DHvA effect

Alphen (dHvA) effect every cycle of the magnetic oscillations is accompanied by a first-order phase transition, and by the appearance of a domain structure. Figure 1, taken from [29], illustrates the splitting of the NMR frequency of Ag109 in metallic silver under the condition of the dHvA effect, which unambiguously testifies to the occurrence of diamagnetic domains. 

In the vicinity of a phase transition a rapid change of magnetic properties with the field intensity occurs. Consequently, a highly uniform magnetic field, comparable to the experimental conditions in the studies of the dHvA effect in metals, is required. 

A variety of substances, manifestating intermediate states, which was earlier represented by type 1 superconductors and weakly magnetic metals under conditions of the dHvA effect, is complemented by antiferromagnetic insulators. 

To illustrate the effect of finite temperatures on the dHvA amplitude further, Fig. 3.1 shows an actual measurement of the dHvA effect in K-(ET)2l3 for different temperatures. This organic superconductor has a simple FS so that for the chosen field and temperature range only one extremal orbit is dominant (see Sect. 4.2.3). With increasing temperature the strong decrease of the oscillating magnetization is clearly seen. From this dependence, the cyclotron effective mass, fj,c, can be extracted either by fitting the relation... 

Although in principle every experimental setup that measures the field dependence of the magnetization or a derivative of M could be used to observe the dHvA effect, usually an apparatus with a very high sensitivity has to be designed to resolve the oscillations. An overview of the different experimental techniques is given in Ref. [249], Two main realizations used to detect dHvA oscillations in organic superconductors are the torque and the modulation-field method. 

Magnetic quantum oscillations in bismuth were first observed in the field dependence of the electrical resistivity by Shubnikov and de Haas [246] shortly before the dHvA effect was discovered. Usually, however, the SdH effect is weak and hard to observe except in semimetals, like bismuth, and semiconductors. 

The next a-phase salt to be discussed is o -(ET)2TlHg(SeCN)4. As already mentioned, this compound is not superconducting down to 80 mK. The measurements of both SdH [285] and dHvA effect [286] revealed a similar picture as for a-(ET)2NH4Hg(SCN)4. Typical dHvA oscillations of one... 

For a perfectly 2D material the usual assumption of a constant field independent chemical potential has to be revised. If in an increasing field the FS is just between two successive Landau levels the chemical potential has to shift with the Landau cylinders and finally jump back for increasing field to the next lower level. An analytical formula for the dHvA effect of a 2D electron gas taking into account finite temperature and fields is given in [326]. The applicability of this formula could not be tested quantitatively. Qualitatively, however, the predicted increased harmonic content and a drastically changed shape of the oscillations was observed. 

The second material is K-(DMET)2AuBr2 with 1.9K [17]. This is the first charge transfer salt with a donor molecule other than ET where the dHvA effect was observed [369]. DMET (= dimethyl-ethylenedithio-diselenedithiafulvalene) is an asymmetric hybrid molecule composed of one... 

The almost perfect 2D FS is responsible for the sometimes unusual behavior of the SdH or dHvA oscillations, like an enhanced anharmonicity or a seemingly field-dependent effective mass. A detailed theoretical understanding of the dHvA effect for 2D materials with a similar powerful equation such as the Lifehitz-Kosevich formula is still missing. The current investigations on magnetic quantum oscillations of 2D materials, especially comparative studies of magnetic (dHvA) and resistive (SdH) measurements, will hopefully help to clarify the open questions. 

As discussed in sect. 2 the observation of the dHvA effect far in the vortex phase B < Bc2) is a sure signature of nodal superconductivity. Although oscillations of the three Fermi surface sheets in URu2Si2 have been seen below Bc2 (Ohkuni et al., 1999) the amplitude falls of quite rapidly with B, especially for field along c. Therefore, these experiments are not able to confirm the existence of nodes in A (k). 

The magnetization or the magnetic susceptibility is the most common one of these physical quantities, and its periodic variation is called the de Haas-van Alphen (dHvA) effect (de Haas and van Alphen 1930, 1932). It provides one of the best tools for the investigation of Fermi surface properties such as the extremal cross-sectional area S, the cyclotron mass w and the scattering lifetime x of metals (Shoenberg 1984). Sometimes other physical quantities are also measured for example, torque, static strain, ultrasonic velocity, and magnetoresistance, etc. The last type of measurement is called the Shubnikov-de Haas effect. 

The measurements of the dHvA effect in LaBe (Suzuki et al. 1988, Ishizawa et al. 1977, 1980, Arko et al. 1976), shown in fig. 8, revealed that the Fermi surface consists of a set of three equivalent nearly spherical ellipsoids, denoted by a,- (/ = 1, 2 and 3), which... 

The Fermi surface of CeB has been seen with the dHvA effect (van Deursen et al. 1985, Joss et al. 1987, 1988, Onuki et al. 1989a, 1990a, Springford 1991). At this field value, CeBg is in an induced ferromagnetic state. In fig. 23, we show the data of Onuki et al. (1989a). The experimental Fermi surface looks identical to that in LaBg,... 

In the case of CeP, no sharp peak in p versus T was observed (Hulliger and Ott 1978). Kwon etal. (1991) grew very good single crystals using a recrystallization method with an excess of P. The temperature dependence of the electrical resistivity of CeP is shown in fig. 121 (Kwon et al. 1991). This result is very similar to that obtained for CeAs (see fig. 120), and in fact the carrier concentration determined by the de Haas-van Alphen (dHvA) effect is nearly the same as that obtained for CeAs (0.001 electron/Ce-atom). 

Of great interest are specific-heat data, since the obtained y-value for CeAs (17mJ/molK ) is nearly the same as those for CeSb and CeBi (Kwon et al. 1991), although CeSb and CeBi have carrier concentrations of about 0.02 electron/Ce-atom (determined by the dHvA effect), with a mass enhancement factor of about 25. Thus, the mass enhancement for CeAs must be very large, and one can consider it as a heavy-fermion system with an extremely low carrier concentration. 

When a high magnetic field H) is applied to lowdimensional conductors at low temperatures, several magnetooscillation phenomena, caused by Landau sublevels passing through the Fermi level, are observed (see [521-531] and references cited therein). In 2D conductors (with closed orbits) the magnetization oscillation is known as the de Haas-van Alphen (dHvA) effect and the magnetoresistance oscillation as the Shubnikov-de Haas (SdH) effect. These effects have been observed firstly in thin metal films [521,522] and more recently in a number of low-dimensional... 

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