本文利用电路量子电动力学微波探针测量微米级超导体/铁磁体双层膜，发现诱导超流密度具有面内二重各向异性和节点 p 波三重态配对特征。
摘要：
混合系统代表了非常规超导研究的前沿之一，也是实现拓扑超导态的有前景平台。由于其介观尺度，这些材料难以用许多常规测量技术探测，需要新的实验探针才能成功表征。在本工作中，我们开发了一种探针，使我们能够利用源自电路量子电动力学（cQED）的微波技术测量微米尺寸超导体的超流密度。我们将该技术应用于一个典型的混合系统——超导体/铁磁体双层膜，发现近邻诱导的超流密度在样品平面内具有二重各向异性，并表现出幂律温度标度，这指示了一种节点超导态。这些实验结果与理论预测的具有节点 p 波序参量的诱导三重态配对特征相一致。此外，我们意外地观察到在铁磁共振附近频率处微波响应发生剧烈改变，表明铁磁层中的自旋动力学与诱导超导序之间存在耦合。我们的结果为超导体/铁磁体异质结构中诱导的非常规超导态提供了新的见解，同时也为研究范德华异质结构等低维材料中脆弱的非常规超导性开辟了新途径。
英文摘要：
Hybrid systems represent one of the frontiers in the study of unconventional superconductivity and are a promising platform to realize topological superconducting states. Owing to their mesoscopic dimensions, these materials are challenging to probe using many conventional measurement techniques, and require new experimental probes to successfully characterize. In this work, we develop a probe that enables us to measure the superfluid density of micron-size superconductors using microwave techniques drawn from circuit quantum electrodynamics (cQED). We apply this technique to a paradigmatic hybrid system, the superconductor/ferromagnet bilayer, and find that the proximity-induced superfluid density is two-fold anisotropic within the plane of the sample and exhibits power law temperature-scaling which is indicative of a nodal superconducting state. These experimental results are consistent with the theoretically predicted signatures of induced triplet pairing with a nodal $p$-wave order parameter. Moreover, we unexpectedly observe drastic modifications to the microwave response at frequencies near the ferromagnetic resonance, suggesting a coupling between the spin dynamics and induced superconducting order in the ferromagnetic layer. Our results offer new insights into the unconventional superconducting states induced in superconductor/ferromagnet heterostructures and simultaneously establish a new avenue for the study of fragile unconventional superconductivity in low-dimensional materials such as van der Waals heterostructures.
We realized point contact spectroscopy experiment on ferromagnet/superconductor bilayers. Differential conductance curves show several features that we explained within Bogoliubov-de Gennes formalism considering the presence of two interfaces in the normal-metal-tip/ferromagnet/superconductor device. We demonstrate that such configuration is suitable as local probe of the spin polarization and thickness of ferromagnetic layer, directly on bilayer areas. This is due to the high sensitivity of the Andreev surface states to the physical properties of the ferromagnetic interlayer.
We study theoretically the magnetic screening properties of thin, diffusive superconductor/ferromagnet bilayers subject to a perpendicular magnetic field. We find that the effective penetration depth characterizing the magnetic response oscillates with the thickness of the ferromagnetic layer on the scale of the ferromagnetic coherence length.
We investigate ferromagnetic resonance (FMR) modulation in $d$-wave superconductor (SC)/ferromagnetic insulator (FI) bilayer systems theoretically. The modulation of the Gilbert damping in these systems reflects the existence of nodes in the $d$-wave SC and shows power-law decay characteristics within the low-temperature and low-frequency limit. Our results indicate the effectiveness of use of spin pumping as a probe technique to determine the symmetry of unconventional SCs with high sensitivity for nanoscale thin films.
We analyze the enhancement of the superconducting critical temperature of superconducting/ferromagnetic bilayers due to the appearance of localized superconducting states in the vicinity of magnetic domain walls in the ferromagnet. We consider the case when the main mechanism of the superconductivity destruction via the proximity effect is the exchange field. We demonstrate that the influence of the domain walls on the superconducting properties of the bilayer may be quite strong if the domain wall thickness is of the order of superconducting coherence length.
