De Haas–van Alphen effect

In solid-state physics of the de Haas -van Alphen - effect describes certain changes in the magnetic properties of a metal in an applied static magnetic field. It is very useful in detailed studies of the electronic band structure.

The effect was first observed in 1930 by hiking Johannes de Haas and PM van Alphen in bismuth, its importance for band structure studies but was not recognized until 1952 by Lars Onsager. At low temperatures and very pure samples of a variation in magnetic susceptibility was observed as a function of applied magnetic field: as a function of inverse field strength, the magnetic susceptibility shows a superposition of periodic oscillations.

Explanation

The applied magnetic field exerts a Lorentz force on the conduction electrons, resulting in a change in the electronic density of states: In a semi-classical description, it can be explained by the fact that due to the Lorentz force, the kinetic energy of the motion component is quantized perpendicular to the field direction. This results in the split into so-called Landau levels. Crucial for most electronic properties of a metal is the density in the vicinity of the Fermi energy. It can be shown that the density of states is singular at the Fermi energy ( and therefore provides the dominant contribution ) when an extremal electron orbit (perpendicular to the field direction ) on the Fermi surface satisfies the quantization condition, which is enforced by the magnetic field. A " extremal orbit " here is a closed electron orbit with minimum or maximum enclosed area to understand. The quantization condition for an extremal electron orbit is fulfilled for various field strengths; Here, the difference between the inverse of two adjacent field strengths, where the quantization is satisfied, a constant. It depends mainly on the surface which is enclosed by the extremal electron orbit:

Thus, all physical quantities (in particular, the magnetic susceptibility ), which depend on the density of states at the Fermi energy, comprising magnetic field-dependent oscillations that are periodic as a function of 1 / H. These include oscillations of the electrical conductivity ( quantum Hall effect and Shubnikov - de Haas effect), magnetostriction ( change in sample dimension) and other sizes. The number of superimposed oscillations corresponds to the number of extremal oriented perpendicular to the field direction orbits on the Fermi surface.

If we consider an oscillating in 1 / B size ( for example, the magnetic moment of a sample at absolute zero ) for magnetic fields the same direction, but different thickness, one can determine the period of oscillation. Because it can be concluded on the area that is enclosed by the living on the Fermi surface extremal orbit. The extreme path ( and thus also the surface S) is perpendicular to the magnetic field. The Fermi surface can thus be reconstructed by sampling different directions.

Experiments

One possibility for the observation of the de Haas -van Alphen - effect is the precise measurement of changes in the magnetic moment of the sample with a torsion balance.

In another method, which is especially suitable for examinations in strong magnetic fields, the sample is located in a coil, and measuring the induced voltage in case of a rapid change in magnetic field. Using the measured induced voltage, as well as the time-resolved induced current can be used to determine the inductance of the coil.

You can now dissolve after, thus obtaining the magnetic susceptibility over the functional relationship of the inductance.