Femtoscale Magnetically Induced Lattice Distortions in Multiferroic TbMnO ₃

Abstract

Magneto-electric multiferroics exemplified by TbMnO 3 possess both magnetic and ferroelectric long-range order. The magnetic order is mostly understood, whereas the nature of the ferroelectricity has remained more elusive. Competing models proposed to explain the ferroelectricity are associated respectively with charge transfer and ionic displacements. Exploiting the magneto-electric coupling, we use an electric field to produce a single magnetic domain state, and a magnetic field to induce ionic displacements. Under these conditions, interference charge-magnetic X-ray scattering arises, encoding the amplitude and phase of the displacements. When combined with a theoretical analysis, our data allow us to resolve the ionic displacements at the femtoscale, and show that such displacements make a significant contribution to the zero-field ferroelectric moment.The discovery of spin-cycloid multiferroics, in which the onset of non-collinear magnetic order leads to a spontaneous ferroelectric polarization, has generated considerable interest in 1 arXiv:1110.2875v1 [cond-mat.str-el] 13 Oct 2011 the control of electric polarization by magnetic fields, and vice versa (1, 2). While comprehensive, microscopic descriptions of their magnetic structures have been obtained (3-11), our understanding of the ferroelectric state is still emerging. Two competing theoretical scenarios have been proposed: one purely electronic, without ionic displacements (12); one based on anti-symmetric exchange interactions, with ionic displacements (13). Experiments have been unable to resolve the individual ionic displacements (14).Spin-cycloid multiferroics exhibit an exceptionally strong cross-coupling between the different types of order, as demonstrated when the electric (magnetic) field E (H) was used to control magnetization M (ferroelectric polarization P) (1,5,(15)(16)(17)(18). Interest in this class of multiferroic has been generated both by the potential for novel devices, and the challenge they represent to our fundamental understanding of ordering phenomena in solids. TbMnO 3 is the prototypical spin-cycloid multiferroic (1). Diffraction studies have established that in its ferroelectric phase below ∼30 K the Mn magnetic moments form a cycloid in the bc plane (3), while the Tb moments order sinusoidally (5), Fig. 1A,B. Formation of the cycloid removes the centre of inversion at the Mn sites and generates a spontaneous P along c. The scenario in which P is generated by ionic displacements has been investigated by ab-initio density functional theory (DFT) (19,20) which makes definite predictions for the displacements of the constituent ions. Experimentally, only an upper limit (of ∼500 fm) has been estimated for the ionic displacements from EXAFS measurements (14); EXAFS has been used to obtain femtoscale displacements in other systems (21). Application of a sufficiently strong magnetic field along either the a or b axis results in the flopping of P from the c to a axis (6, 15). Conventional X-ray scattering in an applied magnetic fie...

Recent Progress of Multiferroic Perovskite Manganites

“…30 In 2011, by using a diffraction technique which exploited the interference between the non-resonant magnetic scattering and the charge scattering arising from the ionic displacements, Walker et al measured the ionic displacements in TbMnO 3 , which obtained very high precision values (up to several femto-meter) and decisively supported the microscopic models that attribute polarization to ionic displacements. 31 …”

Anisotropic resonant X-ray scattering: Beauty of forbidden reflections

“…We cannot review in this short paper other interesting and sometimes controversial phenomena studied via beautiful shine of forbidden reflections: a possible orbital ordering vs. the Jahn-Teller distortions in LaMnO 3 [34,35,53,54], charge ordering vs. atomic displacements during the Verwey transition in magnetite [55][56][57], recent observation of orbital currents in CuO crystals [58] and extremely small atomic displacements in multiferroics [59] (see also numerous references therein). The forbidden reflections are also used very successfully in soft X-ray region near L-or M -edges [60].…”

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