Topological spin configurations in proximity to a superconductor have recently attracted great interest due to the potential application of the former in spintronics and also as another platform for realizing non-trivial topological superconductors. Their application in these areas requires precise knowledge of the existing exchange fields and/or the stray-fields which are therefore essential for the study of these systems. Here, we determine the effective stray-field and the Meissner currents in a Superconductor/Ferromagnet/Superconductor (S/F/S) junction produced by various nonhomogenous magnetic textures in the F. The inhomogeneity arises either due to a periodic structure with flat domain walls (DW) or is caused by an isolated chiral magnetic skyrmion (Sk). We consider both Bloch- and Néel-type Sk and also analyze in detail the periodic structures of different types of DW's-- that is Bloch-type DW (BDW) and Néel-type DW (NDW) of finite width with in- and out-of-plane magnetization vector. The spatial dependence of the fields and Meissner currents are shown to be qualitatively different for the case of Bloch- and Néel-type magnetic textures. While the spatial distributions in the upper and lower S are identical for Bloch-type Sk and DW's they are asymmetric for the case of Néel-type magnetic textures. The depairing factor, which determines the critical temperature and which is related to vector potential of the stray-field, can have its maximum at the center of a magnetic domain but also, as we show, above the DW. For Sk's the maximum is located at a finite distance within the Sk radius. Based on this, we study the nucleation of superconductivity in the presence of DW's. Because of the asymmetry for Néel-type structures, the critical temperature in the upper and lower S is expected to be different. The obtained results can also be applied to S/F bilayers.
Small-angle neutron scattering (SANS) measurements are performed on the ferromagnetic superconductor EuFe$_{2}$(As$_{0.8}$P$_{0.2}$)$_{2}$ ($T\rm_{sc}=22.5\,$K) to probe the delicate interplay between ferromagnetism and superconductivity. A clear signature of large ferromagnetic domains is found below the ferromagnetic ordering temperature $T\rm_{C}$ = 18.5 K. In a small temperature interval of $\sim$ 1.5 K below $T\rm_{C}$, additional SANS signal is observed, of which the indirect Fourier transform reveals characteristic length scales in between $\sim$ 80 nm to $\sim$ 160 nm. These nanometer-…
An increase of the magnetic moment in superconductor/ferromagnet (S/F) bilayers V(40nm)/F [F$=$Fe(1,3nm), Co(3nm), Ni(3nm)] was observed using SQUID magnetometry upon cooling below the superconducting transition temperature Tc in magnetic fields of 10 Oe to 50 Oe applied parallel to the sample surface. A similar increase, often called the paramagnetic Meissner effect (PME), was observed before in various superconductors and superconductor/ferromagnet systems. To explain the PME effect in the presented S/F bilayers a model based on a row of vortices located at the S/F interface is proposed. Acc…
We theoretically find that finite size Fulde-Ferrell (FF) superconductor (which is characterized by spatially nonuniform ground state $Ψ\sim \text{exp}(-i{\bf q}_{FF}{\bf r})$ and $|Ψ|(r)=const$ in the bulk case, where $Ψ$ is a superconducting order parameter) has paramagnetic Meissner, vortex and 'onion' ground states with $|Ψ|(r) \neq const$. These states are realized due to boundary effect when the lateral size of superconductor $L \sim 1/q_{FF}$. We argue, that predicted states could be observed in thin disk/square made of superconductor-ferromagnet-normal metal trilayer with $L \simeq 150…
We study theoretically spontaneous currents and magnetic field induced in a superconductor-ferromagnet (S-F) bilayer due to direct and inverse proximity effects. The induced currents {are Meissner currents that appear even in the absence of an external magnetic field due to the magnetic moment in the ferromagnet }and {to the magnetization } in the superconductor . The latter is induced by the inverse proximity effect over a distance of the order of the superconducting correlation length $ξ_{S}$. On the other hand the magnetic induction $B$, caused by Meissner currents, penetrates the S film ov…
We consider a hybrid quantum Hall-superconductor system, where a superconducting finger with oblique profile is wedged into a two-dimensional electron gas in the presence of a perpendicular magnetic field, as considered by Lee et al., Nat. Phys. 13, 693 (2017). The electron gas is in the quantum Hall regime at filling factor $ν=1$. Due to the Meissner effect, the perpendicular magnetic field close to the quantum Hall-superconductor boundary is distorted and gives rise to an in-plane component of the magnetic field. This component enables nonlocal crossed Andreev reflection between the spin-pol…
