*Stanford University*

We show that non-Abelian topological structure arises inside the momentum space of semimetals and metals under various symmetry settings [1], including PT-symmetric systems with negligible spin-orbit coupling, and C2T-symmetric systems with or without spin-orbit coupling. This results in non-Abelian topological charges of band-structure nodes, similar to those that describe disclinations in biaxial nematics, implying non-trivial braiding phenomena inside the momentum space [2]. We discuss how the non-Abelian band topology can be captured using various mathematical techniques, including homotopy groups, characteristic classes, and Wilson-loop Pfaffians [3]. We conclude the talk by briefly commenting on the interplay of this newly discovered topological structure with space-group symmetry.

[1] Q.S. Wu, A. A. Soluyanov, T. Bzdušek, arXiv:1808.07469 (2018)[2] A. Tiwari and T. Bzdušek, arXiv:1903.00018 (2019)

[3] A. Bouhon, R.-J. Slager, T. Bzdušek, arXiv:1907.10611 (2019) ]]>

*Department of Physics, University of Basel, Basel, Switzerland*

The quest to harness magnonic spin waves, aided by insights from topological matter, has

led to the emergence of the new field of topological magnonics. Among the systems that have

been predicted to support topologically protected magnonic edge states are spatially periodic

noncollinear textures. A noteworthy example are skyrmion crystals, which have garnered

much interest lately due to their topological transport properties and the potential to use

skyrmions as information carriers in future high-density, low-power storage and logic

devices. In this talk I will discuss our latest findings on topologically protected magnonic

edge states in antiferromagnetic as well as ferromagnetic skyrmion crystals.

*1 Institute for Physics, Johannes Gutenberg University Mainz, D-55128 Mainz, Germany
2 Graduate School of Excellence Material Science in Mainz, Staudingerweg 9, 55128, Mainz, Germany
3 Department of Materials Science and Engineering, Technion-Israel Institute of Technology
4 Center for Quantum Spintronics, Norwegian University of Science and Technology, NO-7491 Trondheim, Norway
5 Utrecht University, Princetonplein 5, 3584 CC Utrecht, Netherlands
6 Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
*

In contrast to ferromagnets, antiferromagnets benefit from unparalleled stability with respect to applied external fields, magnetization dynamics at THz frequencies and a lack of stray fields [1]-[2]. Many theoretical studies have been undertaken describing the mechanisms through which antiferromagnets could allow for the propagation of spin current across the long distances which would be required for integration into information transfer and logic devices [3]-[4]. Recently, we demonstrated that in antiferromagnetic insulators, a diffusive magnonic spin current is able to propagate over tens of micrometers carried by the intrinsic Néel order using a single crystal of the most common insulating antiferromagnet, hematite (α-Fe2O3)[5]. With low damping and characteristic frequencies of hundreds of GHz, this compound allows for antiferromagnetic spin-waves to propagate as far as in YIG, a ferromagnetic material with the lowest known damping that is the material of choice for magnonic devices. Through measurements of the spin Hall magnetoresistance, the internal crystal anisotropies can be extracted [6], allowing for a precise determination of critical fields without the need for high frequency resonance experiments.

Here, we grow high quality antiferromagnetic thin films of hematite (< 500 nm) and show that they can also allow pure magnonic current to propagate over long-distances, opening the way towards a development and an integration of antiferromagnetic magnonic devices. We then discuss the role of the growth orientation and of the magnetic fields required to induce transport. By controlling the antiferromagnetic domains, we demonstrate how magnetic textures impact the propagation of polarized magnons [7]. Finally, we discuss the temperature dependence of the magnon propagation for magnons originating from an electrical spin-bias at the interface of hematite and platinum or from thermal heating of the hematite layer, and demonstrate that one can even achieve zero-field, room temperature magnon transport in insulating antiferromagnets.

