Orbital Rashba Effect as a Platform for Robust Orbital Photocurrents.

Orbital current has emerged over the past years as one of the key novel concepts in magnetotransport. Here, we demonstrate that laser pulses can be used to generate large and robust nonrelativistic orbital currents in systems where the inversion symmetry is broken by the orbital Rashba effect. By referring to model and first principles tools, we demonstrate that orbital Rashba effect, accompanied by crystal field splitting, can mediate robust orbital photocurrents without a need for spin-orbit interaction even in metallic systems. We show that such nonrelativistic orbital photocurrents are translated into derivative photocurrents of spin when relativistic effects are taken into account. We thus promote orbital photocurrents as a promising platform for optical generation of currents of angular momentum, and discuss their possible applications.

Topological-chiral magnetic interactions driven by emergent orbital magnetism.

Two hundred years ago, Ampère discovered that electric loops in which currents of electrons are generated by a penetrating magnetic field can mutually interact. Here we show that Ampère's observation can be transferred to the quantum realm of interactions between triangular plaquettes of spins on a lattice, where the electrical currents at the atomic scale are associated with the orbital motion of electrons in response to the non-coplanarity of neighbouring spins playing the role of a magnetic field. The resulting topological orbital moment underlies the relation of the orbital dynamics with the topology of the spin structure. We demonstrate that the interactions of the topological orbital moments with each other and with the spins form a new class of magnetic interactions [Formula: see text] topological-chiral interactions [Formula: see text] which can dominate over the Dzyaloshinskii-Moriya interaction, thus opening a path for realizing new classes of chiral magnetic materials with three-dimensional magnetization textures such as hopfions.

Modification of Dzyaloshinskii-Moriya-Interaction-Stabilized Domain Wall Chirality by Driving Currents.

We measure and analyze the chirality of Dzyaloshinskii-Moriya-interaction (DMI) stabilized spin textures in multilayers of Ta|Co_{20}F_{60}B_{20}|MgO. The effective DMI is measured experimentally using domain wall motion measurements, both in the presence (using spin-orbit torques) and absence of driving currents (using magnetic fields). We observe that the current-induced domain wall motion yields a change in effective DMI magnitude and opposite domain wall chirality when compared to field-induced domain wall motion (without current). We explore this effect, which we refer to as current-induced DMI, by providing possible explanations for its emergence, and explore the possibility of its manifestation in the framework of recent theoretical predictions of DMI modifications due to spin currents.

Femtosecond control of electric currents in metallic ferromagnetic heterostructures.

The idea to use not only the charge but also the spin of electrons in the operation of electronic devices has led to the development of spintronics, causing a revolution in how information is stored and processed. A novel advancement would be to develop ultrafast spintronics using femtosecond laser pulses. Employing terahertz (10(12) Hz) emission spectroscopy and exploiting the spin-orbit interaction, we demonstrate the optical generation of electric photocurrents in metallic ferromagnetic heterostructures at the femtosecond timescale. The direction of the photocurrent is controlled by the helicity of the circularly polarized light. These results open up new opportunities for realizing spintronics in the unprecedented terahertz regime and provide new insights in all-optical control of magnetism.

Electrical switching of an antiferromagnet.

Antiferromagnets are hard to control by external magnetic fields because of the alternating directions of magnetic moments on individual atoms and the resulting zero net magnetization. However, relativistic quantum mechanics allows for generating current-induced internal fields whose sign alternates with the periodicity of the antiferromagnetic lattice. Using these fields, which couple strongly to the antiferromagnetic order, we demonstrate room-temperature electrical switching between stable configurations in antiferromagnetic CuMnAs thin-film devices by applied current with magnitudes of order 10(6) ampere per square centimeter. Electrical writing is combined in our solid-state memory with electrical readout and the stored magnetic state is insensitive to and produces no external magnetic field perturbations, which illustrates the unique merits of antiferromagnets for spintronics.

Ballistic Anisotropic Magnetoresistance of Single-Atom Contacts.

