Fluctuation-Driven Quantum Phase Transitions in Clean Itinerant Ferromagnets

The quantum phase transition in clean itinerant ferromagnets is analyzed. It is shown that soft particle-hole modes invalidate Hertz's mean-field theory for $d \leq 3$. A renormalized mean-field theory predicts a fluctuation-induced first order transition for $1 < d \leq 3$, whose stability is analyzed by renormalization group techniques. Depending on microscopic parameter values, the first order transition can be stable, or be pre-empted by a fluctuation-induced second order transition. The critical behavior at the latter is determined. The results are in agreement with recent experiments.Comment: 4 pp., REVTeX, no figs; final version as publishe

Nature of the Quantum Phase Transition in Clean, Itinerant Heisenberg Ferromagnets

A comprehensive theory of the quantum phase transition in clean, itinerant Heisenberg ferromagnets is presented. It is shown that the standard mean-field description of the transition is invalid in spatial dimensions $d\leq 3$ due to the existence of soft particle-hole excitations that couple to the order parameter fluctuations and lead to an upper critical dimension $d_c^+ = 3$. A generalized mean-field theory that takes these additional modes into account predicts a fluctuation-induced first-order transition. In a certain parameter regime, this first-order transition in turn is unstable with respect to a fluctuation-induced second-order transition. The quantum ferromagnetic transition may thus be either of first or of second-order, in agreement with experimental observations. A detailed discussion is given of the stability of the first-order transition, and of the critical behavior at the fluctuation-induced second-order transition. In $d=3$, the latter is mean field-like with logarithmic corrections to scaling, and in $d<3$ it can be controlled by means of a $3-\epsilon$ expansion.Comment: 15 pp., revtex4, 6 eps 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

Magnetic pair breaking in disordered superconducting films

A theory for the effects of nonmagnetic disorder on the magnetic pair breaking rate $\alpha$ induced by paramagnetic impurities in quasi two-dimensional superconductors is presented. Within the framework of a strong-coupling theory for disordered superconductors, we find that the disorder dependence of $\alpha$ is determined by the disorder enhancements of both the electron-phonon coupling and the spin-flip scattering rate. These two effects have a tendency to cancel each other. With parameter values appropriate for Pb_{0.9} Bi_{0.1}, we find a pair breaking rate that is very weakly dependent on disorder for sheet resistances 0 < R < 2.5 kOhm, in agreement with a recent experiment by Chervenak and Valles.Comment: 6 pp., REVTeX, epsf, 2 eps figs, final version as publishe

Nonanalytic behavior of the spin susceptibility in clean Fermi systems

The wavevector and temperature dependent static spin susceptibility, \chi_s(Q,T), of clean interacting Fermi systems is considered in dimensions 1\leq d \leq 3. We show that at zero temperature \chi_s is a nonanalytic function of |Q|, with the leading nonanalyticity being |Q|^{d-1} for 1<d<3, and Q^2\ln|Q| for d=3. For the homogeneous spin susceptibility we find a nonanalytic temperature dependence T^{d-1} for 1<d<3. We give qualitative mode-mode coupling arguments to that effect, and corroborate these arguments by a perturbative calculation to second order in the electron-electron interaction amplitude. The implications of this, in particular for itinerant ferromagnetism, are discussed. We also point out the relation between our findings and established perturbative results for 1-d systems, as well as for the temperature dependence of \chi_s(Q=0) in d=3.Comment: 12pp., REVTeX, 5 eps figures, final version as publishe

Theory of many-fermion systems II: The case of Coulomb interactions

In a recent paper (cond-mat/9703164) a general field-theoretical description of many-fermion systems with short-ranged interactions has been developed. Here we extend this theory to the case of disordered electrons interacting via a Coulomb potential. A detailed discussion is given of the Ward identity that controls the soft modes in the system, and the generalized nonlinear sigma model for the Coulombic case is derived and discussed.Comment: 12 pp., REVTeX, no figs, final version as publishe

Metamagnetic Quantum Criticality in Sr3Ru2O7

We consider the metamagnetic transition in the bilayer ruthenate, ${\rm Sr_3Ru_2O_7}$, and use this to motivate a renormalization group treatment of a zero-temperature quantum-critical end-point. We summarize the results of mean field theory and give a pedagogical derivation of the renormalization-group equations. These are then solved to yield numerical results for the susceptibility, the specific heat and the resistivity exponent which can be compared with measured data on ${\rm Sr_3Ru_2O_7}$ to provide a powerful test for the standard framework of metallic quantum criticality. The observed approach to the critical point is well-described by our theory explaining a number of unusual features of experimental data. The puzzling behaviour very near to the critical point itself, though, is not accounted for by this, or any other theory with a Fermi surface

The Effects of Electron-Electron Interactions on the Integer Quantum Hall Transitions

We study the effects of electron-electron interaction on the critical properties of the plateau transitions in the {\it integer} quantum Hall effect. We find the renormalization group dimension associated with short-range interactions to be $-0.66\pm0.04$. Thus the non-interacting fixed point (characterized $z=2$ and $\nu\approx 2.3$) is stable. For the Coulomb interaction, we find the correlation effect is a marginal perturbation at a Hartree-Fock fixed point ($z=1$, $\nu\approx 2.3$) by dimension counting. Further calculations are needed to determine its stability upon loop corrections.Comment: 12 pages, Revtex, minor changes, to be published in Phys. Rev. Let

The Eliashberg Function of Amorphous Metals

A connection is proposed between the anomalous thermal transport properties of amorphous solids and the low-frequency behavior of the Eliashberg function. By means of a model calculation we show that the size and frequency dependence of the phonon mean-free-path that has been extracted from measurements of the thermal conductivity in amorphous solids leads to a sizeable linear region in the Eliashberg function at small frequencies. Quantitative comparison with recent experiments gives very good agreement.Comment: 4pp., REVTeX, 1 uuencoded ps fig. Original posting had a corrupted raw ps fig appended. Published as PRB 51, 689 (1995

Metamagnetic Quantum Criticality

A renormalization group treatment of metamagnetic quantum criticality in metals is presented. In clean systems the universality class is found to be of the overdamped, conserving (dynamical exponent z=3) Ising type. Detailed results are obtained for the field and temperature dependence of physical quantities including the differential susceptibility, resistivity and specific heat near the transition. An application of the theory is made to Sr3Ru2O7, which appears to exhibit a metamagnetic critical end-point at a very low temperature and a field of order 5-7T.Comment: 4 pages latex (Revtex 4) and 3 eps figure