Nature of the magnetic order and origin of induced ferroelectricity in TbMnO3

Non-collinear magnetism & multiferroicity: the perovskite case

The most important types of non-collinear magnetic orders that are realized in simple perovskite oxides are outlined in relation to multiferroicity. These orders are classified and rationalized in terms of a mimimal spin Hamiltonian, based on which the notion of spin-driven ferroelectricity is illustrated. These concepts find direct application in reference materials such as BiFeO3, GdFeO3 and TbMnO3 whose multiferroic properties are briefly reviewed.

Control of Chiral Magnetism Through Electric Fields in Multiferroic Compounds above the Long-Range Multiferroic Transition

Polarized neutron scattering experiments reveal that type-II multiferroics allow for controlling the spin chirality by external electric fields even in the absence of long-range multiferroic order. In the two prototype compounds TbMnO_{3} and MnWO_{4}, chiral magnetism associated with soft overdamped electromagnons can be observed above the long-range multiferroic transition temperature T_{MF}, and it is possible to control it through an electric field. While MnWO_{4} exhibits chiral correlations only in a tiny temperature interval above T_{MF}, in TbMnO_{3} chiral magnetism can be observed over several kelvin up to the lock-in transition, which is well separated from T_{MF}.

Tuning the multiferroic mechanisms of TbMnO3 by epitaxial strain

A current challenge in the field of magnetoelectric multiferroics is to identify systems that allow a controlled tuning of states displaying distinct magnetoelectric responses. Here we show that the multiferroic ground state of the archetypal multiferroic TbMnO₃ is dramatically modified by epitaxial strain. Neutron diffraction reveals that in highly strained films the magnetic order changes from the bulk-like incommensurate bc-cycloidal structure to commensurate magnetic order. Concomitant with the modification of the magnetic ground state, optical second-harmonic generation (SHG) and electric measurements show an enormous increase of the ferroelectric polarization, and a change in its direction from along the c- to the a-axis. Our results suggest that the drastic change of multiferroic properties results from a switch of the spin-current magnetoelectric coupling in bulk TbMnO₃ to symmetric magnetostriction in epitaxially-strained TbMnO₃. These findings experimentally demonstrate that epitaxial strain can be used to control single-phase spin-driven multiferroic states.

Non-collinear magnetism in multiferroic perovskites

We present an overview of the current interest in non-collinear magnetism in multiferroic perovskite crystals. We first describe the different microscopic mechanisms giving rise to the non-collinearity of spins in this class of materials. We discuss, in particular, the interplay between non-collinear magnetism and ferroelectric and antiferrodistortive distortions of the perovskite structure, and how this can promote magnetoelectric responses. We then provide a literature survey on non-collinear multiferroic perovskites. We discuss numerous examples of spin cantings driving weak ferromagnetism in transition metal perovskites, and of spin-induced ferroelectricity as observed in the rare-earth based perovskites. These examples are chosen to best illustrate the fundamental role of non-collinear magnetism in the design of multiferroicity.

Multiferroic properties of o-LuMnO3 controlled by b-axis strain

Strain is a leading candidate for controlling magnetoelectric coupling in multiferroics. Here, we use x-ray diffraction to study the coupling between magnetic order and structural distortion in epitaxial films of the orthorhombic (o-) perovskite LuMnO(3). An antiferromagnetic spin canting in the E-type magnetic structure is shown to be related to the ferroelectrically induced structural distortion and to a change in the magnetic propagation vector. By comparing films of different orientations and thicknesses, these quantities are found to be controlled by b-axis strain. It is shown that compressive strain destabilizes the commensurate E-type structure and reduces its accompanying ferroelectric distortion.

Magnetic susceptibility and heat capacity measurements of single crystal TbMnO3

Measurements of the magnetic susceptibility χ and heat capacity C on single crystals of the multiferroic TbMnO3 are presented. A non-magnetic isostructural compound, LaGaO3, was used to isolate the magnetic component of the heat capacity. An anisotropic magnetic susceptibility, deviations from Curie-Weiss behaviour and a significant magnetic entropy above the antiferromagnetic ordering temperature TN1 = 41 K are attributed to a combination of crystal-field effects and short-range order between the Mn moments. Heat capacity in a magnetic field applied along the a axis confirms the saturation of Tb(3+) moments in 90 kOe. A hyperfine contribution from the Tb and Mn nuclear moments that may be convolved with a contribution from low-lying Tb crystal-field levels leads to a low-temperature rise in C(T)/T.

Melting of chiral order in terbium manganate (TbMnO3) observed with resonant x-ray Bragg diffraction

Resonant Bragg diffraction of soft, circularly polarized x-rays has been used to observe directly the temperature dependence of chiral-order melting in a motif of Mn ions in terbium manganate. The underlying mechanism uses the b-axis component of a cycloid, which vanishes outside the polar phase. Melting is witnessed by the first and second harmonics of a cycloid, and we explain why the observed temperature dependence differs in the two harmonics. Conclusions follow from an exact treatment of diffraction by using atomic multipoles in a circular cycloid, since a standard treatment of the diffraction, based on a single material-vector identified with the magnetic dipole, does not reproduce correctly observations at the second harmonic.

