We present an optimal field-free protocol for current-induced switching of a perpendicularly magnetized ferromagnetic insulator nanoelement on the surface of a topological insulator. The time dependence of in-plane components of the surface current, which drives the magnetization reversal via the Dirac spin-orbit torque with minimal Joule heating, is derived analytically as a function of the switching time and material properties. Our analysis identifies that energy-efficient switching is achieved for vanishing damping-like torque. The optimal reversal time that balances switching speed and energy efficiency is determined. When we compare topological insulators to heavy-metal systems, we find similar switching costs for the optimal ratio between the spin-orbit torque coefficients. However, topological insulators offer the advantage of tunable material properties. Finally, we propose a robust and efficient simplified switching protocol using a down-chirped rotating current pulse, tailored to realistic ferromagnetic/topological insulator systems.

Den här studien syftar till att undersöka hur gymnasieelever tolkar visuella representationer av magneter som förekommer i läroböcker i gymnasiet. Genom observationer av elever som löser uppgifter undersöks elevernas tolkningar av representationer som förekommer i fysikundervisning. Data analyseras tematiskt och en induktiv analys görs inom varje tema. Huvudresultaten är att i) eleverna använder spontana metaforer för att förklara magnetiska fenomen samtidigt som de väljer förklaringsmodeller som innehåller elektriska laddningar, samt att ii) eleverna uppfattar flera olika meningsförmedlande faktorer hos magneter i visuella representationer. I mångtydiga visuella representationer av magneter använder eleverna olika huvudsakliga strategier för att analysera representationerna vilket kan leda till motstridiga tolkningar beroende på hur den visuella representationen är utformad. Elevernas spontana metaforer för att beskriva orsaken till permanentmagneters magnetism riskerar att leda till förklaringsmodeller baserade på elektriska laddningar, vilket i sin tur kan ge en bristande insikt i att magnetism hos permanentmagneter är en materialegenskap. Dagens snabba utveckling av magnetiska tillämpningar, såsom magnetiska hårddiskar och magnetiska motorer i elbilar, gör att fysikämnet behöver lyfta aspekter av hållbar utveckling kopplat till magnetiska material då dessa är en ändlig resurs.

The conventional Josephson effect may be modified by introducing spin-active scattering in the interface layer of the junction. Here, we discuss a Josephson junction consisting of two s-wave superconducting leads coupled over a classical spin that precesses with the Larmor frequency due to an external magnetic field. This magnetically active interface results in a time-dependent boundary condition with different tunnelling amplitudes for spin-up and -down quasi- particles and where the precession produces spin-flip scattering processes. As a result, the Andreev states develop sidebands and a non-equilibrium population that depend on the details of the spin precession. The Andreev states carry a steady-state Josephson charge current and a time-dependent spin current, whose current–phase relations could be used to characterize the precessing spin. The spin current is supported by spin-triplet correlations induced by the spin precession and creates a feedback effect on the classical spin in the form of a torque that shifts the precession frequency. By applying a bias voltage, the Josephson frequency adds another complexity to the situation and may create resonances together with the Larmor frequency. These Shapiro resonances manifest as torques and, under suitable 2conditions, are able to reverse the direction of the classical spin in sub-nanosecond time. Another characteristic feature is the subharmonic gap structure in the DC charge current displaying an even–odd effect attributable to precession-assisted multiple Andreev reflections. This article is part of the theme issue ‘Andreev bound states’.

Using the non-equilibrium Green’s function method and the Keldysh formalism, we study the effects of spin–orbit interactions and time-reversal symmetry breaking exchange fields on non-equilibrium quantum transport in graphene armchair nanoribbons. We identify signatures of the quantum spin Hall (QSH) and the quantum anomalous Hall (QAH) phases in nonequilibrium edge transport by calculating the spin-resolved real space charge density and local currents at the nanoribbon edges. We find that the QSH phase, which is realized in a system with intrinsic spin–orbit coupling, is characterized by chiral counter-propagating local spin currents summing up to a net charge flow with opposite spin polarization at the edges. In the QAH phase, emerging in the presence of Rashba spin–orbit coupling and a ferromagnetic exchange field, two chiral edge channels with opposite spins propagate in the same direction at each edge, generating an unpolarized charge current and a quantized Hall conductance  . Increasing the intrinsic spin–orbit coupling causes a transition from the QAH to the QSH phase, evinced by characteristic changes in the non-equilibrium edge transport. In contrast, an antiferromagnetic exchange field can coexist with a QSH phase, but can never induce a QAH phase due to a symmetry that combines time-reversal and sublattice translational symmetry.

