Magnetic Cooling

a method of producing temperatures below 1°K by means of adiabatic demagnetization of paramag-nets. It was proposed by P. Debye and the American physicist W. Giauque (1926) and was first applied in 1933. Magnetic cooling is one of the two practically applicable methods that make possible the production of temperatures below 0.3°K (the other method is the dissolution of liquid ³He in liquid ⁴He).

Salts of rare earths (for example, gadolinium sulfate), as well as potassium chromate alum, ammonium ferric alum, chrome methyl ammonium alum, and a number of other paramagnetic substances, are used in magnetic cooling. The crystal lattice of these substances contains ions of iron, chromium, and gadolinium with incomplete electron shells and nonzero intrinsic magnetic moment (spin). In the crystal lattice the paramagnetic ions are separated by a large number of nonmagnetic atoms. Consequently, the magnetic interaction of ions is weak: even at low temperatures, when thermal motion is significantly reduced, the forces of interaction are not able to order the system of randomly oriented spins.

In the magnetic cooling method a sufficiently strong external magnetic field (of the order of several kilooersteds) is applied; as the field orders the spin directions, it magnetizes the paramagnet. If the external field is shut off (demagnetization of the paramagnet), the spins again assume random orientation under the influence of the thermal motion of the atoms (ions) in the crystal lattice. If the demagnetization occurs adiabatically (under conditions of thermal insulation) the temperature of the paramagnet decreases.

The magnetic cooling process is customarily represented in thermodynamic diagrams in coordinates of temperature T and entropy S (Figure 1). The production of low temperatures is associated with the attainment of states in which a substance exhibits low values of entropy. Both thermal vibrations of the atoms in the crystal lattice (“thermal disorder”) and disorientation of the spins (“magnetic disorder”) contribute to the entropy of the crystalline paramagnet, which characterizes the disorder of its structure. As T —> 0°, the entropy of the lattice S_lat, diminishes faster than the entropy of the spin system S_mag, so that at temperatures T < 1°K, s_iat becomes vanishingly small as compared with Smag. Under such conditions magnetic cooling becomes feasible.

Figure 1. Entropy diagram of a magnetic cooling process (S is entropy, T is temperature). The curve S₀ shows the change in entropy of the working substance versus temperature, without a magnetic field; (S_H) change in entropy of the substance in a field of intensity H, (S_lat) entropy of the crystal lattice (S_lat ~ T³), (T_fin) final temperature of the magnetic cooling cycle.

The cycle of magnetic cooling consists of two stages: isothermic magnetization (line AB ) and adiabatic demagnetization of the paramagnet (line BC ). Before magnetization the temperature of the paramagnet is decreased to T ~ 1°K by means of liquid helium and is then held constant throughout the first stage of magnetic cooling. Magnetization is accompanied by liberation of heat and a decrease in entropy to the value S_H. During the second stage of magnetic cooling, thermal motion destroys the ordering of spins and causes an increase in S_mag. However, during the process of adiabatic demagnetization the total entropy of the paramagnet remains unchanged. The increase in S_mag is compensated by a decrease in S_lat—that is, by cooling of the paramagnet.

The interaction of spins among themselves and with the crystal lattice (spin-lattice interaction) determines the temperature at which a sharp drop in the curve S_mag begins as T —> 0° and at which magnetic cooling becomes possible. The weaker the spin interaction, the lower the temperatures obtainable by magnetic cooling. Paramagnetic salts used in magnetic cooling make it possible to produce temperatures of the order of 10^-3 °K.

Considerably lower temperatures have been produced by using the paramagnetism of atomic nuclei rather than atoms (ions). The magnetic moments of nuclei are about a thousand times smaller than the spin magnetic moments of electrons, which determine the moments of paramagnetic ions. Therefore, the interaction of nuclear magnetic moments is much weaker than the interaction of ion moments. Even at T = 1°K, strong magnetic fields (~ 10₇ oersteds) are required to magnetize a system of nuclear magnetic moments to saturation. In practice, fields of 10₅ oersteds are used, but in this case lower temperatures are needed (~0.01°K). For an initial temperature of 0.01°K the use of adiabatic demagnetization of nuclear spin systems makes possible the production of temperatures from 10~5 to 10~6 °K. The entire sample is not cooled to this temperature. The temperature produced (called the spin temperature) is a measure of the intensity of thermal motion in the nuclear spin system immediately after demagnetization. However, after demagnetization the electrons and the crystal lattice remain at the original temperature ~0.01°K. The subsequent energy transfer between the systems of nuclear and electron spins (by means of spin-spin interaction) can result in the short-duration cooling of the entire substance down to T ~ 10^-4 °K. Low temperatures (~ 10 ~2 °K and lower) are measured using methods of magnetic thermometry.

In practice, magnetic cooling is conducted as follows (Figure 2,a). A block of a paramagnetic salt is suspended in a chamber on brackets made from a material with a low coefficient of thermal conductivity. The chamber is immersed in a cryostat containing liquid ⁴He. By evacuating the helium vapors the temperature in the cryostat is maintained at 1.0°-1.2°K (the use of liquid 3He makes possible a decrease in the original temperature to Ü0.3°K). Heat released in the salt during magnetization is conducted to the liquid helium by the gas in the chamber. Before the magnetic field is cut off, the gas is pumped out of the chamber through a valve; thus, the block of salt is thermally insulated from the liquid helium. After demagnetization the temperature of salt drops and may attain several thousandths of a degree. If any substance is pressed into the block of salt or connected to it by a bundle of thin copper wires, the substance can be cooled to virtually the same temperature.

Figure 2. Diagrams of apparatus for magnetic cooling: (a) one-stage apparatus (N and S are the poles of an electromagnet), (b) two-stage apparatus

The lowest temperatures are produced by a two-stage method of magnetic cooling (Figure 2,b). First, salt C is adiabatically demagnetized, and a previously magnetized salt D is cooled through the thermal switch (thermally conductive jumper). Subsequently, after the switch is opened, salt D is demagnetized and is cooled to a temperature substantially lower than that previously obtained for the salt C. In apparatus of the type described here, the thermal switch usually consists of a small wire made of a superconductor. The thermal conductivity of such a switch in its superconductive state at T ~ 0.1 °K is many times greater than the thermal conductivity in its normal state. Nuclear demagnetization is also conducted according to the diagram shown in Figure 2,b. However, in this case the magnetized salt is replaced, for example, by a copper sample, and the field used to magnetize the sample has an intensity of several dozen kilooersteds.

Magnetic cooling is widely used in the study of the low-temperature properties of liquid helium (such as superfluidity), quantum phenomena in solids (for example, superconductivity), and phenomena of nuclear physics.