Anisotropic magnetoresistance, that is, the sensitivity of the electrical resistance of magnetic materials on the magnetization direction, is expected to be strongly enhanced in ballistic transport through nanoscale junctions. However, unambiguous experimental evidence of this effect is difficult to achieve. We utilize single-atom junctions to measure this ballistic anisotropic magnetoresistance (AMR). Single Co and Ir atoms are deposited on domains and domain walls of ferromagnetic Fe layers on W(110) to control their magnetization directions. They are contacted with nonmagnetic tips in a low-temperature scanning tunneling microscope to measure the junction conductances. Large changes of the magnetoresistance occur from the tunneling to the ballistic regime due to the competition of localized and delocalized d-orbitals, which are differently affected by spin-orbit coupling. This work shows that engineering the AMR at the single atom level is feasible.

Dzyaloshinskii-Moriya Interaction and Hall Effects in the Skyrmion Phase of Mn(1-x) Fe(x)Ge.

We carry out density functional theory calculations which demonstrate that the electron dynamics in the Skyrmion phase of Fe-rich Mn_{1-x}Fe_{x}Ge alloys is governed by Berry phase physics. We observe that the magnitude of the Dzyaloshinskii-Moriya interaction directly related to the mixed space-momentum Berry phases, changes sign and magnitude with concentration x in direct correlation with the data of Shibata et al. [Nat. Nanotechnol. 8, 723 (2013)]. The computed anomalous and topological Hall effects in FeGe are also in good agreement with available experiments. We further develop a simple tight-binding model able to explain these findings. Finally, we show that the adiabatic Berry phase picture is violated in the Mn-rich limit of the alloys.

Effect of magnetism and light sp-dopants on chain creation in Ir and Pt break junctions.

Applying the generalization of the model for chain formation in break-junctions (Di Napoli et al 2012 J. Phys.: Condens. Matter 24 135501), we study the effect of light impurities on the energetics and elongation properties of Pt and Ir chains. Our model enables us to develop a tool ideal for detailed analysis of impurity-assisted chain formation, in which zigzag bonds play an important role. In particular we focus on H (s-like) and O (p-like) impurities and assume, for simplicity, that the presence of impurity atoms in experiments results in a ..M-X-M-X-... (M: metal, X: impurity) chain structure in between the metallic leads. Feeding our model with material-specific parameters from systematic full-potential first-principles calculations, we find that the presence of such impurities strongly affects the binding properties of the chains. We find that, while both types of impurities enhance the probability of chains being elongated, the s-like impurities lower the chain's stability. We also analyze the effect of magnetism and spin-orbit interaction on the growth properties of the chains.

Real-space and reciprocal-space Berry phases in the Hall effect of Mn(1-x)Fe(x)Si.

We report an experimental and computational study of the Hall effect in Mn(1-x)Fe(x)Si, as complemented by measurements in Mn(1-x)Co(x)Si, when helimagnetic order is suppressed under substitutional doping. For small x the anomalous Hall effect (AHE) and the topological Hall effect (THE) change sign. Under larger doping the AHE remains small and consistent with the magnetization, while the THE grows by over a factor of 10. Both the sign and the magnitude of the AHE and the THE are in excellent agreement with calculations based on density functional theory. Our study provides the long-sought material-specific microscopic justification that, while the AHE is due to the reciprocal-space Berry curvature, the THE originates in real-space Berry phases.

Berry phase theory of Dzyaloshinskii-Moriya interaction and spin-orbit torques.

Recent experiments on current-induced domain-wall motion in chiral domain walls reveal important contributions both from spin-orbit torques (SOTs) and from the Dzyaloshinskii-Moriya interaction (DMI). We derive a Berry phase expression for the DMI and show that within this Berry phase theory DMI and SOTs are intimately related, in a way formally analogous to the relation between orbital magnetization (OM) and anomalous Hall effect (AHE). We introduce the concept of the twist torque moment, which probes the internal twist of wavepackets in chiral magnets in a similar way as the orbital moment probes the wavepacket's internal self-rotation. We propose to interpret the Berry phase theory of DMI as a theory of spiralization in analogy to the modern theory of OM. We show that the twist torque moment and the spiralization together give rise to a Berry phase governing the response of the SOT to thermal gradients, in analogy to the intrinsic anomalous Nernst effect. The Berry phase theory of DMI is computationally very efficient because it only needs the electronic structure of the collinear magnetic system as input. As an application of the formalism we compute the DMI in Co/Pt(111), O/Co/Pt(111) and Al/Co/Pt(111) magnetic bi- and trilayers and show that the DMI is highly anisotropic in these systems.

