Accepted Manuscript 23 January 2014
1
This is the author’s version of the work. It is posted here by permission of the
AAAS for personal use, not for redistribution. The definitive version was
published in Science 343, 1333 on March 21, 2014, DOI:
10.1126/science.1242862 .
Large amplitude spin dynamics driven by a THz pulse in resonance with an
electromagnon
Authors: T. Kubacka
1
*, J.A. Johnson
2
, M.C. Hoffmann
3
, C. Vicario
4
, S. de Jong
3
, P. Beaud
2
, S.
Grübel
2
, S-W. Huang
2
, L. Huber
1
, L. Patthey
4
, Y-D. Chuang
5
, J.J. Turner
3
, G.L. Dakovski
3
, W-S.
Lee
3
, M.P. Minitti
3
, W. Schlotter
3
, R.G. Moore
6
, C.P. Hauri
4,7
, S.M. Koohpayeh
8
, V. Scagnoli
2
,
G. Ingold
2
, S.L. Johnson
1
, U. Staub
2
Affiliations:
1
ETH Zurich, Institute for Quantum Electronics, Wolfgang-Pauli-Strasse 16, 8093 Zurich,
Switzerland
2
Swiss Light Source, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland
3
Linac Coherent Light Source, SLAC National Accelerator Laboratory, Menlo Park, California
94025, USA
4
SwissFEL, Paul Scherrer Institut, 5232 Villigen PSI, Switzerland
5
Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720,
USA
6
The Stanford Institute for Materials and Energy Sciences (SIMES), SLAC National Accelerator
Laboratory, Menlo Park, California 94025, USA
7
Ecole Polytechnique Federale de Lausanne, 1015 Lausanne, Switzerland
This document is the accepted manuscript version of the following article:
Kubacka, T., Johnson, J. A., Hoffmann, M. C., Vicario, C., de Jong, S., Beaud, P.,
… Staub, U. (2014). Large-amplitude spin dynamics driven by a THz pulse in
resonance with an electromagnon. Science, 343(6177), 1333-1336.
https://doi.org/10.1126/science.1242862
2
8
Institute for Quantum Matter, Department of Physics and Astronomy, Johns Hopkins
University, Baltimore, MD 21218, USA
*Correspondence to: tkubacka@phys.ethz.ch
Abstract: Multiferroics have attracted strong interest for potential applications where electric
fields control magnetic order. The ultimate speed of control via magnetoelectric coupling,
however, remains largely unexplored. Here we report on an experiment in which we drive spin
dynamics in multiferroic TbMnO
3
with an intense few-cycle terahertz (THz) light pulse tuned to
resonance with an electromagnon, an electric-dipole active spin excitation
.
We observe the
resulting spin motion using time-resolved resonant soft x-ray diffraction. Our results show that it
is possible to directly manipulate atomic-scale magnetic structures using the electric field of light
on a sub-picosecond timescale.
Main Text: Data storage devices based on ferromagnetic or ferroelectric materials depend
strongly on domain reorientation, a process that typically occurs over time scales of several
nanoseconds. Faster reorientation dynamics may be achievable using intense electromagnetic
(EM) pulses (1). The EM pulses can couple to magnetism either indirectly via electronic
excitations (2) or directly via the Zeeman torque induced by the magnetic field (3-5). Direct
excitation has the advantage of minimal excess heat deposition, but requires frequencies in the
10
10
-10
12
Hz range. The low magnetic field strength of currently realizable THz frequency EM
sources poses a formidable challenge for such schemes.
Thanks to the coexistence of different ferroic orders, multiferroics offer new routes to
domain control (6). Particularly strong coupling between the ferroelectric and magnetic order
exists in single-phase frustrated magnets where noncollinear spin structure drives ferroelectricity
as a result of weak relativistic interactions (7-9). Consequently, the magnetic order can be
3
controlled by application of an electric field (10-13). The speed of domain switching triggered by
simple step-function-like electric fields appears, however, to be limited to a timescale of several
milliseconds (14). As an alternate solution, optical pulses have been shown to affect the magnetic
structure of multiferroics on a femto- and picosecond timescale (15-17). It has been predicted
that ultrafast magnetic dynamics can be also triggered by coherent excitation of electromagnons,
electric-dipole active spin excitations directly connected to the magnetoelectric coupling (18).
Here we show experimentally that a few-cycle THz pulse tuned to resonance with an
electromagnon can transiently modify the magnetic structure of multiferroic TbMnO
3
.
TbMnO
3
is a model spin-cycloid multiferroic exhibiting strong magnetoelectric coupling.
