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Classification of composite Weyl nodes

Daniel Gosálbez-Martínez

Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
National Centre for Computational Design and Discovery of Novel Materials MARVEL, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland

Weyl nodes with chiral charge +/-1 are classified as types I and type II according to the tilting of
the conical band dispersion at the band degeneracy. Their Fermi surface, described by a quadratic
form, is different for these two types. We extend this classifcation to the case of composite Weyl
nodes with chiral charge larger than one. When the C4 and C6 rotation symmetries forbid the linear
band dispersion on the plane perpendicular to the symmetry axis, new terms with quadratic and
cubic momentum dependence must be included. Consequently, the Fermi surface produced by these
band degeneracies are described by a 4 or 6 order algebraic surfaces. In this more complex situation,
instead of classifying Fermi surfaces, we study numerically the possible Lifshitz transitions of the
Fermi surface produced by a composite Weyl node as the chemical potential is varied. We use this
methodology to classify the different types the composite Weyl fermions. In particular, for the case
of quadratic Weyl nodes generated by the C4 rotation symmetry. we find four different types band
dispersion morphologies, two analogous to the type-I and type-II case of the conical Weyl nodes,
and two new distinct morphologies within the type-II class. We illustrate the existence of these new
types of band degeneracies in real materials such as ferromagnetic iron.

Nonequilibrium Quantum Dynamics of Magnetic Skyrmions

Christina PSAROUDAKI

Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland

We provide a comprehensive picture of the quantum propagation of skyrmions in
chiral magnets, focusing on the microscopic description of dissipation at zero and
finite temperatures, originating from the interaction of the skyrmion with quantum
fluctuations. The most interesting feature is that the effect of this damping is reduced
to a mass term that is predicted for the first time [1]. We demonstrate that a skyrmion
in a confined geometry behaves as a massive particle, a discovery with great impact
on the technologically important case of linear tracks relevant for magnetic memory
devices [1]. An additional quantum mass term is predicted with an explicit
temperature dependence which remains finite even at zero temperature.
In the presence of time-dependent oscillating magnetic field gradients, the
unavoidable coupling of the external field to the magnons gives rise to timedependent
dissipation for the skyrmion, with measurable consequences on the
skyrmion’s path [2]. These ac fields act as a net driving force on the skyrmion via its
own intrinsic magnetic excitations. We generalize the standard quantum theory of
dissipation to include the effects of the driven bath on the skyrmion dynamics. We
address the stochastic effects of the quantum driven bath on the skyrmion propagation
[3], and provide a generalized version of the nonequilibrium fluctuation-dissipation
relation for externally driven reservoirs.
Our work initiates studies towards the possibility of observing a quantum mechanical
behavior at a mesoscopic scale. I will briefly talk about the observability of tunneling
events, in particular quantum depinning of a magnetic skyrmion out of a pinning
center [4].

[1] C. Psaroudaki, S. Hoffman, J. Klinovaja, and D. Loss, Quantum Dynamics of
Skyrmions in Chiral Magnets, Phys. Rev. X 7, 041045 (2017).
[2] C. Psaroudaki and D. Loss, Skyrmions Driven by Intrinsic Magnons, Phys. Rev.
Lett. 120, 237203 (2018).
[3] C. Psaroudaki, P. Aseev, and D. Loss, "Quantum Brownian Motion of a Magnetic
Skyrmion", arXiv:1904.09215
[4] C. Psaroudaki and D. Loss, "Quantum Deppining of a Magnetic Skyrmion",
manuscript in preparation (2019).

Magnons and Electrons in Magnets with Spin-Orbit Coupling

Alexander MOOK

MPI Halle

The interplay of spin-orbit coupling (SOC) and magnetism gives rise to a plethora of unconventional charge/heat-to-spin conversion phenomena in solids that harbor great potential for spintronic applications. Accounting for both the metallic and insulating states of matter, electrons as well as magnons emerge as two prominent spin carriers.

