This article's lead section may be too long. Please read the length guidelines and help move details into the article's body.(July 2023)
Condensed matter phenomenon; vortex-like magnetic quasiparticle
This article is about the vortex-like magnetic structure. For the general model in particle physics, see skyrmion.
In physics, magnetic skyrmions (occasionally described as 'vortices,'[1] or 'vortex-like'[2]
configurations) are statically stable solitons which have been predicted theoretically[1][3][4] and observed experimentally[5][6][7] in condensed matter systems. Magnetic skyrmions can be formed in magnetic materials in their 'bulk' such as in manganese monosilicide (MnSi),[6] or in magnetic thin films.[1][2][8][9] They can be achiral, or chiral (Fig. 1 a and b are both chiral skyrmions) in nature, and may exist both as dynamic excitations[10] or stable or metastable states.[5] Although the broad lines defining magnetic skyrmions have been established de facto, there exist a variety of interpretations with subtle differences.
Most descriptions include the notion of topology – a categorization of shapes and the way in which an object is laid out in space – using a continuous-field approximation as defined in micromagnetics. Descriptions generally specify a non-zero, integer value of the topological index,[11] (not to be confused with the chemistry meaning of 'topological index'). This value is sometimes also referred to as the winding number,[12] the topological charge[11] (although it is unrelated to 'charge' in the electrical sense), the topological quantum number[13] (although it is unrelated to quantum mechanics or quantum mechanical phenomena, notwithstanding the quantization of the index values), or more loosely as the “skyrmion number.”[11] The topological index of the field can be described mathematically as[11]
(1)
where is the topological index, is the unit vector in the direction of the local magnetization within the magnetic thin, ultra-thin or bulk film, and the integral is taken over a two dimensional space. (A generalization to a three-dimensional space is possible).[citation needed]
Passing to spherical coordinates for the space ( ) and for the magnetisation ( ), one can understand the meaning of the skyrmion number. In skyrmion configurations the spatial dependence of the magnetisation can be simplified by setting the perpendicular magnetic variable independent of the in-plane angle () and the in-plane magnetic variable independent of the radius ( ).
Then the topological skyrmion number reads:
(2)
where p describes the magnetisation direction in the origin (p=1 (−1) for ) and W is the winding number.
Considering the same uniform magnetisation, i.e. the same p value, the winding number allows to define the skyrmion () with a positive winding number and the antiskyrmion with a negative winding number and thus a topological charge opposite to the one of the skyrmion.
What this equation describes physically is a configuration in which the spins in a magnetic film are all aligned orthonormal to the plane of the film, with the exception of those in one specific region, where the spins progressively turn over to an orientation that is perpendicular to the plane of the film but anti-parallel to those in the rest of the plane. Assuming 2D isotropy, the free energy of such a configuration is minimized by relaxation towards a state exhibiting circular symmetry, resulting in the configuration illustrated schematically (for a two dimensional skyrmion) in figure 1. In one dimension, the distinction between the progression of magnetization in a 'skyrmionic' pair of domain walls, and the progression of magnetization in a topologically trivial pair of magnetic domain walls, is illustrated in figure 2. Considering this one dimensional case is equivalent to considering a horizontal cut across the diameter of a 2-dimensional hedgehog skyrmion (fig. 1(a)) and looking at the progression of the local spin orientations.
It is worth observing that there are two different configurations which satisfy the topological index criterion stated above. The distinction between these can be made clear by considering a horizontal cut across both of the skyrmions illustrated in figure 1, and looking at the progression of the local spin orientations. In the case of fig. 1(a) the progression of magnetization across the diameter is cycloidal. This type of skyrmion is known as a hedgehog skyrmion. In the case of fig. 1(b), the progression of magnetization is helical, giving rise to what is often called a vortex skyrmion.
^ abcBogdanov AN, Rössler UK (July 2001). "Chiral symmetry breaking in magnetic thin films and multilayers". Physical Review Letters. 87 (3): 037203. Bibcode:2001PhRvL..87c7203B. doi:10.1103/physrevlett.87.037203. PMID 11461587.
^ abIwasaki J, Mochizuki M, Nagaosa N (October 2013). "Current-induced skyrmion dynamics in constricted geometries". Nature Nanotechnology. 8 (10): 742–7. arXiv:1310.1655. Bibcode:2013NatNa...8..742I. doi:10.1038/nnano.2013.176. PMID 24013132. S2CID 780496.
