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ABSTRACT: We study various aspects of proximity effects in $F/S$
(Ferromagnet/Superconductor) bilayers, where $F$ has a spiral magnetic texture
such as that found in Holmium, Erbium and other materials, and $S$ is a
conventional s-wave superconductor. We numerically solve the Bogoliubov-de
Gennes (BdG) equations self-consistently and use the solutions to compute
quantities relevant to the proximity effects in these bilayers. We obtain the
relation between the superconducting transition temperature $T_c$ and the
thicknesses $d_F$ of the magnetic layer by solving the linearized BdG
equations. We find that the $T_c(d_F)$ curves include multiple oscillations.
Moreover, the system may be reentrant not only with $d_F$, as is the case when
the magnet is uniform, but with temperature $T$: the superconductivity
disappears in certain ranges of $d_F$ or $T$. The $T$ reentrance occurs when
$d_F$ is larger than the spatial period of the conical exchange field. We
compute the condensation free energies and entropies from the full BdG
equations and find the results are in agreement with $T_c$ values obtained by
linearization. The inhomogeneous nature of the magnet makes it possible for all
odd triplet pairing components to be induced. We have investigated their
properties and found that, as compared to the singlet amplitude, both the $m=0$
and $m=\pm 1$ triplet components exhibit long range penetration. For nanoscale
bilayers, the proximity lengths for both layers are also obtained. These
lengths oscillate with $d_F$ and they are found to be long range on both sides.
These results are shown to be consistent with recent experiments. We also
calculate the reverse proximity effect described by the three dimensional local
magnetization, and the local DOS, which reveals important energy resolved
signatures associated with the proximity effects.
10/2012;
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ABSTRACT: We report the results of a study of superconducting proximity effects in
clean Ferromagnet/Ferromagnet/Superconductor (${\rm F_1F_2S}$)
heterostructures, where the pairing state in S is a conventional singlet
s-wave. We numerically find the self-consistent solutions of the Bogoliubov-de
Gennes (BdG) equations and use these solutions to calculate the relevant
physical quantities. By linearizing the BdG equations, we obtain the
superconducting transition temperatures $T_c$ as a function of the angle
$\alpha$ between the exchange fields in $\rm F_1$ and $\rm F_2$. We find that
the results for $T_c(\alpha)$ in ${\rm F_1F_2S}$ systems are clearly different
from those in ${\rm F_1 S F_2}$ systems, where $T_c$ monotonically increases
with $\alpha$ and is highest for antiparallel magnetizations. Here,
$T_c(\alpha)$ is in general a non-monotonic function, and often has a minimum
near $\alpha \approx 80^{\circ}$. For certain values of the exchange field and
layer thicknesses, the system exhibits reentrant superconductivity with
$\alpha$: it transitions from superconducting to normal, and then returns to a
superconducting state again with increasing $\alpha$. This phenomenon is
substantiated by a calculation of the condensation energy. We compute, in
addition to the ordinary singlet pair amplitude, the induced odd triplet
pairing amplitudes. The results indicate a connection between equal-spin
triplet pairing and the singlet pairing state that characterizes $T_c$. We find
also that the induced triplet amplitudes can be very long-ranged in both the S
and F sides and characterize their range. We discuss the average density of
states for both the magnetic and the S regions, and its relation to the pairing
amplitudes and $T_c$. The local magnetization vector, which exhibits reverse
proximity effects, is also investigated.
07/2012;
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ABSTRACT: We study a bilayer consisting of an ordinary superconductor and a magnet with a spiral magnetic structure of the Ho type. We use a self-consistent solution of the Bogolioubov-de Gennes equations to evaluate the pair amplitude, the transition temperature, and the thermodynamic functions, namely, the free energy and entropy. We find that for a range of thicknesses of the magnetic layer the superconductivity is reentrant with temperature T: as one lowers T the system turns superconducting, and when T is further lowered it turns normal again. This behavior is reflected in the condensation free energy and the pair potential, which vanish both above the upper transition and below the lower one. The transition is strictly reentrant: the low and high temperature phases are the same. The entropy further reveals a range of temperatures where the superconducting state is less ordered than the normal one.
Physical Review Letters 03/2012; 108(11):117005. · 7.37 Impact Factor
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ABSTRACT: We study a bilayer consisting of an ordinary superconductor and a magnet with
a spiral magnetic structure of the {\rm Ho} type. We use a self consistent
solution of the Bogolioubov-de Gennes equations to evaluate the pair amplitude,
the transition temperature, and the thermodynamic functions, namely, the free
energy and entropy. We find that for a range of thicknesses of the magnetic
layer the superconductivity is reentrant with {\it temperature} $T$: as one
lowers $T$ the system turns superconducting, and when $T$ is further lowered it
turns normal again. This behavior is reflected in the condensation free energy
and the pair potential, which vanish both above the upper transition and below
the lower one. The transition is strictly reentrant: the low and high
temperature phases are the same. The entropy further reveals a range of
temperatures where the superconducting state is {\it less ordered} than the
normal one.