In this talk, I focus on selected aspects of SOC-driven phenomena in magnets with ferromagnetic or antiferromagnetic textures. Among those are (i) the thermal Hall effect of magnons in magnon Chern phases, (ii) spin-polarized magnon currents in fully compensated antiferromagnets, and (iii) spin current vortices that give rise to a magnetic spin Hall effect, the time-reversal odd cousin of the usual spin Hall effect.

17.09.2019 – Skyrmionics Workshop for Young Researcher

Skyrmionics Workshop for Young Researcher

The recent interest skyrmionic materials have provided a new playground for the study of topological solitons. The topologically non-trivial magnetic spin textures can facilitate fast current-induced magnetization manipulation, which makes these exotic textures widely advantageous for many areas of technology, from spintronics to neuromorphic computing.

The current research effort is to detect, visualize, and manipulate the magnetic states: by momentum space mapping such as small angle neutron scattering, by real space detection such as Lorentz transmissions electron microscopy, by transport such as the topological Hall effect, and manipulation by external fields resulting in the skyrmion Hall effect. The extensive study of their transport properties and the ability to create a controlled environment for the creation and annihilation of magnetic skyrmions are essential steps towards the realization of skyrmion-based devices. Skyrmions can exist in a multitude of systems, bulk, multilayer heterostructures, and films with a variety of shapes due to the internal symmetry and the competition of exchange interactions. The increasing number of skyrmion hosting materials combined with the rapid growth of the research field provides a promising prospect to overcome the challenges for next-generation devices.

For videos of the talks and further information, please visit the workshop home page.

07.07.2019 – Gordon Research Conference

Gordon Research Conference: Spin Transport and Dynamics in New Geometries, Materials and Nanostructures

In recent years the fields of spintronics has greatly expanded towards new materials, new functionalities, and new device concepts. In the new materials front, antiferromagnetic metallic and insulating systems have been shown to be effective transport media of spins, allowing for very high frequency applications and efficient electric control of the magnetic order parameter. There has also been a tremendous progress in the realization of magnetism in two dimensional materials, where new functionalities, such as spin valves, have been also demonstrated recently. Due to their spin-valley coupling these material systems also connect spins with photons. In addition, new forms of spin-orbit coupling have been discovered in magnetic and non-magnetic systems, connecting new materials with topological insulator and Weyl materials that promise new functionalities based on the control of these type of high-energy-like quasiparticles. A remaining materials frontier in spintronics is organic systems, which seems to be very different from solid state spintronics, exhibiting new chiral phenomena which remains to be fully understood. Finally, as an emergent new device concept, the conference will cover the area of neuromorphic computing in spintronics, where Skyrmions, and other spin systems, are being touted as future platforms for such type of brain-inspired devices.

23.10.2018 – Ultrafast Spintronics: from Fundamentals to Technology

Ultrafast Spintronics: from Fundamentals to Technology

The 21st century digital economy and technology is presently facing fundamental scaling limits (heating and the superparamagnetic limit) as well as societal challenges: the move to mobile devices and the increasing demand of cloud storage leads to an enormous increase in energy consumption of our ICT infrastructure. These developments require new strategies and paradigm shifts, such as spin-based technologies and the introduction of photonic processors. Currently, photons are used for information transport, electrons for processing and spins for storage. Future developments will require integration of these separate technologies. Spintronic or spin-based memory such as Spin-torque transfer magnetic Random Access Memory (STT-RAM) is one concept that may revolutionize memory technology. The ability to control spins and macroscopic magnetic ordering by means of femtosecond laser pulses provides an alternative and energy efficient approach to magnetic recording. But this will only provide a novel and energy efficient alternative to current data storage if spintronics can be integrated with photonics. Such integration may also allow faster spin logic. Antiferromagnetic materials may provide another alternative for fast spintronics, but there are still many challenges. In this workshop we want to discuss recent developments in this exciting field as well as the challenges that lay ahead.

