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We investigate the electronic shot noise produced by nanowires of beta-Ta, an archetypal ``bad" metal with resistivity near the Ioffe-Regel localization limit. The Fano factor characterizing the shot noise exhibits a strong dependence on temperature and is suppressed compared to the expectations for quasiparticle diffusion, but hopping transport is ruled out by the analysis of scaling with the nanowire length. These anomalous behaviors closely resemble those of strange metal nanowires, suggesting that beta-Ta may host a correlated electron liquid. This material provides an accessible platform for exploring exotic electronic states of matter., Comment: 4 pages, 4 figures; comments are welcome

We show that electron interaction with the crystal lattice imposes stringent symmetry constrains on the orbital moment propagation. We present examples that elucidate the underlying mechanisms and reveal an additional effect of ultrafast orbital moment oscillations not captured by the semiclassical models. The constraints revealed by our analysis warrant re-interpretation of prior observations, and suggest routes for efficient orbitronic device implementation., Comment: One of the main findings is that the orbital current generated by orbital Hall effect is not a well-defined physical quantity

We use micro-focus Brillouin light scattering spectroscopy to study the effects of spin-orbit torque on thermal spin waves in almost angular-momentum compensated ferrimagnetic CoGd alloy films. The spin-orbit torque is produced by the electric current flowing in the Pt layer adjacent to CoGd. Both the ferromagnetic and the exchange modes are detected in our measurements. The intensity and the linewidth of the ferromagnetic mode are modified by the spin-orbit torque. In contrast, the properties of the exchange mode are unaffected by the spin-orbit torque. We also find that the frequencies and the linewidths of both modes are significantly modified by Joule heating, due to the strong temperature dependence of the magnetic properties of CoGd in the vicinity of angular momentum compensation point. Our results provide insight into the mechanisms that can enable the implementation of sub-THz magnetic nano-oscillators based on ferrimagnetic materials, as well as related effects in antiferromagnets.

We utilize coherent femtosecond extreme ultraviolet (EUV) pulses derived from a free electron laser (FEL) to generate transient periodic magnetization patterns with periods as short as 44 nm. Combining spatially periodic excitation with resonant probing at the dichroic M-edge of cobalt allows us to create and probe transient gratings of electronic and magnetic excitations in a CoGd alloy. In a demagnetized sample, we observe an electronic excitation with 50 fs rise time close to the FEL pulse duration and ~0.5 ps decay time within the range for the electron-phonon relaxation in metals. When the experiment is performed on a sample magnetized to saturation in an external field, we observe a magnetization grating, which appears on a sub-picosecond time scale as the sample is demagnetized at the maxima of the EUV intensity and then decays on the time scale of tens of picoseconds via thermal diffusion. The described approach opens prospects for studying dynamics of ultrafast magnetic phenomena on nanometer length scales.

The field of magnonics, which utilizes propagating spin waves for nano-scale transmission and processing of information, has been significantly advanced by the advent of the spin-orbit torque. The latter phenomenon can allow one to overcome two main drawbacks of magnonic devices - low energy efficiency of conversion of electrical signals into spin wave signals, and fast spatial decay of spin waves in thin-film waveguiding structures. At first glance, the excitation and amplification of spin waves by spin-orbit torques can seem to be straightforward. Recent research indicates, however, that the lack of the mode-selectivity in the interaction of spin currents with dynamic magnetic modes and the onset of dynamic nonlinear phenomena represent significant obstacles. Here, we discuss the possible route to overcoming these limitations, based on the suppression of nonlinear spin-wave interactions in magnetic systems with perpendicular magnetic anisotropy. We show that this approach enables efficient excitation of coherent magnetization dynamics and propagating spin waves in extended spatial regions, and is expected to enable practical implementation of complete compensation of spin-wave propagation losses.

