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Large-Amplitude Spin Dynamics Driven by a THz Pulse in Resonance with an Electromagnon

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Science  21 Mar 2014:
Vol. 343, Issue 6177, pp. 1333-1336
DOI: 10.1126/science.1242862

Ultrafast Manipulation

Multiferroic materials commonly show both magnetism and ferroelectricity, such that the electric field can be used to manipulate the magnetic order, and vice versa. Kubacka et al. (p. 1333, published online 6 March) used a strong terahertz electromagnetic pulse in resonance with an electromagnon—an excitation based on both electric and magnetic ordering—to control the spin dynamics of the multiferroic TbMnO3 on a sub-picosecond time scale and induce the rotation of the spin-cycloid plane of the material.

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 an experiment in which we drove spin dynamics in multiferroic TbMnO3 with an intense few-cycle terahertz (THz) light pulse tuned to resonance with an electromagnon, an electric-dipole active spin excitation. We observed 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 with the electric field of light on a sub-picosecond time scale.

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 by 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 (35). Direct excitation has the advantage of minimal excess heat deposition but requires frequencies in the 1010 to 1012 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 (79). Consequently, the magnetic order can be controlled by application of an electric field (1013). However, the speed of domain switching triggered by simple step-function–like electric fields appears to be limited to a time scale 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 time scale (1517). 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 TbMnO3.

TbMnO3 is a model spin-cycloid multiferroic exhibiting strong magnetoelectric coupling. Although it has a relatively simple perovskite atomic structure, a strong GdFeO3-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 and j gives rise to a ferroelectric polarization Embedded Image (7), and the magnitude of the polarization is further enhanced by lattice displacements (2123). 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).

Fig. 1 Experimental setup.

(A) The magnetic structure of TbMnO3 below 27 K. The spins of the Mn 3d shells (black arrows) form a cycloid propagating within the (bc) crystallographic plane. The oxygens are represented by gray octahedra around the Mn atoms (blue spheres). The black dashed box indicates a unit cell. (B) Schematic of the experiment. A THz pulse resonant with the strongest electromagnon [lower right inset, spectrum measured with orientation of electric (ETHz) and magnetic (HTHz) field of THz denoted in the box (26)] excites spin motion in the sample. An x-ray pulse resonant with the Mn L2 edge (upper inset) measures the response as changes in the intensity of the (0q0) diffraction peak (lower left inset). a.u., arbitrary units.

The EM excitation spectrum of TbMnO3 shows broad peaks in the THz frequency range; these have been assigned to electromagnons (2529) (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 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 antiphase 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 TbMnO3 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 TbMnO3 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 by using optical rectification in a nonlinear organic crystal with a peak electric field of about 300 kV/cm at focus (33). We measured the electric field component of the THz waveform at the sample position by using electrooptic sampling. To see the spin motion resulting from the excitation, we used time-resolved resonant soft x-ray diffraction at the Mn L2 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, Δτ (Fig. 2). At T = 13 K, where TbMnO3 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 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 about 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 TbMnO3 is in the non-multiferroic SDW phase (T = 30 K), the oscillation in the peak intensity after 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).

Fig. 2 Time-dependent behavior.

The magnetic diffraction intensity I of the (0q0) peak of TbMnO3 (blue symbols, left axis) compared with the electric field ETHz of the pump trace (red solid line, right axis) as a function of the time delay. (A and B) The response of the crystal in the multiferroic phase (T = 13 K) for opposite signs of the driving electric field. The solid black lines are based on a model discussed in the text. (C) The response in the SDW phase (T = 30 K). (D) Fourier transform of the THz and x-ray traces from (A). Error bars indicate a standard error for every point (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 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. 2, A and B). 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 oscillations. We consider two components of the induced spin motion, motivated by the current understanding of spin dynamics in this system. In the first component, the spins move in antiphase within the spin-cycloid plane, the pattern widely considered to be responsible for the infrared activity of the 1.8-THz electromagnon (28). The driving electric field applies an effective “force” to this component. In our model of the electromagnon as a harmonic oscillator, this component of the spin motion should then be identified with the “position” of the oscillator. In the proposed pure spin Hamiltonian for this system (18), the conjugate momentum must be a spin motion orthogonal to this position coordinate. Numerical simulations based on this Hamiltonian have predicted that a sufficiently intense THz pulse in resonance with the 1.8-THz electromagnon can induce coherent rotation of the spin-cycloid plane about the b axis until it reaches another stable orientation in either the (ab) or the (bc) plane (18). In our experiment, the effective THz pulse field strength is over two orders of magnitude lower than that used in these simulations (34), and so we do not expect to see a persistent domain reorientation. Instead, we propose to consider a smaller rotation of the spin-cycloid plane about the b axis as a second component of the spin motion that corresponds to the conjugate momentum for the 1.8-THz resonance.

