Anderson-Mott Transition in a Magnetic Field: Corrections to Scaling

It is shown that the Anderson-Mott metal-insulator transition of paramagnetic, interacting disordered electrons in an external magnetic field is in the same universality class as the transition from a ferromagnetic metal to a ferromagnetic insulator discussed recently. As a consequence, large corrections to scaling exist in the magnetic-field universality class, which have been neglected in previous theoretical descriptions. The nature and consequences of these corrections to scaling are discussed.Comment: 5pp., REVTeX, no figs, final version as publishe

Quantum critical behavior in disordered itinerant ferromagnets: Logarithmic corrections to scaling

The quantum critical behavior of disordered itinerant ferromagnets is determined exactly by solving a recently developed effective field theory. It is shown that there are logarithmic corrections to a previous calculation of the critical behavior, and that the exact critical behavior coincides with that found earlier for a phase transition of undetermined nature in disordered interacting electron systems. This confirms a previous suggestion that the unspecified transition should be identified with the ferromagnetic transition. The behavior of the conductivity, the tunneling density of states, and the phase and quasiparticle relaxation rates across the ferromagnetic transition is also calculated.Comment: 15pp., REVTeX, 8 eps figs, final version as publishe

Anomalous Density-of-States Fluctuations in Two-Dimensional Clean Metals

It is shown that density-of-states fluctuations, which can be interpreted as the order-parameter susceptibility \chi_OP in a Fermi liquid, are anomalously strong as a result of the existence of Goldstone modes and associated strong fluctuations. In a 2-d system with a long-range Coulomb interaction, a suitably defined \chi_OP diverges as 1/T^2 as a function of temperature in the limit of small wavenumber and frequency. In contrast, standard statistics suggest \chi_OP = O(T), a discrepancy of three powers of T. The reasons behind this surprising prediction, as well as ways to observe it, are discussed.Comment: 4 pp, revised version contains a substantially expanded derivatio

Nonanalytic Magnetization Dependence of the Magnon Effective Mass in Itinerant Quantum Ferromagnets

The spin wave dispersion relation in both clean and disordered itinerant quantum ferromagnets is calculated. It is found that effects akin to weak-localization physics cause the frequency of the spin-waves to be a nonanalytic function of the magnetization m. For low frequencies \Omega, small wavevectors k, and small m, the dispersion relation is found to be of the form \Omega ~ m^{1-\alpha} k^2, with \alpha = (4-d)/2 (2<d<4) for disordered systems, and \alpha = (3-d) (1<d<3) for clean ones. In d=4 (disordered) and d=3 (clean), \Omega ~ m ln(1/m) k^2. Experiments to test these predictions are proposed.Comment: 4 pp., REVTeX, no fig

Quantum critical behavior of disordered itinerant ferromagnets

The quantum ferromagnetic transition at zero temperature in disordered itinerant electron systems is considered. Nonmagnetic quenched disorder leads to diffusive electron dynamics that induces an effective long-range interaction between the spin or order parameter fluctuations of the form r^{2-2d}, with d the spatial dimension. This leads to unusual scaling behavior at the quantum critical point, which is determined exactly. In three-dimensional systems the quantum critical exponents are substantially different from their finite temperature counterparts, a difference that should be easily observable. Experiments to check these predictions are proposed.Comment: 14pp., REVTeX, 3 eps figs, final version as publishe

Order Parameter Description of the Anderson-Mott Transition

An order parameter description of the Anderson-Mott transition (AMT) is given. We first derive an order parameter field theory for the AMT, and then present a mean-field solution. It is shown that the mean-field critical exponents are exact above the upper critical dimension. Renormalization group methods are then used to show that a random-field like term is generated under renormalization. This leads to similarities between the AMT and random-field magnets, and to an upper critical dimension $d_{c}^{+}=6$ for the AMT. For $d<6$, an $\epsilon = 6-d$ expansion is used to calculate the critical exponents. To first order in $\epsilon$ they are found to coincide with the exponents for the random-field Ising model. We then discuss a general scaling theory for the AMT. Some well established scaling relations, such as Wegner's scaling law, are found to be modified due to random-field effects. New experiments are proposed to test for random-field aspects of the AMT.Comment: 28pp., REVTeX, no figure

Theory of helimagnons in itinerant quantum systems

The nature and effects of the Goldstone mode in the ordered phase of helical or chiral itinerant magnets such as MnSi are investigated theoretically. It is shown that the Goldstone mode, or helimagnon, is a propagating mode with a highly anisotropic dispersion relation, in analogy to the Goldstone mode in chiral liquid crystals. Starting from a microscopic theory, a comprehensive effective theory is developed that allows for an explicit description of the helically ordered phase, including the helimagnons, for both classical and quantum helimagnets. The directly observable dynamical spin susceptibility, which reflects the properties of the helimagnon, is calculated.Comment: 20 pp., 1 eps fig; corrects various typos and incorrect prefactors in Phys Rev B versio

Local field theory for disordered itinerant quantum ferromagnets

An effective field theory is derived that describes the quantum critical behavior of itinerant ferromagnets in the presence of quenched disorder. In contrast to previous approaches, all soft modes are kept explicitly. The resulting effective theory is local and allows for an explicit perturbative treatment. It is shown that previous suggestions for the critical fixed point and the critical behavior are recovered under certain assumptions. The validity of these assumptions is discussed in the light of the existence of two different time scales. It is shown that, in contrast to previous suggestions, the correct fixed point action is not Gaussian, and that the previously proposed critical behavior was correct only up to logarithmic corrections. The connection with other theories of disordered interacting electrons, and in particular with the resolution of the runaway flow problem encountered in these theories, is also discussed.Comment: 17pp., REVTeX, 5 eps figs, final version as publishe

A metal-insulator transition as a quantum glass problem

We discuss a recent mapping of the Anderson-Mott metal-insulator transition onto a random field magnet problem. The most important new idea introduced is to describe the metal-insulator transition in terms of an order parameter expansion rather than in terms of soft modes via a nonlinear sigma model. For spatial dimensions d>6 a mean field theory gives the exact critical exponents. In an epsilon expansion about d=6 the critical exponents are identical to those for a random field Ising model. Dangerous irrelevant quantum fluctuations modify Wegner's scaling law relating the conductivity exponent to the correlation or localization length exponent. This invalidates the bound s>2/3 for the conductivity exponent s in d=3. We also argue that activated scaling might be relevant for describing the AMT in three-dimensional systems.Comment: 10 pp., REvTeX, 1 eps fig., Sitges Conference Proceedings, final version as publishe