Micro-focus Brillouin light scattering is a powerful technique for the spectroscopic and spatial characterization of elementary excitations in materials. However, the small momentum of light limits the accessible excitations to the center of the Brillouin zone. Here, we utilize a metallic nanoantenna fabricated on the archetypal ferrimagnet yttrium iron garnet to demonstrate the possibility of Brillouin light scattering from large-wavevector, high-frequency spin wave excitations that are inaccessible with free-space light. The antenna facilitates sub-diffraction confinement of electromagnetic field, which enhances the local field intensity and generates momentum components significantly larger than those of free-space light. Our approach provides access to high frequency spin waves important for fast nanomagnetic devices, and can be generalized to other types of excitations and light scattering techniques., Comment: 6 pages, 4 figures

We experimentally study the dynamical modes excited by spin current in Spin Hall nano-oscillators based on the Pt/[Co/Ni] multilayers with perpendicular magnetic anisotropy. Both propagating spin wave and localized solitonic modes of the oscillation are achieved and controlled by varying the applied magnetic field and current. At room temperature, the generation linewidth broadening associated with mode hopping was observed at currents close to the transition between different modes and in the mode coexistence regimes. The mode hopping was suppressed at cryogenic temperatures, confirming that the coupling between modes is mediated by thermal magnons. We also demonstrate that coherent single-mode oscillations with linewidth of 5 MHz can be achieved without applying external magnetic field. Our results provide insight into the mechanisms controlling the dynamical coherence in nanomagnetic oscillators, and guidance for optimizing their applications in spin wave-based electronics., Comment: 6 pages, 5 figures

We experimentally demonstrate that both quasi-linear and nonlinear self-localized bullet modes of magnetization auto-oscillation can be excited by dc current in the nano-gap spin Hall nano-oscillator, by utilizing the geometry with an extended gap. The quasi-linear mode is stable at low driving currents, while the bullet mode is additionally excited at larger currents, and becomes increasingly dominant with increasing current. Time-resolved measurements show that the formation of the bullet mode is delayed relative to the quasi-linear mode by up to 100 nanoseconds, demonstrating that the mechanisms of the formation of these modes are fundamentally different. We discuss the relationship between the observed behaviors and the formation of an unstable nonlinear magnon condensate.

We perform electronic measurements of unidirectional spin Hall magnetoresistance (USMR) in a Permalloy/Pt bilayer, in conjunction with magneto-optical Brillouin light spectroscopy of spin current-driven magnon population. We show that the current dependence of USMR closely follows the dipolar magnon density, and that both dependencies exhibit the same scaling over a large temperature range of 80-400 K. These findings demonstrate a close relationship between spin current-driven magnon generation and USMR, and indicate that the latter is likely dominated by the dipolar magnons.

The Hall effect and its varieties such as quantum, anomalous, and spin Hall effects, provide indispensable tools for the characterization of electronic and magnetic properties of materials, metrology, and spintronics. The conventional four-probe Hall configuration is generally not amenable to measurements at nanoscale, due to current shunting by the Hall electrodes. We demonstrate that Hall measurements on the nanoscale can be facilitated by the three-probe Hall configuration that avoids the shunting problem. We illustrate the efficiency of the proposed approach with anomalous Hall effect-based measurements of individual activation events during domain wall motion in magnetic films with perpendicular anisotropy., Comment: 2 figures

We demonstrate a silicon-based, single-layer anti-reflection coating that suppresses the reflectivity of metals at near-infrared frequencies, enabling optical probing of nano-scale structures embedded in highly reflective surroundings. Our design does not affect the interaction of terahertz radiation with metallic structures that can be used to achieve terahertz near-field enhancement. We have verified the functionality of the design by calculating and measuring the reflectivity of both infrared and terahertz radiation from a silicon/gold double layer as a function of the silicon thickness. We have also fabricated the unit cell of a terahertz meta-material, a dipole antenna comprising two 20-nm thick extended gold plates separated by a 2 $\mu$m gap, where the terahertz field is locally enhanced. We used the time-domain finite element method to demonstrate that such near-field enhancement is preserved in the presence of the anti-reflection coating. Finally, we performed magneto-optical Kerr effect measurements on a single 3-nm thick, 1-$\mu$m wide magnetic wire placed in the gap of such a dipole antenna. The wire only occupies 2\% of the area probed by the laser beam, but its magneto-optical response can be clearly detected. Our design paves the way for ultrafast time-resolved studies, using table-top femtosecond near-infrared lasers, of dynamics in nano-structures driven by strong terahertz radiation., Comment: 10 pages, 5 figures

