doi: 10.1038/s41467-019-13642-z.
Creation and annihilation of topological meron pairs in in-plane magnetized films
Affiliations
- PMID: 31811144
- PMCID: PMC6898613
- DOI: 10.1038/s41467-019-13642-z
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Creation and annihilation of topological meron pairs in in-plane magnetized films
Nat Commun.
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Abstract
Merons which are topologically equivalent to one-half of skyrmions can exist only in pairs or groups in two-dimensional (2D) ferromagnetic (FM) systems. The recent discovery of meron lattice in chiral magnet Co8Zn9Mn3 raises the immediate challenging question that whether a single meron pair, which is the most fundamental topological structure in any 2D meron systems, can be created and stabilized in a continuous FM film? Utilizing winding number conservation, we develop a new method to create and stabilize a single pair of merons in a continuous Py film by local vortex imprinting from a Co disk. By observing the created meron pair directly within a magnetic field, we determine its topological structure unambiguously and explore the topological effect in its creation and annihilation processes. Our work opens a pathway towards developing and controlling topological structures in general magnetic systems without the restriction of perpendicular anisotropy and Dzyaloshinskii-Moriya interaction.
Conflict of interest statement
The authors declare no competing interests.
Figures
a Definition and corresponding relation between vortice/antivortice and meron/antimeron, where w denotes the winding number and N denotes the topological number (N = pw/2 with p = +1 for up and p = −1 for down polarity of the cores). It is worth to mention that winding number is always +1 for vortex and −1 for antivortex, and does not depend on the clockwise or counterclockwise circulation direction of the in-plane magnetization. b Schematic drawing of vortex imprinting from a Co disk into a continuous Py film. c Simulation result of the magnetization distribution in a system with a Co disk (40 nm thick and 1 μm radius) on top of a 80 nm thick Py film. The result clearly shows the imprinting of the vortex from Co into Py, as well as a spontaneous creation of an antivortex to pair with the imprinted vortex. The positions of the vortex and antivortex in the Py film are highlighted by “V” and “A” in the zoomed in magnetization profile. The color wheel is shown next to the Co profile (each color on the wheel represents magnetization directing toward the corresponding radial direction outward.) d A simplified illustration of the magnetization profile of the meron pair. e, f Topology of the meron pair depends on their core polarities. Under a continuous spin deformation, the bimeron state (e; N = −1) is transformed into a skyrmion which wraps the full S2 spin space. In contrast, the meron–antimeron pair (f; N = 0) is transformed into a state in which the y > 0 (y < 0) half plane wraps (unwraps) the same half of the S2 spin space, allowing a continuous shrinking of this semisphere to a single point on S2, i.e., a single domain state with N = 0. Note, there are totally four possible combinations of the core polarities. We only show two of them because the other two cases are just mirror reflection of the shown two cases.
a Sample geometry imaged by MTXM at Co L3 edge. b Hysteresis loops of the sample inside and outside the patterned area. c The in-plane magnetic contrast at Co edge at external field of 50 Oe. d The corresponding simulated magnetization profile in Co layer, with the color wheel shown next to it. e The x-component (horizontal) of magnetization in Co layer from simulation. f The in-plane magnetic contrast at Fe edge at external field of 50 Oe. g The corresponding simulated magnetization profile in Py layer. h The x-component (horizontal) of magnetization in Py layer from simulation.
a–d Typical out-of-plane magnetic contrast images at 35 Oe. e–h Corresponding zoomed in images around the cores of the meron pairs. “V” and “A” denote the vortex core and antivortex core, respectively. i–l Corresponding schematic views of the magnetization profiles of the meron pairs. All four combinations of the core polarities are observed. The two cores are always bonded together and locate near either the top or bottom edge of the disk (the choice depends on the in-plane circulation direction of the vortex).
a–i In-plane magnetic contrast at three different states of H<+Hc (a, d, g), +Hc<H<+Hs (b, e, h), and H>+Hs (c, f, i) in the magnetization process. a, b, c The experimental results. The white arrows indicate the direction of surrounding Py magnetization. d, e, f Corresponding magnetization profiles obtained by simulation. g, h, i Corresponding thickness averaged x-component of the simulated magnetization profile in the Py film. j, k, l Out-of-plane magnetic contrast during the magnetization process. At the end of region (1) (e.g., the 15 Oe image in the figures), a meron pair is nucleated at the bottom edge of the disk area; after passing region (2) (e.g., the 45 Oe image in the figures), a new pair forms at the top edge; further increasing the magnetic field makes the distance between the two cores gradually reducing from ~300 nm toward zero (e.g., the 85–155 Oe images in the figures), and finally the meron pair is annihilated at the end of region (3) (e.g., the 175 Oe image in the figures). j The experimental images, where the yellow arrows in the first two images indicate the core position of vortices and antivortices; k thickness averaged z-component of the magnetization in the Py film in a simulation with the same field sequence; l zoomed in view of the magnetization profile close to the meron pairs at the bottom surface of Py from simulations, where the in-plane magnetization profile is plotted by arrows and the out-of-plane component of the magnetization is represented by the colors.
a, b Annihilation of a bimeron (N = −1), where the vortex and antivortex have opposite polarities. c, d Annihilation of a meron–antimeron pair (N = 0), where both the vortex and antivortex have the same polarity. a, c The experimental results; b, d thickness averaged z-component of the Py magnetization in a simulation with similar field sequence. The left schematic drawings show the starting topology of the two cases.
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