Discusión de resultados de los bioprocesos y del efecto de las variables sobre

Single crystals of Sr3Ru2O7 and Sr2RuO4 were grown by a floating-zone tech-

nique in an infra-red image furnace. High purity powders of SrCO3 and RuO2

are mixed, ground and calcinated, pressed into a rod, sintered and the result- ing rod is placed into the image furnace. At the focus of two infra-red lamps, the sintered rod melts, forming a molten zone. The rod is slowly moved through the focus of the lamps until the molten zone has passed its entire

length, leaving behind a single crystal. For Sr3Ru2O7, a detailed study has

been performed to optimise the variety of growth conditions [91], resulting

in single crystals with residual resistivities as low as ρ0 ≈ 0.25µΩcm. The

Sr3Ru2O7 samples used for this project were grown by R.S. Perry, whilst the

Sr2RuO4 samples were grown by A.S. Gibbs.

Significant variations between the qualities of different growths were found [12], so that many batches needed to be grown and characterised in order to select the ones yielding samples sufficiently pure to exhibit the anisotropic phase. Most of the samples used in this project were selected from batches which had undergone extensive characterisation by J.-F. Mercure [12], which enabled us to cut new samples with high confidence of their purity. We

selected samples from batches with ρ0 < 0.7µΩcm, and in which quantum

oscillations had been observed. Over the course of this project, we cut,

mounted and characterised crystals from eight different batches. The crystals used in the eventual measurements are those which were found to be the most homogeneous, with the lowest residual resistivities and the most suitable shapes.

During the course of this project, I mounted and characterised approx- imately 20 crystals; the best 4 of these were selected for the detailed ex- periments described in chapters 4-6. Two samples measured in the vector magnet, which will be described in chapter 5 as ‘needle’ and ‘octagon 1’, had already been mounted and characterised by R.A. Borzi and S.A. Grigera, so that their quality was known before the start of this project.

Sample cutting

Both Sr2RuO4 and Sr3Ru2O7 cleave readily along their ab planes. The ex-

posedabsurface is optically reflective and may have few visible imperfections

over the length scale of a millimetre. The larger the surface of the cleave, the greater the probability that irregularities appear. Cleaves can be initi- ated manually with a sharp scalpel blade. Whilst the cleaves are often of good quality, the scalpel technique is not controlled enough to determine the thickness of the cleaved platelet precisely. In addition, a crystal may spontaneously cleave if it is stressed.

For resistivity samples in which current is passed through the ab plane,

the size of the absolute resistance is inversely proportional to the thickness

of the sample in the c-direction. To reproducibly cleave off thin slabs, we

tried cleaving samples by employing a technique that is widely used in An- gle Resolved Photoelectron Spectroscopy (ARPES). For ARPES, the crystal surface must be cleaved in ultrahigh vacuum. The solution is to stick the crystal down with glue and attach a small object on top of the exposed crys-

it, exposing the cleaved surface. We found that this method works well un- der atmospheric conditions. Glueing a crystal on a microscope slide with

Araldite, with a 0.7mm drill bit attached to the ab plane with Crystalbond,

we obtained good >1mm2 _{area plates, but of widely varying thickness.}

To improve on the different cleaving techniques, we polished a number of crystals down, with good results. We employed a hand held polishing puck made of stainless steel, with a central column onto which end the sample is glued. The column moves up and down freely in the puck, so that the only downward force on the sample is the weight of the column. Samples are attached to their holder with Crystalbond. For the polishing medium we

decided to use self-adhesive abrasive disks1 _{which are pre-coated with fine}

alumina powder. The disks are attached to a thick glass plate for stability. For lubrication machine oil, glycerine and WD40 are all suitable, but tap water works equally well. For the best results, samples are polished on a series of different disks, varying from course to fine grain size. A final polish

with 1µm grains results in a surface which is visually indistinguishable from a

cleaved surface. We were able to polish theac,bc and ab planes equally well.

By polishing, we were able to bring any sample dimension down to about 50

µm. At this thickness, the sample is very brittle and tweezer manipulation

becomes problematic so there is a significant risk of breaking the sample. For these measurements, we wanted to control the direction of current

within the ab plane. Specifically, for needle samples, we wanted the current

to flow along eithera orb. To cut the crystal in theac andbc planes we used

a wire saw2_{. The wire saw operates by rapidly moving a thin (80 µm outer}

diameter) tungsten wire over the sample, feeding the wire through slowly between two spools to prevent excessive wear. The interface between the

wire and the sample is lubricated with a mixture of glycerine and 15µm SiC

powder. A well calibrated wire saw can make very thin cuts in a well defined plane. In practice, our cuts were around twice the wire diameter in width.

