Hysteresis in the de Haas–van Alphen Effect

Abstract

A hysteresis loop is observed for the first time in the de Haas-van Alphen (dHvA) effect of beryllium at low temperatures and quantizing magnetic field applied parallel to the hexagonal axis of the single crystal. The irreversible behavior of the magnetization occurs at the paramagnetic part of the dHvA period in conditions of Condon domain formation arising by strong enough dHvA amplitude. The resulting extremely nonlinear response to a very small modulation field offers the possibility to find in a simple way the Condon domain phase diagram. From a harmonic analysis, the shape and size of the hysteresis loop is constructed.

Giant parametric amplification of the nonlinear response in a single crystal of beryllium in a quantizing magnetic field

“…It is consistent with the previous experiments on observation of the Condon instability at a value of the magnetic field up to~3T. However, it gives overestimated values for higher field and inconsistent with our present experiments and recent publi- cation on the observation of Condon domains in beryllium [10]. Our analysis of experimental data is based on the recent theory of diamagnetic phase transitions [22], which allows one to reconstruct the phase diagrams consistent with present experimental results.…”

“…A complete theory of nonlinear helicon resonance does not exist up to now. The recent experimental study of the dHvA oscillations in single crystal beryllium at low temperatures showed that strong nonlinear response appears even at very low amplitude of excitation in an antinode area of dHvA oscillations [10]. All the above mentioned experiments are related to nonlinear effects, such as self-influence [9], harmonic generation, and/or rectification [8,10].…”

Diamagnetic length scales of the Condon domain phase in Lifschitz–Kosevich–Shoenberg approximation

“…The formation of rather complicated diamagnetic structure in silver was demonstrated by use of a set micro Hall probes [5]. Further development of the experimental technique including the standard ac method with different modulation levels, frequencies and magnetic field ramp rates allowed us to reconstruct the magnetization reversal in beryllium [8]. The detection of giant nonlinear response at the crossing critical point, a →1, where a = µ 0 max{∂M/∂B} is a differential magnetic susceptibility, offered a way to construct the diamagnetic phase diagrams [5], [13]- [15].…”

“…The symmetric pitchfork bifurcation gives rise to the secondorder phase transition on temperature at the center of the dHvA period, while the deviation from the center results in a phase transition of the first order both in temperature and magnetic field. The diamagnetic phase transition has received recently much attention due to a number of unusual phenomena for the physics of diamagnetism, e. g. formation of complex branch structures [3], [5], strong dependence of magnetic phase diagrams on Fermi-surface topology [6], [7], presence of diamagnetic hysteresis in magnetization curves [8], existence of persistent currents [9] which results in a discontinuity of magnetic induction along the interface boundaries of regular domain patterns [2], [5].…”

A Measurement of the neutron electric form factor at very large momentum transfer using polaried electrions scattering from a polarized helium-3 target

“…At Jefferson Lab, the 3 He polarized target has been used successfully in six experiments prior to E02-013 [80,81,82,83,84].…”