Motivated by recent experiments searching for Majorana zero modes in tripartite semiconductor nanowires with epitaxial superconductor and ferromagnetic-insulator layers, we explore the emergence of topological superconductivity in such devices for paradigmatic arrangements of the three constituents. Accounting for the competition between magnetism and superconductivity, we treat superconductivity self consistently and describe the electronic properties, including the superconducting and ferromagnetic proximity effects, within a direct wave-function approach. We conclude that the most viable mechanism for topological superconductivity relies on a superconductor-semiconductor-ferromagnet arrangement of the constituents, in which spin splitting and superconductivity are independently induced in the semiconductor by proximity and superconductivity is only weakly affected by the ferromagnetic insulator.
The proximity effect in mesoscopic ferromagnet/superconductor ($FS$) Ni/Al structures of various geometries was studied experimentally on both $F$- and $S$-sides of the structures. Samples with a wide range of interface transparency were fabricated. The dependence of the effect on $FS$ interface transparency was investigated. The amplitude of this effect was found to be larger than expected from classical theory of proximity effect. Preliminary experiments showed no phase-sensitive oscillations in Andreev interferometer geometry. Various theoretical models are discussed.
Motivated by the recent experiment of Wang et al. [Nature Physics 6, 389 (2010)], who observed a highly unusual transport behavior of ferromagnetic Cobalt nanowires proximity-coupled to superconducting electrodes, we study proximity effect and temperature-dependent transport in such a mesoscopic hybrid structure. It is assumed that the asymmetry in the tunneling barrier gives rise to the Rashba spin-orbit-coupling in the barrier that enables induced p-wave superconductivity in the ferromagnet to exist. We first develop a microscopic theory of Andreev scattering at the spin-orbit-coupled interf…
When a ferromagnet is placed in contact with a superconductor, owing to incompatible spin order, the Cooper pairs from the superconductor cannot survive more than one or two nanometers inside the ferromagnet. This is confirmed in the measurements of ferromagnetic nickel (Ni) nanowires contacted by superconducting niobium (Nb) leads. However, when a 3 nm thick copper oxide (CuO) buffer layer made by exposing an evaporated or a sputtered 3 nm Cu film to air, is inserted between the Nb electrodes and the Ni wire, the spatial extent of the superconducting proximity range is dramatically increased …
We study shot noise of the spin-polarized current in a diffusive ferromagnetic nanowire which contains a ballistic domain wall. We find that the existence of a short domain wall influences strongly the shot noise for sufficiently high spin-polarization of the wire. Compared to the situation of the absence of the domain wall, the shot noise can be reduced or enhanced depending on the length of the domain wall and its relative conductance.
Spin orbit torques are of great interest for switching the magnetization direction in nanostructures, moving skyrmions and exciting spin waves. The standard method of determining their efficiency is by spin torque ferromagnetic resonance (ST-FMR), a technique that involves analyzing the resonance linewidth or lineshape. On microstuctures these two analysis methods are quite consistent. Here we present ST-FMR results on permalloy (Ni$_{80}$Fe$_{20}$) nanowires -- with widths varying from $150$ to 800 nm -- that show that the standard model used to analyze the resonance linewidth and lineshape g…
We represent the results of micromagnetic modeling and experimental magnetic force microscopy investigations of domain wall (DW) pinning-depinning effects in the hybrid systems consisting of ferromagnetic nanowire (NW) and two ferromagnetic nanoparticles (NPs). It was demonstrated that the special NW-NPs configuration including the NW with DW nucleating bulb at one end and two-NP gate enables the realization of controlled DW pinning-depinning based on switching of magnetization in NPs subsystem. The algorithm of external driving field manipulation and independent NPs switching, which allow one…
We report the results of experimental investigations of controlled domain wall (DW) pinning in a ferromagnetic nanowire (NW) by stray fields of two uniformly magnetized bistable ferromagnetic nanoparticles (NPs) placed on either side of the NW and elongated parallel to the NW axis. We show by magnetic force microscopy measurements that DW pinning strength essentially depends on the orientation of the NP magnetic moments relative to the NW magnetization and can reach 20 mT. We also performed micromagnetic simulations confirming the influence of the magnetostatic interaction of the DW with the N…
We present a calculation of the dephasing time of electrons in a ferromagnet relevant for the conductance fluctuations. We focus on the contribution from the interaction with spin waves. Explicit results are presented for a quasi-one-dimensional systems. Going beyond previous calculations, we do not restrict ourselves to the limit of a small exchange splitting compared to the electronic elastic scattering time, nor does our calculation rely on the diffusion approximation to describe electronic transport.