To determine the orientation of the principal crystal axesa andb, we used

a Laue camera at the Centre for Science at Extreme Conditions in Edinburgh. Samples are glued to a wooden holder on a three axis goniometer, which fits both the Laue camera and the wire saw. Broadband X-rays are generated by hitting a metal target with an electron beam. The beam is directed and

collimated to hit the sample normal to its ab plane. This orientation is

determined by using the optical reflectivity of a cleaved surface, and back- reflecting a visible laser beam which travels by the same path as the X- ray beam. X-rays penetrate into the crystal and are back scattered onto a

1_{Buehler FibrMet}

Figure 3.1: Laue X-ray image taken normal to the Sr3Ru2O7 ab plane. In

each case theaandb axes are oriented horizontally and vertically (any differ-

ences between the two are not resolved). Darkness denotes higher intensity.

Left: scan from a photosensitive plate. The white central dot is caused by

a hole in the plate through which the X-ray beam is directed. Right: Simu-

lated pattern using the crystal structure found by Kiyanagi and co-workers [38]. Red lines are guides to the eye to the most visible lines of high intensity peaks, and the angles between them.

photosensitive plate. Spots of high intensity appear on the plate where the Bragg condition is fulfilled. The Laue pattern has the same symmetries as the crystal structure, and rotates as the crystal is rotated around its surface normal. By calculating the expected Laue pattern, or comparing to previous

results, we can determine the orientation of a and b.

Figure 3.1 presents a measured and a simulated Laue pattern side by

side, for an X-ray beam normal to the ab plane and either a or b oriented

vertically. Once the principal axes are identified, the sample can be cut by

wire saw alongac and bc on the same goniometer.

Sample mounting

A typical Sr3Ru2O7 sample with resistivity contacts is shown in figure 3.2.

The pictured sample is bar-shaped, with current contacts at the ends of the bar and a set of voltage contacts at opposite sides of the bar. By comparing voltage measurements from both sets of contacts we can verify that the mea- sured behaviour is independent of details of the contact configuration or local crystal imperfections. Apart from bar-shaped samples, we measured several samples cut as regular octagonal prisms with rectangular sides (I will refer

and cut as a regular octagon in the ab plane. The octagons are mounted using the same technique as for bar-shaped samples, but have one contact attached to the middle of each of the eight faces.

All samples were mounted with permanently attached contacts to gold wires, which lead to large contact pads on a quartz plate. The rationale is that the contacts to the sample only have to be made once. After this, measurement wires on different experimental probes can be attached to the larger pads, which are less fragile than the contacts to the sample itself. This also guarantees that the same contact configuration and spacing are used if a single sample is measured on different probes. The sample mounting tech- nique is well-established in St Andrews, and has been described in previous theses [12, 92].

A sample is mounted on 50 µm gold wires, which suspend the crystal

about 0.3 mm over an amorphous quartz substrate. Contacts between the sample and the wires, and the larger contacts between the wires and the

quartz, are made with high temperature curing silver paste3. The paste

is applied using a ‘paintbrush’ consisting of a single 50 µm wire, and all

contacts are made before the paste is cured. Baking the contacts at 450 ◦C

for 5 minutes results in contact resistances of 1Ω at room temperature.

Differential thermal contraction strains upon cooling the sample in a cryostat

will be absorbed by the soft gold wires. The crystalab plane is approximately

parallel to the quartz surface. Silver paste contacts are applied on the sides of the crystal, ‘shorting out’ the c-axis.

In an effort to improve the sample mounting recipe we tried changing the curing scheme. The manufacturer’s data sheet suggests a 2.5 hour curing

time at temperatures ranging from 200 ◦C to 160 ◦C [93], but after several

attempts we found that the optimum curing seems to be the one described before. For some samples we replaced the amorphous quartz with sapphire, primarily for its much higher thermal conductivity at low temperatures [94].

We also mounted samples thermally anchored to the substrate with grease4_.

In practice, the improvements in thermalisation were minimal, which led us to conclude that the dominant heat flow is through the measurement wires.

3_{DuPont 6838, thinner: hexyl acetate}

Figure 3.2: Photograph of a typical single crystal of Sr3Ru2O7, cut into a

bar shape and mounted for resistivity measurements.