Magnetic droplets are dynamical solitons that can be generated by locally suppressing the dynamical damping in magnetic films with perpendicular anisotropy. To date, droplets have been observed only in nanocontact spin-torque oscillators operated by spin-polarized electrical currents. Here, we experimentally demonstrate that magnetic droplets can be nucleated and sustained by pure spin currents in nanoconstriction-based spin Hall devices. Micromagnetic simulations support our interpretation of the data, and indicate that in addition to the stationary droplets, propagating solitons can be also generated in the studied system, which can be utilized for the information transmission in spintronic applications.

We experimentally study spin-Hall nano-oscillators based on [Co/Ni] multilayers with perpendicular magnetic anisotropy. We show that these devices are capable of single-frequency auto-oscillations at current densities comparable to those in the in-plane magnetized oscillators. The demonstrated oscillators exhibit large magnetization precession amplitudes, and their oscillation frequency is highly tunable by the electric current. These features make them promising for applications in high-speed integrated microwave circuits., Comment: 13 pages, 4 figures

We show experimentally that the spin current generated by the spin Hall effect drives the magnon gas in a ferromagnet into a quasi-equilibrium state that can be described by the Bose-Einstein statistics. The magnon population function is characterized either by an increased effective chemical potential or by a reduced effective temperature, depending on the spin current polarization. In the former case, the chemical potential can closely approach, at large driving currents, the lowest-energy magnon state, indicating the possibility of spin current-driven Bose-Einstein condensation.

We study the effects of electrostatic gating on the magnetization auto-oscillations induced by the local injection of electric current into a ferromagnet/heavy metal bilayer. We find that the characteristic currents required for the excitation, the intensity and the spectral characteristics of the generated dynamical states can be tuned by the voltage applied to the metallic gate separated from the bilayer by a thin insulating layer. We show that the effect of electrostatic gating becomes enhanced in the strongly nonlinear oscillation regime at sufficiently large driving currents. Analysis shows that the observed effects are caused by a combination of electric field-dependent surface anisotropy and electric field-dependent contribution to the current-induced spin-orbit torques. The demonstrated ability to control the microwave emission and spectral characteristics provides an efficient approach to the development of electrically tunable microwave nano-oscillators., Comment: 6 pages, 4 figures

Recent advances in the studies of pure spin currents - flows of angular momentum (spin) not accompanied by the electric currents - have opened new horizons for the emerging technologies based on the electron's spin degree of freedom, such as spintronics and magnonics. The main advantage of pure spin current, as compared to the spin-polarized electric current, is the possibility to exert spin transfer torque on the magnetization in thin magnetic films without electrical current flow through the material. In addition to minimizing Joule heating and electromigration effects, this characteristic enables the implementation of spin torque devices based on the low-loss insulating magnetic materials, and offers an unprecedented geometric flexibility. Here we review the recent experimental achievements in investigations of magnetization oscillations excited by pure spin currents in different magnetic nanosystems based on metallic and insulating magnetic materials. We discuss the spectral properties of spin-current nano-oscillators, and relate them to the spatial characteristics of the excited dynamic magnetic modes determined by the spatially-resolved measurements. We also show that these systems support locking of the oscillations to external microwave signals, as well as their mutual synchronization, and can be used as efficient nanoscale sources of propagating spin waves.

We study experimentally the possibility to utilize pulses of pure spin current, produced via the nonlocal spin injection mechanism, to generate short packets of spin waves propagating in nanoscale magnetic waveguides. The spatially and time-resolved micro-focus Brillouin light scattering spectroscopy measurements demonstrate that the excitation by spin current results in extremely fast transient response, enabling efficient generation of short spin-wave packets with duration down to a few nanoseconds. The proposed method opens a route for the implementation of high-speed magnonic systems for transmission and processing of information on the nanoscale.