We use spin torque ferromagnetic resonance to measure the spectral properties of dipole-exchange spin waves in permalloy nanowires. Our measurements reveal that geometric confinement has a profound effect on the damping of spin waves in the nanowire geometry. The damping parameter of the lowest-energy quantized spin wave mode depends on applied magnetic field in a resonant way and exhibits a maximum at a field that increases with decreasing nanowire width. This enhancement of damping originates from a nonlinear resonant three-magnon confluence process allowed at a particular bias field value d…
We investigate, angle dependent, the magnetoresistance (MR) of individual self-assembled ferromagnetic GaAs/(Ga,Mn)As core-shell nanowires at cryogenic temperatures. The shape of the MR traces and the observed strong anisotropies in transport can be ascribed to the interplay of the negative magnetoresistance effect and a strong uniaxial anisotropy with the magnetic easy direction pointing along the wire axis. The magnetoresistance can be well described by a quantitative analysis based on the concept of the effective magnetic field, usually used to describe ferromagnetic resonance phenomena. Th…
We model the exchange bias effect in thin cylindrical nanowires composed of a ferromagnetic core and an antiferromagnetic shell implementing a classical spin Hamiltonian and Monte Carlo simulations. We address systematically the effect of shell polycrystallinity on the characteristic fields of the isothermal hysteresis loop (coercivity, exchange-bias) and their angular dependence upon the direction of the applied / cooling field. We relate the observed trends to modifications of the underlying magnetization reversal mechanism. We fit our simulation results to an extended Stoner-Wohlfarth model…
Integration of magneto-electric and spintronic sensors presents a massive potential for advancing flexible and wearable technology. Magnetic nanowires are core components for building such devices, and therefore it important to realize flexible magnetic nanowires and uncover magneto-elastic properties, which can propel not only such flexible sensing applications, but can also make new pathways for exploration of flexible magneto-plasmonic devices, and discovering unseen observations at reduced dimensions. Here, we realize ferromagnetic nanowires on flexible substrates for the first time. Throu…
We investigate the spin dynamics including Gilbert damping in the ferromagnetic nanowire arrays. We have measured the ferromagnetic resonance of ferromagnetic nanowire arrays using vector-network analyzer ferromagnetic resonance (VNA-FMR) and analyzed the results with the micromagnetic simulations. We find excellent agreement between the experimental VNA-FMR spectra and micromagnetic simulations result for various applied magnetic fields. We find that the demagnetization factor for longitudinal conditions, Nz (Ny) increases (decreases) as decreasing the nanowire width in the micromagnetic simu…
Recently a long ranged superconductor/ferromagnet (S/F) proximity effect has been reported in Co crystalline nanowires [1, Nature, 6 389 (2010)]. Since the authors of [1] take care to avoid the existence of magnetic domains, the triplet character of the long ranged proximity effect is improbable. Here we demonstrate that in the one-dimensional ballistic regime the standard singlet S/F proximity effect becomes long ranged. We provide an exact solution for the decay of the superconducting correlations near critical temperature ($T_{c}$) and for arbitrary impurities concentration. In particular w…
We study the effects of spin-orbit interaction (SOI) on the current-induced motion of a magnetic (Bloch) domain wall in ultrathin ferromagnetic nanowires. The conspiracy of spin relaxation and SOI is shown to generate a novel strong nonequilibrium Rashba field, which is dominant even for moderate SOI. This field causes intricate spin precession and a transition from translatory to oscillatory wall dynamics with increasing SOI. We show that current pulses of different lengths can efficiently be used to control the domain wall motion.
