Monopole-Induced Emergent Electric Fields in Ferromagnetic Nanowires

Michalis Charilaou, Hans-Benjamin Braun, and Jörg F. Löffler

Phys. Rev. Lett. 121, 097202 – Published 28 August 2018

Abstract

We predict that complete magnetization reversal in simple metallic ferromagnetic nanoparticles is directly linked to the pair creation of topological point defects in the form of hedgehog-antihedgehog pairs. These dynamical point defects move at exceptionally high speeds in excess of $1500 m / s$ , faster than any other known magnetic object. Their rapid motion generates unprecedented solenoidal emergent fields on the order of megavolts per meter, in analogy to the magnetic field of a moving electric charge, providing a striking example that a moving hedgehog constitutes an emergent magnetic monopole.

Received 19 April 2018
Corrected 21 September 2018

DOI:https://doi.org/10.1103/PhysRevLett.121.097202

Physics Subject Headings (PhySH)

Magnetic texture Magnetism Magnetization dynamics

Condensed Matter, Materials & Applied Physics

Corrections

21 September 2018

Correction: The first byline footnote has been restructured for clarity.

Authors & Affiliations

Michalis Charilaou^1,*, Hans-Benjamin Braun^2,3,†, and Jörg F. Löffler¹

¹Laboratory of Metal Physics and Technology, Department of Materials, ETH Zurich, 8093 Zurich, Switzerland
²UCD School of Physics, University College Dublin, Dublin 04 V1W8, Ireland
³School of Theoretical Physics, Dublin Institute of Advanced Studies, Dublin 04 C932, Ireland

^*charilaou@mat.ethz.ch Present address: Department of Physics, University of Louisiana at Lafayette, Lafayette, Louisiana 70504, USA. michalis.charilaou@louisiana.edu
^†bbraun@stp.dias.ie

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand

Issue

Vol. 121, Iss. 9 — 31 August 2018

Reuse & Permissions

Access Options

Author publication services for translation and copyediting assistance advertisement

Images

Figure 1
Snapshots of a micromagnetic simulation showing the initial, reversible stages of the switching process in a cylindrical Permalloy nanowire with diameter 60 nm and length 300 nm: (a) at 0 s, (b) at 100 ps, and (c) at 160 ps, after having applied a constant field of 125 mT along $- z$ . The top panels show vector-field plots, and the bottom panels show contour plots of the $z$ component of the magnetization together with the topological charge density integrated across the cylinder. The initial curling-mode instability develops into the formation of two Skyrmion lines of opposite handedness. The graph in (d) shows the profile across the wire taken 100 nm from its middle, well described by the variational ansatz discussed in the text, and (e) schematically indicates the Skyrmion spin textures of opposite chirality that are obtained in (b) and (c) at sample cross sections at $\pm z_{0}$ , with $z_{0} \approx 50 - 150 nm$ .
Reuse & Permissions
Figure 2
Time evolution of the spatially averaged magnetization ${\bar{m}}_{z}$ during a field pulse, and contour plot of $m_{z} 10 ps$ before the applied magnetic field is switched off: (a) The magnetization process is reversible if the applied field is switched off before the Skyrmion lines break ( $Δ t_{1} = 0.16 ns$ ). (b) Irreversibility sets in only when the Skyrmion line is destroyed via the creation of a hedgehog-antihedgehog pair before switching off the applied field ( $Δ t_{2} = 0.17 ns$ ). Only in the latter case does full magnetization reversal occur ( ${\bar{m}}_{z} \approx - 1$ ).
Reuse & Permissions
Figure 3
Contour plots of $m_{z}$ and $Q_{D}$ as a function of $z$ at (a) $t = 10 ps$ , (b) $t = 30 ps$ , and (c) $t = 50 ps$ after the field has been switched off. The circles in the contour plots indicate the positions of the $Q_{S^{2}} = 1$ (top) hedgehog and the $Q_{S^{2}} = - 1$ (bottom) antihedgehog as a function of time. (d) Detailed view of the moment distribution of a hedgehog at the end of the Skyrmion line. (e) Hedgehog separation (diamonds) and location of the top hedgehog (circles) as a function of time, yielding a maximal relative velocity of $\approx 3 \times 10^{3} m / s$ . (f) Hedgehog speed as a function of the damping constant $α$ at three different external fields. In panels (a)-(e) the values $α = 0.1$ and $μ_{0} H_{ext} = 0.125 T$ were used, as marked with a circle in panel (f).
Reuse & Permissions
Figure 4
(a) Schematic view of the end of a Skyrmion line, where (b) the corresponding magnetization texture is seen to be topologically equivalent to a hedgehog with radially outward-oriented magnetization ( $Q_{S^{2}} = 1$ ). (c) A pair of separating hedgehogs of opposite topological charge ( $Q_{S^{2}} = \pm 1$ ) gives rise to an emergent solenoidal electric field (purple), in analogy to the magnetic field created by a pair of separating electric charges of opposite sign. For the process shown in Fig. 3, the emergent electric field of such a magnetic monopole has a strength of the order of $0.5 MV / m$ .
Reuse & Permissions

Physical Review Letters