A system exhibiting multiple simultaneously broken symmetries offers the opportunity to influence physical phenomena such as tunneling currents by means of external control parameters. In this paper, we consider the broken SU (2) (internal spin) symmetry of ferromagnetic systems coexisting with i) the broken U (1) symmetry of superconductors and ii) the broken spatial inversion symmetry induced by a Rashba term in a spin-orbit coupling Hamiltonian. In order to study the effect of these broken symmetries, we consider tunneling currents that arise in two different systems; tunneling junctions consisting of non-unitary spin-triplet ferromagnetic superconductors and junctions consisting of ferromagnets with spin-orbit coupling. In the former case, we consider different pairing symmetries in a model where ferromagnetism and superconductivity coexist uniformly. An interplay between the relative magnetization orientation on each side of the junction and the superconducting phase difference is found, similarly to that found in earlier studies on spin-singlet superconductivity coexisting with spiral magnetism. This interplay gives rise to persistent spin-and charge-currents in the absence of an electrostatic voltage that can be controlled by adjusting the relative magnetization orientation on each side of the junction. In the second system, we study transport of spin in a system consisting of two ferromagnets with spin-orbit coupling separated by an insulating tunneling junction. A persistent spin-current across the junction is found, which can be controlled in a well-defined manner by external magnetic and electric fields. The behavior of this spin-current for important geometries and limits is studied.

We have performed large-scale Monte Carlo simulations on a two-dimensional generalized Ashkin-Teller model to calculate the thermodynamic properties in the critical region near its transitions. The Ashkin-Teller model has a pair of Ising spins at each site which interact with neighboring spins through pair-wise and four-spin interactions. The model represents the interactions between orbital current loops in CuO 2 plaquettes of high-T c cuprates, which order with a staggered magnetization M s inside each unit cell in the underdoped region of the phase diagram below a temperature T ‫ء‬ ͑x͒ which depends on doping. The pair of Ising spins per unit cell represents the directions of the currents in the links of the current loops. The generalizations are the inclusion of anisotropy in the pair-wise nearest-neighbor current-current couplings consistent with the symmetries of a square lattice and the next-nearest-neighbor pair-wise couplings. We use the Binder cumulant to estimate the correlation length exponent and the order-parameter exponent ␤. Our principal results are that in a range of parameters; the Ashkin-Teller model as well as its generalization has an order-parameter susceptibility which diverges as T → T ‫ء‬ and an order parameter below T ‫ء‬ . Importantly, however, there is no divergence in the specific heat. This puts the properties of the model in accord with the experimental results in the underdoped cuprates. We also calculate the magnitude of the "bump" in the specific heat in the critical region to put limits on its observability. Finally, we show that the staggered magnetization couples to the uniform magnetization M 0 such that the latter has a weak singularity at T ‫ء‬ and also displays a wide critical region, also in accord with recent experiments.

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.

Recent findings of superconductors that simultaneously exhibit multiple spontaneously broken symmetries, such as ferromagnetic order or lack of an inversion center and even combinations of such broken symmetries, have led to much theoretical and experimental research. We consider quantum transport in a junction consisting of a ferromagnetic metal and a non-unitary ferromagnetic superconductor. It is shown that the conductance spectra provides detailed information about the superconducting gaps, and is thus helpful in determining the pairing symmetry of the Cooper pairs in ferromagnetic superconductor.

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