Non-Fermi-liquid behavior in transport through Co-doped Au chains.

We calculate the conductance as a function of temperature G(T) through Au monatomic chains containing one Co atom as a magnetic impurity, and connected to two conducting leads with a fourfold symmetry axis. Using the information derived from ab initio calculations, we construct an effective model H(eff) that hybridizes a 3d(7) quadruplet at the Co site with two 3d(8) triplets through the hopping of 5d(xz) and 5d(yz) electrons of Au. The quadruplet is split by spin anisotropy due to spin-orbit coupling. Solving H(eff) with the numerical renormalization group we find that at low temperatures G(T)=a-b√[T] and the ground state impurity entropy is ln(2)/2, a behavior similar to the two-channel Kondo model. Stretching the chain leads to a non-Kondo phase, with the physics of the underscreened Kondo model at the quantum critical point.

Terahertz spin current pulses controlled by magnetic heterostructures.

In spin-based electronics, information is encoded by the spin state of electron bunches. Processing this information requires the controlled transport of spin angular momentum through a solid, preferably at frequencies reaching the so far unexplored terahertz regime. Here, we demonstrate, by experiment and theory, that the temporal shape of femtosecond spin current bursts can be manipulated by using specifically designed magnetic heterostructures. A laser pulse is used to drive spins from a ferromagnetic iron thin film into a non-magnetic cap layer that has either low (ruthenium) or high (gold) electron mobility. The resulting transient spin current is detected by means of an ultrafast, contactless amperemeter based on the inverse spin Hall effect, which converts the spin flow into a terahertz electromagnetic pulse. We find that the ruthenium cap layer yields a considerably longer spin current pulse because electrons are injected into ruthenium d states, which have a much lower mobility than gold sp states. Thus, spin current pulses and the resulting terahertz transients can be shaped by tailoring magnetic heterostructures, which opens the door to engineering high-speed spintronic devices and, potentially, broadband terahertz emitters.

Disentangling the physical contributions to the electrical resistance in magnetic domain walls: a multiscale study.

We analyze the origin of the electrical resistance arising in domain walls of perpendicularly magnetized materials by considering a superposition of anisotropic magnetoresistance and the resistance implied by the magnetization chirality. The domain wall profiles of L1(0)-FePd and L1(0)-FePt are determined by micromagnetic simulations based on which we perform first-principles calculations to quantify electron transport through the core and closure region of the walls. The wall resistance, being twice as high in L1(0)-FePd than in L1(0)-FePt, is found to be clearly dominated in both cases by a high gradient of magnetization rotation, which agrees well with experimental observations.

Modeling impurity-assisted chain creation in noble-metal break junctions.

In this work we present the generalization of the model for chain formation in break junctions, introduced by Thiess et al (2008 Nano Lett. 8 2144), to zigzag transition-metal chains with s and p impurities. We apply this extended model to study the producibility trends for noble-metal chains with impurities, often present in break junction experiments, namely, Cu, Ag and Au chains with H, C, O and N adatoms. Providing the material-specific parameters for our model from systematic full-potential linearized augmented plane-wave first-principles calculations, we find that the presence of such impurities crucially affects the binding properties of the noble-metal chains. We reveal that both the impurity-induced bond strengthening and the formation of zigzag bonds can lead to a significantly enhanced probability for chain formation in break junctions.

Origin of the planar Hall effect in nanocrystalline Co60Fe20B20.

