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Local Dynamics of Topological Magnetic Defects in the Itinerant Helimagnet Fege

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Local Dynamics of Topological Magnetic Defects in the Itinerant Helimagnet Fege ARTICLE Received 4 Jan 2016 | Accepted 1 Jul 2016 | Published 18 Aug 2016 DOI: 10.1038/ncomms12430 OPEN Local dynamics of topological magnetic defects in the itinerant helimagnet FeGe A. Dussaux1,*, P. Schoenherr2,*, K. Koumpouras3, J. Chico3, K. Chang1, L. Lorenzelli1, N. Kanazawa4, Y. Tokura4,5, M. Garst6, A. Bergman3, C.L. Degen1 & D. Meier2,7 Chiral magnetic interactions induce complex spin textures including helical and conical spin spirals, as well as particle-like objects such as magnetic skyrmions and merons. These spin textures are the basis for innovative device paradigms and give rise to exotic topological phenomena, thus being of interest for both applied and fundamental sciences. Present key questions address the dynamics of the spin system and emergent topological defects. Here we analyse the micromagnetic dynamics in the helimagnetic phase of FeGe. By combining magnetic force microscopy, single-spin magnetometry and Landau–Lifschitz–Gilbert simula- tions we show that the nanoscale dynamics are governed by the depinning and subsequent motion of magnetic edge dislocations. The motion of these topologically stable objects triggers perturbations that can propagate over mesoscopic length scales. The observation of stochastic instabilities in the micromagnetic structure provides insight to the spatio-temporal dynamics of itinerant helimagnets and topological defects, and discloses open challenges regarding their technological usage. 1 Department of Physics, ETH Zu¨rich, Otto Stern Weg 1, Zurich 8093, Switzerland. 2 Department of Materials, ETH Zu¨rich, Vladimir-Prelog-Weg 4, Zurich 8093, Switzerland. 3 Department of Physics and Astronomy, Uppsala University, PO Box 516, Uppsala 75120, Sweden. 4 Department of Applied Physics, University of Tokyo, Tokyo 113-8656, Japan. 5 RIKEN Center for Emergent Matter Science (CEMS), Wako 351-0198, Japan. 6 Institute for Theoretical Physics, Universita¨tzuKo¨ln, Ko¨ln D-50937, Germany. 7 Department of Materials Science and Engineering, Norwegian University of Science and Technology, Trondheim 7491, Norway. * These authors contributed equally to this work. Correspondence and requests for materials should be addressed to C.L.D. (email: [email protected]) or to D.M. (email: [email protected]). NATURE COMMUNICATIONS | 7:12430 | DOI: 10.1038/ncomms12430 | www.nature.com/naturecommunications 1 ARTICLE NATURE COMMUNICATIONS | DOI: 10.1038/ncomms12430 ntriguing states of magnetism1 arise in transition-metal centres, immobilized on the FeGe surface, show that these silicides and germanides of the B20-type such as MnSi2,3, dynamics are intrinsic and highlight their stochastic nature. 4–6 7–9 IFe1 À xCoxSi , and FeGe . The competition of Coarse-grained LLG simulations are applied to analyse the ferromagnetic exchange, Dzyaloshinskii–Moriya (DM) microscopic magnetization dynamics. The simulations demon- interaction, and magnetic anisotropy leads to a variety of strate that the movement and annihilation of topological defects complex magnetic phases with spins forming helical or conical plays a key role for the self-organization of the spin structure and spirals, as well as long-range-ordered lattices of magnetic the development of a long-range-ordered helimagnetic ground whirls10. These spin structures are appealing as they give rise to state. anomalous transport properties11,12, exotic vortex domain walls13 and unusual dynamic spin-wave phenomena14–16. Of particular Results interest is the emergence of topologically protected spin states, that is, stable magnetic configurations that cannot be generated or Helimagnetism in FeGe probed by magnetic force microscopy. destroyed by a continuous transformation of the spin system17. For our studies on the dynamics of topological magnetic defects, we choose cubic FeGe37 as it exhibits helimagnetic order near These topological defects are explicitly robust and may serve as E functional objects in future spintronics devices18,19. At present, room temperature with TN 280 K and because its phase diagram is well-characterized38. Single crystals of FeGe were grown by the however, we are only at the verge of grasping the technological 39 potential of topological spin states20,21 and their complex chemical vapour transport method as explained in the Methods nanoscale physics is still largely unexplored. section. The helical axis of the spin system in FeGe is described by During the last years, research activities in the field mainly a wave vector q, which first points along the crystallographic h001i direction (Fig. 1a), changing to the h111i direction below focused on topologically protected magnetic whirls called 8 skyrmions. Skyrmions arise in