Modified Spin Splitting of Landau Levels Observed in a Kondo System

Abstract

The de Haas-van Alphen effect has been studied in the Kondo system Cu:Cr in magnetic fields up to 55 kG at 1.0 K. In alloys containing ~30 ppm Cr "beat" minima and shifts of the spin-splitting zeros are observed for several orbits. These observations are explained by supposing the normal spin splitting of the Landau levels to be modified by an antiferromagnetic exchange term, so that the effective g factor becomes g-^€ ex /iJ. B H, Some time ago we reported 1 the observation of a sharp minimum in the amplitude of (111) "belly" de Haas-van Alphen (dH-vA) oscillations in very dilute (~30 ppm) Cu:Cr alloys. The effect had the appearance of a "beat" minimum, but could not be ascribed to sample imperfection, so we postulated at the time the existence of an electronscattering anomaly. It now appears probable that we are indeed observing a form of beat and that this is fundamental in origin.The frequencies observed in the dH-vA effect can be related to an extremal area of the Fermi surface and are associated with the spacing of the Landau levels for that cross section. The amplitude of the oscillations is a complex function of magnetic field H and temperature T but is also affected by the electron spin. Each of the Landau levels is split according to the spin direction, introducing into the amplitude a term cos(TTgm*/2m 0 ), where the factor g is usually but not always 2 and m*/m 0 is the cyclotron mass in units of free-electron mass. When the spin splitting is exactly half the spacing of the Landau levels, the amplitude of the fundamental drops to zero; this corresponds to gm*/m 0 taking the value 1, 3, etc.In ferromagnetic systems such as iron, 2 nickel, 3 or palladium with a small concentration of cobalt, 4 an exchange interaction splits the Fermi surface into separate spin-up and spin-down surfaces (with corresponding extremal areas) and the spin-splitting factor is suppressed. This feature is particularly striking in the experiments of Hornfeldt, Ketterson, and Windmiller, 4 where small concentrations of cobalt added to palladium suppressed the spin-splitting zeros, and the nesting spin-up and spin-down Fermi surfaces caused a beat in the dH-vA oscillations. This experiment suggested that we reinterpret our data for Cu:Cr in terms of a beat induced by the localized moment. We used for new experiments a single crystal of copper doped with 35 ppm (nominal) chromium. The resistance ratio of the specimen (room temperature to 4.2 K) was 42, giving a value of 34 ppm using the resistivity data of Daybell and Steyert. 5

Experimental evidence for many-body effects in dilute alloys

“…De Haas-van Alphen experiments, which are closely related to the impurity resistivity, also provide us with direct evidence that the scattering on transition metal impurities has a d-like symmetry. The anisotropy of the conduction electron lifetime due to the particular symmetry of the scattered conduction electrons is different for normal metal and transition metal impurities, and in the latter case the experiments are in agreement with the assumption of pure d-symmetry for Cu-based alloys (Coleridge and Templeton 1970). The conduction electron lifetimes derived from the de Haas-van Alphen experiments were found to be proportional to the transport relaxation times and show the same double-peaked behaviour versus the impurity atomic number in the copper host as shown in fig.…”

“…The thermoelectric power measurements of Boato andVig (1967) andCooper et al (1974) in A1-3d transition metal alloys show the same trend as given by eqn. (25), confirming that the virtual bound state is spin degenerate.…”

Fermi Surface Properties, Metamagnetic Transition and Quantum Phase Transition of CeRu2Si2 and Its Alloys Probed by the dHvA Effect

“…Since the amplitudes of the oscillations from the up and down spin electrons are different due to the spin dependent scattering, the spin splitting zero phenomena observed at a particular field direction changes to the spin splitting minimum in a dilute Kondo alloy. 131,132 Although it may not be apparent from the equations above, it is noted that the electron mean path l is determined from an average distance between impurities and is given approximately by vτ . Here, v is the velocity of the electron.…”

Influence of magnetic impurities on the de Haas‐van Alphen oscillations

“…In dilute Kondo alloys such as Cu(Cr) deviations from the behaviour of pure metals are observed, that provide information about the impurities [3]. One effect of the magnetic impurities shows up in an exponential damping of the oscillations, which also occurs for non magnetic impurities.…”

“…Finally the constant @( = 1/2) in (1) results from the Lifshiz-Onsager-quantization condition, by which the states in the region of k .-space given by condense into the single Landau level with S(E,; k,) = (n + @) 2n/r;. The self-energy C , @, k,; ion) similarly is given by the normalized k,, k,-average over the region defined by (3).…”