We investigate experimentally and theoretically the magnetization reversal process in one-dimensional magnonic structures composed of permalloy nanowires of the two different widths and finite length arranged in a periodic and quasiperiodic order. The main features of the hysteresis loop are determined by different shape anisotropies of the component elements and the dipolar interactions between them. We showed, that the dipolar interactions between nanowires forming a ribbon can be controlled by change a distance between the neighboring ribbons. The quasiperiodic order can influence the hyste…
We have investigated dynamic behaviors of the magnetic domain wall under perpendicular magnetic field pulses in ferromagnetic nanowires using micromagnetic simulations. It has been found that the perpendicular magnetic field pulse can trigger the magnetic domain wall motion, where all the field torques are kept to be on the plane of nanowire strip. The magnetic domain wall speed faster than several hundreds meters per second is predicted without the Walker breakdown for the perpendicular magnetic driving field stronger than $200~\mathrm{mT}$. Interestingly, the dynamic behavior of the moving m…
The Dzyaloshinskii Moriya Interaction (DMI) has laid the foundation for many novel chiral structures such as Skyrmions. In most of the studies so far, the DMI is present in the whole of the magnetic layer. Here, we report our investigations on a ferromagnetic nanowire where DMI is confined to a nanoscale region. We observe that the local modulation of magnetic properties causes oscillation of domain walls under the influence of spin-transfer torque. The oscillation frequency is tunable within a few GHz, making this observation potentially useful for applications in neuromorphic computing.
We study optical properties of arrays of ultrathin nanowires by means of the Brillouin scattering of light on magnons. We employ the Stokes/anti-Stokes scattering asymmetry to probe the circular polarization of a local electric field induced inside nanowires by linearly polarized light waves. We observe the anomalous polarization conversion of the opposite sign than that in a bulk medium or thick nanowires with a great enhancement of the degree of circular polarization attributed to an unconventional refraction in the nanowire medium.
We have measured the electrical resistivity of a single strand of a ferromagnetic Ni nanowire of diameter 55 nm using a 4-probe method in the temperature range 3 K-300 K. The wire used is chemically pure and is a high quality oriented single crystalline sample in which the temperature independent residual resistivity is determined predominantly by surface scattering. Precise evaluation of the temperature dependent resistivity ($ρ$) allowed us to identify quantitatively the electron-phonon contribution (characterized by a Debye temperature $θ_R$) as well as the spin-wave contribution which is s…
We demonstrate that for multilayered magnetic nanowires, where the thickness and composition of the individual layers has been carefully chosen, domain walls can be pinned at non-topographic sites created purely by ion irradiation in a focused ion beam system. The pinning results from irradiation induced alloying leading to magnetic property modification only in the affected regions. Using Lorentz transmission electron microscopy, we have studied the pinning behavior of domain walls at the irradiation sites. Depending on the irradiation dose, a single line feature not only pinned the domain wa…
The dynamics of the low energy excitations in a ferromagnet is studied in case a temperature gradient is coupled to the local magnetization. Due to the different time scales of changing temperature and magnetization it is argued that only the coupling between the spatially varying part of the temperature field and the magnetization is relevant. Using variational principles the evolution equation for the magnetic system is found which is strongly influenced by the local temperature profile. The system offers damped spin wave excitations where the strength of damping is determined by the magneto…
The current mediated domain-wall dynamics in a thin ferromagnetic wire is investigated. We derive the effective equations of motion of the domain wall. They are used to study the possibility to optimize the power supplied by electric current for the motion of domain walls in a nanowire. We show that a certain resonant time-dependent current moving a domain wall can significantly reduce the Joule heating in the wire, and thus it can lead to a novel proposal for the most energy efficient memory devices. We discuss how Gilbert damping, non-adiabatic spin transfer torque, and the presence of Dzyal…
We present a joint experimental and theoretical study of parametric resonance of spin wave eigenmodes in Ni$_{80}$Fe$_{20}$/Pt bilayer nanowires. Using electrically detected magnetic resonance, we measure the spectrum of spin wave eigenmodes in transversely magnetized nanowires and study parametric excitation of these eigenmodes by a microwave magnetic field. We also develop an analytical theory of spin wave eigenmodes and their parametric excitation in the nanowire geometry that takes into account magnetic dilution at the nanowire edges. We measure tuning of the parametric resonance threshold…
We present fractional quantum Hall domain walls confined in a gate-defined wire structure. Our experiments utilize spatial oscillation of domain walls driven by radio frequency electric fields to cause nuclear magnetic resonance. The resulting spectra are discussed in terms of both large quadrupole fields created around the wire and hyperfine fields associated with the oscillating domain walls. This provides the experimental fact that the domain walls survive near the confined geometry despite of potential deformation, by which a localized magnetic resonance is allowed in electrical means.