11/2011;
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ABSTRACT: We study proximity effects in clean nanoscale superconductor-normal
metal-superconductor (S$\mid$N$\mid$S) graphene heterostructures using a
self-consistent numerical solution to the continuum Dirac Bogoliubov-de Gennes
(DBdG) equations. We obtain results for the pair amplitude and the local
density of states (DOS), as a function of doping and of the geometrical
parameters determining the width of the structures. The superconducting
correlations are found to penetrate the normal graphene layers even when there
is extreme mismatch in the normal and superconducting doping levels, where
specular Andreev reflection dominates. The local DOS exhibits peculiar
features, which we discuss, arising from the Dirac cone dispersion relation and
from the interplay between the superconducting and Thouless energy scales. The
corresponding characteristic energies emerge in the form of resonant peaks in
the local DOS, that depend strongly on the doping level, as does the energy
gap, which declines sharply as the relative difference in doping between the S
and N regions is reduced. We also linearize the DBdG equations and develop an
essentially analytical method that determines the critical temperature $T_c$ of
an \sns nanostructure self-consistently. We find that for S regions that occupy
a fraction of the coherence length, $T_c$ can undergo substantial variations as
a function of the relative doping. At finite temperatures and by manipulating
the doping levels, the self consistent pair amplitudes reveal dramatic
transitions between a superconducting and resistive normal state of the
structure. Such behavior suggests the possibility of using the proposed system
as a carbon-based superconducting switch, turning superconductivity on or off
by tuning the relative doping levels.
05/2011;
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ABSTRACT: The superconducting transition temperature T(c) of a ferromagnet (F)-superconductor (S)-ferromagnet trilayer depends on the mutual orientation of the magnetic moments of the F layers. This effect has been previously observed in F/S/F systems as a T(c) difference between parallel and antiparallel configurations of the F layers. Here we report measurements of T(c) in CuNi/Nb/CuNi trilayers as a function of the angle between the magnetic moments of the CuNi ferromagnets. The observed angular dependence of T(c) is in qualitative agreement with a F/S proximity theory that accounts for the odd triplet component of the condensate predicted to arise for noncollinear orientation of the magnetic moments of the F layers.
Physical Review Letters 11/2010; 105(20):207002. · 7.37 Impact Factor
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ABSTRACT: We study triplet pairing correlations induced in an SFS trilayer (where F is a ferromagnet and S an ordinary s-wave superconductor) by spin flip scattering at the interfaces. We derive and solve self consistently the appropriate Bogoliubov-de Gennes equations in the clean limit. We find that the spin flip scattering generates $m=\pm 1$ triplet correlations, odd in time. We study the general spatial behavior of these and of $m=0$ correlations as a function of position and of spin-flip strength, $H_{spin}$. We concentrate on the case where the ferromagnet is half-metallic. We find that for certain values of $H_{spin}$, the triplet correlations pervade the magnetic layer and can penetrate deeply into the superconductor. The behavior we find depends very strongly on whether the singlet order parameter is in the 0 or $\pi$ state, which must in turn be determined self-consistently. We also present results for the density of states (DOS) and for the local magnetization, which, due to spin-flip processes, is not in general aligned with the magnetization of the half metal, and near the interfaces, rotates as a function of position and $H_{spin}$. The average DOS in both F and S is shown to exhibit various subgap bound states positioned at energies that depend strongly on the particular junction state and the spin Comment: 14 pages including figures (some compressed). Good quality figures available from authors
07/2009;
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ABSTRACT: We study induced triplet pairing correlations in clean ferromagnet/superconductor/ferromagnet heterostructures. The pairing state in the superconductor is the conventional singlet s-wave, and the angle $\alpha$ between the magnetizations of the two ferromagnetic layers is arbitrary. We use a numerical fully self-consistent solution of the microscopic equations and obtain the time-dependent triplet correlations via the Heisenberg equations of motion. We find that in addition to the usual singlet correlations, triplet correlations, odd in time as required by the Pauli principle, are induced in both the ferromagnets and the superconductor. These time-dependent correlations are largest at times of order of the inverse of the Debye cutoff frequency, $\omega_D$, and we find that within that time scale they are often spatially very long ranged. We discuss the behavior of the characteristic penetration lengths that describe these triplet correlations. We also find that the ferromagnets can locally magnetize the superconductor near the interface, and that the local magnetization then undergoes strongly damped oscillations. The local density of states exhibits a variety of energy signatures, which we discuss, as a function of ferromagnetic strength and $\alpha$. Comment: 12 pages including 11 figures
03/2008;
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ABSTRACT: We study triplet pairing correlations in clean ferromagnet (F)/superconductor (S) nanojunctions, via fully self-consistent solution of the Bogoliubov-de Gennes equations. We consider FSF trilayers, with S being an s-wave superconductor, and an arbitrary angle alpha between the magnetizations of the two F layers. We find that contrary to some previous expectations, triplet correlations, odd in time, are induced in both the S and F layers in the clean limit. We investigate their behavior as a function of time, position, and alpha. The triplet amplitudes are largest at times on the order of the inverse Debye frequency, and at that time scale they are long-ranged in both S and F. The zero temperature condensation energy is found to be lowest when the magnetizations are antiparallel.