^Rössler UK, Bogdanov AN, Pfleiderer C (August 2006). "Spontaneous skyrmion ground states in magnetic metals". Nature. 442 (7104): 797–801. arXiv:cond-mat/0603103. Bibcode:2006Natur.442..797R. doi:10.1038/nature05056. PMID 16915285. S2CID 4389730.
^Dupé B, Hoffmann M, Paillard C, Heinze S (June 2014). "Tailoring magnetic skyrmions in ultra-thin transition metal films". Nature Communications. 5: 4030. Bibcode:2014NatCo...5.4030D. doi:10.1038/ncomms5030. PMID 24893652.
^ abRomming N, Hanneken C, Menzel M, Bickel JE, Wolter B, von Bergmann K, et al. (August 2013). "Writing and deleting single magnetic skyrmions". Science. 341 (6146): 636–9. Bibcode:2013Sci...341..636R. doi:10.1126/science.1240573. PMID 23929977. S2CID 27222755.
^ abMühlbauer S, Binz B, Jonietz F, Pfleiderer C, Rosch A, Neubauer A, et al. (February 2009). "Skyrmion lattice in a chiral magnet". Science. 323 (5916): 915–9. arXiv:0902.1968. Bibcode:2009Sci...323..915M. doi:10.1126/science.1166767. PMID 19213914. S2CID 53513118.
^Hsu PJ, Kubetzka A, Finco A, Romming N, von Bergmann K, Wiesendanger R (February 2017). "Electric-field-driven switching of individual magnetic skyrmions". Nature Nanotechnology. 12 (2): 123–126. arXiv:1601.02935. Bibcode:2017NatNa..12..123H. doi:10.1038/nnano.2016.234. PMID 27819694. S2CID 5921700.
^Fert A, Cros V, Sampaio J (March 2013). "Skyrmions on the track". Nature Nanotechnology. 8 (3): 152–6. Bibcode:2013NatNa...8..152F. doi:10.1038/nnano.2013.29. PMID 23459548.
^Husain S, Sisodia N, Chaurasiya AK, Kumar A, Singh JP, Yadav BS, et al. (January 2019). "Co2FeAl Heusler Alloy Ultrathin Film Heterostructures". Scientific Reports. 9 (1): 1085. doi:10.1038/s41598-018-35832-3. PMC 6355792. PMID 30705297.
^Sondhi SL, Karlhede A, Kivelson SA, Rezayi EH (June 1993). "Skyrmions and the crossover from the integer to fractional quantum Hall effect at small Zeeman energies". Physical Review B. 47 (24): 16419–16426. Bibcode:1993PhRvB..4716419S. doi:10.1103/physrevb.47.16419. PMID 10006073.
^ abcdHeinze S, Bergmann K, Menzel M, Brede J, Kubetzka A, Wiesendanger R, Bihlmayer G, Blügel S (2011). "Spontaneous atomic-scale magnetic skyrmion lattice in two dimensions". Nature Physics. 7 (9): 713–718. Bibcode:2011NatPh...7..713H. doi:10.1038/nphys2045.
^von Bergmann K, Kubetzka A, Pietzsch O, Wiesendanger R (October 2014). "Interface-induced chiral domain walls, spin spirals and skyrmions revealed by spin-polarized scanning tunneling microscopy". Journal of Physics: Condensed Matter. 26 (39): 394002. Bibcode:2014JPCM...26M4002V. doi:10.1088/0953-8984/26/39/394002. PMID 25214495. S2CID 38343842.
^Finazzi M, Savoini M, Khorsand AR, Tsukamoto A, Itoh A, Duò L, et al. (April 2013). "Laser-induced magnetic nanostructures with tunable topological properties". Physical Review Letters. 110 (17): 177205. arXiv:1304.1754. Bibcode:2013PhRvL.110q7205F. doi:10.1103/physrevlett.110.177205. PMID 23679767. S2CID 21660154.
^Hoffmann M, Zimmermann B, Müller GP, Schürhoff D, Kiselev NS, Melcher C, Blügel S (August 2017). "Antiskyrmions stabilized at interfaces by anisotropic Dzyaloshinskii-Moriya interactions". Nature Communications. 8 (1): 308. arXiv:1702.07573. Bibcode:2017NatCo...8..308H. doi:10.1038/s41467-017-00313-0. PMC 5566362. PMID 28827700.
