We present a model for the fully developed proximity effect in superconductor-ferromagnet heterostructures. Within the circuit-theory approximation, we evaluate the Green functions, the density of states, and the Josephson current which depend essentially on the magnetic configuration. DOI: 10.1103/PhysRevLett.98.077003 PACS numbers: 74.78.Fk, 72.25.Ba, 74.50.+r The research of heterostructures that combine superconducting (S) and ferromagnetic (F) elements gives insight into the problem of the mutual influence of superconductivity and ferromagnetism, allows realization of exotic S states such as the Larkin-Ovchinnikov-Fulde-Ferrell state [1] and triplet ordering [2], and promises applications that utilize the spin degree of freedom [3]. While this research started more than three decades ago [4], interest in the above topics has produced important recent developments, both theoretical and experimental. Those concern Josephson junctions [5,6], triplet superconductivity [2,6,7], and Josephson spin valves [8,9].We refer to the proximity effect that takes place in nonmagnetic dirty superconducting/normal (S/N) structures as ''conventional.'' In the normal part of a S/N structure, S correlations persist at distances of the order of normal-metal coherence length N . This length scale can grow large at sufficiently small temperatures T. In a diffusive material, N @D=2k B T p , D being the diffusivity. In contrast to this, S correlations in a ferromagnet, where an exchange field h is present, are quenched at a much shorter scale h @D=h p . Hence one might conclude that the proximity and Josephson effects are strongly suppressed in S/F heterostructures. However, some experiments [10] seem to contradict this statement, indicating proximity correlations at a much larger scale. Although these experiments may be explained by interface effects [11], they have motivated a proposal of an interesting mechanism for long-range proximity effect in ferromagnets [2,6]. It was shown that inhomogeneity in the direction of exchange field generates S correlations of two electrons with the same spin, i.e., triplet correlations. Such a triplet proximity effect (TPE) is not suppressed by an exchange field and penetrates the ferromagnet at the scale of N . Recently, a substantial Josephson current has been reported for a fully polarized ferromagnet [7]. The experiment can only be explained by TPE.An immediate problem is that the theoretical predictions so far have been elaborated by assuming that TPE is weak and can be treated perturbatively. This makes it difficult to determine an unambiguous experimental signature of TPE to distinguish it from the conventional effect. Experimentally, the Josephson current due to TPE [7] does not seem to be smaller than that due to a fully developed conventional proximity effect.In this work, we address a fully developed TPE, that is, the TPE that significantly changes the density of states (DOS) near the Fermi energy. We show that the DOS increases. This is in contrast with complete suppression of DOS...

This Letter presents a theoretical analysis of propagation of spin waves in a superconducting ferromagnet. The surface impedance was calculated for the case when the magnetization is normal to the sample surface. We found the frequencies at which the impedance and the power absorption have singularities related to the spin wave propagation, and determined the form of these singularities. With a suitable choice of parameters, there is a frequency interval in which two propagating spin waves of the same circular polarization are generated, one of them having a negative group velocity.PACS numbers: 74.25. Nf, 75.30.Ds, 76.50.+g, 74.25.Ha Coexistence of superconductivity (SC) and ferromagnetism (FM) has been a long-standing problem since the beginning of the modern theory of SC [1,2,3]. There has been a renewed interest to this problem, and SC-FM coexistence was discovered recently in various materials such as ruthenocuprates [4,5], ZrZn 2 [6], UGe 2 [7], and URhGe [8]. It was also suggested theoretically that in pwave superconductors, time reversal symmetry is broken, and a non-zero magnetic moment arises [9].The existence of the FM order in a superconductor is hidden by Meissner currents, which create a magnetic moment opposite to the spontaneous magnetic moment. Moreover, in the Meissner state SC eliminates another consequence of the FM order: the equilibrium domain structure [10]. However, the Meissner currents cannot shade such an important manifestation of the FM order as spin waves. A conventional technique to probe spin modes in ferromagnets, both insulators and metals, has been observation of Ferromagnetic Resonance (FMR) [11]. There are also reports on FMR observations in materials with SC-FM coexistence [12].In this work we theoretically investigated propagation of spin waves in a material, which possesses both SC and FM order and is irradiated by an electromagnetic (EM) wave. The first step in this direction was done by Ng and Varma [13], who studied the spectrum of spin waves interacting with vortex modes in the spontaneous vortex phase (mixed state in zero external magnetic field). Here we analyze the boundary problem for the Meissner state: how an incident EM wave can generate spin waves inside a sample. We solved the Landau-Lifshitz equation for the magnetization and the equations of London electrodynamics, assuming that the equilibrium magnetization is normal to the surface and there is no external static magnetic field and, as a result of it, no Meissner currents at equilibrium. We found the spectrum of spin waves for two cases, depending on the stiffness of the spin system. If the stiffness is large enough, the spectrum looks similar to that of a FM insulator, with the minimum wave frequency (threshold for spin wave propagation) equal to the frequency of the uniform FMR, i.e. corresponding to zero wave vector [11]. But the opposite case of small spin stiff-

We develop a theory for frictional drag between two 2D hole layers in a dilute bilayer GaAs hole system, including effects of hole-hole and hole-phonon interactions. Our calculations suggest significant enhancement of hole drag transresistivity over the corresponding electron drag results. This enhancement originates from the exchange induced renormalization of the single layer compressibility and the strong dependence of single layer conductivity on density. We also address the effect of hole-phonon interaction on the drag temperature dependence. Our calculated results are in reasonable quantitative agreement with recent experimental observations.

