Magnetization and magnetotransport measurements have been used to study the composition dependence of the electronic properties of the Ruddlesden-Popper phases Sr 2 NdMn 2 O 7 and Sr 1.9 Nd 1.1 Mn 2 O 7 . Although their behaviour differs in detail, both compounds show a colossal magnetoresistance (CMR) effect (>10 000% in 14 T) in the temperature range 4.2 T /K 100. However, neither material shows a transition to a ferromagnetic state above 4.2 K, and both materials have higher resistivities (>10 3 cm for 4.2 T /K 100) than the metallic oxides previously found to show CMR. In view of the low conductivity and the absence of ferromagnetism, the CMR of these phases is not readily explained by a doubleexchange mechanism.

We report measurements of the longitudinal magnetoresistance and magnetization of in pulsed magnetic fields of up to 50 T and temperatures down to 400 mK, using samples of different purity. Below 2 K the amplitude of the Shubnikov - de Haas oscillations in is found to decrease dramatically with falling temperature. This effect is shown to coincide with quasipersistent eddy current resonances in the magnetization, which are a signature of the quantum Hall effect. Evidence is provided for the existence of a novel interplane conduction mechanism involving highly metallic edge states with supressed scattering at the surface of the sample (a so-called `chiral Fermi liquid'), operational when the chemical potential is between Landau levels in the bulk of the material.

Angle-dependent magnetoresistance oscillations (AMROs) have been studied in the isostructural charge-transfer salts and (where BEDT-TTF is bis(ethylenedithio)tetrathiafulvalene) in steady fields of up to 30 T. The shapes of the approximately elliptical quasi-two-dimensional (Q2D) Fermi surfaces that these organic metals possess have been determined at 30 T and are found to be in broad agreement with recent band-structure calculations. The Fermi surface of the salt undergoes a reconstruction at low fields and temperatures, resulting in a change in the dimensionality of the AMROs from Q2D character to quasi-one-dimensional character. This change is associated with the kink transition that is observed in magnetic field sweeps and is attributed to the formation of a spin-density wave ground state. The phase boundary of the change in the AMRO dimensionality has been followed to both the low-temperature high-field (about 23 T) and low-field high-temperature (about 8 K) extremes. The data are compared with recently proposed models of the AMROs and Fermi surfaces for these materials.

Whilst tight-binding bandstructure calculations are very successful in describing the Fermi-surface configuration in many quasi-two-dimensional organic molecular metals, the detailed topology of the predicted Fermi surface often differs from that measured in experiments. This is very significant when, for example, the formation of a density-wave state depends critically on details of the nesting of Fermi-surface sheets. These differences between theory and experiment probably result from the limited accuracy to which the -orbitals of the component molecules (which give rise to the transfer integrals of the tight-binding bandstructure) are known. In order to surmount this problem, we have derived a method whereby the transfer integrals within a tight-binding bandstructure model are adjusted until the detailed Fermi-surface topology is in good agreement with a wide variety of experimental data. The method is applied to the charge-transfer salt -(BEDT-TTF)2KHg(SCN)4, the Fermi surface of which has been the source of much speculation in recent years. The Fermi surface obtained differs in detail from previous bandstructure calculation findings. In particular, the quasi-one-dimensional component of the Fermi surface is more strongly warped. This implies that upon nesting of these sheets, significant parts of the quasi-one-dimensional sheets remain, leading to a complicated Fermi-surface topology within the low-temperature, low-magnetic-field phase. In contrast to previous models of this phase, the model for the reconstructed Fermi surface in this work can explain virtually all of the current experimental observations in a consistent manner.

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