Frustrated interactions exist throughout nature, with examples ranging from protein folding through to frustrated magnetic interactions. Whilst magnetic frustration is observed in numerous electrically insulating systems, in metals it is a rare phenomenon. The interplay of itinerant conduction electrons mediating interactions between localised magnetic moments with strong spin-orbit coupling is likely fundamental to these systems. Therefore, knowledge of the precise shape and topology of the Fermi surface is important in any explanation of the magnetic behaviour. PdCrO2, a frustrated metallic magnet, offers the opportunity to examine the relationship between magnetic frustration, short-range magnetic order and Fermi surface topology. By mapping the short-range order in reciprocal space and experimentally determining the electronic structure, we have identified the dual role played by the Cr electrons in which the itinerant ones on the nested paramagnetic Fermi surface mediate the frustrated magnetic interactions between local moments.

We show that the Fermi surface can survive the presence of extreme compositional disorder in the equiatomic alloy Ni0.25Fe0.25Co0.25Cr0.25. Our high-resolution Compton scattering experiments reveal a Fermi surface which is smeared across a significant fraction of the Brillouin zone (up to 40% of 2π a ). The extent of this smearing and its variation on and between different sheets of the Fermi surface has been determined, and estimates of the electron mean-free-path and residual resistivity have been made by connecting this smearing with the coherence length of the quasiparticle states.The emergence of the Fermi surface (FS) from the theory of the electronic structure of metals, together with the pioneering experimental determinations of its shape, stand proudly among the greatest achievements of twentieth century physics [1]. The FS, defined by the discontinuity in the momentum distribution, exists even for interacting electrons [2,3], and here we demonstrate its remarkable ability to survive maximal compositional disorder in which the electron mean-free-path (which we can also extract from our measurements) is comparable to the lattice spacing. In disordered systems, the Mott-Ioffe-Regel (MIR) limit describes the semiclassical upper bound for coherent transport in a metal, occuring when the electron mean-free-path becomes comparable with the interatomic spacing [4]. The modern description of the electronic structure of crystalline solidsthe band theory of electrons -depends on the notion of perfect crystals exhibiting long-range order. The Bloch wavefunctions which emerge are a direct consequence of the discrete translational invariance of the potential experienced by the electrons traveling through the ionic lattice. This premise is strongly challenged in substitutionally disordered random alloys (concentrated solid solutions) where there is no such periodicity. Abandoning the familiar concepts associated with a well-defined reciprocal lattice, such as the Brillouin zone (BZ) and indeed the FS, seems inevitable. However, there is considerable theoretical and experimental evidence (e.g. [5, 6]) that by considering an ordered system comprising suitably chosen effective scatterers to restore periodicity, the BZ and FS can be resurrected. The resulting electron states, however, have finite lifetimes due to the presence of disorder, and the "bands" are smeared in both energy, E (resulting in a finite electron lifetime) and crystal mo-mentum, k (finite mean-free-path). This also means that the discontinuity in the momentum distribution associated with the FS is also smeared out in both E and k, with correspondingly reduced Fermi energy electron lifetimes and short mean-free-paths. A sharp FS in an ultrapure metal at cryogenic temperatures is associated with electron mean-free-paths of more than a centimeter [7]. While bulk resistivities of metals are rather well known, comparatively little direct information exists about electron mean-free-paths [8].A new class of metallic alloys, referred to as "high entropy alloys"...

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First-principles calculations of the electronic structure and phonon dispersion relation of the superconducting compound BaSn5 were performed. This has allowed the calculation of the electronphonon matrix elements from which the electron-phonon coupling constant was found to be λep = 0.87. Application of the Allen-Dynes formula with µ * = 0.11 yielded a superconducting transition temperature of Tc = 4.2 K. The calculated Tc agrees well with the available experimental data and indicates that BaSn5 is an electron-phonon superconductor with intermediate strength electronphonon coupling.

The anti-perovskite superconductor MgC0.93Ni2.85 was studied using high-resolution x-ray Compton scattering combined with electronic structure calculations. Compton scattering measurements were used to determine experimentally a Fermi surface that showed good agreement with that of our supercell calculations, establishing the presence of the predicted hole and electron Fermi surface sheets. Our calculations indicate that the Fermi surface is smeared by the disorder due to the presence of vacancies on the C and Ni sites, but does not drastically change shape. The 20% reduction in the Fermi level density-of-states would lead to a significant (~70%) suppression of the superconducting T c for pair-forming electron-phonon coupling. However, we ascribe the observed much smaller T c reduction at our composition (compared to the stoichiometric compound) to the suppression of pair-breaking spin fluctuations.

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