Experimental Studies of Magnetic Field Induced Phase Transitions

Abstract

In the following I shall discuss properties of electrical conducting materials in which the electronic behaviour is well described by electronic energy bands. In a magnetic field (H), the Lorentz force (F) which is perpendicular to the electronic velocity (v) bends the electron trajectory ($\overrightarrow F \:\infty \:\overrightarrow v \: \times \overrightarrow F$). If the relaxation time τ is long enough then the electronic motion, perpendicularly to the magnetic field, becomes periodic with the pulsation ω. This corresponds to the usual relation ω_cτ > 1. The corresponding energies are quantized in ∀ω unit. The energy quantum has to be compared with the relaxation processes connected to the temperature, the purity and the crystallographic quality of the sample. At low temperature, in high quality single crystals of pure material, the effect of the energy quantization can be easily detected by magneto-transport or magnetostatic measurements. But usually the quantization of the energy of conduction electrons only gives rise to oscillations of the free energy of the system and not a discontinuity of any of its derivatives: there are no phase transitions associated with this quantization. The Shubnikov-de Haas effect in magneto-transport and de Haas-van Alphen effect in magneto-static measurements are then signatures of this condensation of the electronic states.