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Figure 3.2: Schematic of the PPMS crysostat probe, taken from [36].

ture dependence ρ(T ) will provide insight into the scattering processes. We therefore require accu- rate control over both applied field and sample temperature, and the ability to reach temperatures of ∼ 1 K.

3.2

Physical Properties Measurement System (PPMS)

3.2.1 Cooling and field

The PPMS cryostat provides a robust and versatile platform for resistivity and heat capacity mea- surements down to 2 K with4_{He, in magnetic fields up to 9 T. It possess a 24 mm bore (setting the}

maximum radius of our pressure cells), with a circle of 12 metallic pins at the bottom, which con- nect to the experiment mounted on a puck. The experiment (whether a pressure cell or samples at ambient presure) must be carefully lowered from the top of the bore with a handheld loading rod to avoid damage to the pins (see Fig. 3.2).

The pins at the bottom of the cryostat are attached to wires that lead back up to to a 12-pin LEMO feedthough at the top. A cable connects this to the measurement electronics and control computer in the instrument rack. The pins are attached to a large block of copper, termed the cooling annulus.

4_{He gas taken from the reservoir is passed through a heat exchanger; electric heaters heat the gas to}

the required temperature, as registered by a field-calibrated thermometer on the annulus. This gas flows past the outside of the cooling annulus, setting its temperature. The sample space contains a low pressure (∼ 4 mbar) of4_{He exchange gas, which improves heat transfer between the annulus}

and the sample.

Experimental methods 3.2 Physical Properties Measurement System (PPMS)

from 0.01 − 15 K/minute can be obtained. The sample thermalises via a combination of metallic contact through the pins and cooling annulus, and conductive heat transfer through the exchange gas. When measurements are being undertaken on piston cylinder cells some care is required: the cell has (particularly at higher temperatures) an extremely large thermal mass. This means that the temperature of the cell and the samples will lag behind the temperature recorded by the cryostat, an error that manifests itself as a clear offset in the data between up and down temperature sweeps. A temperature sweep rate of 2 K/min is far too high and will lead to noticeable thermal lag: for careful temperature sweeps, rates of . 0.3 K/min should be used. Of course, a balance must be struck between minimising thermal lag and completing measurements within a reasonable timescale: a full 2 to 300 K temperature scan at the minimum rate of 0.01 K/min will take around 3 weeks and antagonise other users of the instrument. Typically, for detailed low-temperature measurements we would use a temperature sweep rate of 0.05 K/min, having first performed an up and down temperature sweep at this rate to check for the absence of thermal lag.

Outside the bore of the cryostat sits a superconducting magnet cooled by liquid helium from the reservoir, capable of applying a 9 T field. This magnet can be run in both persistent and driven mode. When driven, the current through the magnet is continuously ramped by a high-current power supply, increasing the field at a constant rate. Alternatively, the magnet can be set to a con- stant field and connected from the driving power supply by means of a superconducting persistent switch, which if allowed to cool will short the current supply leads and permit the continuous cir- culation of any current already present in the magnet. This means a field can be set, the persistent switch closed, and the current supply ramped down again; the magnetic field will stay constant for the duration of the experiment.

One small downside of the magnet is its rather coarse precision and rapid ramp rate. Field sweep rates below 1 mT/s cannot be achieved, and this can prove problematic if very detailed measure- ments are required, e.g. for a quantum oscillation study. For such a measurement, it can be neces- sary to step the field in discrete steps of e.g. 0.5 mT using the persistent switch, which is extremely time-consuming but at least gives a high point resolution.

The major advantage of the PPMS is its reliability: the software and hardware can usually be trusted to provide the desired field and temperature without much effort on the part of the user, and allow the programming of detailed extended measurements encompassing many precisely- controlled temperature and field sweeps. The downside of the system is that, as it allows many types of measurements, it is not entirely optimised for any. The default alternating current (AC) transport option gives both a data acquisition rate and a signal-to-noise ratio around ten times lower than we obtain using our own custom-built setups.

3.2.2 Sample mounting

For ambient-pressure resistivity measurements, samples are mounted on resistivity pucks manu- factured by Quantum Design. The samples are placed on a thin gold-covered copper plate, insu- lated from the plate by a thin layer of paper stuck in place with GE varnish. Traditionalists use cigarette paper, though a small square of half-thickness tissue paper works equally well; the key cri- teria are that the material reliably insulates the sample from electrical shorts to the metallic plate

Experimental methods 3.2 Physical Properties Measurement System (PPMS)

beneath it, and that it allows some heat conduction from the plate to aid in thermalisation of the sample.

The sample is stuck to the insulating paper with a small dab of Dow Corning vacuum grease, which serves to hold it in place and greatly simplifies subsequent soldering of wires from the sam- ple. Once the sample is in place, its four 25 μm Au measurement wires are soldered to pads on the edge of the puck.

This can be a tiresome process, because making four contacts to the sample can take several hours, and when the (very fragile) Au wires are bent to reach the soldering pads, they are prone to breaking at the contact point. This necessitates the removal of the sample and a repeat of the contacting process - made a little more challenging because the sample is now covered in vacuum grease - so great care should be taken to avoid breaking the contacts. We have two approaches. Firstly, for robust metallic samples (like bismuth) where the use of 6838 epoxy allows fairly strong contacts to be made, the wires can be freely bent by tweezers as long as they are supported. Typically the wire will be held in one pair of tweezers close to the contact, and bent around this point using another pair of tweezers or the pressure of a pin.

An alternative approach, more time-consuming but more robust, is necessary for fragile sam- ples, which are prone to breaking in half when any pressure is applied on the contacts. These sam- ples are contacted as normal, and have their dimensions measured, then a small paper stage is made for them. We find the instruction sheet that comes with Double Bubble epoxy (DBE) to be structurally ideal for this purpose. A thin mound of DBE is painted along one side of the stage, and the sample is turned upside down and dropped onto the stage so that the wires - but not the sample itself - are stuck in place by the epoxy. If necessary the wires can be pushed into the epoxy with a pin; care should be taken to ensure the sample itself does not become trapped in the epoxy, or anis- totropic stress may be applied as the epoxy contracts upon cooling. After waiting 20 minutes for the first layer of epoxy to set hard, a second layer of DBE is painted over the wires to ensure they are firmly trapped. Once this epoxy has dried, the wires can be bent around it without any stress being applied to the contacts; the sample can also be tranported by moving the stage around, so there is no need to touch the sample again. This simple technique has proved fairly reliable in contacting extremely fragile and delicate samples which would break upon being squeezed with tweezers.

For measurements in pressure cells, there are two alternatives to connect the cell to the puck. Firstly, the cell can be attached to a T-shaped adapter which fits onto a standard AC transport (ACT) or resistivity puck. Wires from the cell are soldered to the puck pads in the usual PPMS configura- tion. We have found this method rather unreliable: the (very large and heavy) cell exerts a signifi- cant force on the adapter, which can easily loosen or even break the small M1.6 screws holding the T-piece in place. In addition, the large heavy cell applies a significant moment to the puck pins, making it more likely that either the pins will bend, or the cell will simply fall over to one side. This was often observed to happen in our PPMS runs: looking down the PPMS the upper end of the cell was clearly off-centred and at a small angle. Typically this does not affect the measurements - in fact it may have slightly improved thermalisation, as now the top part of the cell is in contact with the cold cryostat wall as well as the bottom part - but it makes extraction of the cell a rather challenging task, so should ideally be avoided.