We report the experimental observation of mutual synchronization of magnetic nanooscillators driven by pure spin current generated by nonlocal spin injection. We show that the oscillators efficiently synchronize due to the direct spatial overlap of the dynamical modes excited by spin current, which is facilitated by the large size of the auto-oscillation area inherent to these devices. The synchronization occurs within an interval of the driving current determined by the competition between the dynamic nonlinearity that facilitates synchronization, and the short-wavelength magnetic fluctuations enhanced by the spin current that suppress synchronization. The demonstrated synchronization effects can be utilized to control the spatial and spectral characteristics of the dynamical states induced by spin currents., Comment: 15 pages, 5 figures

The prediction and realization of magnetic excitations driven by electrical currents via the spin transfer torque effect, enables novel magnetic nano-devices where spin-waves can be used to process and store information. The functional control of such devices relies on understanding the properties of non-linear spin-wave excitations. It has been demonstrated that spin waves can show both an itinerant character, but also appear as localized solitons. So far, it was assumed that localized solitons have essentially cylindrical, $s-$like symmetry. Using a newly developed high-sensitivity time-resolved magnetic x-ray microscopy, we instead observe the emergence of a novel localized soliton excitation with a nodal line, i.e. with $p-$like symmetry. Micromagnetic simulations identify the physical mechanism that controls the transition from $s-$ to $p-$like solitons. Our results suggest a potential new pathway to design artificial atoms with tunable dynamical states using nanoscale magnetic devices.

We studied an electron-induced metal-insulator transition in a two-terminal device based on oxide NdNiO3. In our device, the NdNiO3 is electrostatically doped by the voltage applied between the terminals, resulting in an asymmetric conductivity with respect to the bias polarity. The asymmetry is temperature-dependent and is most significant near the metal-insulator transition. The I-V characteristics exhibit a strong dependence both on the thermal history and the history of the applied voltage bias. Our two-terminal device represents a simple and efficient route for studies of the effect of electron doping on the metal-insulator transition., Comment: 4 pages, 5 Figures

We utilized microwave spectroscopy to study the magnetization oscillations locally induced in a Permalloy film by a pure spin current, which is generated due to the spin Hall effect in an adjacent Pt layer. The oscillation frequency is lower than the ferromagnetic resonance of Permalloy, indicating that the oscillation forms a self-localized nonpropagating spin-wave soliton. At cryogenic temperatures, the spectral characteristics are remarkably similar to the traditional spin-torque nano-oscillators driven by spin-polarized currents. However, the linewidth of the oscillation increases exponentially with temperature and an additional peak appears in the spectrum below the ferromagnetic resonance, suggesting that the spectral characteristics are determined by interplay between two localized dynamical states., Comment: Selected by the editors of PRL to be an Editors' Suggestion and featured in Physics (see Viewpoint: Make your Spins Spin)

We experimentally demonstrate the existence of magnetic coupling between two ferromagnets separated by a thin Pt layer. The coupling remains ferromagnetic regardless of the Pt thickness, and exhibits a significant dependence on temperature. Therefore, it cannot be explained by the established mechanisms of magnetic coupling across nonmagnetic spacers. We show that the experimental results are consistent with the presence of magnetism induced in Pt in proximity to ferromagnets, in direct analogy to the well-known proximity effects in superconductivity., Comment: 4 pages, 3 figures

We propose a method, which enables precise control of magnetic patterns, relying only on the fundamental properties of the wire and the choice of the path in the controlled parameter space but not on the rate of motion along this path. Possible experimental realizations of this mechanism are discussed. In particular, we show that the domain walls in magnetic nanowires can be translated by rotation of the magnetic easy axis, or by applying pulses of magnetic field directed transverse to the magnetic easy axis., Comment: 4 pages, 4 figures

We use a combination of analytic calculations and numerical simulations to demonstrate that electrical current flowing through a magnetic bilayer induces dynamical coupling between the layers. The coupling originates from the dependence of the spin transfer torque exerted on the layers on the relative orientations of their magnetic moments. We demonstrate that such coupling modifies the behaviors of both layers, significantly affecting the the stability of the current-induced dynamical regimes and the efficiency of current-induced magnetic reversal., Comment: 4 pages, 3 figures