Physical Review Letters 10/2007; 99(12):127002. · 7.37 Impact Factor
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ABSTRACT: We study the thermodynamics of clean, layered superconductor/ferromagnet nanostructures using fully self consistent methods to solve the microscopic Bogoliubov-deGennes equations. From these self-consistent solutions the condensation free energies are obtained. The trilayer SFS junction is studied in particular detail: first order transitions between 0 and $\pi$ states as a function of the temperature $T$ are located by finding where the free energies of the two phases cross. The occurrence of these transitions is mapped as a function of the thickness $d_F$ of the F layer and of the Fermi wavevector mismatch parameter $\Lambda$. Similar first order transitions are found for systems with a larger number of layers: examples are given in the 7 layer (3 junction) case. The latent heats associated with these phase transitions are evaluated and found to be experimentally accessible. The transition temperature to the normal state is calculated from the linearized Bogoliubov-deGennes equations and found to be in good agreement with experiment. Thus, the whole three dimensional phase diagram in $T,d_F,\Lambda$ space can be found. The first order transitions are associated with dips in the transition temperature $T_c$ to the non-superconducting state, which should facilitate locating them. Results are given also for the magnetic moment and the local density of states (DOS) at the first order transition.
09/2006;
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ABSTRACT: We study the thermodynamics of clean structures composed of superconductor (S) and ferromagnet (F) layers and consisting of one or more SFS junctions. We use fully self consistent numerical methods to compute the condensation free energies of the possible order parameter configurations as a function of temperature $T$. As $T$ varies, we find that there are phase transitions between states characterized by different junction configurations (denoted as ``0'' or ``$\pi$'' according to the phase difference of the order parameter in consecutive S layers). We show that these transitions are of first order. We calculate the associated latent heats and find them to be measurable. Comment: 4 pages including 3 figures. RevTeX
12/2005;
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ABSTRACT: We study clean ferromagnet-superconductor-ferromagnet (FSF) nanostructures in which the magnetization of the F layers can be parallel (P) or antiparallel (AP). We consider the case where the thickness of the S layer is of order of the coherence length, with thinner F layers. We find that reversing the direction of the magnetization in one of the F layers leads in general to drastic changes in the superconductor's state. Under a wide variety of conditions, the AP geometry favors superconductivity. Magnetization reversal in one of the F layers can lead to the superconductivity turning on and off, or to switching between different states. Our results are obtained via self consistent solution of the Bogoliubov-de Gennes equations and evaluation of the condensation energies of the system. Comment: 4 pages, including 4 figures
06/2005;
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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. Comment: 17 pages, including 14 Figures. Higher resolution figures available from the authors
04/2004;
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ABSTRACT: We investigate clean mutilayered structures of the SFS and SFSFS type, (where the S layer is intrinsically superconducting and the F layer is ferromagnetic) through numerical solution of the self-consistent Bogoliubov-de Gennes equations for these systems. We obtain results for the pair amplitude, the local density of states, and the local magnetic moment. We find that as a function of the thickness $d_F$ of the magnetic layers separating adjacent superconductors, the ground state energy varies periodically between two stable states. The first state is an ordinary "0-state", in which the order parameter has a phase difference of zero between consecutive S layers, and the second is a "$\pi$-state", where the sign alternates, corresponding to a phase difference of $\pi$ between adjacent S layers. This behavior can be understood from simple arguments. The density of states and the local magnetic moment reflect also this periodicity. Comment: 12 pages, 10 Figures
07/2003;
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ABSTRACT: The magnetic field and temperature dependencies of the magnetic moments of superconducting crystals of ${\rm V_{3}Si}$ have been studied. In a constant magnetic field and at temperatures somewhat below the superconducting transition temperature, the moments are hysteretic in temperature. However the magnetic moment-magnetic field isotherms are reversible and exhibit features that formally resemble the pressure-volume isotherms of the liquid-gas transition. This suggests the existence of a first-order phase transition, a two-phase regime, and a critical point in the superconducting phase diagram. The entropy change, determined from the data using the Clausius-Clapeyron equation, is consistent with estimates based on the difference in the vortex densities of the two phases.
