Abstract:Transfer of angular momentum from a spin-polarized current to a ferromagnet provides an efficient means to control the dynamics of nanomagnets. A peculiar consequence of this spin-torque, the ability to induce persistent oscillations of a nanomagnet by applying a dc current, has previously been reported only for spatially uniform nanomagnets. Here we demonstrate that a quintessentially nonuniform magnetic structure, a magnetic vortex, isolated within a nanoscale spin valve structure, can be excited into persistent microwave-frequency oscillations by a spin-polarized dc current. Comparison to micromagnetic simulations leads to identification of the oscillations with a precession of the vortex core. The oscillations, which can be obtained in essentially zero magnetic field, exhibit linewidths that can be narrower than 300 kHz, making these highly compact spin-torque vortex oscillator devices potential candidates for microwave signalprocessing applications, and a powerful new tool for fundamental studies of vortex dynamics in magnetic nanostructures. Pribiag et al.1A spin-polarized electron current can apply a torque on the local magnetization of a ferromagnet. This spin-transfer effect 1,2 provides a new method for manipulating magnetic systems at the nanoscale without the application of magnetic fields and is expected to lead to future data storage and information processing applications 3 . Experiments have demonstrated that spin-torque can be used to induce current-controlled hysteretic switching, as well as to drive persistent microwave dynamics in spin-valve devices 3,4,5,6,7,8,9,10,11,12 . While it is known that spin-torque switching of a magnetic element can sometimes occur via non-uniform magnetic states 13 , a central remaining question is whether spin-torque can be used to efficiently excite steady-state magnetization oscillations in strongly non-uniform magnetic configurations in a manner suitable for fundamental investigations of nanomagnetic dynamics and improved device performance. A relatively simple type of non-uniform magnetic structure is a magnetic vortex, the lowest-energy configuration of magnetic structures just above the singledomain length scale 14 . Previous studies, typically performed on single-layer permalloy (Py) structures, focused on the transient or resonant response of a magnetic vortex to an applied magnetic field and identified the lowest excitation mode of a vortex as a gyrotropic precession of the core 15,16,17,18 . It has also been demonstrated that the vortex core polarization can be efficiently switched by short radio-frequency magnetic field pulses 19 . Recently, the spin-transfer effect has been used to drive a magnetic vortex into resonant precession by means of an alternating current incident on a single Py dot 20 . Here we report by means of direct frequency-domain measurements that a dc spinpolarized current can drive highly coherent gigahertz-frequency steady-state oscillations of the magnetic vortex in a nanoscale magnetic device. The high sensitivity of ou...

Double quantum dot in the few-electron regime is achieved using local gating in an InSb nanowire. The spectrum of two-electron eigenstates is investigated using electric dipole spin resonance. Singlettriplet level repulsion caused by spin-orbit interaction is observed. The size and the anisotropy of singlet-triplet repulsion are used to determine the magnitude and the orientation of the spin-orbit effective field in an InSb nanowire double dot. The obtained results are confirmed using spin blockade leakage current anisotropy and transport spectroscopy of individual quantum dots.PACS numbers: 73.63. Kv, 85.35.Be The spin-orbit interaction (SOI) describes coupling between the motion of an electron and its spin. In one dimension, where electrons can move only to the left or to the right, the SOI couples this left or right motion to either spin-up or spin-down. An extreme situation occurs in what is called a helical liquid [1] where, in the presence of magnetic field, all spin-up electrons move to the left and all spin-down electrons to the right. As proposed recently [2,3], a helical liquid in proximity to a superconductor can generate Majorana fermions [4]. The search for Majorana fermions in 1D conductors is focused on finding the best material in terms of a strong spin-orbit interaction and large Landé g-factors. The latter is required for a helical liquid to exist at magnetic fields that do not suppress superconductivity. High g-factors of the order 50, strong SOI and the ability to induce superconductivity put forward InSb nanowires [5,6] as a natural platform for the realization of 1D topological states.The SOI can be expressed as an effective magnetic field B SO that depends on the electron momentum. An electron moving through the wire undergoes spin precession around B SO with a π rotation over a distance l SO called the spin-orbit length (see Fig. 1(a)). The length l SO is a direct measure of the SOI strength: a stronger SOI results in a shorter l SO . In this letter, we use spin spectra of single electrons in quantum dots [7] to extract l SO and the direction of B SO . In quantum dots, the SOI hybridizes states with different spin [5,8,9]. For a single electron, the SOI-hybridized spin-up and spin-down states form a spin-orbit qubit [10,11]. For two electrons SOI hybridization induces level repulsion between singlet and triplet states. The resulting level-repulsion gap between the well-defined qubit states can be used to measure the SOI: the gap size is determined by l SO [5,8,9] and the gap anisotropy indicates the direction of B SO [12][13][14]. Double quantum dots in InSb nanowires are defined by local gating (Figs. 1(b),1(c)). A finite voltage is applied across the source and drain electrodes; and the current through the nanowire is measured. Five gates underneath the wire create the confinement potential and control the electron number on the two dots [9,15]. We focus on the (1,1) charge configuration ( Fig. 1(d)), in which both the left and the right dot contain exactly one electron, each of them...