We present a circuit model to describe the electron transport through a domain wall in a ferromagnetic nanowire. The domain wall is treated as a coherent 4-terminal device with incoming and outgoing channels of spin up and down and the spin-dependent scattering in the vicinity of the wall is modelled using classical resistances. We derive the conductance of the circuit in terms of general conductance parameters for a domain wall. We then calculate these conductance parameters for the case of ballistic transport through the domain wall, and obtain a simple formula for the domain wall magnetores…
The effect of the domain wall (DW) on the conductance in a ballistic ferromagnetic nanowire (FMNW) is revisited by exploiting a specific perturbation theory which is effective for a thin DW; the thinness is often the case in currently interested conductance measurements on FMNWs. Including the Hund coupling between carrier spins and local spins in a DW, the conductance of a FMNW in the presence of a very thin DW is calculated within the Landauer-Büttiker formalism. It is revealed that the conductance plateaus are modified significantly, and the switching of the quantization unit from $e^2/h$ t…
Spin torque from spin current applied to a nanoscale region of a ferromagnet can act as negative magnetic damping and thereby excite self-oscillations of its magnetization. In contrast, spin torque uniformly applied to the magnetization of an extended ferromagnetic film does not generate self-oscillatory magnetic dynamics but leads to reduction of the saturation magnetization. Here we report studies of the effect of spin torque on a system of intermediate dimensionality - a ferromagnetic nanowire. We observe coherent self-oscillations of magnetization in a ferromagnetic nanowire serving as the…
The current-induced motion of a domain wall in a semicircle nanowire with applied Zeeman field is investigated. Starting from a micromagnetic model we derive an analytical solution which characterizes the domain-wall motion as a harmonic oscillation. This solution relates the micromagnetic material parameters with the dynamical characteristics of a harmonic oscillator, i.e., domain-wall mass, resonance frequency, damping constant, and force acting on the wall. For wires with strong curvature the dipole moment of the wall as well as its geometry influence the eigenmodes of the oscillator. Based…
Hybrid semiconducting nanowire devices combining epitaxial superconductor and ferromagnetic insulator layers have been recently explored experimentally as an alternative platform for topological superconductivity at zero applied magnetic field. In this proof-of-principle work we show that the topological regime can be reached in actual devices depending on some geometrical constraints. To this end, we perform numerical simulations of InAs wires in which we explicitly include the superconducting Al and magnetic EuS shells, as well as the interaction with the electrostatic environment at a self-…
Achieving high velocities of magnetic domain walls is a crucial factor for their use as information carriers in modern nanoelectronic applications. In nanomagnetism and spintronics, these velocities are often limited either by internal domain wall instabilities, known as the Walker breakdown phenomenon, or by spin wave emission, known as the magnonic regime. In the rigid domain wall model, the maximum magnon velocity acts as an effective "speed of light", providing a relativistic analogy for the domain wall speed limitation. Cylindrical magnetic nanowires are an example of systems with the abs…
We study current induced magnetization dynamics in a long thin ferromagnetic wire with Dzyaloshinskii-Moriya interaction (DMI). We find a spiral domain wall configuration of the magnetization and obtain an analytical expression for the width of the domain wall as a function of the interaction strengths. Our findings show that above a certain value of DMI a domain wall configuration cannot exist in the wire. Below this value we determine the domain wall dynamics for small currents, and calculate the drift velocity of the domain wall along the wire. We show that the DMI suppresses the minimum va…
We present magnetoresistance (MR) experiments on an InAs nanowire quantum dot device with two ferromagnetic sidegates (FSGs) in a split-gate geometry. The wire segment can be electrically tuned to a single dot or to a double dot regime using the FSGs and a backgate. In both regimes we find a strong MR and a sharp MR switching of up to 25\% at the field at which the magnetizations of the FSGs are inverted by the external field. The sign and amplitude of the MR and the MR switching can both be tuned electrically by the FSGs. In a double dot regime close to pinch-off we find {\it two} sharp trans…
