Stability of $\pi$ junction configurations in ferromagnet-superconductor heterostructures

Abstract

We investigate the stability of possible order parameter configurations in clean layered heterostructures of the $SFS...FS$ type, where $S$ is a superconductor and $F$ a ferromagnet. We find that for most reasonable values of the geometric parameters (layer thicknesses and number) and of the material parameters (such as magnetic polarization, wavevector mismatch, and oxide barrier strength) several solutions of the {\it self consistent} microscopic equations can coexist, which differ in the arrangement of the sequence of ``0'' and ``$\pi$'' junction types (that is, with either same or opposite sign of the pair potential in adjacent $S$ layers). The number of such coexisting self consistent solutions increases with the number of layers. Studying the relative stability of these configurations requires an accurate computation of the small difference in the condensation free energies of these inhomogeneous systems. We perform these calculations, starting with numerical self consistent solutions of the Bogoliubov-de Gennes equations. We present extensive results for the condensation free energies of the different possible configurations, obtained by using efficient and accurate numerical methods, and discuss their relative stabilities. Results for the experimentally measurable density of states are also given for different configurations and clear differences in the spectra are revealed. Comprehensive and systematic results as a function of the relevant parameters for systems consisting of three and seven layers (one or three junctions) are given, and the generalization to larger number of layers is discussed.

arXiv comment17 pages, including 14 Figures. Higher resolution figures available from the authors

References in corpus (15)

• Coupling of two superconductors through a ferromagnet : evidence for a pi-junction
• Josephson current in superconductor-ferromagnet structures with a nonhomogeneous magnetization
• Periodic alternating $0,\pi$-junction structures as realization of $\varphi$-Josephson junctions
• Controllable Josephson current through a pseudo-spin-valve structure
• Proximity effects at ferromagnet-superconductor interfaces
• Josephson effect in double-barrier superconductor-ferromagnet junctions
• Dynamics of semifluxons in Nb long Josephson 0-pi junctions
• Free Energy of an Inhomogeneous Superconductor: a Wave Function Approach
• Proximity effects and characteristic lengths in ferromagnet-superconductor structures
• $\pi -0$ Transition in Superconductor-Ferromagnetic-Superconductor Junctions
• Layered ferromagnet-superconductor structures: the $\pi$ state and proximity effects
• Local spectroscopy of a proximity superconductor at very low temperature
• Analytical analysis of ground states on 0-$\pi$ long Josephson junctions
• Phase diagram of a superconductor / ferromagnet bilayer
• Quasiclassical theory of superconductivity: interfering paths

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• Local Density of States and Order Parameter Configurations in Layered Ferromagnet-Superconductor Structures
• Phase separation and proximity effects in itinerant ferromagnet-superconductor heterostructures