Coexistence of superconductivity and ferromagnetism in ferromagnetic metals

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.     

Coexistence of superconductivity and ferromagnetism in two dimensions

Ferromagnetism is usually considered to be incompatible with conventional superconductivity, as it destroys the singlet correlations responsible for the pairing interaction. Superconductivity and ferromagnetism are known to coexist in only a few bulk rare-earth materials. Here we report evidence for their coexistence in a two-dimensional system: the interface between two bulk insulators, LaAlO(3) (LAO) and SrTiO(3) (STO), a system that has been studied intensively recently. Magnetoresistance, Hall, and electric-field dependence measurements suggest that there are two distinct bands of charge carriers that contribute to the interface conductivity. The sensitivity of properties of the interface to an electric field makes this a fascinating system for the study of the interplay between superconductivity and magnetism.     

Coexistence of ferromagnetism and superconductivity in Cu-rich lanthanum Cu-oxides

We have measured the zero field and field cooled magnetization of the lightly oxygen doped Cu-rich La₂CuO _{4 + δ} in a wide temperature range (5 K to 350 K). The data together with the evolution of the magnetic hysteresis loop suggest that the ferromagnetism with Curie temperature of 280 K coexists with superconductivity below the transition temperature ∼ 34 K. The coexistence occurs in the hole-rich clusters of size ? 150 nm, which are electronic phase separated from the hole-poor antiferromagnetic background. Received 17 October 2001     

Coexistence of ferromagnetism and superconductivity in Ni/Bi bilayers

In spite of a lack of superconductivity in bulk crystalline Bi, thin film Bi deposited on thin Ni underlayers are strong-coupled superconductors below approximately 4 K. We unambiguously demonstrate that by tuning the Ni thickness the competition between ferromagnetism and superconductivity in the Ni/Bi can be tailored. For a narrow range of Ni thicknesses, the coexistence of both a superconducting energy gap and conduction electron spin polarization are visible within the Ni side of the Ni/Bi bilayers, independent of any particular theoretical model. We believe that this represents one of the clearest observations of superconductivity and ferromagnetism coexisting.     

Coexistence of superconductivity and ferromagnetism in ferromagnet/superconductor proximity structures

The Nambu spinor Green's function approach is applied to calculating the density of states (DOS) and superconducting order parameter in normal-metal/insulator/ferromagnet/superconductor (NM/I/FM/SC) junctions. It is found that the s-wave superconductivity and ferromagnetism can coexist near the FM/SC interface, which is induced by proximity effect. On the SC side, the spin-dependent DOS appears both within and without the energy gap. On the FM side, the superconducting order parameter displays a damped oscillation and the DOS exhibits some superconducting behavior. The calculated result for the DOS in FM for “0 state” and “π state” can reproduce recent tunneling spectra in Al/Al₂O₃/PdNi/Nb tunnel junctions. Received 1st July 2002 Published online 19 November 2002     

Coexistence of superconductivity and ferromagnetism in hybrid rutheno-cuprate superconductors RuSr2RCu2O8

I consider the extended two-band s–f model with additional terms, describing inter-site Cooper pairs interaction between two-subsystems s and f, respectively. Following Green’s function technique and equation of motion method self-consistent equations for superconducting order parameter (Δ) and magnetic order parameter (m_f) are derived. The expressions for specific heat, density of states, and free energy are also derived. The theory has been applied to explain the coexistence of superconductivity and ferromagnetism in hybrid rutheno-cuprate superconductors RuSr₂RECu₂O₈ (RE = Gd, Eu). The theory shows that it is possible to become superconducting via a second order phase transition if the system is already ferromagnetic. The agreement between theory and experimental observations is quite satisfactory.     

Coexistence of superconductivity and magnetism

A model consisting of the B.C.S.-Hamiltonian and Zener's s-d exchange interaction is solved rigorously in the thermodynamic limit. Coexistence of superconductivity and magnetism is only possible for an impurity spin concentration smaller than a half at T ≠ 0.     

