Magnetic skyrmions: Review of recent advances

Magnetic skyrmions: advances in physics and potential applications.
Albert Fert, Nicolas Reyren,Vincent Cros
Nature Reviews Materials 2, 17031 (2017)

Skyrmions in Noncentrosymmetric Magnets: Review

Noncentrosymmetric Magnets Hosting Magnetic Skyrmions.

Naoya Kanazawa, Shinichiro Seki, and Yoshinori Tokura

Advanced Materials 29, 1603227 (2017)

Skyrmion excitations in a magnonic crystal

Collective dynamical skyrmion excitations in a magnonic crystal.

M. Mruczkiewicz, P. Gruszecki, M. Zelent, and M. Krawczyk
Phys. Rev. B 93, 174429 (2016)

Spatial maps of the x, y, and z components of the dynamic magnetization vector δm of (a) the 0.98 GHz clockwise gyrotropic mode, and (b) the 13.24 GHz breathing mode, obtained from FDTD simulations in a 30-nm nanodot under magnetic field Bz=0.1 T. Left and right columns show the absolute value and phase, respectively, of each δm component.

Multidomain Skyrmion Lattice

Multidomain Skyrmion Lattice State in Cu2OSeO3.

S. L. Zhang, A. Bauer, D. M. Burn, P. Milde, E. Neuber, L. M. Eng, H. Berger, C. Pfleiderer, G. van der Laan, and T. Hesjedal

 Nano Letters (ACS Publications)

Bubble and skyrmion crystals

Bubble and skyrmion crystals in frustrated magnets with easy-axis anisotropy.
Satoru Hayami, Shi-Zeng Lin, and Cristian D. BatistaPhys. Rev. B 93, 184413 (2016)

Schematic views of (a) a noncoplanar skyrmion texture and (b) a collinear bubble. Triangular crystals of these structures are induced by magnetic field and easy-axis anisotropy in high-symmetry frustrated magnets.

Thermally activated helicity reversals of skyrmions

Thermally activated helicity reversals of skyrmions.
X. Z. Yu, K. Shibata, W. Koshibae, Y. Tokunaga, Y. Kaneko, T. Nagai, K. Kimoto, Y. Taguchi, N. Nagaosa, and Y. Tokura
Phys. Rev. B 93, 134417 (2016)

Schematic of a bubble with winding number 1. Arrows show that the magnetic moments and concentric rings are a bubble domain wall. ϕ, φ, and ψ denote the polar angle, azimuthal angle, and the angle between the magnetic moment and the $x$ direction, respectively.

Antiferromagnetic Skyrmions: Applied Current and Temperature

Static and Dynamical Properties of Antiferromagnetic Skyrmions in the Presence of Applied Current and Temperature.
Joseph Barker and Oleg A. Tretiakov
Phys. Rev. Lett. 116, 147203 (2016)

The spin texture of a $G$-type AFM Skyrmion. (a) Top view of the Skyrmion, white lines show contours of constant $n_z$. The radius is 2.1 nm. (b) Cross section of the Skyrmion. The core is not a single spin but a compensated structure combining the two sublattices.

Generation of magnetic skyrmion bubbles

Generation of magnetic skyrmion bubbles by inhomogeneous spin Hall currents.
Olle Heinonen, Wanjun Jiang, Hamoud Somaily, Suzanne G. E. te Velthuis, and Axel Hoffmann
Phys. Rev. B 93, 094407 (2016)

The left panel shows a contour plot of the out-of-plane component of the magnetization director of a skyrmion bubble. The right panel shows the out-of-plane component of the magnetization across the line indicated in the left panel. The domain-wall width estimated from $m_z=0.9$ to $m_z=-0.9$ is about 30 nm.

High-topological-number magnetic skyrmions

High-topological-number magnetic skyrmions and topologically protected dissipative structure.

Xichao Zhang, Yan Zhou, and Motohiko Ezawa
Phys. Rev. B 93, 024415 (2016)

Time evolution of the high-Q skyrmion (Q=2). (a) Time evolution of the total energy Etotal, the DMI energy EDMI, the topological number Q, the in-plane (mx,my) and out-of-plane mz components of magnetization averaged over the simulation area, and the dissipation functions W. A high-Q skyrmion with Q=2 is created nearly at t=0.38 ns. The DMI constant D=2 mJ m−2. The spin current density j=3×1012 A m−2. The external magnetic field Bz=250 mT. (b) Top views of the magnetization distributions mx,my, and mz of the FM nanodisk, the corresponding topological charge density distribution q, and the Rayleigh dissipation function W at selected times. The green circle indicates the spin current injection region. The nucleation of a high-Q skyrmion with Q=2 occurs nearly at t=0.38 ns, where the dissipation function spreads all over the FM nanodisk, implying that the spin wave propagates. The DMI is turned off at t=10 ns. It is remarkable that the high-Q skyrmion remains stable even if the DMI is switched off, which demonstrates the topological protection against the change of a variable, that is, the DMI.