Topological superconductivity is an exotic state of matter that supports Majorana zero-modes, which have been predicted to occur in the surface states of three-dimensional systems, in the edge states of two-dimensional systems, and in one-dimensional wires. Localized Majorana zero-modes obey non-Abelian exchange statistics, making them interesting building blocks for topological quantum computing. Here, we report superconductivity induced in the edge modes of semiconducting InAs/GaSb quantum wells, a two-dimensional topological insulator. Using superconducting quantum interference we demonstrate gate-tuning between edge-dominated and bulk-dominated regimes of superconducting transport. The edge-dominated regime arises only under conditions of high-bulk resistivity, which we associate with the two-dimensional topological phase. These experiments establish InAs/GaSb as a promising platform for the confinement of Majoranas into localized states, enabling future investigations of non-Abelian statistics.

We use magnetoconductance measurements in dual-gated InSb nanowire devices, together with a theoretical analysis of weak antilocalization, to accurately extract spin-orbit strength. In particular, we show that magnetoconductance in our three-dimensional wires is very different compared to wires in two-dimensional electron gases. We obtain a large Rashba spin-orbit strength of 0.5-1 eVÅ corresponding to a spin-orbit energy of 0.25-1 meV. These values underline the potential of InSb nanowires in the study of Majorana fermions in hybrid semiconductor-superconductor devices. Hybrid semiconductor nanowire-superconductor devices are a promising platform for the study of topological superconductivity [1]. Such devices can host Majorana fermions [2,3], bound states with non-Abelian exchange statistics. The realization of a stable topological state requires an energy gap that exceeds the temperature at which experiments are performed (∼50 mK). The strength of the spin-orbit interaction (SOI) is the main parameter that determines the size of this topological gap [4] and thus the potential of these devices for the study of Majorana fermions. The identification of nanowire devices with a strong SOI is therefore essential. This entails both performing measurements on a suitable material and device geometry as well as establishing theory to extract the SOI strength.InSb nanowires are a natural candidate to create devices with a strong SOI, since bulk InSb has a strong SOI [5,6]. Nanowires have been used in several experiments that showed the first signatures of Majorana fermions [7][8][9][10]. Nanowires are either fabricated by etching out wires in planar heterostructures or are grown bottom up. The strong confinement in the growth direction makes etched wires two dimensional (2D) even at high density. SOI has been studied in 2D InSb wires [11] and in planar InSb heterostructures [12], from which a SOI due to structural inversion asymmetry [13], a Rashba SOI α R of 0.03 eVÅ has been obtained [12]. Bottom-up grown nanowires are three dimensional (3D) when the Fermi wavelength is smaller than the wire diameter. In InSb wires of this type, SOI has been studied by performing spectroscopy on quantum dots [14,15] [19,20]. Our approach is to use a high-k dielectric in combination with a top gate that covers the InSb nanowire. The standard method to extract SOI strength in extended regions is through low-field magnetoconductance (MC) measurements [21,22]. Quantum interference (see Fig. 1) in the presence of a strong SOI results in an increased conductance, called weak antilocalization (WAL) [23], that reduces to its classical value when a magnetic field is applied [24]. From fits of MC data to theory a spin relaxation length is extracted. If spin relaxation results from inversion asymmetry, a spin precession length and SOI strength can be defined. To extract SOI strength in nanowires the theory should contain (1) the length over which the electron dephases in the presence of a magnetic field, the magnetic dephasing length [25], and (...