Competition between nuclear ferromagnetism and superconductivity

A qualitative theory of nuclear magnetism against a background of superconductivity in metals is proposed. Even though the superconducting transition temperature is much higher than the nuclear ordering temperature, nuclear ferromagnetism can partially or completely destroy superconductivity. An experimental method of determining the effective electron-nuclear spin-spin interaction constant for superconductors is discussed. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 10, 772–775 (25 May 1997)     

Coexistence of ferromagnetism and superconductivity close to a quantum phase transition: the Heisenberg- to Ising-type crossover

A microscopic mean-field theory of the phase coexistence between ferromagnetism and superconductivity in the weakly ferromagnetic itinerant electron system is constructed, while incorporating a realistic mechanism for superconducting pairing due to the exchange of critical spin fluctuations. The self-consistent solution of the resulting equations determines the superconducting transition temperature which is shown to depend strongly on the exchange splitting. The effect of phase crossover from isotropic (Heisenberg-like) to uniaxial (Ising-like) spin fluctuations near the quantum phase transition is analyzed and the generic phase diagram is obtained. This scenario is then applied to the case of itinerant ferromagnet ZrZn2, which sheds light on the proposed phase diagram of this compound. A possible explanation of superconductivity in UGe2 is also discussed.     

On the coexistence of superconductivity and ferromagnetism

The magnetic scattering of electrons is studied, paying special attention to the problem of coexistence of superconductivity and ferromagnetism. The utilized model consists of two electronic bands, one of which can become superconducting, and a system of localized spins. The calculated transition temperatures of the superconduction and the magnetic subsystems show regions of coexistence for not too large exchange interactions. Generally speaking, coexistence is favoured due to spin-orbit scattering as well as due to the interaction of the superconducting band with the normal band in certain cases.     

Coexistence of superconductivity and magnetic order

The microscopic theory of simple antiferromagnetic superconductors is extended to structures where the magnetic order is described by a spin-density wave. For the case where the magnetic system is inherently ferromagnetic, the free energy of the combined system is minimized with respect to the amplitude and the wave vector of the spin-density wave. It is found that the wave vector depends very weakly on temperature. We apply the theory to the coexistence region in ErRh₄B₄, finding a first-order re-entry transition.     

Coexistence problem of magnetism and superconductivity

The recent development of the problem of coexistence of magnetism and superconductivity will be reviewed. The possible coexistence of superconductivity with various types of magnetism carried by localized magnetic moments and itinerant electrons is critically discussed in connection with several existing materials such as rare earth ternary compounds [(RE)Mo₆S₈, (RE)Mo₆Se₈ and (RE)Rh₄B₄], newly synthesized organic superconductors [(TMTSF)₂X] and Y₉Co₇. In order to obtain a coherent picture for the understanding the rich phenomena associated with the interplay between two mutually exclusive types of long-range order, a unified point of view based on a key concept of the partial gapping model proposed by the author is introduced as a working hypothesis.     

Coexistence of superconductivity and magnetic order

Experimental work on systems showing evidence of the coexistence of superconductivity and magnetic order is reviewed. The presently known systems are shown to be “superconducting spin glasses” rather than “ferromagnetic superconductors”. In those systems where the magnetic order is expected to be long-ranged (up to now) superconductivity vanishes as soon as the magnetic order appears. But it is not excluded that magnetic order with a correlation length larger than the superconductive coherence length can coexist with superconductivity.     

Coexistence of s-wave superconductivity and antiferromagnetism

We study the phase diagram of a new model that exhibits a first order transition between s-wave superconducting and antiferromagnetic phases. The model, a generalized Hubbard model augmented with competing spin-spin and pair-pair interactions, was investigated using the projector quantum Monte Carlo method. Upon varying the Hubbard U from attractive to repulsive, we find a first order phase transition between superconducting and antiferromagnetic states.     

Magnetic nesting and coexistence of ferromagnetism and superconductivity

If the condition ε_σ(p)=ε_?σ(?p+nI/v_F) for magnetic nesting is fulfilled for the electron dispersion law with spin σ along a certain preferential direction n, ferromagnetism and the inhomogeneous superconducting state can coexist up to a very high magnetization I. This fact was used to explain the coexistence of ferromagnetism and superconductivity for layered cuprates of the RuSr₂GdCu₂O₈ type, which possess a finite, though rather high, critical magnetization, because the conditions for magnetic nesting are fulfilled only approximately.     

Possible phase change between itinerant ferromagnetism and superconductivity

It is pointed out theoretically that a single electron band model is able to exhibit the interchange of two phases: itenerant band ferromagnetism and superconductivity. Our theory is based on the molecular field approximation applied for a simplified electron-electron interaction. Possible phase changes are discussed in connection with two phase transitions of ferromagnetism and superconductivity in the intermetallic compound Y₄Co₃.     

Interplay between ferromagnetism and superconductivity in tunneling currents

We study tunneling currents in a model consisting of two nonunitary ferromagnetic spin-triplet superconductors separated by a thin insulating layer. We find a novel interplay between ferromagnetism and superconductivity, manifested in the Josephson effect. This offers the possibility of tuning dissipationless currents of charge and spin in a well-defined manner by adjusting the magnetization direction on either side of the junction.