various B20 materials under 211 K on cooling . We begin our discussion with the spatially magnetic fields and represent particle-like entities that can be resolved MFM measurements shown in Fig. 1b–e. The MFM data moved12, written and erased on demand22. Although it is known are collected in two-path mode, recording first the topography in that the formation of skyrmions is facilitated by superior semi-contact and then the magnetic response with a fixed topological defects that develop in the helimagnetic ground state23, little attention has been paid to the latter ones. In the a M helimagnetic phase topological defects arise, for example, in the form of magnetic edge dislocations24,25. Analogous to edge dislocations in crystals and nematics, these magnetic edge dislocations naturally develop where helical spin textures of n1 unequal phase meet, compensating for the local mismatch. At the n bulk level, such line-like topological defects are often neglected as 2 q they affect only a small fraction of the volume. At the nanoscale, n3 however, the defects and their dynamics become crucial as they can lead to significant perturbations in the electronic structure in 265 K c 270 K itinerant helimagnets. Thus, due to the close relation to the b formation of the skyrmion phase and their general significance for the research on topological states, a detailed knowledge about the dynamics of topological defects in the helimagnetic state is q1 highly desirable. The probing of intrinsic micromagnetic instabilities at the nanoscale in a non-invasive way is a well-known challenge. q2 Conventional microscopy methods, such as Lorentz transmission electron microscopy, magnetic force microscopy (MFM)26 and scanning tunnelling microscopy27, make either use of an electron beam or a magnetic probe tip and can themselves influence the behaviour of the spin structure. As a consequence, it is difficult to d 275 K e 280 K unambiguously separate between intrinsic and extrinsic, probe- induced dynamical effects. Nitrogen vacancy (NV) centre-based magnetometry28,29 is a rather new experimental method that, in principle, is capable of providing the desired information. This technique has already been used successfully to study, for example, vortices30, domain walls31,32 and spin wave excitations33,34 in ferromagnets, but it has never been used to probe (helical) antiferromagnetic spin arrangements and rarely been applied under cryogenic conditions35,36. In this article, we study emergent micromagnetic dynamics in the helimagnetic phase of FeGe based on MFM, NV centre magnetometry, and Landau–Lifschitz–Gilbert (LLG) simulations. Figure 1 | Temperature dependence of the helimagnetic domain structure The MFM measurements reveal temperature-driven local changes in FeGe. (a) Schematic of the helimagnetic spin order and wave vector q. in the magnetic domain structure, as well as jump-like collective Colour-coded planes indicate wave fronts of the magnetization M that are movements of the helical spin texture that propagate over defined by uniformly oriented spins. (b) MFM image in the helimagnetic mesoscopic length scales. The collective movements are driven by state. q1 and q2 indicate two magnetic domains. Scale bar, 500 nm. the depinning and subsequent motion of topological magnetic (c,d) With increasing temperature, local variations are observed in the edge dislocations by which the system relaxes its magnetic domain structure while the period of the helimagnetic order within domains structure. Single-spin magnetometry experiments with NV is unaffected. (e) The magnetic contrast vanishes when approaching TN. 2 NATURE COMMUNICATIONS | 7:12430 | DOI: 10.1038/ncomms12430 | www.nature.com/naturecommunications NATURE COMMUNICATIONS | DOI: 10.1038/ncomms12430 ARTICLE tip-surface distance of about 30 nm (a representative topography l ¼ 70±5 nm, which is consistent with neutron scattering image is shown in Supplementary Fig. 1; see Methods section for data8. The measurement in Fig. 1b further reveals micrometer- further technical details). After cooling the sample to 265 K, sized magnetic domains with different orientation of the wave alternating bright and dark lines are clearly visible, indicating a vector q, that are separated by a so-called vortex-free domain wall periodic magnetic structure. To relate the MFM data to the as detailed in ref. 13. microscopic spin arrangement, we calculate the magnetic stray To investigate the stability of the helimagnetic order, we field for helimagnetic order with periodicity l and a constant perform additional MFM scans at elevated temperature as magnetization amplitude |M| ¼ M (see Fig. 1a for a schematic illustrated in Fig. 1c–e. A comparison of the MFM images shows illustration of the helical spin structure). The magnetic structure that the magnetic stray field associated with the structure of the can be described as domain
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