An efficient matrix formalism for finding power series solutions to boundary value problems typical for technological plasticity is developed. Hyperbolic system of two first order quasilinear PDEs that models two-dimensional plastic flow of von Mises material is converted to the telegraph equation by the hodograph transformation. Solutions to the boundary value problems are found in terms of hypergeometric functions. Convergence issue is also addressed. The method is illustrated by two test problems of metal forming., Comment: 17 pages, 6 figures

While magnetoresistance (MR) has generally been found to be symmetric in applied field in non-magnetic or magnetic metals, we have observed antisymmetric MR in Co/Pt multilayers. Simultaneous domain imaging and transport measurements show that the antisymmetric MR is due to the appearance of domain walls that run perpendicular to both the magnetization and the current, a geometry existing only in materials with perpendicular magnetic anisotropy. As a result, the extraordinary Hall effect (EHE) gives rise to circulating currents in the vicinity of the domain walls that contributes to the MR. The antisymmetric MR and EHE have been quantitatively accounted for by a theoretical model., Comment: 17 pages, 4 figures

According to the spin-torque model, current-driven magnetic dynamics in ferromagnetic multilayers is determined by the transfer of electron spin perpendicular to the layers' magnetizations. By separating the largest contributions to the magnetic dynamics, we demonstrate that the dominant effect of spin-torque is rather due to the electron spin parallel to the field. We show that this effect can be equivalently described as stimulated current-driven excitation of spin-waves, and discuss four specifically quantum-mechanical aspects of spin-transfer, not described by the spin-torque., Comment: 4 pages

In epitaxial (111) oriented Ni$_{80}$Fe$_{20}$/Fe$_{50}$Mn$_{50}$ bilayers, we separate two distinct behaviors: unidirectional anisotropy (exchange bias) in thick Fe$_{50}$Mn$_{50}$, and enhanced coercivity in thin Fe$_{50}$Mn$_{50}$. By measuring the magnetization response to a rotating magnetic field, we quantitatively determine the relevant anisotropies, and demonstrate that the enhanced coercivity is related to the rotatable magnetic anisotropy of Fe$_{50}$Mn$_{50}$. We also demonstrate the consequences of the anisotropy changes with temperature., Comment: 4 pages, 4 figures

We summarize our recent findings on how current-driven magnetization switching and magnetoresistance in nanofabricated magnetic multilayers are affected by varying the spin-scattering properties of the non-magnetic spacers, the relative orientations of the magnetic layers, and spin-dependent scattering properties of the interfaces and the bulk of the magnetic layers. We show how our data are explained in terms of current-dependent effective magnetic temperature., Comment: 6 pages, 6 figures, submitted to MMM'04 proceedings

We study the dependence of perpendicular-current magnetoresistance in magnetic multilayers on the angle between the magnetizations of the layers. This dependence varies with the thickness of one of the layers, and is different for multilayers with two and three magnetic layers. We derive a system of equations representing an extension of the two-current series resistor model, and show that the angular dependence of magnetoresistance gives information about the noncollinear spin-transport in ferromagnets., Comment: 4 pages, 3 figures

Combining pairs of ferromagnetic metals with different signs of scattering anisotropies, let us independently invert the magnetoresistance and the direction of current-driven switching in ferromagnetic/non-magnetic/ferromagnetic metal nanopillars. We show all four combinations of normal and inverse behaviors, at both room temperature and 4.2K. In all cases studied, the direction of switching is set by the net scattering anisotropy of the fixed (polarizing) ferromagnet. We provide simple arguments for what we see., Comment: 4 pages, 5 figures, submitted to PRL

We summarize our recent findings on how the current-driven magnetization switching in nanofabricated magnetic multilayers is affected by an applied magnetic field, changes of temperature, magnetic coupling between the ferromagnetic layers, variations in the multilayer structure, and the relative rotation of the layers' magnetizations. We show how these results can be interpreted with a model describing current-driven excitations as an effective current-dependent magnetic temperature., Comment: 6 pages, 6 figures To be published in JAP, MMM'04 proceedings

We provide new data on current-driven switching in Permalloy (Py = Ni84Fe16) based nanopillars at room temperature and 4.2K that confirm and extend previously published work. We present data for both uncoupled and antiferromagnetically coupled samples. The latter confirm prior results for Co/Cu/Co. We show that inserting sufficiently strong spin-flip-scattering into the Cu layer eliminates hysteretic current-driven switching. This result may have ramifications for understanding current-driven switching., Comment: ISAMT'03 (Taiwan) proceedings, to be published in JMMM