Skyrmions in chiral magnets with Rashba and Dresselhaus spin-orbit coupling

Skyrmions in chiral magnets with Rashba and Dresselhaus spin-orbit coupling.
James Rowland, Sumilan Banerjee, and Mohit Randeria
Phys. Rev. B 93, 020404 (2016)

Phase diagrams as a function of $AJ/D^2$ and $HJ/D^2$ for four values of $D_{\perp }/D_{\parallel }$. Easy-axis anisotropy corresponds to $A<0$ while easy-plane anisotropy to $A>0$. The cone, elliptic cone, and tilted FM phases are shown schematically, with the $Q$ vector shown in red and the texture traced out by spins shown in black.

Topological and thermodynamic stabilityskyrmion lattice

Interplay between topological and thermodynamic stability in a metastable magnetic skyrmion lattice.

Hiroshi Oike, Akiko Kikkawa, Naoya Kanazawa, Yasujiro Taguchi, Masashi Kawasaki, Yoshinori Tokura & Fumitaka Kagawa

Nature Physics 12, 62 (2016)

Creation and annihilation of the metastable skyrmion lattice through thermal control.

Stability of skyrmionic bits

Stability of single skyrmionic bits.
J. Hagemeister, N. Romming, K. von Bergmann, E. Y. Vedmedenko & R. Wiesendanger
Nature Communications 6, 8455 (2015)

(a) Triangular spin lattice with a hexagonal boundary shape containing a single skyrmion at k_BT=0.05 J and μB=0.1 J. (b) The inset displays the DM energy as a function of the Monte Carlo step (MCS) for different magnetic field strengths at k_BT=0.61 J exhibiting a two-state behaviour due to the ongoing creation and annihilation of a single skyrmion. The size of the system is such that it contains a maximum of one skyrmion at a given MCS. The histogram of the DM energy shows two peaks corresponding to the FM and Sk states. The Sk and FM states are populated with equal probability at the critical field B_c and the areas underneath the peaks of the histogram are equal.

Néel skyrmions in confined geometries

Degeneracies and fluctuations of Néel skyrmions in confined geometries.
Rick Keesman, A. O. Leonov, P. van Dieten, Stefan Buhrandt, G. T. Barkema, Lars Fritz, and R. A. Duine 
Phys. Rev. B 92, 134405 (2015)

Simulations snapshots of spin systems of size L×L=3 for different parameter values and temperatures with the parameter D/Jchosen such that the pitch length p=8. The periodic boundary is drawn as a red solid line and spin vectors are represented by colored arrows where the color scales linearly with the zˆ component of the vector to highlight spin texture

Dynamically stabilized magnetic skyrmions

Dynamically stabilized magnetic skyrmions.

Y. Zhou, E. Iacocca, A. A. Awad, R. K. Dumas, F. C. Zhang, H. B. Braun and J. Åkerman
Nature Communications 6, 8193 (2015)

(a) A bubble skyrmion stabilized by dipolar interactions which may exist as a left- or right-handed version. Its size typically exceeds that of skyrmions stabilized by DMI. (b,c) DMI stabilized skyrmions: (b) A chiral skyrmion as favoured in B20-type materials such as MnSi. (c) A hedgehog skyrmion as favoured by interfacial DMI.(d) Dynamically stabilized magnetic skyrmion which requires neither dipolar interactions nor DMI and which exhibits precession around the (vertical) easy-axis anisotropy. (e) For vanishing dipolar interactions (DDI), DMI and Oe fields, and in absence of damping, the skyrmion precesses uniformly and breathing disappears.

Magnetic skyrmions beyond room temperature

A new class of chiral materials hosting magnetic skyrmions beyond room temperature.

Y. Tokunaga, X. Z. Yu, J. S. White, H. M. Rønnow, D. Morikawa, Y. Taguchi, Y. Tokura

Nature Communications 6, 7638 (2015) 

Lorentz transmission electron microscopy (LTEM) of skyrmion crystal.

Neel-type skyrmion lattice

Néel-type skyrmion lattice with confined orientation in the polar magnetic semiconductor GaV4S8.
I. Kézsmárki, S. Bordács, P. Milde, E. Neuber, L. M. Eng, J. S. White, H. M. Rønnow, C. D. Dewhurst, M. Mochizuki, K. Yanai, H. Nakamura, D. Ehlers, V. Tsurkan & A. Loidl

Nature Materials 14, 1116 (2015) 

a, In a Bloch-type skyrmion, the spins rotate in the tangential planes—that is, perpendicular to the radial directions—when moving from the core to the periphery. b, In a Néel-type skyrmion, the spins rotate in the radial planes from the core to the periphery. The cross-section of the vortex is also depicted in both cases.

