Platinum Metals Rev., 1996, 40, (3), 112
Electronic and Nuclear Magnetism in Platinum-Iron at Ultralow Temperatures
Low Temperature World Record Established
In February 1996, physicists at the University of Bayreuth claimed a world record for producing the lowest temperature yet achieved when they announced the results of their work with platinum. They cooled 31.4 grams of platinum to 2 millionths of a degree Celsius above absolute zero temperature, -273.15°C. In this paper they describe the theory and the practical work behind this accomplishment. Research in low temperature physics involves the construction of detailed and precise knowledge of the atomic and nuclear structures and their interactions in atoms. Some effects due to atomic and nuclear structure, particularly magnetic effects, are only seen at very low temperatures; however their effects have consequences at higher temperatures, although these are not usually observed. Thus, this and other low temperature work is contributing to a fundamental understanding of the magnetic behaviour of materials.
The study of magnetism is one of the most interesting fields in solid state physics. Electronic magnetism shows a wide spectrum of different ordering phenomena at temperatures from about 103 K, where the ferromagnetic phase transition in iron occurs, to about 10-3 K, where Ce3+ ions in the paramagnetic salt CMN order magnetically. (CMN is cerium magnesium nitrate. 2Ce3+(NO3)43Mg(NO3)224H2O, which previously found application for electronic demagnetisation refrigeration before 3He-4He dilution refrigerators were used (1). Nowadays some research groups use it for thermometry at mK temperatures, but we used a PdFe thermometer in this temperature range).
Interacting magnetic moments of localised electronic shells or itinerant electrons are responsible for phenomena such as ferro-, ferri-, antiferro- and meta-magnetism or spin glass freezing. However, many elements and compounds do not contain such electronic magnetic moments, but very often their nuclei carry a magnetic moment due to the nuclear spin. Since nuclear magnetic moments are three orders of magnitude smaller than their electronic coun-terparts, and as the interaction energy is proportional to the square of the magnetic moment, ordering phenomena in the nuclear spin system are expected to occur only in the microkelvin temperature range or at even lower temperatures.
Apart from solid 3He with its strong quantum-mechanical direct exchange force, and the Van Vleck paramagnets with hyperfine enhanced magnetic moments, one has to distinguish between two groups of nuclear spin systems:
those in insulators and metals with a weak coupling between the nuclei and the conduction electrons, and
those in metals with a strong coupling between the nuclei and the conduction electrons.
The Korringa constant, k, is an important parameter to characterise the strength of this interaction. The Korringa constant is given by the conduction electron temperature, Telectron, multiplied by the spin lattice relaxation time, τ1.
For the first group of materials, the Korringa constant is larger than 1 Ks. As the spin lattice relaxation time τ1 becomes very long at temperatures below 1 mK (τ1 > 1000 s), it is possible to cool only the nuclear spin system to nanokelvin or even picokelvin temperatures for a time long enough to perform nuclear magnetic investigations, while the conduction electrons stay at a much higher temperature (Telectron > 100 μK). For systems such as these, nuclear magnetic ordering phenomena have been observed in silver (k = 12 Ks, Tc = 0.6 nK) and copper (k = 1.3 Ks, Tc = 60 nK) (2).
However, it is much more difficult to observe nuclear magnetic ordering phenomena in the second group, since in this case, the whole system has to be cooled because of the strong coupling between the electrons and the nuclei. On the other hand the indirect exchange interaction between nuclei in these systems is stronger than the dipole-dipole interaction, and therefore ordering phenomena are expected to occur at temperatures of up to tens of microkelvin.
Work with Platinum as a Strong Coupling System
Recently, we have been able to observe a nuclear ferromagnetic transition of this type with the113,115In nuclei in AuIn2 (k = 0.11 Ks) at a temperature of 35 μK (3). Another very interesting material in this group is platinum, which has a very small Korringa constant, of size only k ≥ 0.03 Ks. The nuclear magnetic moment of 195Pt is a factor of 10 smaller than that of the indium nuclei and only 33.8 per cent of the platinum nuclei carry the rather small magnetic moment of 0.597 μn (nuclear magneton μn = 5.05 × 10-27 Am2). Therefore, it is necessary to reach temperatures below 1 μK to observe nuclear magnetic ordering in platinum (4).
The additional interest in platinum comes from the fact that electronic magnetic 3d impurities, such as iron, form so-called giant moments in this strongly enhanced electronic Pauli para-magnet. (Platinum and also palladium are both strongly exchange enhanced Pauli paramagnets.) The giant moments show spin glass freezing at temperatures of a few mK at concentrations of ppm (5). This system of randomly distributed electronic magnetic moments may have a strong influence on the nuclear magnetic properties.
Searching for Nuclear Magnetic Ordering in Platinum
In order to search for a possible nuclear magnetic ordering of 195Pt and to study the above mentioned interaction between nuclear and electronic magnetism, we have investigated platinum samples containing magnetic impurities at concentrations of 11 and 41 ppm. The impurities were mainly iron, carrying an electronic magnetic “giant” moment of eight times the Bohr magneton μB (μB = 9.274 × 10-24 Am2). The properties that we measured were:
heat capacity in magnetic fields, B; (0 ± 0.05) mT ≤ B ≤ 248 mT
AC susceptibility at B = (0 ± 0.05) mT and
nuclear magnetic resonance at fields 2.5 mT ≤ B ≤ 22.8 mT.
