Haas-van Alphen effect

Up to this point we have treated the electrons as a set of classical charge carriers, except for the confinement in the z direction which introduces quantization of the motion along z, and localization in the xy plane. Now we introduce the effects of quantization in the remaining two dimensions. The behavior of electrons in the plane exhibits quantization in two ways, which are actually related (see Problem 4). Here we give only a qualitative discussion of these two levels of quantization. 

In the presence of a perpendicular magnetic field H = i/i the electron orbits are quantized in units of the cyclotron frequency 

The corresponding energy levels are equally spaced, separated by intervals hcoc, these are called Landau levels. This is intuitively understood as the quantization of circular motion due to a harmonic oscillator potential. 

The number of electronic states that each Landau level can accommodate is determined by the quantization of magnetic flux. This is intuitively understood as a consequence of the fact that there exist spatial limitations in the placement of the circular orbits. 

The total magnetic flux through the plane where the electrons are confined is H W L), where W is the width and L the length of the plane we define the area A of the plane as A = WL. The number of flux quanta corresponding to this total flux is 

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Shoenberg, D. (1960) The de Haas-van Alphen effect in copper, silver and gold, Phil. Mag., 5, 105-110. 

Detailed studies - band structure calculations, de Haas-van Alphen effect and polarized neutron diffraction - have evidenced the strong hybridization of 5 f bands either with p anions bands (USi3, UGes, USns) or 4d bands (URhs, UIts). 

So it cannot contribute to the magnetic oscillations giving rise to the de Haas-van Alphen effect. Fig. 8 (inset) shows the dHvA oscillations for the present salt at 1.5 K and the FFT is shown in Fig. 8. Only two frequencies, a and P, can be seen so that this can be taken as an additional confirmation of the fact that the (P-a) and (P-2a) frequencies are really connected with a QI effect. 

Falicov L.M. and Stachowiak H. (1966) The Theory of de Haas-van Alphen Effect in a system of Coupled Orbits. Application to Magnesium, Phys. Rev. 147,505-515. 

FIGURE 23 de Haas-van Alphen effect in superconducting YNi2B2C. The field-dependent torque signal is observed at 0.45 K. The magnetic field is rotated 45° from [001] to [100], arrows indicate the field-sweep directions. In the inset, after background subtraction, dHvA oscillations can be seen more clearly (Ignatchik et al., 2005). 

Keywords Antiferromagnet, phase transition, magnetic properties, de Haas-van Alphen effect... 

J.H. Condon, Nonlinear de Haas-van Alphen effect and Magnetic Domains in Beryllium, Phys.Rev. 145, 526-535 (1966)... 

Wang, G., P. K. Ummat, and W. R. Datars. 1988. De Haas-van Alphen effect of potassium intercalated graphite. Extended Abstracts, Graphite Intercalation Compounds, 217-219, Materials Research Society, Fall Meeting, Pittsburg, PA. 

It is most convenient to begin by constructing a (110) plane in wave number space, with the wave number lattice as shown in Fig. 16-12. The electron density is l6/because there are four atoms per cube and four electrons per atom, so the Fermi wave number can be obtained in units of Inja. Either a graphical solution or an approximate geometrical solution is adequate. These areas are directly measured in the de Haas van Alphen effect. The experimental values (Gold, 1958) are 1.00 and 0.11 times ftn/aY for the second band and third band, respectively. 

NOZ/KOB] Nozue, T., Kobayashi, H., Sato, M., Uesawa, A., Suzuki T., Kamimura, T., Specific heat and de Haas-van Alphen effect in NiAs, Physica B (Amsterdam), (1997), 174-176. Cited on page 211. 

De Haas-Van Alphen effect - An effect observed in certain metals and semiconductors at low temperatures and high magnetic fields, characterized by a periodic variation of magnetic susceptibility with field strength. 

Bucher et al. (1970) and Kayser (1970) independently reported that the stable low temperature phase of Yb is hep rather then fee. Tanuma et al. (1970) reexamined the de Haas-van Alphen effect and confirmed that Yb transforms to hep after a cooling cycle to 1.2 K. A specimen prepared in this way may be predominantly in the hep phase, but it inevitably contains some amount of the fee phase. To what extent this mixture of phases may affect the de Haas-van... 

The de Haas-van Alphen effect in ferromagnetic Gd has been observed by two groups, using crystals purified by the same electrotransport technique. Young et al. (1973) obtained a crystal with resistivity ratio 240. They carried out the measurement at 0.9 K over various field directions and observed a total of seven oscillations. By varying the temperature from 2K to 0.9 K Young and Hulbert (1974) determined the cyclotron mass of four of the orbits. Schirber et al. reported nine orbits on a specimen with resistivity ratio 260. The three orbits with largest areas have been identified. 

Plots of the hyperfine coupling constant at uranium nuclei by Mossbauer spectroscopy and the cyclotron masses obtained by de Haas-van Alphen effect measurements in the series of uranium dipnictides. 

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