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Enhanced stability of magnetic skyrmion lattice phase under a tilted magnetic field in two-dimensional chiral magnet Chao Wang, Haifeng Du, Xuebing Zhao, Chiming Jin, Mingliang Tian, Yuheng Zhang, and Renchao Che Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.7b00135 • Publication Date (Web): 28 Mar 2017 Downloaded from http://pubs.acs.org on March 29, 2017
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Enhanced stability of magnetic skyrmion lattice
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phase under a tilted magnetic field in two-
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dimensional chiral magnet
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Chao Wang┴,†, Haifeng Du┴,‡,§, Xuebing Zhao┴,†, Chiming Jin‡,§, Mingliang Tian*,‡,§, Yuheng
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Zhang‡,§ and Renchao Che*,†
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†Advanced Materials Laboratory, Fudan University, Shanghai 200433, China;
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‡High Magnetic Field Laboratory, Chinese Academy of Science (CAS), Hefei230031, Anhui
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Province, China;
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§Collaborative Innovation Center of Advanced Microstructures, Nanjing210093, Jiangsu
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Province, China
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Corresponding Author
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*
[email protected] 17
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[email protected] ACS Paragon Plus Environment
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ABSTRACT: Magnetic skyrmion is a topologically stable vortex-like spin texture that offers
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great promise as information carriers for future spintronic devices. In a two-dimensional chiral
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magnet, it was generally considered that a tilted magnetic field is harmful to its formation and
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stability. Here we investigated the angular dependent stability of magnetic skyrmions in FeGe
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nanosheets by using high-resolution Lorentz transmission electron microscopy (Lorentz TEM).
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Besides the theoretically predicted destruction of skyrmion lattice state by an oblique magnetic
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field as temperature closes to its magnetic Curie temperature Tc~278 K, we also observed an
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unexpected reentry-like phenomenon at the moderate temperatures near the border between
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conical and skyrmion phase, Tt~240 K. This behavior is completely beyond the theoretical
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prediction in a conventional two-dimensional (2D) system. Instead, a three-dimensional (3D)
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model involving the competition between conical phase and skyrmions is likely to play a crucial
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role.
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KEYWORDS: Skyrmion, Lorentz TEM, Stability, FeGe
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In 1980s, a pioneered theoretical work by Bogdanov and Yablonskii investigated magnetic
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vortices in magnetically ordered crystals lacking inversion symmetry, which was lately named
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magnetic skyrmions1. Its first experimental confirmation was performed in 2009 by Mühlbauer
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et al.2 with neutron scattering in a chiral magnet MnSi bulk, and subsequently a real space
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imaging of such a skyrmion lattice was verified by Yu et al.3 with Lorentz TEM. Since then, a
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rich of interesting properties relative to the magnetic skyrmions were reported, such as the
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controllable size, topological stability, and low critical current density required for motion4-8.
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These properties make magnetic skyrmions hold great promise to be information carrier in next-
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generation low consumption memory or logic devices.
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According to the Bogdanov’s theory, an important ingredient for stabilizing magnetic
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skyrmions in chiral magnets is the antisymmetric Dzyaloshinskii-Moriya interaction (DMI),
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which favors non-collinear arrangements of spins9-11. Competition between the DMI and the
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conventional ferromagnetic exchange coupling results in a spin helix ground state with a fixed
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propagation wave-vector k and a fixed period, LD, where the k and LD are, respectively,
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determined by the weak magnetic anisotropy and the energy ratio of these two interactions.
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When an external magnetic field, H, is applied, the spin helix generally evolves into a conical
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phase with kǁH and then into a saturated ferromagnetic state at high H. Skyrmions appear in the
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form of a lattice with a fixed lattice constant and an approximate circular shape, but it survives
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only in a small pocket just below the ferromagnetic transition temperature Tc in the magnetic
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field (H) and temperature (T) isotherm2,12,13. Further experimental studies also demonstrated that
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the stability of skyrmions can be enhanced significantly by lowering the dimensionality of chiral
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magnets from a bulk to thin film14,15, which was considered theoretically to be a result of the
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uniaxial anisotropy or three-dimensional modulated skyrmion arrangement in thin film species16-
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beneficial to the exploration of skyrmion physics. However, the existing work on skyrmions in
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thin film of chiral magnets is mostly restricted to the case with an applied magnetic field normal
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to the film plane. From the viewpoint of topology, the skyrmion structure is topologically
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protected and thus should be robust to the external perturbative magnetic field. Therefore, it is a
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fundamental interest to investigate the formation and stability of magnetic skyrmions in the
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presence of a tilted field.