We introduce the general formalism to describe spin torques induced by the supercurrents injected from the adjacent superconducting electrodes into the spin-textured ferromagnets. By considering the adiabatic limit for the equal-spin superconducting correlations in the ferromagnet we show that the supercurrent can generate both the field-like spin transfer torque and the spin-orbital torque. These dissipationless spin torques are expressed through the current-induced corrections to the effective field derived from the system energy. The general formalism is applied to show that the supercurren…
When a magnetic field is applied to a ferromagnetic body it starts to spin (Einstein-de Haas effect). This demonstrates the intimate connection between the electron's magnetic moment $μ_B=e\hbar/2m_ec$, associated with its spin angular momentum $S=\hbar/2$, and ferromagnetism. When a magnetic field is applied to a superconducting body it also starts to spin (gyromagnetic effect), and when a normal metal in a magnetic field becomes superconducting and expels the magnetic field (Meissner effect) the body also starts to spin. Yet according to the conventional theory of superconductivity the elect…
Since the discovery of the long-range superconducting proximity effect, the interaction between spin-triplet Cooper pairs and magnetic structures such as domain walls and vortices has been the subject of intense theoretical discussions, while the relevant experiments remain scarce. We have developed nanostructured Josephson junctions with highly controllable spin texture, based on a disk-shaped Nb/Co bilayer. Here, the vortex magnetization of Co and the Cooper pairs of Nb conspire to induce long-range triplet (LRT) superconductivity in the ferromagnet. Surprisingly, the LRT correlations emerge…
Magnetic texture modulated superconductivity in superconductor/ferromagnet shells of semiconductor nanowires
Stanford University（斯坦福大学）；SLAC National Accelerator Laboratory（SLAC国家加速器实验室）；Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔研究所）；Universidad de Chile（智利大学）；Danish Fundamental Metrology（丹麦基础计量）；Universidad de Santiago de Chile（圣地亚哥德智利大学）
We consider physical properties of a superconductor with a recently proposed type of odd-frequency pairing that exhibits diamagnetic Meissner response ("odd-dia state"). Such a state was suggested in order to address stability issues arising in an odd-frequency superconducting state with paramagnetic Meissner response ("odd-para state"). Assuming the existence of an odd-dia state (due to a proper retarded interaction), we study its coexistence with an odd-para state. The latter is known to be generated as an induced superconducting component in, e.g., singlet superconductor/ferromagnet proximi…
An important feature of strong correlated electron systems is the tunability between interesting ground states such as unconventional superconductivity and exotic magnetism. Pressure is a clean, continuous and systematic tuning parameter. However, due to the restricted accessibility introduced by high-pressure devices, compatible magnetic field sensors with sufficient sensitivity are rare. This greatly limits the detections and detailed studies of pressure-induced phenomena. Here, we utilize nitrogen vacancy (NV) centers in diamond as a powerful, spatially-resolved vector field sensor for mate…
The existence of spin-triplet superconductivity in non-collinear magnetic heterostructures with superconductors is by now well established. This observation lays the foundation of superconducting spintronics with the aim to create a low-power consuming devices in order to replace the conventional electronics limited by heating. From a fundamental point of view the investigation of the structure and properties of spin-triplet Cooper pairs continues. Recently, spectroscopic evidence has shown to offer more detailed insights in the structure of triplet Cooper pairs than the supercurrent. Hence, w…
The coupling of a superconductor to a different material often results in a system with unconventional superconducting properties. A conventional superconductor is a perfect diamagnet expelling magnetic fields out of its volume, a phenomenon known as Meissner effect. Here, we show that the simple adsorption of a monolayer of chiral molecules, which are non-magnetic in solution, onto the surface of a conventional superconductor can markedly change its diamagnetic Meissner response. By measuring the internal magnetic field profile in superconducting Nb thin films under an applied transverse fiel…