Although it has a relatively simple perovskite atomic structure, a strong GdFeO
3
-type distortion
gives rise to a variety of spin-frustrated phases (19, 20). At room temperature, the crystal is
paramagnetic. Below 42 K the Mn spins form a paraelectric sinusoidally modulated spin density
wave (SDW) state which transforms into a spin-cycloid state below 27 K. In this phase the spins
form a cycloid within the (bc) crystallographic plane (Fig. 1A) and a spontaneous ferroelectric
polarization along the c axis develops. Microscopically, the spin current between canted spins on
neighboring sites i, j gives rise to a ferroelectric polarization
( )
ij ij i j
prSSµ´ ´
(7), and the
magnitude of the polarization is further enhanced by lattice displacements (21-23). In all these
spin frustrated phases the magnetic structure of the Mn spins is incommensurate with the lattice,
characterized by a wave vector k = (0,q,0), where q » 0.28 changes very slowly in the SDW
phase with temperature (24).
The EM excitation spectrum of TbMnO
3
shows broad peaks in the THz frequency range;
these have been assigned to electromagnons (25-29) (Fig. 1B, lower inset). The strongest feature
at 1.8 THz is activated with the electric component of light parallel to the a axis and is absent in
4
other geometries (26). It has been proposed that the oscillating electric field along the a axis
modifies the nearest neighbor ferromagnetic exchange constant in the (ab) plane, resulting in
anti-phase spin oscillations within the spin cycloid plane (28, 30). Weaker spectral features at
lower frequencies have been proposed to arise from the higher harmonics of the spin cycloid and
coupling to the strongest electromagnon (30), and from out-of-plane spin cycloid motions (28,
31, 32).
To investigate whether excitation of electromagnons in TbMnO
3
is a viable route for
magnetic order control, we performed a THz pump and soft x-ray probe experiment (Fig. 1B).
The sample is a single crystal of TbMnO
3
cut to the (010) surface, oriented so that the a axis is at
45° with respect to the horizontal scattering plane. We generated few-cycle, phase stable THz
pulses with a center frequency of 1.8 THz using optical rectification in a nonlinear organic
crystal with a peak electric field of approximately 300 kV/cm at focus (33). We measured the
electric field component of the THz waveform at the sample position using electro-optical
sampling. To see the spin motion resulting from the excitation we used time-resolved resonant
soft x-ray diffraction at the Mn L
2
edge and measured the intensity of the first order (0q0)
cycloid reflection (34).
The spin dynamics can be extracted from the behavior of the intensity of the (0q0)
diffraction peak as a function of pump-probe delay time Dt (Fig. 2). At T = 13 K, where
TbMnO
3
is deep in the multiferroic phase, the x-ray signal shows oscillations resembling the
shape of the THz pump pulse electric field (Fig. 2A). The observed modulation of the diffraction
peak intensity is over an order of magnitude larger than expected for unconstrained spin
precession driven directly by the magnetic field component of the THz pulse (34). The Fourier
transform of the x-ray trace (Fig. 2D) shows that the material response has essentially the same
5
frequency spectrum as both the pump and the electromagnon. The delay between the first
maximum of the pump trace and the first maximum of the x-ray trace is 250 fs, corresponding to
approximately half of a single oscillation cycle. Inverting the sign of the electric field of the
pump pulse results in an opposite sign of changes in the diffraction intensity transients (Fig. 2B).
Such behavior is expected when it is the electric field, and not simple heating, that drives the
spin motion. When TbMnO
3
is in the non-multiferroic SDW phase (T = 30 K), the oscillation in
the peak intensity following the pump is strongly suppressed (Fig. 2C). This temperature
dependence gives strong evidence that the THz-induced spin motion is correlated with the
presence of multiferroicity. At 30 K we tentatively attribute the slight drop of overall intensity
after the pump to heating effects from absorption of the THz pulse, which leads to an estimated
temperature increase of less than 0.05 K (34).
To better understand the time dependence of the spin response, we construct a very
simple model of the system as two independent simple harmonic oscillators at the electromagnon
resonance frequencies of 0.7 THz and 1.8 THz (34). Although not a perfect match to the data, the
behavior of the conjugate momentum of the higher frequency oscillator successfully reproduces
the general shape of the oscillation and the delay between the driving electric field and the
changes in x-ray diffraction (Fig. 2A and 2B). The agreement is much worse for either canonical
coordinate of the lower frequency oscillator, suggesting that off-resonant excitation of the lower
energy electromagnon or other purely magnetic modes is not consistent with the measured shape
or delay of the response (34).
Resonant x-ray scattering at the Mn L-edge is predominantly sensitive to the magnetic
moment of the Mn 3d shell (35). An analysis of how different spin motions contribute to the
intensity of the diffraction peak allows us to test which of them are involved in the observed
