangement.

An important consideration in hysteresis loop measurements, especially when hoping to fit these to a Langevin equation (see chapter 4), is the demagnetisation effect. Demagnetisation fields are a consequence of the fact that, inside a magnetised sample o f finite dimensions, the magnetisation M and the applied field H point in different directions. It is possible to determine a

demagnetising field present whenever magnetic poles are created in a

material. The demagnetisation field depends on the magnetisation M and the

shape o f the sample. Thus, = N^M, where is a shape-dependent

demagnetisation factor, which is a dimensionless number provided H and M are both measured in the same unit. A/m. An exact analytical solution for Ad is only possible for ellipsiods, but approximations can be obtained experimentally. In the experiments in this thesis, a variety o f sample-mounting procedures have been attempted in order to minimise demagnetisation effects. The best results finally

came by measuring pressed discs o f powder, that had been prepared in a pneumatic press, and then mounted in-plane with the field. The demagnetisation factor for an infinite plane taken parallel to the surface is zero, so this configuration gives negligible A^d-

The hysteresis data in this project were obtained on an Aerosonic 3001 Vibrating Sample Magnetometer, using an electromagnet capable o f fields up to 7000 Oe. For much o f the project, only fields up to 5000 Oe were used, as they were deemed sufficient for the purposes o f the project, thus sacrificing magnitude for the sake o f stability.

a. SQUID m a g n e t o m e t r y - t„, = JO^ s

SQUID is an acronym deriving from the words Superconducting Quantum Interference Device. SQUIDs are now the ultimate technique for field measurements. The SQUID data in this thesis were obtained on a Quantum Design MPMS SQUID magnetometer.

Josephson junction Superconducting current h Superconducting circuit

Figure 3.3. A schematic diagram o f the mechanism behind a SQUID.

A SQUID consists o f a superconducting ring with a small insulating layer known as a Josephson junction (figure 3.3). The junction can just as easily consist o f a small gap in a ring o f superconducting material. In the SQUID used in this experiment, the sample is not placed in the centre o f the ring, but through a superconducting coil that produces a field at the ring shown in fig. 3.3. Due to the

Meissner effect, magnetic fields cannot penetrate a superconductor, either in or out. The gap, however, is permeable to flux, and if this gap is thin enough, the supercurrent can still flow, typically restricted to less than 10'^ A [Jiles, 1991]. Thus, flux can enter the ring. The relation between the flux density in the ring <Z>,

and the flux density due to an applied field (^, is = cP» + Lh. L is the inductance

o f the ring, and h the supercurrent, producing the flux d>s =LIs. h is related to the

critical current 7c, such that A = 7c sin 0, where 0 is the phase difference of the

electron wavefimctions across the weak link. Therefore, (Z>= <Pa + Lie sin 6.

Flux is quantised in a superconducting ring, such that O = The phase

angle ^depends on the flux as

2n N- 2;r(<P/<^) = sin = -sin {IkOIOq) (3.1)

since A is an integer. Therefore

0 — (Pa ~ Lie sin { 2 7 t 0 ! (3.2)

The flux quantum o f the applied field is 2.067 x 10'^^ Wb [Jiles, 1991]. Whenever

0/0Q does not equal d^/(P, and the flux is not an integral multiple o f the quantum,

voltage pulses due to the quantum jump are produced. These can be detected by wrapping an induction coil around the SQUID. The signal recorded was averaged over three sweeps, lasting about thirty seconds each, for a total measurement timescale o f 10^ s.

Hi. Mossbauer - Tm = 10'^ s

In this project, Mossbauer Spectroscopy represents the shortest measurement timescale, o f the order of nanoseconds. Mossbauer is also a nuclear technique, not a bulk technique like SQUID and VSM.

570 keV -^'C o

electron capture, = 270 days

13 7 k eV -^ T e* • > y /=7: 14.4 k eV -" T e* •>Y /= V ;

Figure 3.4. The emission scheme o f ^^Co.

The Mossbauer effect relies upon the fact that a nucleus can emit recoilless y-rays if bound to a solid. This was noted in 1939 by Lamb, and experimentally verified by Rudolf Mossbauer, in 1958 [Greenwood and Gibb, 1971]. The most common Mossbauer set-ups use ^^Co nuclei, which decay into ^^Fe nuclei (fig. 3.4). The y- rays are absorbed by ^^Fe in the sample, an isotope which constitutes 2% of normal iron. Usually the sample will be a thin foil or a dispersion of a powder, such that y-rays can traverse the sample to a detector and Single Channel Analyser (SCA). By oscillating the source or the sample at a few mm/s, a narrow band o f y- ray energies can be obtained through the Doppler effect. The absorption peaks can then be obtained and analysed.

In ^^Fe Mossbauer, there are three main effects. The first is the isomer

shift, which is a shift in the energy levels by 5. One reason for this is the differing

sizes o f the source and absorber nuclei, giving rise to a difference in the Coulomb interaction between the nucleus and the surrounding electrons. The isomer shift can also be caused by a temperature difference between the emitter and absorber [Pankhurst and Pollard, 1993].