[2] V. Baltz et al., Rev. Mod. Phys. 90, 015005 (2018)

[3] S. Takei et al., Phys. Rev. B, 90, 94408 (2014)

[4] S. Bender et al., Phys. Rev. Lett. 19, 056804 (2017)

[5] R. Lebrun et al., Nature 561, 222-225 (2018)

[6] R. Lebrun et al., Communications Physics 2 50 (2019)

[7] A. Ross et al., arXiv:1907.02751 (2019) ]]>

*Weizmann Institute of Science*

Symmetry protected topological (SPT) phases are gapped phases of matter that cannot be deformed to a trivial phase without breaking the symmetry or closing the bulk gap. In this talk I will introduce a new notion of a topological obstruction that is not captured by bulk energy gap closings in periodic boundary conditions. More specifically, we say two bulk Hamiltonians belong to distinct boundary obstructed topological `phases' (BOTPs) if they can be deformed to each other on a system with periodic boundaries, but cannot be deformed to each other for symmetric open boundaries without closing the gap at at least one high symmetry region on the surface. I will discuss the double-mirror quadrupole model [Science, 357(6346), 2018] and a dimerized weak topological insulator [arxiv 1809.03518] as examples of BOTPs. I will describe the general framework to study boundary obstructions in free-fermion systems in terms of Wannier band representations (WBR), an extension of the recently-developed band representation formalism to Wannier bands. WBRs capture the notion of topological obstructions in the Wannier bands which can then be used to study topological obstructions in the boundary spectrum by means of the correspondence between the Wannier and boundary spectra. This establishes a form of bulk-boundary correspondence for BOTPs by relating the bulk band representation to the boundary topology.

]]>*EPFL*

Heusler compounds are exciting materials for future spintronics applications because they display a wide range of tunable electronic and magnetic interactions such as metallicity, superconductivity, and giant magneto-resistance. However, the ultimate speed at which spins can be manipulated in materials is still an open question. In this work, we use a femtosecond light pulse to directly transfer spin polarization from one element to another in a half-metallic Heusler material, Co2MnGe. This spin transfer initiates as soon as light is incident on the material, showing that we can spatially transfer angular momentum between neighboring atomic sites on timescales less than 10 fs. Using ultrafast high harmonic pulses to simultaneously and independently probe the magnetic state of two elements during laser excitation, we find that the magnetization of Co is enhanced, while that of Mn rapidly quenches. By comparing our measurements to density functional theory, we show that the optical excitation directly transfers spin from one magnetic sub-lattice to another, via preferred spin-polarized excitation pathways. This direct manipulation of spins via light provides a path towards spintronic logic devices such as switches that can operate on few femtosecond or even faster timescales.

]]>*IMDEA NANOSCIENCE, Campus de Cantoblanco, Madrid, Spain*

The development of room temperature magnetic devices exploiting Spin Orbit effects is at the forefront of actual research. A major challenge for future spintronics is to develop suitable spin transport channels with superior properties such as long spin lifetime and propagation length. Graphene can meet these requirements, even at room temperature [1]. However, the development of all-graphene spintronic devices requires that, in addition to its passive capability to transmit spins over long distances, other active properties are incorporated to graphene. The generation of long range magnetic order and spin filtering in graphene have been recently achieved by molecular functionalization [2,3] as well as by the introduction of giant spin-orbit coupling (SOC) in the electronic bands of graphene [4]. On the other side, taking advantage of the fast motion of perpendicular magnetic anisotropy (PMA) chiral spin textures, i.e., Néel-type domain walls (DWs) and magnetic skyrmions, can satisfy the demands for high-density data storage, low power consumption and high processing speed [5].

