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DOE OSTI2024

Readout of Oriented Triplet Excitons in Linear Acenes via Room-Temperature Electrically Detected Magnetic Resonance

In this study, optically generated molecular spin centers offer an attractive platform for room-temperature spintronic and quantum applications. The linear acene family of molecules are especially good candidates due to their efficient generation of highly polarized triplet excitons via singlet fission. However, the direct detection and manipulation of these spin centers in thin films via the electrical means desirable for ultimate microelectronic devices has proven challenging. In particular, highly oriented triplet features have previously been detected in crystalline anthracene but longer acenes reveal only doublet features in Electrically-Detected Magnetic Resonance (EDMR). In this work we present EDMR spectra of highly oriented triplet excitons in pentacene for the first time, using a host-guest style device made of tetracene and pentacene. The guest acts as an energetic trap site, permitting the isolation and detection of molecular triplets at room temperature. Modeling of these results shows that the observed resonance features correspond to triplet sublevel transitions on isolated pentacene guest molecules. Rotation of the applied field confirms the tendency of the linear acenes to self-orient with the longest molecular axis perpendicular to the device substrate. Lastly, we find the disappearance of resonant triplet features in the neat acenes is not primarily due to the effects of exciton delocalization, but a broader mechanism of spin relaxation primarily influenced by exciton diffusivity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Spatial separation of triplet excitons drives endothermic singlet fission

Molecules that undergo singlet fission, converting singlet excitons into pairs of triplet excitons, have potential as photovoltaic materials. The possible advantages of endothermic singlet fission (enhanced use of photon energy and larger triplet energies for coupling with common absorbers) motivated us to assess the role of exciton delocalization in the activation of this process. Here we report the synthesis of a series of linear perylene oligomers that undergo endothermic singlet fission and have endothermicities in the range 5-10 kBT at room temperature in solution. We study these compounds using transient spectroscopy and modelling to unravel the singlet and triplet dynamics. We show that the minimal number of coupled chromophores needed to undergo endothermic singlet fission is three, which provides sufficient statistical space for triplet excitons to separate and avoid annihilation - and a subsequent fast return to the singlet state. Our data additionally suggest that torsional motion of chromophores about the molecular axis following triplet-pair separation contributes to the increase in entropy, thus lengthening the triplet lifetime in longer oligomers.

14 SOLAR ENERGY↗

DOE OSTI2014

Triplet correlation functions in liquid water

Triplet correlations have been shown to play a crucial role in the transformation of simple liquids to anomalous tetrahedral fluids [M. Singh, D. Dhabal, A. H. Nguyen, V. Molinero, and C. Chakravarty, Phys. Rev. Lett. 112, 147801 (2014)]. Here we examine triplet correlation functions for water, arguably the most important tetrahedral liquid, under ambient conditions, using configurational ensembles derived from molecular dynamics (MD) simulations and reverse Monte Carlo (RMC) datasets fitted to experimental scattering data. Four different RMC data sets with widely varying hydrogen-bond topologies fitted to neutron and x-ray scattering data are considered [K. T. Wikfeldt, M. Leetmaa, M. P. Ljungberg, A. Nilsson, and L. G. M. Pettersson, J. Phys. Chem. B 113, 6246 (2009)]. Molecular dynamics simulations are performed for two rigid-body effective pair potentials (SPC/E and TIP4P/2005) and the monatomic water (mW) model. Triplet correlation functions are compared with other structural measures for tetrahedrality, such as the O–O–O angular distribution function and the local tetrahedral order distributions. In contrast to the pair correlation functions, which are identical for all the RMC ensembles, the O–O–O triplet correlation function can discriminate between ensembles with different degrees of tetrahedral network formation with the maximally symmetric, tetrahedral SYM dataset displaying distinct signatures of tetrahedrality similar to those obtained from atomistic simulations of the SPC/E model. Triplet correlations from the RMC datasets conform closely to the Kirkwood superposition approximation, while those from MD simulations show deviations within the first two neighbour shells. The possibilities for experimental estimation of triplet correlations of water and other tetrahedral liquids are discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Collider probes of real triplet scalar dark matter