We propose a Hamiltonian dynamics formalism for the current and magnetic field driven dynamics of ferromagnetic and antiferromagnetic domain walls in one dimensional systems. To demonstrate the power of this formalism, we derive Hamilton equations of motion via Poisson brackets based on the Landau-Lifshitz-Gilbert phenomenology, and add dissipative dynamics via the evolution of the energy. We use this approach to study current induced domain wall motion and compute the drift velocity. For the antiferromagnetic case, we show that a nonzero magnetic moment is induced in the domain wall, which in…
We study current-induced domain-wall motion in a narrow ferromagnetic wire. We propose a way to move domain walls with a resonant time-dependent current which dramatically decreases the Ohmic losses in the wire and allows to drive the domain wall with higher speed without burning the wire. For any domain wall velocity we find the time-dependence of the current needed to minimize the Ohmic losses. Below a critical domain-wall velocity specified by the parameters of the wire the minimal Ohmic losses are achieved by dc current. Furthermore, we identify the wire parameters for which the losses red…
We theoretically investigate the interlayer dipolar and exchange couplings for an array of metallic magnetic nanowires grown on top of an extended ultrathin yttrium iron garnet film. The calculated interlayer dipolar coupling agrees with observed anticrossings [Chen \emph{et al.}, Phys. Rev. Lett. \textbf{120}, 217202 (2018)], concluding that the interlayer exchange coupling is suppressed by a spacer layer between the nanowires and film. The Kittel mode in the nanowire array couples chirally to spin waves in the film, even though Damon-Eshbach surface modes do not exist. The chirality is suppr…
Iron phthalocyanine (FePc) is a molecular semiconductor whose building blocks are one-dimensional ferromagnetic chains. We show that its optical and magnetic properties are controlled by the growth strategy, obtaining extremely high coercivities of over 1 T and modulating the exchange constant between 15 and 29 K through tuning the crystal phase by switching from organic molecular beam deposition, producing continuous thin films of nanocrystals with controlled orientations, to organic vapour phase deposition, producing ultralong nanowires. Magnetisation measurements are analysed using a suite …
We theoretically investigate the transport properties of a quasi one dimensional ferromagnet-superconductor junction where the superconductor consists of mixed singlet and triplet pairings. We show that the relative orientation of the stoner field ($\bf{\tilde{h}}$) in the ferromagnetic lead and the $\bf{d}$ vector of the superconductor acts like a on-off switch for the zero bias conductance of the device. In the regime, where triplet pairing amplitude dominates over the singlet counterpart (topological phase), a pair of Majorana zero modes appear at each end of the superconducting part of the…
Motivated by a recent experiment in which zero-bias peaks have been observed in scanning tunneling microscopy (STM) experiments performed on chains of magnetic atoms on a superconductor, we show, by generalizing earlier work, that a multichannel ferromagnetic wire deposited on a spin-orbit coupled superconducting substrate can realize a non-trivial chiral topological superconducting state with Majorana bound states localized at the wire ends. The non-trivial topological state occurs for generic parameters requiring no fine tuning, at least for very large exchange spin splitting in the wire. We…
We quantify the probability per unit Euclidean-time of reversing the magnetization of a $π$-Bloch vector, which describes the Ferromagnetic Domain Walls of a Ferromagnetic Nanowire at finite-temperatures, by evaluating the saddlepoint solution of the grand canonical partition function for the Ferromagnetic Nanowire consisting of $N$ such soliton and anti-soliton states. Our approach, based on Langer's Theory, treats the double Sine-Gordon model that defines the $π$-Bloch vectors via a procedure of nonperturbative renormalization, and uses importance sampling methods to minimise the free energy…
To understand quantum mechanical transport in ferromagnetic semiconductor the knowledge of basic material properties like phase coherence length and corresponding dephasing mechanism are indispensable ingredients. The lack of observable quantum phenomena prevented experimental access to these quantities so far. Here we report about the observations of universal conductance fluctuations in ferromagnetic (Ga,Mn)As. The analysis of the length and temperature dependence of the fluctuations reveals a T^{-1} dependence of the dephasing time.
