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Helicon propagation in aluminium spheres Feser, Siegfried


Theoretical and experimental studies have been made of the propagation characteristics of helicon waves in metallic spheres; the helicon wave is a branch of the magnetoplasma wave spectrum in the presence of a uniform, static magnetic field. Our theoretical considerations have shown that for an infinitely conducting sphere the helicon wave inside the sphere can be described to good approximation by a single cylindrical wave. This model leads to a simple, approximate, analytic understanding of the resonant mode structure and of the helicon field distribution inside the sample. The resonant modes can be described as a doubly infinite series, labelled by (m,n), where m indicates the number (odd) of half wavelengths along the magnetic field direction nearly equalling the sample diameter and n indicates the same condition perpendicular to the magnetic field. An exact numerical calculation for a sphere of finite scalar resistivity has been carried out by representing the helicon wave inside the sphere by a superposition of cylindrical waves. In this way one is able to calculate the absorption peak heights and widths as well as the resonant frequencies for the first few modes. These results are found to be in good agreement with those calculated independently by Ford and Werner using vector spherical harmonics throughout. Whereas the formalism of Ford and Werner is preferred for computational accuracy, their approach is physically less transparent. Experimentally, we have substantiated the results of the calculations by using single-crystal spheres of aluminium with a residual resistance ratio of about 4000. The resonant modes were studied for two distinct geometries of the excitation and detection coils: the "parallel" geometry had the axes of the coils collinear but at right angles to the static magnetic field, whereas the "perpendicular" geometry had the excitation coil, the detection coil and the magnetic field all mutually perpendicular. The anisotropy of the fundamental (1,1) absorption peak amplitude is about 20% and that of the resonant frequency is about 1% for an applied magnetic field of 35 k0e. The helicon data are interpreted in terms of the anisotropics of the transverse magnetoresistivity (20%) and of the Hall coefficient (1%). For the first time in a helicon experiment an adequate sampling of crystallographic orientations has been made using the same sample throughout. The principal feature of the (1,1) peak height anisotropy is the presence of a narrow trough - typically 1° wide - whenever the static magnetic field lies in a {100} plane. This feature, which corresponds to an equally sharp ridge in the anisotropy of the transverse magnetoresistivity, has escaped detection in all previous studies of the magnetoresistivity (by helicons and otherwise), and it is a consequence of the magnetic breakthrough which is required by the Ashcroft model of the Fermi surface of aluminium. The transverse magnetoresistivity oscillates (periodically in 1/B) whenever the magnetic field is parallel to a direction and this feature is likewise consistent with the Ashcroft model. Other quantum oscillations have been observed superimposed on the helicon resonance and their periodicities are found to agree closely with those in the de Haas-van Alphen effect.

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