We study discovery prospects for a real triplet extension of the Standard Model scalar sector at the Large Hadron Collider (LHC) and a possible future 100 TeV $\mathcal{pp}$ collider. We focus on the scenario in which the neutral triplet scalar is stable and contributes to the dark matter relic density. When produced in $\mathcal{pp}$ collisions, the charged triplet scalar decays to the neutral component plus a soft pion or soft lepton pair, yielding a disappearing charged track in the detector. We recast current 13 TeV LHC searches for disappearing tracks, and find that the LHC presently excludes a real triplet scalar lighter than 248 (275) GeV, for a mass splitting of 172 (160) MeV with $\mathcal{L}$ = 36 fb –1 . The reach can extend to 497 (520) GeV with the collection of 3000 fb –1 . We extrapolate the 13 TeV analysis to a prospective 100 TeV pp collider, and find that a ~ 3 TeV triplet scalar could be discoverable with $\mathcal{L}$ = 30 ab –1 , depending on the degree to which pile up effects are under control. We also investigate the dark matter candidate in our model and corresponding present and prospective constraints from dark matter direct detection. We find that currently XENON1T can exclude a real triplet dark matter lighter than ~ 3 TeV for a Higgs portal coupling of order one or larger, and the future XENON20T will cover almost the entire dark matter viable parameter space except for vanishingly small portal coupling.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Screened Range-Separated Hybrid Functional with Polarizable Continuum Model Overcomes Challenges in Describing Triplet Excitations in the Condensed Phase Using TDDFT

Long range-corrected (LRC) or range-separated hybrid (RSH) functionals where the long-range (LR) limit of electronic interactions is set to the exact exchange have been shown to correct the tendency of traditional density functional theory (DFT) to underestimate the frontier orbital gap. Consequently, the use of such functionals in calculating electronic excited states using linear response based time-dependent DFT (TDDFT) has been successful in correcting the tendency for underestimating the energies of charge transfer states by DFT-based calculations. More recently formulations of functionals that attenuate the LR limit to address condensed-phase effects to polarize the electronic density have been reported. In particular screened RSH (SRSH) combined with polarizable continuum model (PCM) was benchmarked successfully in reproducing the fundamental gap and charge transfer state energies of molecular systems in the condensed phase. Here we use SRSH-PCM to address triplet excited states, and show its success in obtaining correspondence of the low-lying triplet states to the singlet–triplet gap in a similar way that the fundamental orbital gap corresponds to electron removal and addition energies. Importantly, the accuracy of the SRSH-PCM in calculating triplet excitations stands on the polarization consistent framework in addressing the scalar dielectric constant and without affecting the optimal tuning by triplet energies. Finally, the prospect of even further improving the SRSH-PCM accuracy in calculating triplet states can be achieved by optimal tuning on the basis of the spin multiplicity gap.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Ultrafast Triplet Generation at the Lead Halide Perovskite/Rubrene Interface

Triplet sensitization of rubrene by bulk lead halide perovskites has recently resulted in efficient infrared-to-visible photon upconversion via triplet-triplet annihilation. Notably, this process can occur under solar relevant fluxes, potentially paving the way toward integration with photovoltaic devices. In order to further improve the upconversion efficiency, the fundamental photophysical pathways at the perovskite/rubrene interface must be clearly understood to maximize charge extraction. Here, we utilize ultrafast transient absorption spectroscopy to elucidate the processes underlying triplet generation at the perovskite/rubrene interface. In this work, our results point to a triplet generation mechanism based on hot carriers; thermally excited charge carriers in the perovskite cool more rapidly in the presence of rubrene, suggesting rapid extraction of these thermally excited carriers on the picosecond time scale. Subsequent triplet formation in rubrene is observed on a subnanosecond time scale.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2017

An assessment of low-lying excitation energies and triplet instabilities of organic molecules with an ab initio Bethe-Salpeter equation approach and the Tamm-Dancoff approximation