We model these two spin-motion patterns separately as distortions to the equilibrium magnetic structure that influence the magnetic structure factor (34). We then calculate the intensity of the (0q0) diffraction peak as a function of each coordinate of the spin motion (Fig. 3). For the in-plane motion, the intensity of the diffraction peak is an even function of the spin coordinate, giving a decrease of the diffracted intensity with twice the frequency of the spin motion (Fig. 3A). For the spin-cycloid plane rotation, the change of diffracted intensity is an odd function of the rotation angle. This motion then leads to a modulation of the diffraction intensity with the same frequency as the spin motion (Fig. 3B). For a field-driven excitation process, we expect the spin-motion frequency to be the same as the frequency of THz pump. We conclude that the main motion visible in our experiment is a rotation of the spin-cycloid plane. The in-plane spin motion may also be present, but its response would be suppressed at the current experimental time resolution. This is consistent with our harmonic oscillator model, which suggests that we see primarily dynamics of the conjugate momentum of the resonance.

Fig. 3 Spin-motion patterns analyzed to interpret the time-dependent data.

The illustrations depict the different patterns of how the magnetic structure changes. Black arrows denote how the spins are oriented in the ground state. Color arrows indicate the spin directions at one of the extremes of the excited motion. Tb ions have been removed for clarity. The graphs show calculations of the changes in (0q0) peak intensity as a function of the motion coordinate. (A) Antiphase oscillation within the spin-cycloid plane, parameterized by using the spin rotation coordinate ϕ and viewed along the a axis. (B) Coherent rotation of the spin-cycloid plane by an angle ϕ′ about the crystallographic b axis viewed along the b axis.

For π-polarized x-rays at the Mn L2 edge, the scattering intensity is a strongly varying function of the sample azimuth (rotation about the Bragg wave vector) (34). Rotation of the spin-cycloid plane about the b axis induced by the THz pulse is equivalent to rotating the sample about the (0q0) scattering vector. Hence, we interpret the data quantitatively by comparing the change of the intensity of the diffraction peak seen in the pump-probe trace with the change seen upon rotating the sample by a small angle around the azimuth of 45° in equilibrium conditions (Fig. 4). We estimate that the observed 1.35% ± 0.12% (SE) maximum change of peak intensity corresponds to an amplitude of spin-cycloid plane rotation equal to 4.2° ± 0.4° (34). We expect that higher fields will lead to larger spin-cycloid rotations. A simple linear extrapolation suggests that THz pulses with an amplitude of 1 to 2 MV/cm inside the sample could lead to spin-cycloid rotations on the order of 90°. We can compare this against the model of (18), which predicts switching at 14 to 15 MV/cm for single-cycle THz pulses.

Fig. 4 The diffracted intensity versus spin-cycloid rotations.

(Left) Azimuthal dependence of the (0q0) peak for the π-polarized incident x-rays divided by the diffracted intensity at an azimuth of 45°. (Right) Time-resolved diffracted intensity normalized to the intensity before excitation. The blue plane represents a plane of a single spin cycloid propagating along the crystallographic b axis. The a axis is marked with red. The angles of rotation in the drawing have been exaggerated for clarity.

Our results show that intense THz pulses can modify the magnetic order in a multiferroic. Given that TbMnO3 is a model compound for a large group of materials with noncollinear spin order, our results serve as a proof of principle for a wide range of compounds. Moreover, the presence of magnetoelectric coupling in multiferroic heterostructures encourages a search for similar mechanisms as a basis for technologically feasible multiferroic devices.

Supplementary Materials

www.sciencemag.org/content/343/6177/1333/suppl/DC1

Materials and Methods

Figs. S1 to S3

References (3647)

References and Notes

  1. See supplementary materials on Science Online.
  2. Acknowledgments: This research was carried out on the SXR Instrument at the LCLS, a division of SLAC and an Office of Science user facility operated by Stanford University for the U.S. Department of Energy (DOE). The SXR Instrument is funded by a consortium including the LCLS, Stanford University through SIMES, Lawrence Berkeley National Laboratory, the University of Hamburg through the BMBF priority program FSP 301, and the Center for Free Electron Laser Science (CFEL). This research was supported by the National Center for Competence in Research (NCCR) Molecular Ultrafast Science and Technology and NCCR Materials with Novel Electronic Properties, funded by the Swiss National Science Foundation, and by the Swiss National Science Foundation (grant no. 200021_144115). Our ultrafast activities are supported by the ETH Femtosecond and Attosecond Science and Technology (ETH-FAST) initiative as part of the NCCR MUST program. The Advanced Light Source is supported by DOE under contract no. DE-AC02-05CH11231. Crystal growth work at IQM was supported by DOE, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering under award DE-FG02-08ER46544. W.-S.L., Y.-D.C., and R.G.M. are supported by DOE, Office of Basic Energy Sciences, Materials Sciences and Engineering Division, under contract DE-AC02-76SF00515.
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