We study the ac Josephson effect in a superconductor-ferromagnet heterostructure with a variable magnetic configuration. The system supports triplet proximity correlations whose dynamics is coupled to the magnetic dynamics. This feedback dramatically modifies the behavior of the junction. The currentphase relation becomes double periodic at both very low and high Josephson frequencies ! J . At intermediate frequencies, the periodicity in ! J t may be lost. DOI: 10.1103/PhysRevLett.100.207001 PACS numbers: 74.78.Fk, 72.25.Ba, 74.50.+r Spin-dependent transport through hybrid structures combining ferromagnets (F) and normal metals has recently attracted a lot of interest, motivated by the prospect of potential technological applications in the field of spintronics [1]. Particular attention is given to two complementary effects involving mutual influence between electric current and magnetic configuration. The first is giant magnetoresistance [2] in which the conductance is much larger when different magnetic regions have their magnetic moments aligned than when they are antialigned. The opposite effect is the appearance of torques acting on magnetic moments when an electric current flows through the system [3]. These nonequilibrium current-induced torques appear due to nonconservation of spin currents accompanying a flow of charge through ferromagnetic regions. They allow manipulation of the magnetic configuration, including switching between the opposite directions or steady-state precession, without application of magnetic fields [4]. The two effects combined promise important practical applications in nonvolatile memory, programmable logic, and microwave oscillators.A conceptually different situation occurs when a ferromagnet is coupled to a superconductor (S), since the spin current through the superconducting part vanishes [5]. This additional constraint modifies the nonequilibrium torques, opening the possibility of perpendicular alignment of magnetic moments. Furthermore, if a magnetic structure is contacted by two superconductors, the proximity effect may be present, leading to a finite Josephson current through the structure at equilibrium. The torques generated by this current correspond to an equilibrium effective exchange interaction between the magnetic moments which can be controlled by the phase difference between the superconductors [6]. The same mechanism enables the reciprocal effect in which the supercurrent depends on the magnetic configuration.For a uniform ferromagnet, the observation of these effects requires a very thin magnetic layer, since the proximity effect is suppressed at short distances. However, in nonuniform ferromagnets, a long-range proximity effect can exist due to triplet superconducting correlations [7]. This triplet proximity effect (TPE) strongly enhances the associated Josephson current. It is important that TPE essentially depends on the magnetic configuration of the system [7]. Hence S/F multilayers exhibiting TPE are especially suitable for studying the Josephson-ind...

We present a theory of orbital magnetic dynamics for a chiral p-wave superconductor with broken time-reversal symmetry. In contrast to the common Landau-Lifshitz theory for spin ferromagnets, the case of orbital magnetism cannot be described in terms of local magnetization density. Hence it is impossible to define unambiguously the spontaneous magnetic moment: the latter would depend on conditions of its experimental investigation. As an example of this we consider orbital magnetization waves and the domain structure energy.PACS numbers: 74.20. Rp, 74.25.Ha, 74.25.Nf Superconductors with unconventional pairing mechanisms have attracted a lot of attention during the past decade. A prominent feature characteristic of unconventional superconductivity is the possibility of states with broken time-reversal symmetry (TRS), which is expressed in the presence of magnetic structure in these materials. Broken TRS has been detected in several superconductors, including . Such an order parameter has a non-zero orbital momentwhich should lead, in principle, to spontaneous magnetization like in usual ferromagnets. However, coexisting superconductivity screens out this magnetization, making its experimental detection rather difficult. As a possible way to overcome this difficulty, it was proposed [10] to perform microwave response measurements, where excitation of spin waves would provide an immediate signature for the presence of magnetic order. Previous works [9,10,11,12,13] which considered magnetic dynamics in superconductors with coexisting magnetism (SCFM), assumed a phenomenological model in which the magnetization was independent from the superconducting order parameter, and its dynamics was described by the Landau-Lifshitz equation (LL dynamics).[14] This model, however, is not so obvious for materials such as Sr 2 RuO 4 , where TRS is broken at the superconducting transition, and the magnetic properties are expected to stem from the orbital part of the multicomponent superconducting order parameter. Therefore a proper treatment of magnetic dynamics in such materials should derive it from the dynamics of the superconducting order parameter. An analogous derivation has been done [15] for the A phase of superfluid 3 He ( 3 He-A); then a modification of the theory taking into account the charge of Cooper pairs would yield magnetic orbital dynamics for an isotropic p-wave superconducting electron liquid. However, such a derivation cannot be applied directly to the case of a superconducting metal because of the crystal-field anisotropy.In this paper, we address this problem and derive an effective orbital magnetic dynamics for a p-wave superconductor in a strong crystal-field potential. The resulting dynamics is not equivalent to the phenomenological LL SCFM magnetization dynamics, except for some simple cases. Moreover, in general, it cannot be described in terms of local magnetization at all! Instead, we show that it can be described with the help of a unit vector l, corresponding to the angular momentum of Cooper pai...