Superconductor/ferromagnet bilayers are known to exhibit nontrivial dependence of the critical temperature T_c on the thickness d_f of the ferromagnetic layer. We develop a general method for investigation of T_c as a function of the bilayer's parameters. It is shown that interference of quasiparticles makes T_c(d_f) a nonmonotonic function. The results are in good agreement with experiment. Our method also applies to multilayered structures.
We calculate the density of states (DOS) in a diffusive superconducting/ferromagnetic bilayer with a spin-active interface. We use a self-consistent numerical treatment to make a systematic study of the effects of the Spin-Dependence of Interfacial Phase Shifts (SDIPS) on the self-consistent superconducting gap and the DOS. Strikingly, we find that the SDIPS can induce a double gap structure (DGS) in the DOS of the ferromagnet, even when the superconducing layer is much thicker than the superconducting coherence lenght. We thus obtain DOS curves which have interesting similarities with those o…
Using scanning tunneling microscopy and Ginzburg-Landau simulations we explore vortex configurations in magnetically coupled NbSe$_2$-Permalloy superconductor-ferromagnet bilayer. The Permalloy film with stripe domain structure induces periodic local magnetic induction in the superconductor creating a series of pinning-antipinning channels for externally added magnetic flux quanta. Such laterally confined Abrikosov vortices form quasi-1D arrays (chains). The transitions between multichain states occur through propagation of kinks at the intermediate fields. At high fields we show that the syst…
We study the transport properties of vortex matter in a superconducting thin film separated by a thin insulator layer from a ferromagnetic layer. We assume an alternating stripe structure for both FM and SC layers as found in [7]. We calculate the periodic pinning force in the stripe structure resulting from a highly inhomogeneous distribution of the vortices and antivortices. We show that the transport properties in FM-SC bilayer are highly anisotropic. In the absence of random pinning it displays a finite resistance for the current perpendicular to stripes and is superconducting for the curr…
The interfacial coupling between electrons and magnons in adjacent layers can mediate an attractive electron-electron interaction and induce superconductivity. We consider magic-angle twisted bilayer graphene sandwiched between two ferromagnetic insulators to optimize this effect. As a result, magnons induce an interlayer superconducting state characterized by $p$-wave symmetry. We investigate two candidate ferromagnets. The van der Waals ferromagnet CrI$_3$ stands out because it allows compression to tune the superconducting state with an exponential sensitivity. This control adds a new dimen…
Thermally induced magnetization dynamics is currently a flourishing field of research due to its potential application in information technology. We study the paradigmatic system of a magnetic domain wall in a thermal gradient which is interacting with an adjacent superconductor. The spin-transfer torques arising in this system due to the combined action of the giant thermoelectric effect and the creation of equal-spin pairs in the superconductor are large enough to give rise to high domain wall velocities $10^3$ times larger than previously predicted.