. Such an extended region of the skyrmion phase in the H-T space is attractive and indeed
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Recent topological Hall effect measurements in epitaxial Mn1-xFexSi thin films observed a
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sharp reduction in the topological Hall resistivity in the process of inclining the magnetic field,
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which was associated with the destruction of two-dimensional (2D) skyrmion structures20,21.
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More recently, Monte Carlo simulations in single-layer thin films of chiral magnets showed that
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the shape of an individual skyrmion is noncircular and the skyrmion density decreases with the
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increase of the tilted magnetic field22. Meanwhile, the triangular lattice of skyrmions at a
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perpendicular magnetic field is distorted into a centered rectangular lattice at an inclined
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magnetic field.
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In comparison with the magneto-transport measurements and numerical calculation, we
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performed real-space observations of magnetic skyrmions in FeGe nanosheets at a tilted
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magnetic field by using high resolution Lorentz TEM. We found that both the stability and
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morphology of skyrmions depend on the temperatures. At high temperatures near Tc, the
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observed behavior follows the theoretical predication that the density of magnetic skyrmions
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with noncircular shape decreases with the increase of the tilted angles. However, as the
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temperature is slightly reduced to near the border between conical and skyrmion phase, at which
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the nanosheets only support isolated skyrmions at perpendicular magnetic field, the system
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presents an unexpected behavior from skyrmion clusters state to skyrmion lattice with non-
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triangular arrangement at an inclined magnetic field.
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Bulk FeGe has a near room Curie temperature Tc ~ 278 K and the spin helix possesses a long
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period LD ~ 70 nm6,15. Two FeGe nanosheets with a thickness of 90 and 104 nm were carved
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from the bulk crystal using focused ions beam (FIB) technique (See the details in the Supporting
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Information Note 1). Both samples have a high quality and good flatness with a surface
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roughness of only about ±2 nm (see Figs. S1, S2). The representative Lorentz TEM data
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discussed in the main text are from the nanosheet with the thickness of 90 nm. The others are
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shown in the Supporting Information and the different samples show very similar features
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qualitatively.
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The schematic experimental configuration was shown in Fig. 1a, in which the inclined
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magnetic field H was realized by tilting the FeGe nanosheet, while the magnetic field is always
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fixed along the direction of electron beam. The parameter θ is defined as the angle between the
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magnetic field and the right direction of the nanosheet. Lorentz TEM measurements were
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performed at varied temperatures and magnetic fields. The limitation of Lorentz TEM is that
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only the in-plane magnetic structure normal to the direction of electron beam can be detected.
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This quantitative planar magnetic distributions were obtained by the magnetic transport-of-
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intensity equation (TIE) analyses of high-resolution Lorentz TEM data (See the details in
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Lorentz TEM measurements section in Supporting Information Note 1)23,24.
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Figure 1. (a) The schematically experimental configurations. θ is the tilted angle. The sample
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has a thickness of t ~ 90 nm. The projected magnetic fields normal and parallel to the sample
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plane are defined as H⊥ and Hǁ, respectively. Direction of electron beam is applied along the H. n
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is the unit vector normal to the sample plane. (b)The temperature - field (T - H) phase diagram
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for θ= 0°, i.e. the magnetic field is perpendicular to the sample plane. The colored map is
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constructed to show the normalized skyrmion density, i.e., the ratio of the actual skyrmion
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number to the maximum number that can be accommodated in the sample. The open dots are
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data points from the Lorentz TEM measurement. The helical state is observed at low magnetic
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field. At increased magnetic field, the skyrmion lattice exists only between 240 K
