The interplay between superconductivity and magnetism gives rise to many intriguing and exciting phenomena. In this Letter we report about a novel manifestation of this interplay: a temperature induced phase transition between different spontaneous vortex phases in lead superconducting films with embedded magnetic nanoparticles. Unlike common vortices in superconductors the vortex phase appears without any applied magnetic field. The vortices nucleate exclusively due to the stray field of the magnetic nanoparticles, which serve the dual role of providing the internal field and simultaneously acting as pinning centers. As in usual superconductors, one can move the spontaneous vortices with an applied electric current. Transport measurements reveal dynamical phase transitions that depend on temperature (T) and applied field (H) and support the obtained (H-T) phase diagram. In particular, we used a scaling analysis to characterize a transition from a liquid to a novel disordered solid resembling a vortex glass.
The mechanism of the interplay between superconductivity and magnetism is one of the intriguing and challenging problems in physics. Theory has predicted that the ferromagnetic order can coexist with the superconducting order in the form of a spontaneous vortex phase in which magnetic vortices nucleate in the absence of an external field. However, there has been no rigorous demonstration of spontaneous vortices by bulk magnetic measurements. Here we show the results of experimental observations of spontaneous vortices using a superconductor/ferromagnet fractal nanocomposite, in which supercond…
Recently, interest in Superconductor (S)-Normal (N) interfaces was renewed by the observation of exotic proximity effects in various systems, including S/semiconductor, S/ferromagnet, and S/topological insulator. In general, the proximity effect is enhanced in transparent weak links where coherent Andreev reflection is possible. Also, it is a common knowledge that the proximity effect is, by definition, is a localized phenomenon that can only be active in each S/N interface region. However, here we show that a three-dimensional (3D) macroscale proximity effect is realized in few-micrometer-thi…
We present the generalized quasiclassical theory of the long-range superconducting proximity effect in heterostructures with strong ferromagnets, where the exchange splitting is of the order of Fermi energy. In the ferromagnet the propagation of spin-triplet Cooper pairs residing on the spin-split Fermi surfaces is shown to be governed by the spin-dependent Abelian gauge field which results either from the spin-orbital coupling or from the magnetic texture. The additional gauge field enters into the quasiclassical equations in superposition with the usual electromagnetic vector potential and r…
We investigate superconducting phase transition in superconductor(S)/ferromagnet(F) bilayer with Rasba spin-orbit interaction at S/F interface. This spin-orbit coupling produces spontaneous supercurrents flowing inside the atomic-thickness region near the interface, which are compensated by the screening Meissner currents [S. Mironov and A. Buzdin, Phys. Rev. Lett \textbf{118}, 077001 (2017)]. In the case of thin superconducting film the emergence of the spontaneous surface currents causes the increase of the superconducting critical temperature and we calculate the actual value of the critica…
Using low-temperature Magnetic Force Microscopy (MFM) we provide direct experimental evidence for spontaneous vortex phase (SVP) formation in EuFe$_2$(As$_{0.79}$P$_{0.21}$)$_2$ single crystal with the superconducting $T^{\rm 0}_{\rm SC}=23.6$~K and ferromagnetic $T_{\rm FM}\sim17.7$~K transition temperatures. Spontaneous vortex-antivortex (V-AV) pairs are imaged in the vicinity of $T_{\rm FM}$. Also, upon cooling cycle near $T_{\rm FM}$ we observe the first-order transition from the short period domain structure, which appears in the Meissner state, into the long period domain structure with …
I apply the recently developed formalism of generalized quasiclassical theory to show that using hybrid superconducting systems with non-collinear strong ferromagnets one can realize the Josephson junction between Berezinskii-type superconductors. The reported calculation reproduces main features observed in the recent experiment, namely the the slightly asymmetric double-slit Fraunhofer interference pattern of the Josephson current through the ferromagnetic vortex. The double-slit structure results from the spatially inhomogeneous Berezinskii state with the amplitude controlled by the local a…
On the dc Magnetization, Spontaneous Vortex State and Specific Heat in the superconducting state of the weakly ferromagnetic superconductor RuSr$_{2}$GdCu$_{2}$O$_{8}$
Spontaneous vortex phase (SVP) is an exotic quantum matter in which quantized superconducting vortices form in the absence of external magnetic field. Although being predicted theoretically nearly 40 years ago, its rigorous experimental verification still appears to be lacking. Here we present low-field magnetic measurements on single crystals of the iron-based ferromagnetic superconductor Eu(Fe$_{0.91}$Rh$_{0.09}$)$_{2}$As$_{2}$ which undergoes a superconducting transition at $T_\mathrm{sc}$ = 19.6 K followed by a magnetic transition at $T_\mathrm{m}$ = 16.8 K. We observe a characteristic fir…
Using the Gorkov equations, we provide an exact solution for a one-dimensional model of superconductivity in the presence of a conical helicoidal exchange field. Due to the special type of symmetry of the system, the superconducting transition always occurs into a nonuniform superconducting phase (in contrast with the Fulde-Ferrell-Larkin-Ovchinnikov state, which appears only at low temperatures). We directly demonstrate that the uniform superconducting state in our model carries a current and thus does not correspond to the ground state. We study in the framework of the Bogoliubov-de Gennes a…
The theoretical description and the survey of physical properties of superconducting states in the uranium ferromagnetic materials are presented. On the basis of microscopic theory is shown that the coupling between the electrons in these ferromagnetic metals by means of magnetization fluctuations gives rise the triplet pairing superconducting state and the general form of the order parameter dictated by the symmetry is established. The theory allows to explain some specific observations including peculiar phenomenon of reentrant superconductivity in URhGe in magnetic field perpendicular to th…
Ferromagnetic superconductor URhGe has orthorhombic structure and possesses spontaneous magnetisation along the c-axis. Magnetic field directed along the $b$-axis suppresses ferromagnetism in $c$-direction and leads to a metamagnetic transition into polarised paramagnetic state in the $b$-direction. The theory of these phenomena based on the specific magnetic anisotropy of this material in $(b,c)$ plane is given. Line of the first order metamagnetic transition ends at a critical point. The Van der Waals - type description of behaviour of physical properties near this point is developed. The tr…