Here, I report on high quality, epitaxial graphene/Co(111)/Pt(111) stacks grown on (111)-oriented insulating oxide crystals, characterized by STM, LEED, STEM, Kerr Magnetometrry and Microscopy, XAS-XMCD, XMRS and SP-ARPES, which exhibit enhanced PMA for Co layers up to 4 nm thick and left-handed Néel-type chiral DWs stabilized by interfacial Dzyaloshinskii-Moriya interaction (DMI) localized at both graphene/Co and Co/Pt interfaces with opposite sign [6]. While the DMI at Co/Pt side is due to the intrinsic SOC [7], the sizeable DMI experimentally found at the Gr/Co interface has Rashba origin [6]. The active magnetic texture is protected by the graphene monolayer and stable at 300 K in air, and, since it is grown on an insulating substrate, amenable to transport measurements.

[2] M. Garnica et al., Long range magnetic order in a purely organic 2D layer adsorbed on epitaxial graphene, Nature Phys. 9, 368–374 (2013).

[3] D. Maccariello, et al., Spatially resolved, site-dependent charge transfer and induced magnetic moment in TCNQ adsorbed on graphene, Chemistry of Materials 26 (9), 2883-2890 (2014).

[4] F. Calleja et al., Spatial variation of a giant spin–orbit effect induces electron confinement in graphene on Pb islands, Nature Physics 11, 43–47 (2015).

[5] A. Fert, V. Cros and J. Sampaio, Skyrmions on the track, Nat. Nanotech. 8, 152–156 (2013).

[6] F. Ajejas, et al., Unravelling Dzyaloshinskii–Moriya interaction and chiral nature of Graphene/Cobalt interface, Nano Lett. 18(9), 5364-5372 (2018).

[7] F. Ajejas, et al., Tuning domain wall velocity with Dzyaloshinskii-Moriya interaction, Appl. Phys. Lett. 111, 202402 (2017). ]]>

*(1) Department of Physics, University of Zurich,
Winterthurerstrasse 190, 8057 Zurich, Switzerland
(2) Department of Theoretical Physics, Wroc law University of Science and Technology,
Wybrze_ze Wyspianskiego 27, 50-370 Wroc law, Poland*

Existing classications of topological phases are based on the presence (or absence) of

symmetries and the number of spatial dimensions being an integer. However, equipped with

a notion of locality and the possibility to take a thermodynamic limit, the classication

schemes can be extended in order to include quantum states on general graphs. In particular,

one can consider a class of self-similar geometries characterized by a fractional dimension.

In this talk, I will focus on two fractal lattices, Sierpinski carpet and gasket, exposed to an

external magnetic eld and described within tight-binding approximation. By investigating

spectral and localization properties, together with the real-space Chern number calculations

and level spacings analysis in the presence of disorder, I will show that these systems exhibit

features similar to quantum Hall states in almost two dimensions.

*Fraunhofer Institute for Photonic Microsystems, Group Spin-based Computing Königsbrücker Str. 178, 01099 Dresden, Germany*

In semiconductor industry, the introduction and integration of unconventional materials, technologies and devices for new applications is a very challenging process with a lot of limitations and demands. Even if the expected benefit is tremendous, like it is foreseen for many spintronic applications, partially immense hurdles have to be mastered. First, the established contamination management of a Fab leads to a lot of restrictions and a limited availability with regard to approved elements from the periodic table. Furthermore, the Environmental, Health and Safety conditions from industry add various constraints, which lead to further limitations. Perhaps, the most important condition in semiconductor industry is the cost-of-ownership. The restrictions lead to a limited usability of known materials and difficulties to explore unconventional phases and compounds. Despite the restrictions, there is still plenty of room and a lot of new technologies were developed in recent years especially in the memory business.

