Study of the Fine Structure in the High-Field Galvanomagnetic Properties and the Fermi Surface of Copper

Abstract

Extensive high-field galvanomagnetic data for high-purity single crystals of copper are reported and analyzed in terms of current theory. Special attention is given to the study and identification of the higher order open orbits, commonly called "whiskers," and to an understanding of their presence and extent. Accurate measurements of the Hall constant for the field orientations (111) and (100) were made and values significantly different from those reported earlier were obtained. Our experimental results are in good agreement with theoretical predictions based on Roafs best phenomenological Fermi-surface model (CU VI).

Galvanomagnetic effects in anisotropic metals

“…The presence of open orbits therefore effectively introduces an anisotropy into the conductivity, so that a monocrystM of a cubic metal, for example, which has an isotropic conductivity in the field-free case, has an effectively anisotropic conductivity when open orbits are operative in a plane perpendicular to B. This anisotropy gives rise to a transverse even field analogous to the planar effect, and it has been utilized to determine the directions of open orbits in a metal as well as to demonstrate rather directly the concept of open orbits (Klauder andKunzler 1961, Klauder, l~eed, Brennert andKunzler 1966). The experimental geometry employed by these workers is shown in fig.…”

“…There is, however, the possibility of current channelling down these orbits if the current contacts do not entirely cover the sample's faces, and this has the repercussions in the longitudinal magnetorcsistance referred to at the end of § 4.3.5.] In the high-field limit, when all the conduction in the x'y' plane is effectively along the open orbit, the inclination of the orbit's axis to the x-direction is given by (Liick and Saeger In principle, this permits • to be determined from the even fields measured transversely and longitudinally with respect to the x' axis, but an alternative and perhaps more practical specification of the open orbit's direction with respect to the sample's faces has been given by Klauder and Kunzler (1961). This involves the measurement of the transverse even voltage appearing between P1 and Pe on the y axis (say Vv), together with that between similar contacts on the faces intersected by the z axis (say Vz).…”

“…Illustrating the experimental arrangement used by Klauder and Kunzler (1961) to study the transverse even field arising from the anisotropic conductivity produced by operative open orbits in the sample. E 0 is the component of the total electric field which arises along the open orbit's axis as they become operative.…”

“…18 (a), a transverse even voltage will appear between P1 and P2 whenever ¢ is such that an operative open orbit in the sample lies in the y'x' plane. (Klauder andKunzler 1961, andMarcus 1962, show rotation diagrams to illustrate this in Cu and Ga, respectively.) The transverse even field is given by :…”

Doppler-Shifted Cyclotron Resonances with Helicons in Copper

“…Electrons are the majority carriers, with 0.51 net electrons per atom. 11 Thus, helicons exist and their dispersion relation gives the above "charge density." 12 We have computed from Roaf's parameters 10 …”