Einstein-de Haas Effect
The only experimental work ever published by Albert Einstein was carried out in 1915 in collaboration with Wander Johannes de Haas, who was the son-in-law of H. A. Lorentz. Einstein had long contemplated Ampère's conjecture in 1820 that magnetism is caused by circulation of electric charge. This Demonstration describes a technologically updated version of the original Einstein–de Haas experiment. A cylindrical soft-iron magnet is supported by a thin quartz fiber attached to a mirror. The magnet is suspended within a solenoid connected to a reversible DC power source. The current is large enough to create a magnetic field strong enough to saturate the cylinder's magnetization in either direction. If Ampère was right, this should create an angular displacement of the magnet, which can be detected by deflection of a laser beam directed at the rotating mirror.[more]
The saturation magnetization of iron at room temperature is 1707 gauss. (It is most convenient to use cgs units here.) Magnetization represents net magnetic dipole moment per unit volume, thus , where , the volume of the cylindrical magnet. The conjectured association between magnetism and charge circulation can be represented by , where is the angular momentum of the charge and the proportionality constant is called the magnetogyric ratio. As we now know, the circulating particles are electrons, with charge and mass , so that ( is the speed of light, which occurs in cgs electromagnetic formulas). We denote this quantity by . More generally, we write , where the -factor equals 1 for electron orbital motion (), but 2 for electron spin (). Einstein and de Haas originally obtained results consistent with , but more refined repetitions of the experiment eventually led to , consistent with our understanding that ferromagnetism in iron is caused by unpaired electron spins in the conduction band.
The quartz wire serves as a very sensitive torsion balance, with a torsional constant of the order of dyne-cm/rad. The deflection of the laser beam will be in the range of 1–2° (exaggerated in the graphic), which can be detected on a screen placed some distance from the mirror. A simulated experimental error is added, so results obtained in different runs will show variation.[less]
An iron cylinder with a saturation magnetization of gauss has a net magnetic dipole moment of directed along the axis of the solenoid. If this magnetic dipole is associated with charge circulation, then , where is the angular momentum of the magnet and is the magnetogyric ratio. The maximum kinetic energy of rotation equals , where is the moment of inertia of the magnet. This is converted into potential energy of the torsional balance at its maximum angular displacement, given by . From the preceding formulas, the -factor is determined by , where (expressed in degrees) is the maximum deflection of the reflected laser beam. Reversing the magnetization of the iron should create an angular displacement in the opposite direction as the angular momentum of the charge carriers is reversed.