The magnetoelectric effect--the induction of magnetization by means of an electric field and induction of polarization by means of a magnetic field--was first presumed to exist by Pierre Curie, and subsequently attracted a great deal of interest in the 1960s and 1970s (refs 2-4). More recently, related studies on magnetic ferroelectrics have signalled a revival of interest in this phenomenon. From a technological point of view, the mutual control of electric and magnetic properties is an attractive possibility, but the number of candidate materials is limited and the effects are typically too small to be useful in applications. Here we report the discovery of ferroelectricity in a perovskite manganite, TbMnO3, where the effect of spin frustration causes sinusoidal antiferromagnetic ordering. The modulated magnetic structure is accompanied by a magnetoelastically induced lattice modulation, and with the emergence of a spontaneous polarization. In the magnetic ferroelectric TbMnO3, we found gigantic magnetoelectric and magnetocapacitance effects, which can be attributed to switching of the electric polarization induced by magnetic fields. Frustrated spin systems therefore provide a new area to search for magnetoelectric media.

Magnetic control of ferroelectric polarization

A general introduction to x-ray diffraction and its application to the study of surfaces and interfaces is presented. The application of x-ray diffractkm to various problems in surface and interface science is illustrated through five different techniques: crystal truncation rod analysis, two-dimensional crystallography, three-dimensional structure analysis, the evanescent wave method and lineshape analysis. These techniques are explained with numerous examples from recent experiments and with the aid of an extensive bibliography.

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Surface X‐Ray Diffraction

X-ray techniques have been used for more than a century to study the atomic and electronic structure in practically any type of material. The advent of correlated electron systems, in particular complex oxides, brought about new scientific challenges and opportunities for the advancement of conventional X-ray methods. In this context, the need for new approaches capable of selectively sensing new forms of orders involving all degrees of freedom—charge, orbital, spin, and lattice—paved the way for the emergence and success of resonant X-ray scattering, which has become an increasingly popular and powerful tool for the study of electronic ordering phenomena in solids. We review the recent resonant X-ray scattering breakthroughs in the copper oxide high-temperature superconductors, in particular regarding the phenomenon of charge order, a broken-symmetry state occurring when valence electrons self-organize into periodic structures. After a brief historical perspective on charge order, we outline the mileston...

Resonant X-Ray Scattering Studies of Charge Order in Cuprates

A comprehensive review and state of the art in the field of surface, interface, and thin-film magnetism is presented. New growth techniques which produce atomically engineered novel materials, special characterization techniques to measure magnetic properties of low-dimensional systems, and computational advances which allow large complex calculations have together stimulated the current activity in this field and opened new opportunities for research. The current status and issues in the area of material growth techniques and physical properties, characterization methods, and theoretical methods and ideas are reviewed. A fundamental understanding of surface, interface, and thin-film magnetism is of importance to many applications in magnetics technology, which is also surveyed. Questions of fundamental and technological interest that offer opportunities for exciting future research are identified.

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Surface, interface, and thin-film magnetism

Structural studies of alkali metal adsorption and coadsorption on metal surfaces

We present the results of magnetic x-ray scattering experiments on the rare-earth metal holmium using synchrotron radiation. Direct high-resolution measurements of the nominally incommensurate magnetic satellite reflections reveal new lock-in behavior which we explain within a simple spin-discommensuration model. As a result of magnetoelastic coupling, the spin-discommensuration array produces additional x-ray diffraction satellites. Their observation further substantiates the model and demonstrates additional advantages of synchrotron radiation for magnetic-structure studies.

Magnetic x-ray scattering studies of holmium using synchro- tron radiation

The analysis of data obtained in magnetic X-ray scattering experiments on rare earth metals, particularly holmium, has led to a phenomenological model for one-dimensional spatially propagating magnetic structures. Based on the concept of spin slips or discommensurations, this model explains the observed lock-in transitions in the magnetic spirals of the rare earths in terms of simple commensurate structures. Further, the anomalous intensities of previously observed higher harmonic magnetic satellites, as well as the qualitative behavior of the magnetic wave vector in the presence of a magnetic field, are understood directly within the spin slip description. We discuss how the presence of spin slips in the magnetic structure can lead to modulations of the crystal lattice as demonstrated by a recent magnetic X-ray study of holmium.

Spin slips and lattice modulations in holmium: A magnetic x-ray scattering study

We review the results of X-ray scattering studies of the rare earth metals and present related new results for superlattices and thin slabs. In rare earth crystals we have observed weak structural modulations which accompany the magnetic ordering. The wave length of this modulation can be derived from a spin-slip model in accordance with symmetry considerations. X-ray scattering of both the charge and magnetization density modulations allow for highly accurate determination of the magnetic wave vector. The physical basis of our discussion is given in the context of lattice modulations. The implications of these results for the understanding of magnetic structure of rare earth superlattices are also discussed in the light of recent neutron diffraction studies of holmium-yttrium superlattices. The effect of the finite size of the magnetic block in a superlattice is considered and it is shown that significantly different behavior than in bulk is expected. In particular it is found that for thin slabs the ferromagnetic phase has the lowest energy.

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Diffraction studies of rare earth metals and superlattices

We report high resolution x-ray diffraction studies of the structures and phase transitions of monolayer krypton, adsorbed on both powder and single crystal graphite substrates. A comprehensive series of powder diffraction profiles is used to construct the two dimensional phase diagram. The melting of the
 
$$\sqrt 3 x\sqrt 3$$

 commensurate solid is shown to be strongly first order throughout the region where tricritical behavior was previously thought to occur; fluid solid coexistence extends up to the termination of the commensurate phase at 130 K. A disordered weakly incommensurate phase is shown to be a reentrant fluid, a system which may be described as a disordered network of domain walls and which evolves continuously into a more conventional 2D fluid. This evolution is marked by the disappearance of satellite peaks which are caused by the modulation of the overlayer by the substrate. The freezing of the reentrant fluid into the commensurate phase is shown to be consistent with a chiral Potts transition, its freezing into the incommensurate solid consistent with a dislocation binding transition. Single crystal experiments reveal the orientation of the weakly incommensurate phase. The reentrant fluid is found to have no visible orientational fluctuations, manifesting isotropic diffraction peaks. This is attributed to the strong epitaxy of domain walls. The incommensurate solid is shown to undergo an aligned-rotated transition which is well described by zerotemperature calculations.

Phase diagram and phase transitions of Krypton on graphite in the extended monolayer regime

Synchrotron x-ray diffraction studies of the orientational epitaxy of krypton on single-crystal graphite are reported. The system displays a continuous transition from an aligned to a rotated orientation with increasing mean misfit in a manner predicted by a hexagonal-domain-wall model of the weakly incommensurate phase. A hysteresis at the critical misfit is observed. The results are discussed in light of current views of the structure of the incommensurate phase.

K.L. D'Amico

Papers

Magnetic x-ray scattering studies of holmium using synchro- tron radiation

Spin slips and lattice modulations in holmium: A magnetic x-ray scattering study

Diffraction studies of rare earth metals and superlattices

Phase diagram and phase transitions of Krypton on graphite in the extended monolayer regime

Rotational Transition of Incommensurate Kr Monolayers on Graphite