Annual Report 2011 / 2012 - E21 - Technische Universität München

Chapter 1. Magnetism and Superconductivity 11
Emergent Electrodynamics of Skyrmions in a Chiral Magnet
Tomek Schulz 1 , Robert Ritz 1 , Andreas Bauer 1 , Marco Halder 1 , Michael Wagner 1 ,
Christian Franz 1 , Christian Pfleiderer 1 , Karin Everschor 2 , Markus Garst 2 , Achim Rosch 2
1 Physik-Department E21, Technische Universität München, D-85748 Garching, Germany.
2 Institut für theoretische Physik, Universität zu Köln, D-50937 Köln, Germany.
When an electron moves in a smoothly varying non-collinear
magnetic structure, its spin orientation adapts constantly,
thereby inducing forces that act both on the magnetic structure
and on the electron. These forces may be described
by electric and magnetic fields of an emergent electrodynamics
[1–4]. The topologically quantized winding number of
so-called skyrmions, a type of magnetic whirl discovered recently
in chiral magnets [5–7], has been predicted to induce
exactly one quantum of emergent magnetic flux per skyrmion.
A moving skyrmion is therefore expected to induce an
emergent electric field following Faraday’s law of induction,
which inherits this topological quantization [8].
Through measuring the temperature dependence of the
Hall resistivity,ρ xy (T), in the skyrmion lattice phase of MnSi
under a large applied d.c. electric current, we can show that
the topological Hall effect contribution, signature of the
skyrmion lattice, is suppressed through an emergent electric
field E e that builds up in the opposite direction of the
Hall voltage (fig. 1).
At a certain threshold j c of the applied d.c. current, the
skyrmion lattice depins and begins to drift. In agreement
with previous SANS experiments [9] we find an exceptionally
low j c ≈ 10 6 Am −2 that is five orders of magnitude smaller
than observed in conventional systems (fig. 2). From the
observed changes in the Hall resistivity ρ xy we are able to
directly calculate the emerging electric field E e and the drift
velocity v d‖ , and hence track the motion of the drifting skyrmion
lattice (fig. 3). Thereby, our measurements establish
quantitatively the predicted emergent electrodynamics [10].
In summary, we are able to directly observe the emergent
electric field of skyrmions and measure their depinning
transition and subsequent motion quantitatively. This offers
fundamental insights into the connection between the
emergent and real electrodynamics of skyrmions in chiral
magnets. Furthermore, this opens the possibility to address
fundamental questions of the coupling of magnetism, electric
currents and defects, respectively. The control and detection
of the motion of magnetic whirls (skyrmions) by
the interplay of emergent and real electrodynamics therefore
promises to become an important route towards spintronic
applications.
Figure 1: Temperature dependence of the Hall resistivity, ρ xy,
in the skyrmion lattice phase of MnSi under a large applied d.c.
electric current. To study the effect of the applied d.c. current it
is superimposed on a small a.c. excitation which allows detection
of the signal. Shown is the Hall resistivity for various magnetic
fields. Under an applied d.c. current of 2.81×10 6 Am −2 the Hall
signal is suppressed in the entire skyrmion phase (green shading).
Figure 3: Scaling plot of the transverse electric field, ∆E ⊥ =
−jρ xy , in units of j cρ ∞ xy, induced by the moving skyrmion lattice.
As E ⊥ is proportional to the emergent field E e , this also
constitutes a scaling plot of the emergent electric field E e (in
units of v pin B e ) or of the drift velocity v d‖ in units of the pinning
velocity v pin .
References
[1] G. Volovik, J. Phys. C 20, L87 (1987).
[2] S.A. Yang et al., Phys. Rev. Lett. 102, 067201 (2009).
[3] P.N. Hai et al., Nature 458, 489-492 (2009).
[4] S.E. Barnes et al., Phys. Rev. Lett. 98, 246601 (2007).
Figure 2: Typical variation of the Hall resistivity, ρ xy, of MnSi
as a function of applied d.c. current at B = 250mT and for
T = 27.02K. For temperatures in the skyrmion lattice phase, like
shown here, the signal is suppressed above an ultralow current
density, j c , and converges towards a constant value for large
currents. Absolute data values are given on the left-hand side
and the relative change with respect to j = 0 is given on the
right-hand side.
[5] S. Mühlbauer et al., Science 323, 915-919 (2009).
[6] A. Neubauer et al., Phys. Rev. Lett. 102, 186602 (2009).
[7] X.Z. Yu et al., Nature 465, 901-904 (2010).
[8] J. Zang et al., Phys. Rev. Lett. 107, 136804 (2011).
[9] F. Jonietz et al., Science 330, 1648-1651 (2010).
[10] T. Schulz et al., Nature Physics 8, 301-304 (2012).