Abstract
The thermomagnetic properties of a free-electron gas coupled to an external helical magnetic field is considered. The one-particle energy spectrum problem is reduced to a one-dimensional quantum pendulum. For sufficiently strong magnetic fields ( approximately 104 G) and long pitched magnetic helices ( approximately 10 cm), the resulting energy eigenvalues and their corresponding degeneracies are calculated. The free energy of an N electron system in the low-temperature regime is computed and the diamagnetic behaviour is obtained. The resulting expressions for the non-oscillatory magnetisation and susceptibility behave very differently from the usual Landau result. In fact, the dominant terms are shown to depend like B-3 and B-4 as functions of the external field, respectively. The usual Landau field-independent susceptibility is found to yield only a small correction. Also an oscillating component of the magnetisation is found which is not a simple periodic function of B-1. Finally, the effect of the spin is shown to give the usual constant-field paramagnetic results.
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