The de Haas-van Alphen effect and the Fermi surfaces of rare earth metals

Abstract

The de Haas-van Alphen effect is described. Experimental results for Y, Pr and Gd are interpreted in terms of Fermi surface models which all relate to a basic rare earth band structure. The q-vector for spiral magnetic structures in Y(Gd) alloys is found to be consistent with the experimental Fermi surface for Y. 1. Introduction. - Almost all useful information on Fermi surfaces comes from experiments at liquid He temperatures on specimens with long conduction electron means free path (n. Assessing Thy residual resistivity ratio (3 = p,,3,/p,,,), many elements can be refined to 3 values of lo4 or more. For these there is a wide choice of Fermi surface experiments. Where (some transition metals, rare earths, inter- metallic compounds) it is difficult to achieve an & of even lo3 the only useful methods are the de Haas- van Alphen (dHvA) effect and to a lesser extent the high field magnetoresistance (MR). The dHvA effect can in principle determine all Fermi surface information. For a particular orbit it can measure the area, cyclotron mass (m,), relaxation time (7) and average g-factor and these can be con- verted to local values of k,, velocity, T and g by para- meterisation. MR requires a little larger 3t than dHvA but is of particular value for examining topological properties of Fermi surfaces. Only with the application of solid state electro- transport refining has a high enough % value been achieved for Fermi surface investigation of rare earth metals. Substantial dHvA results have now been reported for Y (I), Gd (2) and Pr (3). Also reported for Gd is the MR (4) and the pressure dependence of dHvA (5). One dHvA frequency has been reported for Lu (6) and several for Tb (7). 2. The de Haas-van Alphen (dHvA) effect. - The dHvA effect arises from the quantisation of the energy states of conduction electrons in a magnetic field. The motion of an electron is determined by the response of its k vector to the Lorentz force :