For videos of the talks and further information, please visit the workshop home page.

Magneto-optical constants and their transient changes in ultrafast XUV spectroscopy

Time: Friday, October 25th, 11:00
Speaker: Felix WILLEMS, Berlin

With the advent of new free-electron and laboratory-based high harmonic radiation sources ultrafast magnetic spectroscopy at 3p to 3d transitions (M-edges) has started to develop into a widely used experimental technique. The advantages of this technique are manifold: (a) it leads to the element-specific response of complex multi-component magnetic systems simultaneously in a single measurement [1, 2] (b) it enables ultrafast distinction between the physics of various energy scales; exchange and spin-orbit interaction as well as collective spin excitations and (c) the wavelength of XUV radiation allows to directly probe nanoscale length scales via small angle X-ray scattering [2] and coherent imaging methods [2, 3]. However, to quantitatively interpret increasingly complex experimental data from this technique, the scientific community relies on fundamental experimental and theoretical groundwork. The lack of such a systematic and thorough study has resulted in a number of controversies in literature stemming mostly from difficulties to separate possibly overlapping resonances and from a non-zero off-resonant magnetic signal at lower photon energies. In our work we address all these important questions by presenting a complete measurement of the complex dichroic index of refraction for Co, Fe and Ni (i.e. both the dispersive and absorptive contributions) and comparing it with state-of-the-art ab-initio density functional theory (DFT) calculations [4].
Furthermore, in a time resolved high harmonic experiment, we measure the transient changes of the absorptive refractive index displaying distinct femtosecond dynamics depending on the polarization state of the probing XUV light. Doing so we can distinguish the between excitation of the pure electronic and the spin system. A comparison with time dependent DFT simulations suggests an explanation based on ultrafast, spin-orbit mediated spin-flips [4].

[1] F. Willems et al., Physical Review B 92, 220405(R) (2015)
[2] F. Willems et al., Structural Dynamics 4, 014301 (2017)
[3] C. von Korff Schmising et al., Phys. Rev. Lett., 112, 217203 (2014)
[4] F. Willems et al., in preparation

Intersublattice exchange interaction probed with high order harmonics over multiscale dynamics

Time Friday, October 26th, 10:10
Speaker: Marie BARTHELEMY, Strasbourg

Over the past few years, optically induced ultrafast magnetization dynamics has been investi-gated in alloyed ferromagnets by probing core level to 3d band optical transitions of transition metals [1,2]. Those chemical selective measurements are sensitive to the sub-lattices interaction processes during the transient magnetization dynamics. For example, it has been found that the inter-sub-lattice exchange interaction has to be taken into account if the demagnetization times of each sub-lattice of the ferromagnet are considered [3,5]. In this work, permalloy sub-lattices magnetic momenta dynamics are measured simultaneously with a table top Transverse Magneto Optical Kerr Effect by probing with High order Harmonics (20-70 eV range) over a broad tempo- ral scale (Figure1). The Landau-Lifshitz-Bloch equation associated to Langevin formalism can be used to deduce the demagnetization time t ε attributed to each element ε, by taking exchange interaction into account [5]. From our measurements in permalloy, both elements demagnetize simultaneously and precess in phase with same period and Gilbert damping due to strong exchange interaction. It will be shown that the ratio between effective exchange interaction constants of Ni and Fe can be retrieved from those measurements. Moreover, the dependence of relaxation rate upon the pump density of excitation will be discussed considering a multiscale approach including tem-perature dependent exchange parameters.