In physics, magneticskyrmions (occasionally described as 'vortices,' or 'vortex-like' configurations) are statically stable solitons which have been predicted...
especially in the emerging technology of spintronics. A two-dimensional magneticskyrmion, as a topological object, is formed, e.g., from a 3D effective-spin...
antiferromagnet. The interaction is fundamental to the production of magneticskyrmions and explains the magnetoelectric effects in a class of materials termed...
ring-shaped topological spin texture and is closely related to the magneticskyrmion. The topological charge can be defined as follows. Q = ∫ m → ( r →...
topic in the history of science. Loop quantum gravity Magneticskyrmion, a vortex-like magnetic quasiparticle Quantum vortex, a quantised flux circulation...
Europhysics Prize in condensed matter physics for theoretical studies on magneticskyrmion phases in MnSi, a new phase of matter. He is one of the recipients...
In particle physics, a magnetic monopole is a hypothetical elementary particle that is an isolated magnet with only one magnetic pole (a north pole without...
and the magnetic monopole in electromagnetism, the Skyrmion and the Wess–Zumino–Witten model in quantum field theory, the magneticskyrmion in condensed...
collaborators have led to the opening of new sub-fields of physics, such as magneticskyrmion spintronics, antiferromagnetic spintronics, and cold-atom spintronics...
ferromagnets. As a result, skyrmions have potential application in ultrahigh-density magnetic storage devices. The helical, conical and skyrmion structures are not...
As of 2021, Cu2OSeO3 is the only insulating material that hosts magneticskyrmions. Cu2OSeO3 polycrystals can be grown by heating a 2:1 molar mixture...
exist: The skyrmion models the nucleon as a topological soliton in a nonlinear SU(2) pion field. The topological stability of the skyrmion is interpreted...
islands. In magnetic systems where interfacial Dzyaloshinskii–Moriya interactions stabilize magnetic textures known as magneticskyrmions, scanning-probe...
other and can result in versatile magnetic spin textures such as magneticskyrmions. Superexchange was theoretically proposed by Hendrik Kramers in 1934...
be controlled by applied electric currents and magnetic fields. Antisymmetric exchange Magneticskyrmion Ferromagnetic resonance Perreault, Christopher...
arrangement of electron spins in MnSi changes with magnetic field, forming helical, conical, skyrmion, and regular ferromagnetic phases. Manganese monosilicide...
exhibit unusual spatial arrangements of electron spin, which were named magneticskyrmion, tetrahedral and cubic hedgehog lattices. Their structure can be controlled...
another polar metal at room temperature was reported which was also magnetic, skyrmions and the Rashba–Edelstein effect were observed. P. W. Anderson and...
His most recent works are on the topologically protected magnetic solitons called skyrmions and on the conversion between charge current and spin current...
observed in certain materials where electrical resistance vanishes and magnetic fields are expelled from the material. Any material exhibiting these properties...
especially crystal plasticity. In magnetic systems, topological defects include 2D defects such as skyrmions (with integer skyrmion charge), or 3D defects such...
nuclei in (mostly organic) molecules by nuclear magnetic resonance. This method uses the quantized spin magnetic moment of the proton, which is due to its angular...
own magnetic moment. Simplistically, the magnetic moment of the neutron can be viewed as resulting from the vector sum of the three quark magnetic moments...
could be detected on Earth by converting them to photons, using a strong magnetic field, motivating a number of experiments. For example, the Axion Dark...
topological structure. They are the three-dimensional counterparts of 2D skyrmions, which exhibit similar topological properties in 2D. Hopfions are widely...
local field. Magnetic polarizability likewise refers to the tendency for a magnetic dipole moment to appear in proportion to an external magnetic field. Electric...
study it using muon spin spectroscopy (μSR), a magnetic resonance technique analogous to nuclear magnetic resonance (NMR) or electron spin resonance (ESR)...
Mott transition, colossal magnetoresistance, Multiferroics, and magneticskyrmions. Tokura was born in Nishiwaki, Hyōgo, Japan. He holds a: B.S. in Applied...
prediction, experimental discovery and theoretical analysis of a magneticskyrmion phase in MnSi, a new state of matter. 2014: Harold Y. Hwang, Jochen...