We study theoretically the influence of spin accumulation on superconductivity in a superconductor/ferromagnet bilayer. It is well-known that the superconductivity in S/F bilayers is suppressed by the proximity to a ferromagnet. The spin accumulation by itself is also a depairing factor. But here we show that creation of the spin accumulation on top of effective exchange depairing, caused by the proximity to a ferromagnet, can lead to an opposite result. The superconductivity can be partially recovered by spin-dependent quasiparticle distribution. The systems with realistic parameters are cons…
We demonstrate that the hybrid structures consisting of a superconducting layer with an adjacent spin-textured ferromagnet demonstrate the variety of equilibrium magnetoelectric effects originating from coupling between the conduction electron spin and superconducting current. By deriving and solving the generalized Usadel equation which takes into account the spin-filtering effect we find that a supercurrent generates spin polarization in the superconducting film which is non-coplanar with the local ferromagnetic moment. The inverse magnetoelectric effect in such structures is shown to result…
Scanning tunneling spectroscopy measurements conducted on epitaxially grown bilayers of half-metallic ferromagnetic La2/3Ca1/3MnO3 (LCMO) on superconducting (SC) (100)YBa2Cu3O7-delta (YBCO) reveal long-range penetration of superconducting order into the LCMO. This anomalous proximity effect manifests itself in the tunneling spectra measured on the LCMO layer as gaps and zero bias conductance peaks. Remarkably, these proximity-induced spectral features were observed for bilayers with LCMO thickness of up to 30 nm, an order of magnitude larger than the expected ferromagnetic coherence length in …
Scanning tunneling spectroscopy measurements on thin epitaxial SrRuO3/(100)YBCO ferromagnet/superconductor bilayers, reveal localized regions in which the superconductor order parameter penetrates the ferromagnet to more than 26 nm, an order of magnitude larger than the coherence length in the ferromagnetic layer. These regions consist of narrow (< 10 nm) and long strips, separated by at least 200 nm, consistent with the known magnetic domain wall structure in SrRuO3. We attributed this behavior to Crossed Andreev Reflections, taking place in the vicinity of the magnetic domain walls.
The excitation spectrum of clean ferromagnet-superconductor bilayers is calculated within the framework of the self-consistent Bogoliubov-de Gennes theory. Because of the proximity effect, the superconductor induces a gap in the ferromagnet spectrum, for thin ferromagnetic layers. The effect depends strongly on the exchange field in the ferromagnet. We find that as the thickness of the ferromagnetic layer increases, the gap disappears, and that its destruction arises from those quasiparticle excitations with wavevectors mainly along the interface. We discuss the influence that the interface qu…
Scanning tunneling spectroscopy of thin epitaxial $SrRuO_{3}/(110)YBa_2Cu_3O_{7-δ}$ ferromagnet/superconductor bilayers, reveal a clear penetration of the Andreev bound states into the ferromagnetic layer. The penetration is manifested in the density of states of the ferromagnet as a split zero bias conductance peak with an imbalance between peak heights. Our data indicate that the splitting occurs at the superconductor side as a consequence of induced magnetization, confirming recent theoretical predictions. The imbalance is attributed to the spin polarization in the ferromagnet.
Vortex pinning in a type-II superconducting Pb film covering a Co/Pt multilayer with perpendicular magnetic anisotropy is investigated. Different stable magnetic domain patterns like band and bubble domains can be created in the Co/Pt multilayer, clearly influencing the vortex pinning in the superconducting Pb layer. Most effective pinning is observed for the bubble domain state. We demonstrate that the pinning properties of the superconductor/ferromagnet bilayer can be controlled by tuning the size, density and magnetization direction of the bubbles.
The theoretical description of the Fulde-Ferrell-Larkin-Ovchinnikov like state establishing in nanostructered bilayers of ferromagnetic (F) and superconducting (S) material leads to critical temperature oscillations and reentrant superconductivity as the F-layer thickness gradually increases. The experimental realization of these phenomena is an important prerequisite for the fabrication of the Ferromagnet/Superconductor/Ferromagnet core structure of the superconducting spin-valve. A switching of the spin-valve is only expected if such non-monotonic critical temperature behavior is observed in…
We use local and global magnetometry measurements to study the influence of magnetic domain width w on the domain-induced vortex pinning in superconducting/ferromagnetic bilayers, built of a Nb film and a ferromagnetic Co/Pt multilayer with perpendicular magnetic anisotropy, with an insulating layer to eliminate proximity effect. The quasi-periodic domain patterns with different and systematically adjustable width w, as acquired by a special demagnetization procedure, exert tunable vortex pinning on a superconducting layer. The largest enhancement of vortex pinning, by a factor of more than 10…
We report the first measurements of the effective superfluid density n_S(T) \propto λ^{-2}(T) of Superconductor-Ferromagnet (SC/FM) bilayers, where λis the effective magnetic field penetration depth. Thin Nb/Ni bilayers were sputtered in ultrahigh vacuum in quick succession onto oxidized Si substrates. Nb layers are 102 A thick for all samples, while Ni thicknesses vary from 0 to 100 A. T_C determined from λ^{-2}(T) decreases rapidly as Ni thickness d_Ni increases from zero to 15 A, then it has a shallow minimum at d_Ni \approx 25 A. λ^{-2}(0) behaves similarly, but has a minimum several times…
Measurements of the polar Kerr effect using a zero-area-loop Sagnac magnetometer on Pb/Ni and Al/(Co-Pd) proximity-effect bilayers show unambiguous evidence for the "inverse proximity effect," in which the ferromagnet (F) induces a finite magnetization in the superconducting (S) layer. To avoid probing the magnetic effects in the ferromagnet, the superconducting layer was prepared much thicker than the light's optical penetration depth. The sign and size of the effect, as well as its temperature dependence agree with recent predictions by Bergeret et al..
