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We address the question of coexistence of superconductivity and ferromagnetism. Using a field theoretical approach we study a one-fermion effective model of a ferromagnetic superconductor in which the quasiparticles responsible for the ferromagnetism form the Cooper pairs as well. For the first time we solve self-consistently the mean-field equations for the superconducting gap and the spontaneous magnetization. We discuss the physical features which are different in this model and the standard BCS model and consider their experimental consequences.

Superconductivity mediated by spin fluctuations in weak and nearly ferromagnetic metals is studied close to the zero-temperature magnetic transition. We solve analytically the Eliashberg equations for p-wave pairing and obtain the quasiparticle self-energy and the superconducting transition temperature T(c) as a function of the distance to the quantum critical point (QCP). We show that the reduction of quasiparticle coherence and lifetime due to scattering by quasistatic spin fluctuations is the dominant pair-breaking process, which leads to a rapid suppression of T(c) to a nonzero value near the QCP. We point out the differences and similarities of the problem to that of paramagnetic impurities in superconductors.

We calculate the entropy of a two-dimensional Fermi Liquid(FL) using a model with a contact interaction between fermions. We find that there are T 2 contributions to the entropy from interactions separate from those due to the collective modes.These T 2 contributions arise from non-analytic corrections to the real part of the selfenergy which may be calculated from the leading log dependence of the imaginary part of the self-energy through the Kramers-Kronig relation. We find no evidence of a breakdown in Fermi Liquid theory in 2D and conclude that FL in 2D are similar to 3D FL's. 05.30.Fk, 65.70+y, 67.50g Typeset Using REVTEX 1

We show that the effective spin Hamiltonian used previously to describe the CuO planes of La2Cu04 does not lead to a net ferromagnetic moment for CuO planes and hence does not describe the metamagnetic behavior seen experimentally. %'e construct for the first time a Hamiltonian from the symmetries of the crystal structure which does lead to metamagnetism. The linear spin-wave spectrum is also calculated. This work points to the necessity of constructing effective spin Hamiltonians for metamagnetic systems which have the same symmetries as the system they are to describe.We construct for the first time an effective spin Hamiltonian for the CuO planes of undoped La2Cu04 whose classical ground state has a small ferromagnetic moment and calculate the corresponding linear spin-wave spectrum. The CuO planes are known to have a small ferromagnetic moment from the metamagnetic behavior seen in measurements of the static magnetic susceptibility, ' although the interactions are predominantly antiferromagnetic. This weak ferromagnetism (WF) is present in other materials and Dzyaloshinskii proposed that this could be accounted for by the presence of an extra term in the Hamiltonian beyond the isotropic antiferromagnetic (AF) Heisenberg term of the form D S, XSJ, where S; and S are spins at the sites i and j. He pointed out that this contribution is not forbidden by symmetry in an expansion of the free energy if the symmetry of the system is sufficiently low. Moriya then showed that this extra term arises from the effect of the spin-orbit interaction on the superexchange characterized by the Heisenberg J.He showed that~D~-(b,g/g)J, where g is the value of the free-electron gyromagnetic ratio and bg was the shift in that value due to the spin-orbit interaction. He also gave rules for determining the direction of D from the symmetries of the spin system. This extra term, the Dzyaloshinskii-Moriya (DM) term, has been applied by a number of authors' ' to the description of WF and has more recently been used to describe the metamagnetism' or spin-Aop transition, the magnetoresistance, and the conductivity of undoped La2Cu04. In the present work we show that the inclusion of the original DM term, where 0 is taken to be a constant, in an effective spin Hamiltonian does not lead to a description of WF but that a generalization of the DM term, which is determined by the symmetry properties of the crystal structure, does lead to a net ferromagnetic moment in the ground state. We consider as an explicit example the CuO planes of La2Cu04 and show that the important symmetry of the crystal structure which leads to the CuO planes having a net ferromagnetic moment is that each Cu site should be a center of inversion. We note in passing that an alternative model for WF was introduced by Borovik-Romanov and Orlova" and is discussed in detail in Ref. 4. In this model WF arises because there are different g tensors for different sublattices.The WF is only manifest in applied fields and since there is evidence for WF in the absence of applied ma...