Signatures of Majorana zero modes (MZMs), which are the building blocks for fault-tolerant topological quantum computing, have been observed in semiconductor nanowires (NW) with strong spin-orbital-interaction (SOI), such as InSb and InAs NWs with proximity-induced superconductivity. Realizing topological superconductivity and MZMs in this most widely-studied platform also requires eliminating spin degeneracy, which is realized by applying a magnetic field to induce a helical gap. However, the applied field can adversely impact the induced superconducting state in the NWs and also places geome…
We study the effect of a domain wall on the electronic transport in ferromagnetic quantum wires. Due to the transverse confinement, conduction channels arise. In the presence of a domain wall, spin up and spin down electrons in these channels become coupled. For very short domain walls or at high longitudinal kinetic energy, this coupling is weak, leads to very few spin flips, and a perturbative treatment is possible. For very long domain wall structures, the spin follows adiabatically the local magnetization orientation, suppressing the effect of the domain wall on the total transmission, but…
Spin-polarized electric current exerts torque on local magnetic spins, resulting in magnetic domain-wall (DW) motion in ferromagnetic nanowires. Such current-driven DW motion opens great opportunities toward next-generation magnetic devices controlled by current instead of magnetic field. However, the nature of the current-driven DW motion--considered qualitatively different from magnetic-field-driven DW motion--remains yet unclear mainly due to the painfully high operation current densities J_OP, which introduce uncontrollable experimental artefacts with serious Joule heating. It is also cruc…
We consider interaction effects related to a nonuniform magnetization in ferromagnetic nanowires and their possible generalization to nanorings. First we show that the electric current in a ferromagnetic nanowire with more than one domain wall induces an exchange coupling between the walls mediated by the spin-dependent interference of scattered carriers. This interaction reveals a complex behavior as a function of mutual orientations and separation of the domain walls, thus affecting the domain wall dynamics. Then we consider how the theory should be modified in the case of a magnetized quant…
We report Coulomb blockade transport studies of semiconducting InAs nanowires grown with epitaxial superconducting Al and ferromagnetic insulator EuS on overlapping facets. Comparing experiment to a theoretical model, we associate cotunneling features in even-odd bias spectra with spin-polarized Andreev levels. Results are consistent with zero-field spin splitting exceeding the induced superconducting gap. Energies of subgap states are tunable on either side of zero via electrostatic gates.
A new type of magnonic crystals, curvature induced ones, is realized in ferromagnetic nanowires with periodically deformed shape. A magnon band structure of such crystal is fully determined by its curvature: the developed theory is well confirmed by simulations. An application to nanoscale spintronic devises with the geometrically tunable parameters is proposed, namely, to filter elements.
We report that the irreversible magnetization switching process in ferromagnetic nanoparticles is governed by the formation and dynamics of topological point-defects in the form of hedgehog-antihedgehog pairs. After nucleation, these pairs rapidly separate with speeds exceeding domain wall velocities, and they generate an emergent electric field of solenoidal character and substantial magnitude.
We solve the Landau-Lifshitz-Gilbert equation in the finite-temperature regime, where thermal fluctuations are modeled by a random magnetic field whose variance is proportional to the temperature. By rescaling the temperature proportionally to the computational cell size $Δx$ ($T \to T\,Δx/a_{\text{eff}}$, where $a_{\text{eff}}$ is the lattice constant) [M. B. Hahn, J. Phys. Comm., 3:075009, 2019], we obtain Curie temperatures $T_{\text{C}}$ that are in line with the experimental values for cobalt, iron and nickel. For finite-sized objects such as nanowires (1D) and nanolayers (2D), the Curie …
We report on the observation of weak localization in arrays of (Ga,Mn)As nanowires at millikelvin temperatures. The corresponding phase coherence length is typically between 100 nm and 200 nm at 20 mK. Strong spin-orbit interaction in the material is manifested by a weak anti-localization correction around zero magnetic field.
Nitrogen-vacancy centers in diamond have recently been established as effective sensors of the magnetization dynamics in vicinal ferromagnetic materials. We demonstrate sub-100 nm placement accuracy of nitrogen-vacancy-containing nanodiamonds and use these as local sensors that probe optically detected ferromagnetic resonance in mesoscopically patterned Permalloy islands. These measurements reveal variations in the ferromagnetic resonance signal at different sites on these structures with distinct behavior in the edge and the bulk of patterned features. These test measurements establish an eas…
