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...

Structural and magnetic chiralities are found to coexist in a small group of materials in which they produce intriguing phenomenologies such as the recently discovered Skyrmion phases. Here, we describe a previously unknown manifestation of this interplay in MnSb(2)O(6), a trigonal oxide with a chiral crystal structure. Unlike all other known cases, the MnSb(2)O(6) magnetic structure is based on corotating cycloids rather than helices. The coupling to the structural chirality is provided by a magnetic axial vector, related to the so-called vector chirality. We show that this unique arrangement is the magnetic ground state of the symmetric-exchange Hamiltonian, based on ab initio theoretical calculations of the Heisenberg exchange interactions, and is stabilized by out-of-plane anisotropy. MnSb(2)O(6) is predicted to be multiferroic with a unique ferroelectric switching mechanism.

The coupling of magnetic chiralities to the ferroelectric polarization in multiferroic RbFe(MoO4)2 is investigated by neutron spherical polarimetry. Because of the axiality of the crystal structure below T(c)=190   K, helicity and triangular chirality are symmetric-exchange coupled, explaining the onset of the ferroelectricity in this proper-screw magnetic structure--a mechanism that can be generalized to other systems with ferroaxial distortions in the crystal structure. With an applied electric field, we demonstrate control of the chiralities in both structural domains simultaneously.