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

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

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

Metallic Continuum Quantum Ferromagnets at Finite Temperature

We study via renormalization group (RG) and large N methods the problem of continuum SU(N) quantum Heisenberg ferromagnets (QHF) coupled to gapless electrons. We establish the phase diagram of the dissipative problem and investigate the changes in the Curie temperature, magnetization, and magnetic correlation length due to dissipation and both thermal and quantum fluctuations. We show that the interplay between the topological term (Berry's phase) and dissipation leads to non-trivial effects for the finite temperature critical behavior.Comment: Corrected typos, new discussion of T=0 results, to appear in Europhys. Let

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

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

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

Coulomb Blockade of Tunneling between Disordered Conductors

We determine the zero-bias anomaly of the conductance of tunnel junctions by an approach unifying the conventional Coulomb blockade theory for ultrasmall junctions with the diffusive anomalies in disordered conductors. Both, electron-electron interactions within the electrodes and electron-hole interactions between the electrodes are taken into account nonperturbatively. Explicit results are given for one- and two-dimensional junctions, and the crossover to ultrasmall junctions is discussed.Comment: 4 pages, 1 figure. Final version published in Phys. Rev. Let

Coexistence of ferromagnetism and superconductivity

A comprehensive theory is developed that describes the coexistence of p-wave, spin-triplet superconductivity and itinerant ferromagnetism. It is shown how to use field-theoretic techniques to derive both conventional strong-coupling theory, and analogous gap equations for superconductivity induced by magnetic fluctuations. It is then shown and discussed in detail that the magnetic fluctuations are generically stronger on the ferromagnetic side of the magnetic phase boundary, which substantially enhances the superconducting critical temperature in the ferromagnetic phase over that in the paramagnetic one. The resulting phase diagram is compared with the experimental observations in UGe_2 and ZrZn_2.Comment: 16 pp., REVTeX, 6 eps figs; final version as publishe

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