The accurate prediction of singlet and triplet excitation energies is an area of intense research of significant fundamental interest and critical for many applications. Most calculations of singlet and triplet energies use time-dependent density functional theory (TDDFT) in conjunction with an approximate exchange-correlation functional. In this work, we examine and critically assess an alternative method for predicting low-lying neutral excitations with similar computational cost, the ab initio Bethe-Salpeter equation (BSE) approach, and compare results against high-accuracy wavefunction-based methods. We consider singlet and triplet excitations of 27 prototypical organic molecules, including members of Thiel’s set, the acene series, and several aromatic hydrocarbons exhibiting charge-transfer-like excitations. Analogous to its impact in TDDFT, we find that the Tamm-Dancoff approximation (TDA) overcomes triplet instabilities in the BSE approach, improving both triplet and singlet energetics relative to higher level theories. Lastly, we find that BSE-TDA calculations built on effective DFT starting points, such as those utilizing optimally tuned range-separated hybrid functionals, can yield accurate singlet and triplet excitation energies for gas-phase organic molecules.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2019

Quintet-triplet mixing determines the fate of the multiexciton state produced by singlet fission in a terrylenediimide dimer at room temperature

Singlet fission (SF) is a photophysical process in which one of two adjacent organic molecules absorbs a single photon, resulting in rapid formation of a correlated triplet pair (T 1 T 1 ) state whose spin dynamics influence the successful generation of uncorrelated triplets (T 1 ). Femtosecond transient visible and near-infrared absorption spectroscopy of a linear terrylene-3,4:11,12-bis(dicarboximide) dimer (TDI 2 ), in which the two TDI molecules are directly linked at one of their imide positions, reveals ultrafast formation of the (T 1 T 1 ) state. The spin dynamics of the (T 1 T 1 ) state and the processes leading to uncoupled triplets (T 1 ) were studied at room temperature for TDI 2 aligned in 4-cyano-4′-pentylbiphenyl (5CB), a nematic liquid crystal. Time-resolved electron paramagnetic resonance spectroscopy shows that the (T 1 T 1 ) state has mixed 5 (T 1 T 1 ) and 3 (T 1 T 1 ) character at room temperature. This mixing is magnetic field dependent, resulting in a maximum triplet yield at ∼200 mT. The accessibility of the 3 (T 1 T 1 ) state opens a pathway for triplet–triplet annihilation that produces a single uncorrelated T 1 state. The presence of the 5 (T 1 T 1 ) state at room temperature and its relationship with the 1 (T 1 T 1 ) and 3 (T 1 T 1 ) states emphasize that understanding the relationship among different (T 1 T 1 ) spin states is critical for ensuring high-yield T 1 formation from singlet fission.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Enhanced spin-triplet pairing in magnetic junctions with s -wave superconductors

A common path to superconducting spintronics, Majorana fermions, and topologically protected quantum computing relies on spin-triplet superconductivity. While naturally occurring spin-triplet pairing is elusive, and even common spin-triplet candidates, such as Sr 2 RuO 4 , support alternative explanations, proximity effects in heterostructures can overcome these limitations. It is expected that robust spin-triplet superconductivity in magnetic junctions should rely on highly spin-polarized magnets or complex magnetic multilayers. Instead, we predict that the interplay of interfacial spin-orbit coupling and the barrier strength in simple magnetic junctions, with only a small spin polarization and s -wave superconductors, can lead to nearly complete spin-triplet superconducting proximity effects. This peculiar behavior arises from an effective perfect transparency: interfacial spin-orbit coupling counteracts the native potential barrier for states of a given spin and wave vector. We demonstrate that the enhanced spin-triplet regime is characterized by a huge increase in conductance magnetoanisotropy, orders of magnitude larger than in the normal state.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2012