Antiferromagnets may exhibit spin superfluidity since the dipole interaction is weak. We seek toestablish that this phenomenon occurs in insulators such as NiO, which is a good spin conductor accordingto previous studies. We investigate nonlocal spin transport in a planar antiferromagnetic insulator witha weak uniaxial anisotropy. The anisotropy hinders spin superfluidity by creating a substantial thresholdthat the current must overcome. Nevertheless, we show that applying a high magnetic field removes thisobstacle near the spin-flop transition of the antiferromagnet. Importantly, the spin superfluidity can thenpersist across many micrometers, even in dirty samples.

Inelastic tunneling of electrons can generate the emission of photons with energies intuitively limited by the applied bias voltage. However, experiments indicate that more complex processes involving the interaction of electrons with plasmon polaritons lead to photon emission with overbias energies. We recently proposed a model of this observation in Phys. Rev. Lett. 113, 066801 (2014), in analogy to the dynamical Coulomb blockade, originally developed for treating the electromagnetic environment in mesoscopic circuits. This model describes the correlated tunneling of two electrons interacting with a local plasmon-polariton mode, represented by a resonant circuit, and shows that the overbias emission is due to the non-Gaussian fluctuations. Here we extend our model to study the overbias emission at finite temperature. We find that the thermal smearing strongly masks the overbias emission. Hence, the detection of the correlated tunneling processes requires temperatures k(B)T much lower than the bias energy eV and the plasmon energy h omega(0), a condition which is fortunately realized experimentally.

Understanding tunneling from an atomically sharp tip to a metallic surface requires to account for interactions on a nanoscopic scale. Inelastic tunneling of electrons generates emission of photons, whose energies intuitively should be limited by the applied bias voltage. However, experiments [Phys. Rev. Lett. 102, 057401 (2009)] indicate that more complex processes involving the interaction of electrons with plasmon polaritons lead to photon emission characterized by over-bias energies. We propose a model of this observation in analogy to the dynamical Coulomb blockade, originally developed for treating the electronic environment in mesoscopic circuits. We explain the experimental finding quantitatively by the correlated tunneling of two electrons interacting with an LRC circuit modeling the local plasmon-polariton mode. To explain the over-bias emission, the non-Gaussian statistics of the tunneling dynamics of the electrons is essential.

In ferromagnets, magnons may condense into a single quantum state. Analogous to superconductors,this quantum state may support transport without dissipation. Recent works suggest that longitudinal spintransport through a thin-film ferromagnet is an example of spin superfluidity. Although intriguing, thistantalizing picture ignores long-range dipole interactions; here, we demonstrate that such interactionsdramatically affect spin transport. In single-film ferromagnets,“spin superfluidity”only exists at lengthscales (a few hundred nanometers in yttrium iron garnet) somewhat larger than the exchange length. Overlonger distances, dipolar interactions destroy spin superfluidity. Nevertheless, we predict the reemergenceof spin superfluidity in trilayer ferromagnet-normal metal-ferromagnet films that are∼1μm in size. Suchsystems also exhibit other types of long-range spin transport in samples that are several micrometers in size.

Understanding tunneling from an atomically sharp tip to a metallic surface requires us to account for interactions on a nanoscopic scale. Inelastic tunneling of electrons generates emission of photons, whose energies intuitively should be limited by the applied bias voltage. However, experiments [G. Schull et al., Phys. Rev. Lett. 102, 057401 (2009)] indicate that more complex processes involving the interaction of electrons with plasmon polaritons lead to photon emission characterized by overbias energies. We propose a model of this observation in analogy to the dynamical Coulomb blockade, originally developed for treating the electronic environment in mesoscopic circuits. We explain the experimental finding quantitatively by the correlated tunneling of two electrons interacting with a LRC circuit modeling the local plasmon-polariton mode. To explain the overbias emission, the non-Gaussian statistics of the tunneling dynamics of the electrons is essential.