We have observed the evolution of phase diagram and vortex pinning using a single ferromagnet/superconductor bilayer of [Co/Pt]8/Nb through a special demagnetization procedure. It induces a continuous and reversible change of the domain width with equal positive/negative domains enabling the observation of the predicted tunable phase diagram. The tunable domain pattern also systematically affects vortex pinning. We have determined the dependence of the activation energy of vortex pinning on domain width, temperature, and magnetic field.
The continuum theory of domain structures in ferromagnetic/superconducting bilayers fails when the equilibrium domain size becomes comparable with effective penetration depth $Λ$. Instead, a lattice of discrete vortices must be considered. Here, we report our results on the discrete vortex lattices in stripe domain structures of ferromagnetic/superconducting bilayers. The vortices are assumed to be situated periodically on chains in stripe domains. We study the configurations containing up to three chains per domain, and calculate their equilibrium energies, equilibrium domain size and vortex …
We study the electronic instabilities of doped bilayer silicene using the random phase approximation. In contrast to the singlet $d+id'$ superconductivity at the low doping region, we find that the system is an itinerant ferromagnet in the narrow doping regions around the Van Hove singularities, and a triplet $p+ip'$ superconductor in the vicinity of these regions. Adding a weak Kane-Mele spin-orbit coupling to the system further singles out the time-reversal invariant equal-spin helical $p+ip'$ pairing as the leading instability. The triplet pairing identified here is driven by the ferromagne…
Vortex motion in ferromagnetic-superconducting bilayers constituted by thin YBa$_2$Cu$_3$O$_{7-δ}$ film deposited on the top of thin manganite La$_{0.67}$Sr$_{0.33}$MnO$_3$ film has been investigated. Both films were deposited on uniformly twinned single-crystalline substrates and patterned into strips directed at different angles to the twin lines pattern. These conditions lead to the guided vortex motion at different angles to the periodic pinning potential. It has been established that critical current and flux flow resistance in such an anisotropic pinning landscape-scale follow the ellipt…
Superconducting spintronics in hybrid superconductor/ferromagnet (S-F) heterostructures provides an exciting potential new class of device. The prototypical super-spintronic device is the superconducting spin-valve, where the critical temperature, $T_c$, of the S-layer can be controlled by the relative orientation of two (or more) F-layers. Here, we show that such control is also possible in a simple S/F bilayer. Using field history to set the remanent magnetic state of a thin Er layer, we demonstrate for a Nb/Er bilayer a high level of control of both $T_c$ and the shape of the resistive tran…
Epitaxial bilayers of ferromagnetic La2/3Ca1/3MnO3 (LCMO) and superconducting YBa2Cu3O7-d (YBCO) have been grown on single-crystalline SrTiO3 (STO) substrates by pulsed laser deposition. The Manganese magnetization profile across the FM layer has been determined with high spatial resolution at low temperatures by X-ray resonant magnetic reflectivity (XRMR). It is found that not only the adjacent superconductor but also the substrate underneath influences the magnetization of the LCMO film at the interfaces at low temperatures. Both effects can be investigated individually by XRMR.