07/2002;
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ABSTRACT: We present an extensive theoretical investigation of the proximity effects that occur in Ferromagnet/Superconductor ($F/S$) systems. We use a numerical method to solve self consistently the Bogoliubov-de Gennes equations in the continuum. We obtain the pair amplitude and the local density of states (DOS), and use these results to extract the relevant lengths characterizing the leakage of superconductivity into the magnet and to study spin splitting into the superconductor. These phenomena are investigated as a function of parameters such as temperature, magnet polarization, interfacial scattering, sample size and Fermi wavevector mismatch, all of which turn out to have important influence on the results. These comprehensive results should help characterize and analyze future data and are shown to be in agreement with existing experiments. Comment: 24 pages, including 26 figures
05/2002;
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ABSTRACT: We study proximity effects at ferromagnet superconductor interfaces by self-consistent numerical solution of the Bogoliubov-de Gennes equations for the continuum, without any approximations. Our procedures allow us to study systems with long superconducting coherence lengths. We obtain results for the pair potential, the pair amplitude, and the local density of states. We use these results to extract the relevant proximity lengths. We find that the superconducting correlations in the ferromagnet exhibit a damped oscillatory behavior that is reflected in both the pair amplitude and the local density of states. The characteristic length scale of these oscillations is approximately inversely proportional to the exchange field, and is independent of the superconducting coherence length in the range studied. We find the superconducting coherence length to be nearly independent of the ferromagnetic polarization. Comment: 13 Pages total. Compressed .eps figs might display poorly, but will print fine
07/2001;
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ABSTRACT: We examine recent high-precision experimental data on the magnetic field, ${\bf H}$, dependence of the penetration depth $\lambda(H)$ in $\rm{YBa_2Cu_3O_{7-\delta}}$ (YBCO) for several field directions in the $a-b$ plane. In a new theoretical analysis that incorporates the effects of orthorhombic symmetry, we show that the data at sufficiently high magnetic fields and low temperatures are in quantitative agreement with the theoretical predictions of the nonlinear Meissner effect. Comment: 4 text pages plus 3 postscript figures
11/2000;
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ABSTRACT: We examine the Meissner state nonlinear electrodynamic effects on the field and angular dependence of the low temperature penetration depth, $\lambda$, of superconductors in several kinds of unconventional pairing states, with nodes or deep minima (``quasinodes'') in the energy gap. Our calculations are prompted by the fact that, for typical unconventional superconducting material parameters, the predicted size of these effects for $\lambda$ exceeds the available experimental precision for this quantity by a much larger factor than for others. We obtain expressions for the nonlinear component of the penetration depth, $\Delta\lambda$, for different two- and three- dimensional nodal or quasinodal structures. Each case has a characteristic signature as to its dependence on the size and orientation of the applied magnetic field. This shows that $\Delta\lambda$ measurements can be used to elucidate the nodal or quasinodal structure of the energy gap. For nodal lines we find that $\Delta\lambda$ is linear in the applied field, while the dependence is quadratic for point nodes. For layered materials with $\rm{YBa_2Cu_3O_{7-\delta}}$ (YBCO) type anisotropy, our results for the angular dependence of $\Delta\lambda$ differ greatly from those for tetragonal materials and are in agreement with experiment. For the two- and three- dimensional quasinodal cases, $\Delta\lambda$ is no longer proportional to a power of the field and the field and angular dependences are not separable, with a suppression of the overall signal as the node is filled in. Comment: 16 pages plus nine figures
07/2000;
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ABSTRACT: We consider the Maxwell-London electrodynamics of three dimensional superconductors in p-wave pairing states with nodal points or lines in the energy gap. The current-velocity relation is then nonlinear in the applied field, cubic for point nodes and quadratic for lines. We obtain explicit angular and depth dependent expressions for measurable quantities such as the transverse magnetic moment, and associated torque. These dependences are different for point and line nodes and can be used to distinguish between different order parameters. We discuss the experimental feasibility of this method, and bring forth its advantages, as well as limitations that might be present. Comment: Fourteen pages RevTex plus four postscript figures
03/2000;