Weak-triplet, color-octet scalars and the CDF dijet excess

We extend the standard model to include a weak-triplet and color-octet scalar. This 'octo-triplet' field consists of three particles, two charged and one neutral, whose masses and renormalizable interactions depend only on two new parameters. The charged octo-triplet decay into a W boson and a gluon is suppressed by a loop factor and an accidental cancellation. Thus, the main decays of the charged octo-triplet may occur through higher-dimensional operators, mediated by a heavy vectorlike fermion, into quark pairs. For an octo-triplet mass below the tb¯ threshold, the decay into Wb b¯ through an off-shell top quark has a width comparable to that into cs¯ or cb¯. Pair production with one octo-triplet decaying to two jets and the other decaying to a W and two soft b jets may explain the dijet-plus-W excess reported by the CDF Collaboration. The same higher-dimensional operators lead to CP violation in B s -B¯ s mixing.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Understanding and Controlling the Formation of Nonradiative Defects in Blue Organic Triplet Emitters

Phosphorescent organic light-emitting devices (PHOLEDs) suffer from destructive molecular processes due to triplet-polaron and triplet-triplet annihilation. These processes are energetically driven and hence are particularly active in decreasing the lifetime of blue PHOLEDs. It has recently been shown that increasing triplet radiative rates via the Purcell effect effectively extends the device operational lifetime by reducing the triplet radiative lifetime, thus decreasing their density and the probability of triplet-annihilation reactions. We provide an analytical framework using Marcus theory to explain the observed, approximately exponential relationship between exciton energy and device lifetime. From transient drift-diffusion dynamics, we show that the Purcell effect reduces the exciton density in the steady state and increases the photoluminescent yield, thereby reducing defect generation rates and extending the device lifetime. We control the radiative rate of excitons in microcavities, thereby connecting the exciton energy and decay rates with the observed device lifetime. The device lifetime is shown to follow a power-law dependence on the Purcell factor ( PF m ) with m = 1.5 to 2.5, dependent on the TTA-to-TPA ratio and photoluminescence quantum yield. From our analysis, a fivefold increase in PF has the potential to extend the blue PHOLED lifetime by up to 2 orders of magnitude, making the blue PHOLED lifetime comparable to that of state-of-the-art green PHOLEDs. Published by the American Physical Society 2024

Zhao, Haonan (ORCID:0000000190584422)↗

NASA NTRS1990

Dynamics and configurations of galaxy triplets

The purpose is to infer the probable dynamical states of galaxy triplets by the observed data on their configurations. Two methods are proposed for describing the distributions of the triplet configuration parameters characterizing a tendency to alignment and hierarchy: (1) obtaining a representative sample of configurations and determining its statistical parameters (moments and percentages); and (2) dividing the region of possible configurations of triple systems (Agekian and Anosova, 1967) into a set of segments and finding the probabilities for the configurations to find themselves in each of them. Both these methods allow representation of the data by numerical simulations as well as observations. The effect of projection was studied. It rather overestimates the alignment and hierarchy of the triple systems. Among the parameters of interest there are found some parameters that are least sensitive to projection effects. The samples consist of simulated galaxy triplets (with hidden mass) as well as of 46 probably physical triple galaxies (Karachentseva et al., 1979). The observed triples as well as numerical models show a tendency to alignment. The triple galaxies do not show any tendency to hierarchy (formation of the temporary binaries), but this tendency may be present for simulated triplets without significant dark matter. The significant hidden mass (of order ten times the total mass of a triplet) decreases the probability of forming a binary and so weakens the hierarchy. Small galaxy groups consisting of 3 to 7 members are probably the most prevalent types of galaxy aggregate (Gorbatsky, 1987). Galaxy triplets are the simplest groups, but dynamically nontrivial ones.

Anosova, Joanna P.↗

NASA NTRS1993

The photophysics of monomeric bacteriochlorophylls c and d and their derivatives: properties of the triplet state and singlet oxygen photogeneration and quenching