The Zeeman splitting by the internal magnetic field shifts the energy by E

= Iz is the component o f nuclear spin parallel to H\, the internal

unit o f nuclear magnetic moment, A/n = {ehlAnm^). For ^^Fe this results in a splitting into four levels fo r /= V2, and two for/ = V2 (fig. 3.5).

The third effect is quadrupole splitting. The quadrupole moment o f a nucleus is given by eQ = i ! j - r^) d v, where p is the electric charge density,

r is the radial vector o f the charge, and z is the co-ordinate axis parallel to the nuclear spin. In the ground state there is no quadrupolar splitting, but in the excited state the levels are split by A£ = V4 e^qQ (3cos^ 6 - l)/2, where q is the

field gradient. /=/2 à I /z = - .. h=- \ r

Isomer shift Zeeman splitting Quadrupole splitting

Emission

Figure 3.5. The absorption scheme o f ^^Fe.

Between these levels, there are six possible transitions (numbered 1-6 in fig. 3.5), that obey the exclusion rule A/z = 0 or ±1, which is the rule o f

conservation o f angular momentum. For a-Fe, the room temperature Mossbauer spectrum with no applied field manifests itself as a row o f six absorption lines (fig. 3.6).

0 0

10.0

2 0 . 0

alpha-Fe Mossbauer spectrum

- 6 - 3 0 3

Velocity (m m /s )

Figure 3.6. A room temperature Mossbauer spectrum o f a-Fe.

iv./uSR- T„, = I f f " - l a ' ” s

The acronym pSR can be used to stand for any o f three different techniques, namely Muon Spin Rotation, Resonance or Relaxation. Muon Spin Rotation refers to the implantation o f positive polarised muons into a sample in a magnetic field normal to the direction o f muon spin polarisation. The muons will precess in this field and the depolarisation is monitored. Muon Spin Resonance refers to the application o f an alternating field in an attempt to induce a resonance. Muon Spin Relaxation is the implantation o f polarised muons into a sample in no external field or a field parallel to the direction o f muon spin polarisation.

In this thesis, we shall concentrate on Muon Spin Relaxation experiments. Thus, unless specified otherwise, the acronym pSR as used in this thesis always refers to Muon Spin Relaxation.

The muon, as a particle, is part o f the lepton family, and can be viewed as a heavier cousin o f the electron. The muon has ^ I the mass o f a proton. It is a spin-V: particle, and has a charge of e. The muon also has a strong magnetic

moment, about three times the size of that o f the proton. Muons are produced from the decay o f pions. The pion decays after approximately 26 nanoseconds to

create a muon and a muon neutrino. In the case o f a the decay scheme is

(3.3)

Because the pion has spin zero, and all neutrinos are polarised in the same direction, the muons created in this way are 100% spin polarised. Beams o f spin- polarised muons are used at facilities like ISIS in the UK, PSI in Switzerland, TRIUMF in Canada and KEK in Japan. The normal procedure is to direct a beam of polarised positive muons into a sample, where they will be implanted. While pSR experiments with negative muons are possible and have been done; this field is at this time not pursued much in Condensed Matter science.

Inside the sample, the muon spin will behave like a lightweight proton. The motion o f a muon, and the coupling and de-coupling to electrons and atoms, present a formidable theoretical challenge, in response to which much research is being done. Fortunately, the muon tends to adopt similar behaviour to protons, which makes comparative studies possible.

Primarily, the electrostatic interaction determines the choice of crystallographic or molecular sites. Muons, like protons, are far too reactive as

particles to remain as and will couple with an electron to form muonium (Mu)

after thermalisation. Muonium is reasonably stable and can be detected as a paramagnetic defect in some solids.

The mechanisms by which the muons stop or thermalise within the sample are fast compared to the decay time of the muon. Furthermore, the primary processes include only electrostatic interactions, which are not spin-dependent, so there is little loss o f initial polarisation. [Ford and Mullin, 1957; Brewer et al., 1975] Of course, its interactions with any magnetic moments in the sample are spin-dependent and will affect the depolarisation signal.

In the sample, the muons precess about any moment not parallel with their

an average lifetime o f 2 . 2 microseconds, a lifetime which is independent o f the

chemical state o f the muon. It decays spontaneously by p-decay as

(3.4)

The positron is emitted preferentially in the direction o f the muon polarisation (fig. 3.7.) These positrons are sufficiently energetic to leave the sample. By detecting the positron emission, one gets an image o f the change in muon polarisation since implantation, due to the magnetic environment around the muon. Considering the shape in figure 3.7, it can be seen that in the three-body decay the initial positron decay asymmetry in the direction o f the polarisation will be about 25% anisotropy [Blundell, 1999]. This will later disappear as the muons become depolarised in the sample.

a = V3

Figure 3.7. The angular distribution P{9) = \ a cos ^ o f the positron emission from a collection o f muons, in the direction 0, with respect to the muon

polarisation, where a is degree o f polarisation o f the muons ( 1 = highest energy,