Today, data is the life blood that is disrupting many industries. The vast majority of these data are stored in the form of non-volatile magnetic bits in hard disk drives, a technology developed more than half a century ago, that has reached fundamental scaling limits that impedes further increases in storage capacity. New approaches are needed. Based on very recent discoveries, spin-based implementations like e.g. Magnetic Random Access Memory (MRAM) or Racetrack Memory (RTM) are such approaches. The charge-to-spin-conversion and vice versa is a key element in spin-based computing systems and is addressed in recent research. Spin-Orbit-Coupling phenomena play a vital role in both, Spin-Orbit-Torque MRAM and RTM, where new materials with high Spin-Hall-Angles are needed. Therefore, several materials ranging from (heavy) metals to binary compounds are considered, like e.g. CoSi or TaP. A CoSi process sequence including wet chemical silicon oxide removal, Cobalt CVD deposition with annealing is available [1]. For TaP a thin film process is not yet available. Both CMOS-compatible compounds are considered to belong to the class of Weyl semimetals, which are theoretically proven to have high Spin Hall Angles [2,3]. Several open questions, like e.g. influences on the topological properties of interfaces or grain boundaries have to be addressed in order to pave the way for new unconventional approaches.

[2] Hu, J.; Liu, J. Y.; Graf, D.; Radmanesh, S. M. A.; Adams, D. J.; Chuang, A. et al. π Berry phase and Zeeman splitting of Weyl semimetal TaP. Scientific reports 6 (2016) 18674.

[3] D.A. Pshenay-Severin, Y.V. Ivanov, A.A. Burkov, A.T. Burkov. Band structure and unconventional electronic topology of CoSi. J. Phys.: Condens. Matter 30 (2018) 135501. ]]>

*Leibniz Institute Dresden*

Weyl semimetals exhibit interesting electronic properties due to their topological band structure.

In particular, large anomalous Hall and anomalous Nernst signals are often reported, which allow for

a detailed and quantitative study of subtle features. We pattern single crystals of the magnetic Weyl

semimetal Co3Sn2S2 into nanoribbon devices using focused ion beam cutting and optical lithography.

This approach enables a very precise study of the galvano- and thermomagnetic transport properties.

Indeed, we found interesting features in the temperature dependency of the anomalous Hall and

Nernst effects. We present an analysis of the data based on the Mott relation and identify in the

Nernst response signatures of magnetic fluctuations enhancing the anomalous Nernst conductivity

at the magnetic phase transition.

*1 Advanced Science Research Center, Japan Atomic Energy Agency
2 School of Mathematical Sciences, University of Adelaide
3 Fachbereich Physik and Landesforschungszentrum OPTIMAS, Technische Universität Kaiserslautern
4 Center for Spintronics, Korea Institute of Science and Technology
5 Institut für Physik, Johannes Gutenberg-Universität Mainz
6 Department of Applied Physics, University of Tokyo
7 Institute for Materials Research, Tohoku University
*

Magnetostatic surface spin waves (a.k.a Damon-Eshbach mode) have long been known to have the largest decay lengths of all available modes and be robust against surface shapes and disorders [1-3]. Combined with their chiral and unidirectional propagation with respect to the direction of the ground state magnetisation, these features remind one of topologically protected edge states of quantum Hall systems. We present a topological characterisation of the dipolar spin wave Hamiltonian, which predicts, via the bulk-edge correspondence, the presence of robust surface spin wave modes without explicitly calculating eigenmodes of a system with boundaries [4].

While the characterisation is based on the symmetry class CI of electronic topological band theory, it is reformulated for the particular dynamical structure of classical Hamiltonian systems in which symplectic, rather than unitary, structure plays an essential role. By suitably identifying the symplectic structure with the chiral symmetry of class CI, assuming a preferred metric tensor in the space of canonical coordinates, we show that the surface spin waves appear not in a gap of bulk frequency spectrum, consistent with the magnetostatic surface spin waves.

[1] A. V. Chumak et al., Appl. Phys. Lett. 94, 172511 (2009).[2] M. Mohseni et al., Phys. Rev. Lett. 122, 197201 (2019).

[3] T. Yu et al., Phys. Rev. B 99, 174402 (2019).

[4] K. Yamamoto et al., Phys. Rev. Lett. 122, 217201 (2019). ]]>