Measurements of pigment triplet-triplet absorption, pigment phosphorescence and photosensitized singlet oxygen luminescence were carried out on solutions containing monomeric bacteriochlorophylls (Bchl) c and d, isolated from green photosynthetic bacteria, and their magnesium-free and farnesyl-free analogs. The energies of the pigment triplet states fell in the range 1.29-1.34 eV. The triplet lifetimes in aerobic solutions were 200-250 ns; they increased to 280 +/- 70 microseconds after nitrogen purging in liquid solutions and to 0.7-2.1 ms in a solid matrix at ambient or liquid nitrogen temperatures. Rate constants for quenching of the pigment triplet state by oxygen were (2.0-2.5) x 10(9) M-1 s-1, which is close to 1/9 of the rate constant for diffusion-controlled reactions. This quenching was accompanied by singlet oxygen formation. The quantum yields for the triplet state formation and singlet oxygen production were 55-75% in air-saturated solutions. Singlet oxygen quenching by ground-state pigment molecules was observed. Quenching was the most efficient for magnesium-containing pigments, kq = (0.31-1.2) x 10(9) M-1 s-1. It is caused mainly by a physical process of singlet oxygen (1O2) deactivation. Thus, Bchl c and d and their derivatives, as well as chlorophyll and Bchl a, combine a high efficiency of singlet oxygen production with the ability to protect photochemical and photobiological systems against damage by singlet oxygen.

NASA Discipline Number 52-30↗

DOE OSTI2024

Distinct Mechanisms of Triplet Pair Decay in Amorphous and Crystalline Heteroacene Thin Films

Triplet pairs (TT) in crystalline molecular semiconductors have unique spin properties of interest for quantum information or enhancing solar photoconversion. The population and diffusion dynamics of TT have been the subject of recent studies, both in covalent dimers and in crystalline systems. Here, in this study, we monitor the triplet population in neat polycrystalline and amorphous films of a heteroacene with known TT spectral properties and tunable spin polarization depending on the intermolecular geometry. Transient measurements reveal an anomalous power dependence in polycrystalline films that we attribute to the fast diffusion and interaction of dissociated triplet pairs confined to one-dimensional stacks of strongly coupled molecules. The nongeminate triplet interaction after dephasing facilitates conversion to the triplet 3 TT and eventually T 1 +S 0 . Amorphous films have no power dependence and proceed directly from 1 TT to 3 TT and subsequently T 1 +S 0 via state mixing facilitated by nonparallel geometries and weak exchange coupling.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

Interligand Coupling Drives Fast Triplet Energy Transfer Routes in PbS/Tetracene Quantum Dot Hybrids

The binding of photoactive organic ligands to inorganic quantum dots (QDs) creates a versatile hybrid architecture that allows access to photophysical processes such as efficient triplet exciton generation with near-infrared radiation. Here we report the subnanosecond generation of a hybrid triplet state with mixed ligand-QD character by replacing native oleate ligands on small PbS QDs with 5,12-tetracenepropiolic acid, a bifunctional ligand with two carboxylic acids that tends to lie face-on with the QD surface at low loadings. The face-on geometry engenders a regime of strong electronic coupling that is evident in steady-state absorption and hastens triplet energy flow by several orders of magnitude compared with more typical tetracene-based ligands exhibiting weak coupling. We further determined via Fourier transform infrared (FTIR) and supported by density functional theory (DFT)-based geometry optimizations that high ligand loading causes a shift in QD-ligand mutual disposition toward an edge-on geometry that instigates the formation of intermolecular excited states characterized by triplet excimer-like features in photoluminescence and transient absorption. Our results demonstrate the ability to control strongly coupled ligand-QD systems toward ultrafast generation of photophysically relevant species such as triplets that are valuable for photon upconversion and catalysis.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Conversion between triplet pair states is controlled by molecular coupling in pentadithiophene thin films

In singlet fission (SF) the initially formed correlated triplet pair state, 1 (TT), may evolve toward independent triplet excitons or higher spin states of the (TT) species. The latter result is often considered undesirable from a light harvesting perspective but may be attractive for quantum information sciences (QIS) applications, as the final exciton pair can be spin-entangled and magnetically active with relatively long room temperature decoherence times. In this study we use ultrafast transient absorption (TA) and time-resolved electron paramagnetic resonance (TR-EPR) spectroscopy to monitor SF and triplet pair evolution in a series of alkyl silyl-functionalized pentadithiophene (PDT) thin films designed with systematically varying pairwise and long-range molecular interactions between PDT chromophores. The lifetime of the (TT) species varies from 40 ns to 1.5 μs, the latter of which is associated with extremely weak intermolecular coupling, sharp optical spectroscopic features, and complex TR-EPR spectra that are composed of a mixture of triplet and quintet-like features. On the other hand, more tightly coupled films produce broader transient optical spectra but simpler TR-EPR spectra consistent with significant population in 5 (TT) 0 . These distinctions are rationalized through the role of exciton diffusion and predictions of TT state mixing with low exchange coupling J versus pure spin substate population with larger J. The connection between population evolution using electronic and spin spectroscopies enables assignments that provide a more detailed picture of triplet pair evolution than previously presented and provides critical guidance for designing molecular QIS systems based on light-induced spin coherence.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2014

