Magneto-electric multiferroics are materials in which mutually-coupled magnetic and ferroelectric order-parameters coexist in a single phase. The recent discovery of such systems has lead to a boom in research in this field, not only due to their potential for technological application, but also because they offer an opportunity for detailed studies of coupled, and often competing order parameters [1]. In certain rare-earth manganites complex magnetic structures, such as cycloidal spin density waves, break inversion symmetry: the essential ingredient to obtain a spontaneous ferroelectric polarisation. Strong, intrinsic magneto-electric coupling can give rise to the condition whereby it is possible to manipulate the spontaneous electric polarisation by applying an external magnetic field, and thus produce a potentially important sensor material. For example, at low temperature TbMn2O5 displays a complete reversal of electric polarisation upon application of a modest external magnetic field of 2 T [2]. To completely understand this mechanism and to predict the macroscopic properties observed, it is vital to unravel the complex magnetic structure. Ultimately this will allow the fabrication and optimisation of new devices. On substitution of the rare-earth ion, the RMn2O5 series (R = rare-earth, Bi or Y) displays a rich phase diagram with a diverse range of macroscopic properties. Resonant X-ray scattering (RXS) selectively probes the long-range magnetic order present on a particular atomic species by tuning to an atomic transition corresponding to the excitation of a core electron. The subsequent recombination of the excited electron with the core hole emits a photon whose polarisation encodes precious information on the magnetic state of the resonating ions.

Fig. 104: Top: Experimental set up for full linear polarisation analysis. A diamond phase plate used in transmission geometry rotates the incident X-ray polarisation. The polarisation of the scattered beam may be measured in terms of Poincaré-Stokes parameters (P1 and P2) using an analyser crystal. Bottom: P1 and P2 of the (4.5, 4, -0.25) magnetic reflection at the E1-E1 transition at 25 K as a function of incident polarisation.

We have employed RXS to investigate the magnetic behaviour of the terbium ions in TbMn2O5 at 25 K, where the electric polarisation is most evident [3]. An energy scan through the terbium LIII absorption edge at a constant wave-vector clearly showed two resonances, one just above the absorption edge and the other 8 eV lower. These originate from E1-E1 and E2-E2 transitions, respectively. In contrast to the E1-E1 transitions probing the band-like 5d levels that may hybridise with the neighbouring ions, the E2-E2 transitions directly probe the magnetism of the terbium 4f shell. The polarisation of the emitted photons is dependent upon the incident X-ray polarisation, magnetic moment direction and, in the case of the E2-E2 transition, wave-vector. This dependence is probed by full linear polarisation analysis as shown in Figure 104, a technique recently developed at beamline ID20. Simulations based upon the theory of Hannon et al. [4], of the scattered polarisation measured as a function of incident polarisation, allows one to refine the magnetic moment directions associated with both the terbium 5d and 4f states.

Fig. 105: The refined terbium magnetic structure of TbMn2O5 at 25 K. The magnetic moments lie in the ab-plane with a slight offset in the c-axis direction. Terbium ions are shown in purple, oxygen in red and Mn4+ and Mn3+ in dark and light green octahedral and square-based pyramid oxygen co-ordinations, respectively.

In TbMn2O5, manganese ions are found in two sublattices, Mn3+ ions coordinated in MnO5 square based pyramids and Mn4+ ions in MnO6 octahedra. These sublattices order below a Néel temperature of 43 K. It had been hypothesised that the magnetic order on the terbium sublattice is induced through nearest neighbour interactions solely with Mn4+ ions [5]. We have confirmed this scenario through the measurement of a superlattice reflection sensitive to the long range ordering of the magnetic moments which is shown to resonate at the binding energy for terbium, confirming an ordering of the terbium sublattice. Further analysis of the incident and exit photon polarisation confirms that the induced polarisation arises solely through interaction with Mn4+ ions, shown by the red line in Figure 104. We were unable to reproduce the data when assuming a polarisation of the terbium ions due to the Mn3+ ions, confirming the hypothesis of Blake et al. [5]. By performing a least squares fit to the polarisation analysis, taken when tuned to the E2-E2 resonance, we have refined the magnetic structure of the terbium ion sublattice as illustrated in Figure 105.


Principal publication and authors

R.D. Johnson (a), S.R. Bland (a), C. Mazzoli (b), T.A.W. Beale (a), C-H. Du (c), C. Detlefs (b), S.B. Wilkins (d) and P.D. Hatton (a), Phys. Rev. B 78, 104407 (2008).
(a) Department of Physics, Durham University (UK)
(b) ESRF
(c) Department of Physics, Tamkang University, Tamsui (Taiwan)
(d) Department of Condensed Matter Physics and Materials Science, Brookhaven National Laboratory, Upton (USA)


[1] M. Fiebig, J. Phys. D: Appl. Phys. 38, R123-R152 (2005).
[2] N. Hur et al., Nature 429, 392 (2004).
[3] L.C. Chapon et al., Phys. Rev. Lett. 93, 177402 (2004).
[4] J.P. Hannon et al., Phys. Rev. Lett. 61, 1245 (1988).
[5] G.R. Blake et al., Phys. Rev. B 71, 214402 (2005).