Measurements were taken at temperatures Tnuclear ≥ 0.3 μK, and Telectron ≥ 2 μK, the latter being the lowest temperature to which electrons and phonons of a material have ever been refrigerated.
Lowering the Platinum Temperature
The ultralow temperatures that are necessary for these experiments were obtained by using the adiabatic nuclear demagnetisation technique. First, 17 kg copper were precooled in the Bayreuth nuclear demagnetisation refrigerator (6) (6.5 kg in an external field of 8 T) by a commercial 3He-4He dilution refrigerator to a temperature of 11 mK.
Then, after a thermal decoupling of the copper nuclear refrigeration stage from the mixing chamber of the dilution refrigerator, the external magnetic field was slowly reduced. At the end of this process the copper stage reached temperatures of about 50 μK. The platinum sample (n = 161 mmole of weight 31.4 grams) was exposed to a magnetic field of 0.37 T and thermally connected to the copper stage via a superconducting aluminium heat switch. The platinum was then precooled, by the copper stage, to a temperature of approximately 100 μK.
Subsequently, the platinum stage was thermally decoupled from the copper stage and the field was reduced. Eventually, in external fields of B ≤ 0.05 mT, the temperature of the nuclear spin system of platinum reached 0.3 μ. In these fields (B ≤ 0.05 mT) the temperature of the nuclei, Tnuclear , was lower than the temperature of the conduction electrons Telectron .
If the adiabatic demagnetisation was stopped at somewhat higher fields, for example 2.5 mT, nuclear temperatures of (0.8 ± 0.2) μK could be measured directly after demagnetisation. Taking the measured heat leak of (12 ± 2) pW into the platinum sample into account and the measured Korringa constant k = (7 ± 3) mKs for platinum in these fields, the temperature of the conduction electrons has to be below 2 μK.
During the next three hours after finishing the demagnetisation the conduction electrons stayed below 3 μK. The small value of 7 mKs for the Korringa constant, in contrast to its literature value of 30 mKs, is caused by magnetic impurities.
Measurement of the Platinum Temperature
The temperature of the platinum was determined from the magnetisation of its nuclear spin system, using pulsed nuclear magnetic resonance (NMR) in fields B ≥ 2.5 mT and the AC susceptibility technique in fields B = (0 ± 0.05) mT. At temperatures of ≥ 20 μK the NMR signal was calibrated against an independent platinum-wire-NMR thermometer, which is itself calibrated against the paramagnetic susceptibility of a PdFex sample at temperatures T ≥ 10 mK (1).
For the temperature calibration we assume that the magnetisation, detected by the NMR signal and the measurement of nuclear AC sus-ceptibility, follows a Curie law (X ~ 1/Tnuclear ) at low polarisation. If it follows a Curie-Weiss law (X ~1/(Tnuclear -Θn )), we would have to correct our temperature scale by Θ (see below).
The measured heat capacity data of the two PtFex samples in different magnetic fields is shown in Figure 1. The solid lines show the nuclear paramagnetic behaviour. In a magnetic field of 248 mT, there is a good agreement at T ≤ 1 mK. However, at higher temperatures the measured heat capacities are larger than expected and scale with the impurity concentration. At lower fields, such as 22.8 mT, this effect is much more pronounced, and at 2.5 mT or in zero field we observe an enhanced heat capacity over almost the whole temperature range. This effect can be described by a spatially varying internal field caused by the electronic magnetic impurities, assuming that this field behaves in a similar way to the electronic polarisation cloud in the conduction electron system - which forms the giant electronic moment. The dashed lines in Figure 1 are calculated using only two fitting parameters. There is a good agreement with the measured data. Therefore, we are able to describe the internal field in platinum as being due to electronic magnetic impurities.
Does Platinum Have Nuclear Magnetic Ordering?
In order to search for a nuclear magnetic ordering transition in platinum, we have measured the nuclear and electronic AC susceptibilities of the two platinum samples in an external field B ≤ 0.05 mT. The results are shown in Figure 2. The two maxima at millikelvin temperatures are caused by the “spin glass freezing” of the magnetic 3d impurities in platinum at freezing temperature, Tf . At temperatures T <: Tf the AC susceptibility shows Curie behaviour with Curie constants C11ppm = 122 μK and C41ppm = 448 μK, determined at 1.6 ≤ T ≤ 40 K in a commercial SQUID magnetometer.
We used this known behaviour (5) to scale our measured data in units of differential volume susceptibility. At T < Tf the susceptibility decreases linearly with temperature and increases again at T < 0.1 mK. The latter increase is caused by the nuclear paramagnetic behaviour of the 195Pt nuclei with a Curie constant of Cpt = 0.0185 μK. No maximum in the susceptibility was found and therefore no evidence for nuclear ordering in our samples could be detected down to the minimum nuclear temperature reached of 0.3 μK.
The temperatures achieved in our platinum samples, for the conduction electrons and phonons, which are below 2 μK, are the lowest temperatures ever reached in equilibrium. No evidence of nuclear magnetic ordering in platinum could be detected. This shows that the temperatures achieved were still measured in the nuclear paramagnetic state where the Curie (or Curie-Weiss) law is valid, and therefore our determination of temperature, assessed via this law is correct.
This work should aid in extending understanding of the interplay between electronic and nuclear magnetism at very low temperatures.
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