Spin patterns in the magnetic phases of GaV₄S₈.

Skyrmions in MnSi Nanowires

Stabilized Skyrmion Phase Detected in MnSi Nanowires by Dynamic Cantilever Magnetometry
A. Mehlin, F. Xue, D. Liang, H. F. Du, M. J. Stolt, S. Jin, M. L. Tian, and M. Poggio
Nano Letters 15, 4839 (2015)

Using dynamic cantilever magnetometry we measure an enhanced skyrmion lattice phase extending from around 29 K down to at least 0.4 K in single MnSi nanowires (NWs). Although recent experiments on two-dimensional thin films show that reduced dimensionality stabilizes the skyrmion phase, our results are surprising given that the NW dimensions are much larger than the skyrmion lattice constant. Furthermore, the stability of the phase depends on the orientation of the NWs with respect to the applied magnetic field, suggesting that an effective magnetic anisotropy, likely due to the large surface-to-volume ratio of these nanostructures, is responsible for the stabilization. The compatibility of our technique with nanometer-scale samples paves the way for future studies on the effect of confinement and surfaces on magnetic skyrmions.

Skyrmion deformation in strained crystals

Large anisotropic deformation of skyrmions in strained crystal.

K. Shibata, J. Iwasaki, N. Kanazawa, S. Aizawa, T. Tanigaki, M. Shirai, T. Nakajima, M. Kubota, M. Kawasaki, H. S. Park, D. Shindo, N. Nagaosa & Y. Tokura

Nature Nanotechnology 10, 589 (2015)

Evaluation of SkX deformation in reciprocal space. a,b, FFT patterns of the over-focused Lorentz TEM images in Fig. 1c (at 260 K) and
Fig. 1d (94 K). c,d, FFT patterns of simulated SkX spin configurations under isotropic and anisotropic DMIs, respectively. Fitting ellipses of the six spots corresponding to magnetic modulation vectors are denoted by dashed curves in a–d. e, SkX deformation parameters a (long axis of the fitting ellipse), b (short axis) and f = 1 − b/a as functions of temperature T (upper abscissa) and estimated strain ε (lower abscissa). f, SkX deformation parameters a, b and f in simulated SkX spin configurations as a function of the degree of introduced DMI anisotropy η = 1 − Dx/Dy.

 

Skyrmion magnonic crystals

Skyrmion-Based Dynamic Magnonic Crystal.
Fusheng Ma, Yan Zhou, H. B. Braun, and W. S. Lew

Nano Letters 15, 4029 (2015)

A linear array of periodically spaced and individually controllable skyrmions is introduced as a magnonic crystal. It is numerically demonstrated that skyrmion nucleation and annihilation can be accurately controlled by a nanosecond spin polarized current pulse through a nanocontact. Arranged in a periodic array, such nanocontacts allow the creation of a skyrmion lattice that causes a periodic modulation of the waveguide’s magnetization, which can be dynamically controlled by changing either the strength of an applied external magnetic field or the density of the injected spin current through the nanocontacts. The skyrmion diameter is highly dependent on both the applied field and the injected current. This implies tunability of the lowest band gap as the skyrmion diameter directly affects the strength of the pinning potential. The calculated magnonic spectra thus exhibit tunable allowed frequency bands and forbidden frequency bandgaps analogous to that of conventional magnonic crystals where, in contrast, the periodicity is structurally induced and static. In the dynamic magnetic crystal studied here, it is possible to dynamically turn on and off the artificial periodic structure, which allows switching between full rejection and full transmission of spin waves in the waveguide. These findings should stimulate further research activities on multiple functionalities offered by magnonic crystals based on periodic skyrmion lattices.

  

Writing and Deleting Single Magnetic Skyrmions

Writing and Deleting Single Magnetic Skyrmions.
Niklas Romming, Christian Hanneken, Matthias Menzel, Jessica E. Bickel, Boris Wolter,

Kirsten von Bergmann, André Kubetzka, Roland Wiesendanger

Science 341, 636 (2015)

Magnetic field dependence of the PdFe bilayer on the Ir(111) surface at T = 8 K. (A to C) Perspective sketches of the magnetic phases. (D) Overview SP-STM image, perspective view of constant-current image colorized with its derivative. (E to G) PdFe bilayer at different magnetic fields (U = +50 mV, I = 0.2 nA, magnetically out-of-plane sensitive tip). (E) Coexistence of spin spiral and skyrmion phase. (F) Pure skyrmion phase. (G) Ferromagnetic phase. A remaining skyrmion is marked by the white circle.