Magnetic thermometer

(solid-state physics) A sample of a paramagnetic salt whose magnetic susceptibility is measured and whose temperature is then calculated from the inverse relationship between the two quantities; useful at temperatures below about 1 K.

A thermometer whose operation is based on Curie's law, which states that the magnetic susceptibility of noninteracting (that is, paramagnetic) dipole moments is inversely proportional to absolute temperature. Magnetic thermometers are typically used at temperatures below 1 K (−458°F). The magnetic moments in the thermometric material may be of either electronic or nuclear origin. Generally the magnetic thermometer must be calibrated at one (or more) reference temperatures. See also Electron; Nuclear moments.

At temperatures from a few millikelvins upward, the thermometric material is preferably an electronic paramagnet, typically a nonconducting hydrous rare-earth salt. For higher temperatures, an ion is selected with a large magnetic moment in a crystalline environment with a high density of magnetic ions. In contrast, for low temperature use the magnetic exchange interactions between the magnetic ions should be small, which is accomplished by selecting an ion with a well-localized moment and by maintaining a large separation between the magnetic ions by means of diamagnetic atoms. This is the case in cerium magnesium nitrate (CMN) [2Ce(NO₃)₃ · 3Mg(NO₃)₃· 24H₂O]. Here, the Ce³⁺ ion is responsible for the magnetic moment, which is well localized within the incompletely filled 4f shell relatively deep below the outer valence electrons. To reduce the magnetic interactions between the Ce³⁺ ions further, Ce³⁺ may be partly substituted with diamagnetic La³⁺ ions. Lanthanum-diluted CMN has been used for thermometry to below 1 mK. See also Exchange interaction.

A mutual-inductance bridge, originally known as the Hartshorn bridge, has been the most widely employed measuring circuit for precision thermometry. The bridge is driven by a low-frequency alternating-current source. The inductance at low temperatures consists of two coils, which are as identical as possible. The voltages induced across them by the drive current are compared by means of a high-input-impedance ratio transformer. The output level of this voltage divider is adjusted to equal that of the midpoint between the two coils, using asnull indicator a narrow-band preamplifier and a phase-sensitive (lock-in) detector. Thus,without a paramagnetic specimen, the bridge is balanced with the decade divider adjusted atits midpoint, while with the specimen inside one of the coils the change in the divider readingat bridge balance is proportional to the sample magnetization. For high-resolution thermometryit has become standard practice to replace the room-temperature zero detector with a SQUIDmagnetometer circuit. This also allows the mass of the sample to be reduced from several gramsto the 1-mg level. See also Inductance measurement; Squid.

Nuclear magnetic moments are smaller by a factor of 10³ and are used forthermometry only in the ultralow-temperature region. For this the Curie-law behavior isgenerally sufficient down to the lowest temperatures. The nuclear paramagnetic thermometerloses adequate sensitivity for calibration purposes above 50–100 millikelvins, unless itis operated in a high polarizing field (H greater than 0.1 tesla). It can be utilizedas a self-calibrating primary thermometer if the spin-lattice relaxation time is measured inparallel with the nuclear Curie susceptibility. Pulsed NMR measurement on the ¹⁹⁵Ptisotope in natural platinum metal provides presently the most widely used thermometry attemperatures below 1 mK. In the Curie-susceptibility measuring mode, it has been extendeddown to 10 μK. See also Low-temperature thermometry; Magnetic relaxation; Nuclear magnetic resonance (NMR).