An angle dependent analysis of the planar Hall effect (PHE) in nanocrystalline single-domain Co(60)Fe(20)B(20) thin films is reported. In a combined experimental and theoretical study we show that the transverse resistivity of the PHE is entirely driven by anisotropic magnetoresistance (AMR). Our results for Co(60)Fe(20)B(20) obtained from first principles theory in conjunction with a Boltzmann transport model take into account the nanocrystallinity and the presence of 20 at. % boron. The ab initio AMR ratio of 0.12% agrees well with the experimental value of 0.22%. Furthermore, we experimentally demonstrate that the anomalous Hall effect contributes negligibly in the present case.

Spin-orbit strength driven crossover between intrinsic and extrinsic mechanisms of the anomalous hall effect in the epitaxial L1{0}-ordered ferromagnets FePd and FePt.

We determine the composition of intrinsic as well as extrinsic contributions to the anomalous Hall effect (AHE) in the isoelectronic L1_{0} FePd and FePt alloys. We show that the AHE signal in our 30 nm thick epitaxially deposited films of FePd is mainly due to an extrinsic side jump, while in the epitaxial FePt films of the same thickness and degree of order the intrinsic contribution is dominating over the extrinsic mechanisms of the AHE. We relate this crossover to the difference in spin-orbit strength of Pt and Pd atoms and suggest that this phenomenon can be used for tuning the origins of the AHE in complex alloys.

Magnetically hindered chain formation in transition-metal break junctions.

Based on first-principles calculations, we demonstrate that magnetism impedes the formation of long chains in break junctions. We find a distinct softening of the binding energy of atomic chains due to the creation of magnetic moments that crucially reduces the probability of successful chain formation. Thereby, we are able to explain the long standing puzzle why most of the transition metals do not assemble as long chains in break junctions and thus provide indirect evidence that in general suspended atomic chains in transition-metal break junctions are magnetic.

Theory and application of chain formation in break junctions.

We introduce a generic model of chain formation in break junctions by formulating criteria for the stability and producibility of suspended monatomic chains based on total energy arguments. Using ab initio calculations including spin-polarization and spin-orbit coupling, we apply our model to the formation of monatomic 4d and 5d transition metal (TM) chains. We explain the physical origin of the experimentally observed general trend of increasing probability for the creation of long chains for late 5d TMs and suppressed chain formation for 4d TMs. We also clarify why the probability of chain elongation can be greatly enhanced by the presence of adsorbates in experiments.

Controlling the magnetization direction in molecules via their oxidation state.

By means of ab initio calculations we predict that it is possible to manipulate the magnetization direction in organic magnetic molecules by changing their oxidation state. We demonstrate this novel effect on the Eu2(C8H8)3 molecule, in which the hybridization of the outer pi ring states with the Eu 4f states causes a redistribution of the orbitals around the Fermi level leading to a strong ferromagnetism due to a hole-mediated exchange mechanism. As a key result, we predict an oscillatory behavior of the easy axis of the magnetization as a function of the oxidation state of the molecule-a new effect, which could lead to new technological applications.

The interplay of structure and spin-orbit strength in the magnetism of metal-benzene sandwiches: from single molecules to infinite wires.

Based on first-principles density functional theory calculations, we explore the electronic and magnetic properties of experimentally producible sandwiches and infinite wires made of repeating benzene molecules and transition-metal atoms of V, Nb, and Ta. We describe the bonding mechanism in the molecules and in particular concentrate on the origin of magnetism in these structures. We find that all the considered systems have sizable magnetic moments and ferromagnetic spin ordering, with the single exception of the V(3)Bz(4) molecule. By including the spin-orbit coupling into our calculations we determine the easy and hard axes of the magnetic moment, the strength of the uniaxial magnetic anisotropy energy (MAE), relevant for the thermal stability of magnetic orientation, and the change of the electronic structure with respect to the direction of the magnetic moment, important for spin-transport properties. While for the V-based compounds the values of the MAE are only of the order of 0.05-0.5 meV per metal atom, increasing the spin-orbit strength by substituting V with heavier Nb and Ta allows one to achieve an increase in anisotropy values by one to two orders of magnitude. The rigid stability of magnetism in these compounds together with the strong ferromagnetic ordering makes them attractive candidates for spin-polarized transport applications. For a Nb-benzene infinite wire the occurrence of ballistic anisotropic magnetoresistance is demonstrated.