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…
We show that a wide class of layered superconductor-ferromagnet (S/F) hybrids demonstrate the emergence of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase well below the superconducting transition temperature. Decreasing the temperature one can switch the system from uniform to the FFLO state which is accompanied by the damping of the diamagnetic Meissner response down to zero and also by the sign change in the curvature of the current-velocity dependence. Our estimates show that an additional layer of the normal metal (N) covering the ferromagnet substantially soften the conditions required…
With the ever-increasing energy need to process big data, the realization of low-power computing technologies, such as superconducting logic and memories, has become a pressing issue. Developing fast and non-volatile superconducting memory elements, however, remains a challenge. Superconductor-ferromagnet hybrid devices offer a promising solution, as they combine ultra-fast manipulation of spins with dissipationless readout. Here, we present a new type of non-volatile Josephson junction memory that utilizes the bistable magnetic texture of a single mesoscopic ferromagnet. We use micromagnetic …
Theory of superconducting and magnetic proximity effect in S$\mid$F structures with inhomogeneous magnetization textures and spin-active interfaces
我们研究了超导体$\mid$铁磁双层中的邻近效应和逆邻近效应，并考虑了迄今为止文献中大多被忽视的几个重要因素。这些包括自旋相关的界面相移（自旋-DIPS）和非均匀的纹理中的铁磁层的磁化强度，这两者都预计将存在于真实的实验样品。我们的方法是数值，使我们能够访问完整的邻近效应制度。在第一部分中，我们研究了具有非平凡磁织构的非均匀铁磁体中的超导邻近效应和由此产生的局域态密度。我们在第一部分中的两个主要结果是布洛赫和内尔畴壁如何影响邻近诱导的超导关联的研究和研究的超导邻近效应在锥形铁磁体。后一个主题应该是相关的铁磁体何，这是最近在实验中使用，以证明产生和维持长程三重态超导关联的可能性。在这项工作的第二部分中，我们调查的逆邻近效应，强调在超导区域的感应磁化强度的结果的“泄漏”的铁磁区域。结果表明，自旋-DIPS的存在下修改先前在文献中获得的结论，在超导区域的感应磁化。特别是，我们发现自旋DIPS可以触发磁化的反屏蔽效应，导致在超导区域与\textit{the same sign}在邻近铁磁体的感应磁化。
Majorana bound states are zero-energy states predicted to emerge in topological superconductors and intense efforts seeking a definitive proof of their observation are still ongoing. A standard route to realize them involves antagonistic orders: a superconductor in proximity to a ferromagnet. Here we show this issue can be resolved using antiferromagnetic rather than ferromagnetic order. We propose to use a chain of antiferromagnetic skyrmions, in an otherwise collinear antiferromagnet, coupled to a bulk conventional superconductor as a novel platform capable of supporting Majorana bound state…
Anderson-Higgs mechanism of mass generation is a generic concept in high-energy and condensed matter physics. It shows up through the Meissner effect providing the expulsion of static and low-frequency magnetic fields from superconductors. However, it does not affect propagating electromagnetic waves with a spectrum gap determined by the plasma frequency, which is too large to be sensitive to the superconducting transition. Here we demonstrate the spectroscopic manifestation of the Anderson-Higgs mass, showing that it determines the spectrum gap of magnons in superconductor/ferromagnet/superco…
Recently discovered superconducting P-doped EuFe$_2$As$_2$ compounds reveal the situation when the superconducting critical temperature substantially exceeds the ferromagnetic transition temperature. The main mechanism of the interplay between magnetism and superconductivity occurs to be an electromagnetic one and a short period magnetic domain structure was observed just below Curie temperature [Stolyarov et al., Sci. Adv. \textbf{4}, eaat1061 (2018)]. We elaborate a theory of such transition and demonstrate how the initial sinusoidal magnetic structure gradually transforms into a soliton-lik…
The interaction between superconductivity and ferromagnetism in thin film superconductor/ferromagnet heterostructures is usually reflected by a change in superconductivity of the S layer set by the magnetic state of the F layers. Here we report the converse effect: transformation of the magnetocrystalline anisotropy of a single Fe(001) layer, and thus its preferred magnetization orientation, driven by the superconductivity of an underlying V layer through a spin-orbit coupled MgO interface. We attribute this to an additional contribution to the free energy of the ferromagnet arising from the c…
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 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…
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 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 …