In bilayers consisting of ferromagnetic and superconducting films, the ferromagnetic film in its domain state induces inhomogeneous distribution of magnetic fields in the superconducting film. When the ferromagnetic film has bubble magnetic domains in a labyrinth structure, it has been found that the pinning of the vortices increases; hence, the critical current of the superconducting film becomes larger. Here we study the effect of parallel ferromagnetic domain structure in Nb/SrRuO3 on the critical current of Nb with current flowing perpendicularly to the domains and find that in this case t…
We have made an experimental study of the tunneling density of states (DOS) in strong ferromagnetic thin films (CoFe) in proximity with a thick superconducting film (Nb) as a function of $d_F$, the ferromagnetic thickness. Remarkably, we find that as $d_F$ increases, the superconducting DOS exhibits a scaling behavior in which the deviations from the normal-state conductance have a universal shape that decreases exponentially in amplitude with characteristic length $d^*\approx 0.4$ nm. We do not see oscillations in the DOS as a function of $d_F$, as expected from predictions based on the Usade…
The discrete vortex lattices in a ferromagnet/superconductor bilayer are studied when the ferromagnet has periodic stripe domains with an out-of-plane magnetization. The vortices are assumed to be situated periodically on chains in the stripe domains. Only up to two vortex chains per domain configurations are considered. When the domain period is fixed, the threshold magnetization is calculated at which the transition from the Meissner state to the mixed state occurs. When the domain period is not fixed, the equilibrium domain size and vortex positions are calculated, depending on the domain's…
We report detailed studies on ferromagnet--superconductor bilayer structures. Epitaxial bilayer structures of half metal--colossal magnetoresistive La$_{\mathrm{2/3}}$Ca$_{\mathrm{1/3}}$MnO$_{\mathrm{3}}$ (HM--CMR) and high--$T_{\mathrm{c}}$ superconducting YBa$_{\mathrm{2}}$Cu$_{\mathrm{3}}$O$_{\mathrm{7-δ}}$(HTSC) are grown on SrTiO$_3$ (100) single--crystalline substrates using pulsed laser deposition. Magnetization $M$(T) measurements show the coexistence of ferromagnetism and superconductivity in these structures at low temperatures. Using the HM--CMR layer as an electrode for spin polari…
We investigated the pinning of flux lines in a superconducting film by a regular array of magnetic antidots. The sample consists of a Co/Pt multilayer with perpendicular magnetic anisotropy in which a regular pattern of submicron holes is introduced and which is covered by a type-II superconducting Pb film. The resulting ferromagnetic/superconducting heterostructure shows a pronounced asymmetric magnetization curve with respect to the field polarity. This asymmetry clearly demonstrates that the magnetic contribution dominates the pinning potential imposed by the magnetic antidots on the superc…
We demonstrate that Josephson devices with nontrivial phase difference $% 0<φ_g <π$ in the ground state can be realized in structures composed from longitudinally oriented normal metal (N) and ferromagnet (F) films in the weak link region. Oscillatory coupling across F-layer makes the first harmonic in the current-phase relation relatively small, while coupling across N-layer provides negative sign of the second harmonic. To derive quantitative criteria for a $φ$-junction, we have solved two-dimensional boundary-value problem in the frame of Usadel equations for overlap and ramp geometries of …
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…
The magnetic field (H) - temperature (T) phase diagram of a superconductor is significantly altered when domains are present in an underlying ferromagnet with perpendicular magnetic anisotropy. When the domains have a band-like shape, the critical temperature Tc of the superconductor in zero field is strongly reduced, and the slope of the upper critical field as a function of T is increased by a factor of 2.4 due to the inhomogeneous stray fields of the domains. Field compensation effects can cause an asymmetric phase boundary with respect to H when the ferromagnet contains bubble domains. For…
