On the Lowest Temperatures*

W. de Haas, Leiden

As is known, the lowest temperatures have hitherto been achieved with the aid of liquid helium boiling at low pressure. This method requires the fulfillment of two conditions: it is necessary to use pumps with a high pumping speed and, as far as possible, to eliminate heat exchange by radiation completely. In this way Kamerlingh Onnes, toward the end of his life, attained a temperature of 0.82 abs. Keesom later reached a temperature of 0.71 abs. His diffusion pumps had approximately 15 times greater power than the pumps of Kamerlingh Onnes. However, it is difficult to advance much farther along this path.

Debye, already in 1926, observed (and also Giauque in 1927) that, in the adiabatic demagnetization of magnetized bodies, the temperature should decrease. Langevin had earlier expressed the same idea as applied to oxygen. Debye’s observations concern gadolinium sulfate. His considerations may be formulated as follows: when some body is magnetized, the elementary magnets, which we must imagine as existing in this body, are arranged in an ordered manner. In such a case the part of the entropy associated with this ordering decreases, and since we imagine the whole process as isentropic, the part of the entropy associated with statistical motions must increase. Conversely, when as a result of demagnetization the disorder in the arrangement of the elementary magnets increases, the part of the entropy associated with magnetization increases, while the part associated with statistical motions decreases and the body is cooled.

In order to obtain distinct results, it is necessary to take into account a number of circumstances: 1) the elementary magnets must not already be ordered (the body must not be ferromagnetic); 2) the elementary magnets must possess as large a magnetic moment as possible, since this is not in contradiction with what was said in point 1; at low temperatures the effect will be strongest, since under these conditions the part of the entropy pertaining to the ordered state must be comparable with the other part, while at the same time the degree of order increases greatly. The experimental conditions follow—

* Nature, 132, No. 3332, p. 372 (9 Sept.), 1933; Naturwiss, 21, 732 (No. 41, 13 Oktober), 1933.

...following: one may hope to obtain very low temperatures if radiation and convection are eliminated as far as possible. In the experiments described, these conditions were fulfilled.

The substance being cooled also serves as the thermometer. The arrangement of the experiment is shown in a very schematic form in Fig. 1. Rod \(A\) is attached to a balance. At the lower end of this rod a small vacuum vessel is suspended. In this vessel there is, as shown in the figure, a glass rod \(B\), to the lower end of which is attached a tube filled with \(\mathrm{CeF}_3\) (\(\mathrm{CeF}_3\) was chosen on the recommendation of G. A. Kramers; see Leipz. Vorträge, 1933). The whole apparatus is placed between the poles of a large Leiden magnet—and is positioned in such a way that the \(\mathrm{CeF}_3\) is at the place where \(H \dfrac{dH}{dx}\) has its greatest value (\(x\) is the vertical coordinate). The entire lower end of the rod with the small vacuum vessel is completely surrounded by liquid helium boiling at \(1.26^\circ\ \mathrm{K}\). The thermal insulation of \(\mathrm{CeF}_3\) is so good that 4–5 hours must pass before the very small amount of salt, with its exceedingly negligible heat capacity, cools to \(1.26^\circ\ \mathrm{K}\) (the heat capacity decreases in proportion to \(T^3\)). But how is it known that the indicated temperature is ultimately reached? It turns out that \(\mathrm{CeF}_3\) indicates its own temperature. A paramagnetic body is drawn into a field (31 K∅) with a force \(K = M \cdot \dfrac{dH}{dx}\), where \(M\) is the total moment acting on the body. Since \(M = \varphi(H,T)\) and since \(H\) is constant, by measuring \(K\) one can easily establish the moment when \(T\) becomes constant. As soon as this occurs, demagnetization is performed; in the first experiments this demagnetization was carried out down to 2.4 K∅, and in subsequent ones down to 1000 and 500. In this weak field we measure the force acting on the balance as a function of time and thus obtain the curve shown in Fig. 2.

Fig. 1. Schematic arrangement of the experiment for obtaining very low temperatures. The tube at the lower end \(B\) contains \(\mathrm{CeF}_3\). The magnet poles are indicated on both sides of the vessel.

Point \(A\) on the curve corresponds to the force at the very lowest temperature, whereas the asymptote corresponds to the force at \(1.26^\circ\ \mathrm{K}\), which is established after the lapse of a long time. The steep drop of the curve at the beginning is explained by the fact that traces of helium (\(10^{-7}\ \mathrm{mm}\)) were deliberately left in the vacuum vessel for thermal contact. Gaseous helium condenses and gives up its heat of condensation. If an even smaller amount of helium is left, the shape of the curve changes and the warming proceeds very slowly with time. The cold is, as it were, “trapped.” To a certain extent an absolute vacuum arises, and heat is no longer supplied.

The magnitudes of the force are directly proportional to the moments, and it remains only to determine what temperatures correspond to these moments. The relation between temperature and moment was found between 4.2° K and 1.3° K. This relation was extrapolated linearly, although the curve shows a less rapid increase of the moment than would correspond to a linear extrapolation. We can, therefore, indicate only an upper limit of the temperature.

The first experiments, in March—April 1933, were carried out with cerium fluoride and gave, for the upper limit of the temperature, 0.27° K. Later experiments with dysprosium ethyl sulfate gave an upper limit of 0.14° K. Finally, experiments in July 1933 with cerium ethyl sulfate gave, as the upper limit, 0.085° K. It is quite possible that, with the experimental arrangement chosen by us, considerably lower temperatures can be attained. The success of further experiments is determined by the choice of a suitable substance. I am convinced that the experimental arrangement will lead to the theoretically possible limiting value.

Fig. 2. Example of measuring temperature by determining the force on a specimen in a magnetic field: heating of the specimen after demagnetization A to 2.16° K.

The concept of temperature is established with the aid of an ideal gas. The determination of temperature is carried out with the aid of a helium thermometer, taking into account the necessary corrections. However, at the low temperatures reached by us, as far as I could ascertain, any possibility of determining temperature by a gas thermometer is excluded. It is necessary to correlate with the absolute temperature scale some other process and, in particular, the magnetic scale may be used. Just as this is done in gas thermometry, certain substances must be found which, within a sufficiently broad interval of temperatures, behave in the same way. The development of the corresponding theory in this case will make possible the creation of magnetic thermometry possessing the same reliability as gas thermometry.

It should be noted, however, that a reservation must be made for the case when the substance used, at very low temperatures, might acquire

ferromagnetic properties, or reveal some new and peculiar kind of ferromagnetism. In this case little can be said about the temperature.

A further major difficulty follows from this: if, by means of the process described, one needs to cool another body, then questions of thermal contact create great difficulties. Radiation has an immeasurably small value, and the elasticity of helium is likewise so small that thermal contact by means of gaseous helium can hardly be taken into account.

The experiments described above were carried out together with the conservator of the Leiden cryogenic laboratory, Dr. E. Wiersma, to whom I am very much indebted for his assistance and numerous suggestions. Likewise, I am very much indebted to Prof. H. A. Kramers for valuable theoretical considerations.