[1] I. Radu, C. Stamm, A. Eschenlohr, F. Radu, R. Abrudan, K. Vahaplar, T. Kachel, N. Pontius, R. Mitzner, K. Holldack, et al., SPIN 5, 1550004 (2015).
[2] C. La-O-Vorakiat, M. Siemens, M. M. Murnane, H. C.Kapteyn, S. Mathias, M. Aeschlimann, P. Grychtol, R. Adam, C. M. Schneider, J. M. Shaw, et al., Phys.Rev. Lett. 103, 257402 (2009).
[3] S. Mathias, C. La-O-Vorakiat, P. Grychtol, P. Granitzka,E. Turgut, J. Shaw, R. Adam, H. Nembach, M. Siemens, S. Eich, et al., Proc. Natl. Acad. Sci. 109, 4792 (2012).
[4] A. J. Schellekens and B. Koopmans, Phys. Rev. B 87,020407 (2013).
[5] D. Hinzke, U. Atxitia, K. Carva, P. Nieves,O. Chubykalo-Fesenko, P. M. Oppeneer, and U. Nowak, Phys. Rev. B 92, 054412 (2015).

Tutorial: Ultrafast spin and magnetization dynamics in rare earth metals

Time. Friday, October 26th, 9:00
Speaker: Martin WEINELT, Berlin

On which timescale do the electronic band structure and spin polarization of a ferromagnet change after femtosecond laser excitation and how do they react to spin transport and spin-flip scattering?
To answer these questionswe perform time-, spin-, and angle-resolved photoemission experiments with optical laser pulses and higher-order harmonic radiation and investigate the transient magnetization by time-resolved X-ray magnetic circular dichroism in reflection.
For the local ferromagnets gadolinium and terbium and their combination in bilayers, we show that exchange splitting, spin polarization, and transient magnetic moment can respond on significantly different timescales. This allows us to distinguish between contributions of spin-flip scattering, spin-lattice coupling, and spin transport to the ultrafast magnetization dynamics.

Photocurrents in magnetic bilayers for ultrafast spinorbitronics

Time: Thursday, October 25th, 16:00
Speaker: Frank FREIMUTH, Julich

Spin photocurrents excited by femtosecond laser pulses bring spinorbitronics to ultrafast timescales. Using the Keldysh formalism we systematically identify mechanisms behind the generation of spin photocurrents and charge photocurrents by femtosecond laser pulses. Noncentrosymmetric crystals and inversion asymmetric magnetic bilayers exhibit several mechanisms of photocurrent generation that are absent in centrosymmetric systems. First, there is the circular photogalvanic effect [1,2]. While previous works on the circular photogalvanic effect have focused on nonmagnetic semiconductors, we will discuss the magnetic photogalvanic effect in metallic magnetic bilayers [3]. Second, when magnetic solids are excited by femtosecond laser pulses, superdiffusive spin currents are generated, which are converted into charge currents by the inverse spin Hall effect [4,5]. Third, laser pulses excite magnetization dynamics due to the inverse Faraday effect and the optical spintransfer torque, which we will discuss for Fe, Co and FePt [6]. This magnetization dynamics generates photocurrents, because electrical currents are pumped by the inverse spin‐orbit torque [7,8]. Fourth, we find that also demagnetization drives photocurrents due to the collapse of the exchange field [9]. Based on density‐functional theory calculations we investigate these effects in Co/Pt and Mn/W bilayers.

[1] J. W. McIver et al., Nature Nanotechnology 7, 96 (2012)
[2] S. D. Ganichev and W. Prettl, JPCM 15, R935 (2003)
[3] F. Freimuth et al., arXiv:1710.10480 (2017)
[4] T. Kampfrath et al., Nature Nanotechnology 8, 256 (2013)
[5] T. Seifert et al., Nature Photonics 10, 483 (2016)
[6] F. Freimuth, S. Blügel and Y. Mokrousov, PRB 94, 144432 (2016)
[7] T. J. Huisman et al., Nature Nanotechnology 11, 455 (2016)
[8] F. Freimuth, S. Blügel and Y. Mokrousov, PRB 92, 064415 (2015)
[9] F. Freimuth, S. Blügel and Y. Mokrousov, PRB 95, 094434 (2017