The existence of coherent magnetic correlations in the normal phase of cuprate high-temperature superconductors has proven difficult to measure directly. Here we report on a study of ferromagnetic-superconductor bilayers of La2/3Ca1/3MnO3/YBa2Cu3O7 (LCMO/YBCO) with varying YBCO layer thicknesses. Using x-ray magnetic circular dichroism, we demonstrate that the ferromagnetic layer induces a Cu magnetic moment in the adjacent high-temperature superconductor. For thin samples, this moment exists at all temperatures below the Curie temperature of the LCMO layer. However, for a YBCO layer thicker t…
We report the superconducting transition temperature $T_c$ vs. thickness $d_F$ of Ferromagnet/Superconductor (F/S) bilayers, where F is a strong $3d$ ferromagnet (Ni, Ni$_{0.81}$Fe$_{0.19}$ (Permalloy), Co$_{0.5}$Fe$_{0.5}$) and S = Nb, taken from superfluid density measurements rather than resistivity. By regrouping the many physical parameters that appear in theory, we show that the effective exchange energy is determined from the F film thickness $d_F$ where $T_c$ vs. $d_F$ begins to flatten out. Using this rearranged theory we conclude: 1) the effective exchange energy, $E_{ex}$, is about …
The pinning properties of type-II superconductors can be efficiently controlled by using laterally nanostructured ferromagnet / superconductor bilayers. This will be illustrated by studying the flux pinning in thin superconducting Pb films which are deposited on top of two types of magnetic nanostructures with out-of-plane magnetisation: (i) an array of dots, and (ii) an array of antidots, both made from a Co/Pt multilayer. The magnetisation curves of the Pb film are extremely asymmetric with respect to the polarity of the magnetic field when the magnetic moments in the Co/Pt multilayer were a…
A resonant enhancement of the neutron standing waves is proposed to use in order to increase the magnetic neutron scattering from a "superconductor/ferromagnet"(S/F) bilayer. The model calculations show that usage of this effect allows to increase the magnetic scattering intensity by factor of hundreds. Aspects related to the growth procedure (order of deposition, roughness of the layers etc) as well as experimental conditions (resolution, polarization of the neutron beam, background etc) are also discussed. Collected experimental data for the S/F heterostructure Cu(32nm)/V(40nm)/Fe(1nm)/MgO c…
We report the observation of a pronounced dip in the in-plane field (H//) dependence of the critical current density Jc(H) and a peak in resistance R(H) of a NbN-HoNi5 bilayer at temperatures below the magnetic ordering temperature (TCurie ~ 5.5 K) of HoNi5, which is lower than the onset temperature (~ 9 K) of superconductivity in the NbN layer. The extrema in Jc(H) and R(H) appear at fields much below the upper critical field of NbN. It is suggested that the origin of this feature is linked with the non-collinear magnetization of HoNi5 whose normal component assists in depairing of Pearl vort…
Extraordinary Hall effect (EHE) in bilayer F/S(N) was investigated theoretically. The conductivity tensor $σ_{αβ}$ is calculated in the Kubo formalism with Green functions found as the solutions of the Gorkov equations. We considered diffuse transport in the ferromagnetic layer, taking into account as a main mechanism of electron resistivity s-d scattering. In this model Gorkov equations for s-electrons in the ferromagnetic layer remain linear and are solved easily. It is shown that Hall field $E^H$ for both F/S and F/N contacts are step-functions of the coordinate perpendicular to the planes …
We report on the first observation of a pronounced re-entrant superconductivity phenomenon in superconductor/ferromagnetic layered systems. The results were obtained using a superconductor/ferromagnetic-alloy bilayer of Nb/Cu(1-x)Ni(x). The superconducting transition temperature T_{c} drops sharply with increasing thickness d_{CuNi} of the ferromagnetic layer, until complete suppression of superconductivity is observed at d_{CuNi}= 4 nm. Increasing the Cu(1-x)Ni(x) layer thickness further, superconductivity reappears at d_{CuNi}=13 nm. Our experiments give evidence for the pairing function osc…