Triplet state photochemistry and the three-state crossing of acetophenone within time-dependent density-functional theory

Even though time-dependent density-functional theory (TDDFT) works generally well for describing excited states energies and properties in the Franck-Condon region, it can dramatically fail in predicting photochemistry, notably when electronic state crossings occur. Here, we assess the ability of TDDFT to describe the photochemistry of an important class of triplet sensitizers, namely, aromatic ketones. We take acetophenone as a test molecule, for which accurate ab initio results exist in the literature. Triplet acetophenone is generated thanks to an exotic three-state crossing involving one singlet and two triplets states (i.e., a simultaneous intersystem crossing and triplet conical intersection), thus being a stringent test for approximate TDDFT. We show that most exchange-correlation functionals can only give a semi-qualitative picture of the overall photochemistry, in which the three-state crossing is rather represented as a triplet conical intersection separated from the intersystem crossing. The best result overall is given by the double hybrid functional mPW2PLYP, which is even able to reproduce quantitatively the three-state crossing region. We rationalize this results by noting that double hybrid functionals include a larger portion of double excitation character to the excited states.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

Proximity induced vortices and long-range triplet supercurrents in ferromagnetic Josephson junctions and spin valves

Using a spin-parameterized quasiclassical Keldysh-Usadel technique, we theoretically study supercurrent transport in several types of diffusive ferromagnetic (F)/superconducting (S) configurations with differing magnetization textures. We separate out the even- and odd-frequency components of the supercurrent within the low proximity limit and identify the relative contributions from the singlet and triplet channels. We first consider inhomogeneous one-dimensional Josephson structures consisting of a uniform bilayer magnetic S/F/F/S structure and a trilayer S/F/F/F/S configuration, in which case the outer F layers can have either a uniform or conical texture relative to the central uniform F layer. Our results demonstrate that for supercurrents flowing perpendicular to the F/F interfaces, incorporating a conical texture yields the most effective way to observe the signatures of long-ranged spin-triplet supercurrents. We also consider three different types of finite-sized two-dimensional magnetic structures subjected to an applied magnetic field normal to the junction plane: a S/F/S junction with uniform magnetization texture and two S/F/F/S configurations with differing F/F bilayer arrangements. In one case, the F/F interface is parallel with the S/F junction interfaces while in the other case, the F/F junction is oriented perpendicular to the S/F interfaces. We then discuss the proximity vortices and corresponding spatial maps of currents inside the junctions. For the uniform S/F/S junction, we analytically calculate the magnetic field induced supercurrent and pair potential in both the narrow and wide junction regimes, thus providing insight into the variations in the Fraunhofer diffraction patterns and proximity vortices when transitioning from a wide junction to a narrow one. Our extensive computations demonstrate that the induced long-range spin-triplet supercurrents can deeply penetrate uniform F/F bilayers when spin-singlet supercurrents flow parallel to the F/F interfaces. This is in stark contrast to configurations where a spin-singlet supercurrent flows perpendicular to the F/F interfaces. We pinpoint the origin of the induced triplet and singlet correlations through spatial profiles of the decomposed total supercurrents. We find that the penetration of the long-range spin-triplet supercurrents associated with supercurrents flowing parallel to the F/F interfaces is more pronounced when the thicknesses of the F strips are unequal. Finally, if one of the S terminals is replaced with a finite-sized normal metal, we demonstrate that the corresponding experimentally accessible S/F/F/N spin valve presents an effective platform in which the predicted long-range effects can be effectively generated and probed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