Circularly polarised X-rays as a probe of non-collinear magnetic order in multiferroic TbMnO3


A circularly polarised incident beam for non-resonant X-ray magnetic scattering together with full polarisation analysis of the diffracted beam has allowed ESRF scientists to shed light on the complex non-collinear magnetic structure of multiferroic TbMnO3, a challenging test case due to its two magnetic sublattices. A key feature of this study was the ability to control the population of the cycloidal magnetic domains by the application of an electric field.

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The discovery of a large magneto-electric coupling in TbMnO3 [1] has led to a resurgence of interest in magnetoelectric multiferroics, materials in which the onset of spontaneous non-collinear antiferromagnetic order simultaneously drives the formation of a ferroelectric state. This class of magnetic materials is a good candidate in the search for materials with strong coupling between magnetic and electric polarisations, leading to potential applications in spintronics technology, such as for data processing and data storage devices. While such particular “improper ferroelectrics” usually order at very low temperature, they are of fundamental interest because the coupling between the magnetic and electric degrees of freedom is so profound. Nevertheless, a picture for the underlying microscopic interaction mechanism is still missing. TbMnO3 is the canonical magnetoelectric multiferroic, in which the phase transition to a non-collinear cycloidal spin arrangement at T=27 K is concomitant with the onset of electric polarisation as a result of the breaking of inversion symmetry [2]. Here we show a new application of non-resonant X-ray magnetic diffraction which exploits circularly polarised photons combined with full polarisation analysis of the diffracted beam, to provide a unique insight into the description of cycloidal magnetic domain state, since the handedness of the circular polarisation naturally couples to the sense of rotation of the magnetic moments.

Since the first demonstration of non-resonant magnetic X-ray scattering by de Bergevin and Brunel in 1972 [3], the technique of non-resonant magnetic scattering has been rarely used, mostly due to the significant technical problems presented by the very weak intensities involved. However, recent instrumental developments on the ID20 magnetic scattering beamline now allow the detection of non-resonant magnetic scattering signals a factor of 10 million times smaller than standard charge Bragg peaks, and to extract the rich information encoded in the X-ray non-resonant magnetic scattering amplitudes.

In this experiment, a new specially commissioned electric stick has been used, which allows the application of an electric field of up to 800 kV/m at low temperatures and in magnetic fields. The sample was cooled to low temperature with an applied electric field E to produce a single magnetic domain in the sample. We established the experimental sensitivity to the imbalance in the magnetic domain populations produced by application of this electric field by demonstrating the complementary behaviour of the intensities of the four magnetic satellites (4 ±τ ±1) for left circular polarisation (LCP), and right circular polarisation (RCP) depending on the sign of τ, as shown in Figure 1. This differs strongly from the expected results for equi-populated domains in which case the signal should be very similar for LCP (red dots) and RCP (green dots). Note that when the linear incident polarisation p is selected, all the satellite reflections have nearly the same intensities (black dots). By switching the electric field, the LCP and RCP produce a reversal in behaviour of the magnetic satellite intensities, because the magnetic cycloid changes its sense of rotation. This is clearly demonstrated in Figure 2a, where the polarisation of the scattered X-rays is analysed in detail for two magnetic satellites as a function of two electric fields with opposite polarity.

Experimental setup and polarisation dependence of non-commensurate satellite magnetic reflections in TbMnO3

Figure 1. Experimental setup and polarisation dependence of (4 ±τ ±1) non-commensurate satellite magnetic reflections in TbMnO3. Data are taken in the low temperature ferroelectric phase (T= 15K) after annealing the sample with an applied negative electric field E<0.

Whilst magnetic structure determination typically involves refining the intensity data for as wide a range of magnetic satellites as possible, we took advantage of the scattering cross-section for non-resonant X-ray magnetic scattering instead. The coupling of the polarisation state and the experimental geometry enables refinement of the magnetic structure using the full polarisation dependence of only four satellite magnetic reflections (see Figure 2a). Not only does this technique provides unique insight into the formation of cycloidal domains, leading to a quantitative description of the domain state, but it also allows refinement of the magnetic structure obtained from an earlier neutron diffraction study. In particular, the absolute sense of rotation and the phase shifts of individual magnetic sublattices has been analysed in detail. The resultant magnetic structure is shown in Figure 2b in which both the Tb and Mn magnetic moments are represented. 

Polarisation dependence of of magnetic satellites for two reversal applied electric fields and magnetic structure of TbMnO3

Figure 2. a) Polarisation dependence of of magnetic satellites (4,±t,-1) for two reversal applied electric field directions (top) and projection in the b-c plane of the two cycloidal magnetic domains (bottom). Broken (continuous) lines are calculations based on a neutron (X-ray) scattering model. b) Magnetic structure of TbMnO3 determined by the present work.

This experiment takes full advantage of the properties of ESRF synchrotron radiation such as high Q-resolution, beam stability, polarisation properties of the beam and its high incident flux. It was only possible thanks to improvements in: 1) the avalanche photo diode detector system, with energy optimisation; 2) the new in-vacuum phase-plate setup, which allows circularly polarised light to be produced with a polarisation factor close to ~99%, and 3) new high-quality polarisation analysers.

This method opens the way to a new class of experiments in which the magnetic state of complex magnetic materials can be probed and the magnetoelectric domain formation controlled under applied external electric and magnetic fields. Other interesting possibilities would be to combine the advantages of this technique with highly focused X-ray beams to provide real-space images of the formation of non-collinear magnetic domains. The future ESRF upgrade programme could allow the extension of this technique to very high magnetic fields.


[1] T. Kimura et al., Nature 426, 55 (2003).
[2] M. Kenzelmann et al., Phys. Rev. Lett. 95, 087206 (2005).
[3] F. de Bergevin and M. Brunel, Phys. Lett. A 39, 141 (1972).


Principal publication and authors
F. Fabrizi (a), H.C. Walker (a), L. Paolasini (a), F. De Bergevin (a), A.T. Boothroyd (b), D. Prabhakaran (b), D.F. McMorrow (c), Circularly Polarized X-Rays as a Probe of Noncollinear Magnetic Order in Multiferroic TbMnO3, Phys. Rev. Lett. 102, 237205 (2009).
(a) ESRF
(b) University of Oxford (UK)
(c) University College London (UK)