Frank Freimuth

Symmetry and magnitude of spin-orbit torques in ferromagnetic heterostructures

Recent demonstrations of magnetization switching induced by in-plane current injection in heavy metal/ferromagnetic heterostructures have drawn increasing attention to spin torques based on orbital-to-spin momentum transfer. The symmetry, magnitude and origin of spin-orbit torques (SOTs), however, remain a matter of debate. Here we report on the three-dimensional vector measurement of SOTs in AlOx/Co/Pt and MgO/CoFeB/Ta trilayers using harmonic analysis of the anomalous and planar Hall effects. We provide a general scheme to measure the amplitude and direction of SOTs as a function of the magnetization direction. Based on space and time inversion symmetry arguments, we demonstrate that heavy metal/ferromagnetic layers allow for two different SOTs having odd and even behaviour with respect to magnetization reversal. Such torques include strongly anisotropic field-like and spin transfer-like components, which depend on the type of heavy metal layer and annealing treatment. These results call for SOT models that go beyond the spin Hall and Rashba effects investigated thus far.

Electrical switching of an antiferromagnet

Manipulating a stubborn magnet Spintronics is an alternative to conventional electronics, based on using the electrons spin rather than its charge. Spintronic devices, such as magnetic memory, have traditionally used ferromagnetic materials to encode the 1s and 0s of the binary code. A weakness of this approach—that strong magnetic fields can erase the encoded information—could be avoided by using antiferromagnets instead of ferromagnets. But manipulating the magnetic ordering of antiferromagnets is tricky. Now, Wadley et al. have found a way (see the Perspective by Marrows). Running currents along specific directions in the thin films of the antiferromagnetic compound CuMnAs reoriented the magnetic domains in the material. Science, this issue p. 587; see also p. 558 Transport and optical measurements are used to demonstrate the switching of domains in the antiferromagnetic compound CuMnAs. [Also see Perspective by Marrows] 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 106 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.

Localized edge states in two-dimensional topological insulators: Ultrathin Bi films

We theoretically study the generic behavior of the penetration depth of the edge states in two-dimensional quantum spin Hall systems. We found that the momentum-space width of the edge-state dispersion scales with the inverse of the penetration depth. As an example of well-localized edge states, we take the Bi(111) ultrathin film. Its edge states are found to extend almost over the whole Brillouin zone. Correspondingly, the bismuth (111) 1-bilayer system is proposed to have well-localized edge states in contrast to the HgTe quantum well.

Terahertz spin current pulses controlled by magnetic heterostructures

1. Department of Physical Chemistry, Fritz Haber Institute, Berlin, Germany. 2. Department of Physics and Astronomy, Uppsala University, Uppsala, Sweden. 3. I. Physikalisches Institut, Georg-August-Universität Göttingen, Göttingen, Germany. 4. Helmholtz-Zentrum Berlin fϋr Materialien und Energie, Berlin, Germany. 5. Peter Grünberg Institute and Institute for Advanced Simulation, Forschungszentrum Jülich and JARA, Jülich, Germany.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.

Efficient metallic spintronic emitters of ultrabroadband terahertz radiation

Ultrashort pulses covering the 1–30 THz range are generated from a W/CoFeB/Pt trilayer and originate from photoinduced spin currents, the inverse spin Hall effect and a broadband Fabry–Perot resonance. The resultant peak fields are several 100 kV cm–1.

Anisotropy of spin relaxation and transverse transport in metals

Using first-principles methods we explore the anisotropy of the spin relaxation and transverse transport properties in bulk metals with respect to the real-space direction of the spin-quantization axis in paramagnets or of the spontaneous magnetization in ferromagnets. Owing to the presence of the spin-orbit coupling the orbital and spin character of the Bloch states depends sensitively on the orientation of the spins relative to the crystal axes. This leads to drastic changes in quantities which rely on interband mixing induced by the spin-orbit interaction. The anisotropy is particularly striking for quantities which exhibit spiky and irregular distributions in the Brillouin zone, such as the spin-mixing parameter or the Berry curvature of the electronic states. We demonstrate this for three cases: (i) the Elliott-Yafet spin-relaxation mechanism in paramagnets with structural inversion symmetry; (ii) the intrinsic anomalous Hall effect in ferromagnets; and (iii) the spin Hall effect in paramagnets. We discuss the consequences of the pronounced anisotropic behavior displayed by these properties for spin-polarized transport applications.

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 wavepackets 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.

All-electrical manipulation of magnetization dynamics in a ferromagnet by antiferromagnets with anisotropic spin Hall effects

We investigate spin-orbit torques of metallic CuAu-I-type antiferromagnets using spin-torque ferromagnetic resonance tuned by a dc-bias current. The observed spin torques predominantly arise from diffusive transport of spin current generated by the spin Hall effect. We find a growth-orientation dependence of the spin torques by studying epitaxial samples, which may be correlated to the anisotropy of the spin Hall effect. The observed anisotropy is consistent with first-principles calculations on the intrinsic spin Hall effect. Our work suggests large tunable spin-orbit effects in magnetically-ordered materials.

Spin-orbit torques in Co/Pt(111) and Mn/W(001) magnetic bilayers from first principles

An applied electric current through a space-inversion asymmetric magnet induces spin-orbit torques (SOTs) on the magnetic moments, which holds much promise for future memory devices. We discuss general Greens function expressions suitable to compute the linear-response SOT in disordered ferromagnets. The SOT can be decomposed into an even and an odd component with respect to magnetization reversal, where in the limit of vanishing disorder the even SOT is given by the constant Berry curvature of the occupied states, while the odd part exhibits a divergence with respect to disorder strength. Within this formalism, we perform first principles density-functional theory calculations of the SOT in Co/Pt(111) and Mn/W(001) magnetic bilayers. We find the even and odd torque components to be of comparable magnitude. Moreover, the odd torque depends strongly on an additional capping layer, while the even torque is less sensitive. We show that the even torque is nearly entirely mediated by spin currents in contrast to the odd torque, which can contain an important contribution not due to spin transfer. Our results are in agreement with experiments, showing that our linear response theory is well-suited for the description of SOTs in complex ferromagnets.

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.