Resonant elastic soft x-ray scattering

Resonant (elastic) soft x-ray scattering (RSXS) offers a unique element, site and valence specific probe to study spatial modulations of charge, spin and orbital degrees of freedom in solids on the nanoscopic length scale. It is not only used to investigate single-crystalline materials. This method also enables one to examine electronic ordering phenomena in thin films and to zoom into electronic properties emerging at buried interfaces in artificial heterostructures. During the last 20 years, this technique, which combines x-ray scattering with x-ray absorption spectroscopy, has developed into a powerful probe to study electronic ordering phenomena in complex materials and furthermore delivers important information on the electronic structure of condensed matter. This review provides an introduction to the technique, covers the progress in experimental equipment, and gives a survey on recent RSXS studies of ordering in correlated electron systems and at interfaces.

Origin of the large polarization in multiferroic YMnO3 thin films revealed by soft- and hard-X-ray diffraction

We investigated the magnetic structure of an orthorhombic YMnO(3) thin film by resonant soft x-ray and hard x-ray diffraction. We observed a temperature-dependent incommensurate magnetic reflection below 45 K and a commensurate lattice-distortion reflection below 35 K. These results demonstrate that the ground state is composed of coexisting E-type and cycloidal states. Their different ordering temperatures clarify the origin of the large polarization to be caused by the E-type antiferromagnetic states in the orthorhombic YMnO(3) thin film.

Femtoscale Magnetically Induced Lattice Distortions in Multiferroic TbMnO3

Magneto-electric multiferroics exemplified by TbMnO3 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 used an electric field to produce a single magnetic domain state, and a magnetic field to induce ionic displacements. Under these conditions, interference between charge and magnetic x-ray scattering arose, 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 substantial contribution to the zero-field ferroelectric moment.

Coupled magnetic cycloids in multiferroic TbMnO3 and Eu3/4Y1/4MnO3

Based on the detailed Mn L(2,3)-edge x-ray resonant scattering results, we report a new complexity in the magnetic order of multiferroic orthomangnites, which has been considered as the simple A-type cycloid order inducing ferroelectricity. The Dzyaloshinskii-Moriya interaction involved in the orthorhombic distortion brings on F-type canting from the A type, and the ordering type becomes the off-phase synchronized bc cycloid in TbMnO(3) or the tilted antiphase ab cycloid in Eu(3/4)Y(1/4)MnO(3). The F-type canting is responsible for the magnetic field-driven multiferroicity to weak ferromagnetism transition.

Cycloidal order of 4f moments as a probe of chiral domains in DyMnO₃

Using soft x-ray diffraction at the Dy-M₅ resonance, pronounced circular dichroism in the ferroelectric phase of DyMnO₃ is observed in connection with sizable b and c components of the Dy-4f magnetic moments. This provides strong evidence for cycloidal order of the 4f moments, corroborating that inversion-symmetry breaking in this material is not accomplished by the Mn spins alone. The 4f circular dichroism allows us to image multiferroic domains that are imprinted on the surface of DyMnO₃ using the local charging by the x-ray beam via the photoelectric effect.

Antiferromagnetically spin polarized oxygen observed in magnetoelectric TbMn2O5

We report the direct measurement of antiferromagnetic spin polarization at the oxygen sites in the multiferroic TbMn2O5, through resonant soft x-ray magnetic scattering. This supports recent theoretical models suggesting that the oxygen spin polarization is key to the magnetoelectric coupling mechanism. The spin polarization is observed through a resonantly enhanced diffraction signal at the oxygen K edge at the commensurate antiferromagnetic wave vector. Using the fdmnes code we have accurately reproduced the experimental data. We have established that the resonance arises through the spin polarization on the oxygen sites hybridized with the square based pyramid Mn3+ ions. Furthermore we have discovered that the position of the Mn3+ ion directly influences the oxygen spin polarization.

RASOR: an advanced instrument for soft x-ray reflectivity and diffraction

We report the design and construction of a novel soft x-ray diffractometer installed at Diamond Light Source. The beamline endstation RASOR is constructed for general users and designed primarily for the study of single crystal diffraction and thin film reflectivity. The instrument is comprised of a limited three circle (theta, 2theta, and chi) diffractometer with an additional removable rotation (phi) stage. It is equipped with a liquid helium cryostat, and post-scatter polarization analysis. Motorized motions are provided for the precise positioning of the sample onto the diffractometer center of rotation, and for positioning the center of rotation onto the x-ray beam. The functions of the instrument have been tested at Diamond Light Source, and initial test measurements are provided, demonstrating the potential of the instrument.