We probe the Meissner effect in our superconducting measurements with DC SQUID magnetome- try, the most precise probe of magnetisation in existence. This allows the measurement of sample magnetic moments as small as Z = 10−12A m2.
Obtaining a measured moment Z from such a magnetometer is a two-step process which relies on physically moving the sample through a superconducting coil set connected to a SQUID sensor; for this reason this technique is often termed extraction magnetometry. At each physical position z of the sample in the coil, the voltage across the SQUID sensor is measured to obtain a voltage curve V (z). This curve is then fit to that expected for an ideal magnetic dipole, to obtain a quantitative value for Z.
The analysis procedure to obtain Z from V (z) is described in some detail later, so here we focus on the first step. The critical component of the sensor is a superconducting coil through which the sample is passed, coupled via a flux transformer to a SQUID. The SQUID itself consists of two paral- lel Josephson junctions (physically, a superconducting ring whose two halves are separated by very narrow strips of non-superconducting material). When there is no external magnetic field, current flows equally across each junction; when an external field is applied (in this case, by the flux trans- former, which essentially applies the field generated by the sample’s magnetisation to the SQUID sensor), the SQUID is constrained by the Aharonov-Bohm effect to allow only an integer multiple of the flux quantum Φ0 = h/2ethrough the ring. It does this by modifying the flow of supercurrent
around the ring, which produces its own magnetic field, thereby changing the flux through the ring so it remains an integer multiple of Φ0. If this supercurrent is larger than the Josephson junctions’
critical current, a voltage appears across the SQUID [34, 37].
The result is a voltage across the junction that depends on the applied magnetic flux: the SQUID acts as an (extremely sensitive) flux-to-voltage converter. An observation of the voltage as a function of sample position can then be compared to that expected for an ideal dipole, to give an absolute value of the sample’s dipole moment.
3.4.3 Cooling and field
We use a Cryogenic S700 commercially-available cryostat implementing the DC SQUID extraction magnetometry technique, as shown in Fig. 3.5. The sample is mounted on the end of a long rod, and lowered into the bore of the cryostat, where it sits in an atmosphere of ∼ 10 mbar of flowing
4He gas.
Temperature control is provided by first passing the4He through a heat exchanger. The bore of
Experimental methods 3.4 Magnetisation measurements
Figure 3.5: Diagram of the Cryogenic S700 DC SQUID magnetometer, from [34].
bath through a needle value and heat exchanger. A thermometer and heater on the heat exchanger, operating a PID loop controlled by a Lakeshore 340 resistance bridge, ensures that the low-pressure helium gas that flows into the cryostat sample space is at the desired temperature. The actual tem- perature of the sample space is measured by a secondary thermometer.
This design ensures the sample is well-thermalised with its surroundings, as it sits in a low pres- sure of exchange gas. It also provides highly-responsive temperature control (at least at low temper- atures where the heat capacity of the sample space is small); the temperature can be changed from 2 to 30 K in less than 10 seconds. The sample can also be inserted while the sample space is at low temperatures; fully inserting an ambient-pressure sample and allowing it to cool to 10 K takes only ∼ 10 minutes. The rod on which the sample is mounted should be lowered in smoothly in several steps - if it is inserted all the way in at once, the heat of the sample will rapidly warm the helium in the sample space, and we have found this results in a much longer total insertion time than if the sample is inserted in a controlled fashion.
There are two downsides to the design of the temperature control system. Firstly, temperatures below 2.15 K cannot be reliably stabilised: typically, the sample space begins to fill with liquid4He
rather than gas at the desired temperature, which results in a drop in the cavity pressure, followed by a rapid fall in the sample space temperature to below 1.7 K (as now significant quantities of liquid4He are being pumped on). To remove this liquid, the sample space must be warmed to
5 K for several minutes. In principle, obtaining lower temperatures would be possible by careful manipulation of the needle valve to ensure a sufficient flow of helium gas, coupled with use of a heater in the sample space itself to prevent the collection of any liquid, but in practice this is very seldom worth the time or effort. Secondly, temperature control is done using a thermometer on the heat exchanger, which is often around 0.2 K lower than the actual temperature of the sample space. This is a minor problem for temperature sweeps, but it means taking points at exactly the required temperature can be challenging.
Experimental methods 3.4 Magnetisation measurements
the sample space. The magnet is cooled with the liquid4He bath, and (as with the PPMS) possesses
a superconducting persistent switch. This is particularly important for the SQUID, as to ensure only the sample’s magnetisation is being measured (rather than the applied magnetic field), the field must be extremely stable when the extraction magnetometry procedure is conducted. This means field sweeps with the SQUID are rather slow, as the field must be stabilised and the persistent switch closed at every point (unlike in a PPMS resistivity field sweep, where the field can be ramped continuously).