We measure the dynamic resistance of a Co/Cu/Co trilayer nanopillar at varied magnetic field $H$ and current $I$. The resistance displays the usual behavior, almost symmetric in $H$, both when magnetization switching is hysteretic at small $I,H$, and reversible at larger $I,H$. We show differences in the $I,H$ magnetization stability diagram measured by holding $I$ fixed and varying $H$ and vice versa. We also show how the peak in $dV/dI$ associated with telegraph noise in the reversible switching regime, is calculated from the telegraph noise variations with $I$. Lastly, we show data for a similar sample that displays behavior asymmetric in $H$, and a negative reversible switching peak instead of a usual positive one., Comment: To appear in the proceedings of the NATO advanced research workshop (2003)

In 1996, Berger and Slonczewski independently predicted that a large enough spin-polarized dc current density sent perpendicularly through a ferromagnetic layer could produce magnetic excitations (spin-waves) or reversal of magnetization (switching). In the past few years, both current-driven switching and current-driven excitation of spin-waves have been observed. The switching is of potential technological interest for direct 'writing' of magnetic random access memory (MRAM) or magnetic media. The spin-wave generation could provide a new source of dc generated microwave radiation. We describe what has been learned experimentally about these two related phenomena, and some models being tested to explain these observations., Comment: 5 pages, 7 figures, expected to appear in conf. proceedings

We report the results of a cryogenic study of the modification of YBa2Cu3O7-delta surface electronic properties with the probe of a scanning tunneling microscope (STM). A negative voltage applied to the sample during STM tunneling is found to modify locally the conductance of the native degraded surface layer. When the degraded layer is removed by etching, the effect disappears. An additional surface effect is identified using Scanning Kelvin Probe Microscopy in combination with STM. We observe reversible surface charging for both etched and unetched samples, indicating the presence of a defect layer even on a surface never exposed to air., Comment: 6 pages, 4 figures. To appear in Superconductor Science and Technology

We study current-driven magnetization switching in nanofabricated magnetic trilayers, varying the magnetoresistance in three different ways. First, we insert a strongly spin-scattering layer between the magnetic trilayer and one of the electrodes, giving increased magnetoresistance. Second, we insert a spacer with a short spin-diffusion length between the magnetic layers, decreasing the magnetoresistance. Third, we vary the angle between layer magnetizations. In all cases, we find an approximately linear dependence between magnetoresistance and inverse switching current. We give a qualitative explanation for the observed behaviors, and suggest some ways in which the switching currents may be reduced., Comment: 3 pages, 4 figures

We develop a quantum analog of the classical spin-torque model for current-driven magnetic dynamics. The current-driven magnetic excitation at finite field becomes significantly incoherent. This excitation is described by an effective magnetic temperature rather than a coherent precession as in the spin-torque model. However, both the spin-torque and effective temperature approximations give qualitatively similar switching diagrams in the current-field coordinates, showing the need for detailed experiments to establish the proper physical model for current-driven dynamics., Comment: 5 pages, 2 figures

We show that dipole-field induced antiferromagnetic coupling, or RKKY ferromagnetic coupling, between Co layers can strongly affect the low magnetic field switching behavior of Co/Cu/Co nanopillars. Whereas current-assisted switching at low fields in uncoupled nanopillars is always hysteretic, strong coupling of either kind can change the switching to non-hysteretic (reversible). These differences can be understood with a simple picture of current-assisted thermal activation over a barrier., Comment: 2 pages, 2 figures

We compare magnetization switching in Co/Cu/Co nanopillars with uncoupled and dipole-field coupled Co layers. In uncoupled nanopillars, current-driven switching is hysteretic at low magnetic field H and changes to reversible, characterized by telegraph noise, at high H. We show that dipolar coupling both affects the switching current and causes the switching to become reversible at small H. The coupling thus changes the switching to reversible, hysteretic, and then reversible again as H increases. We describe our results in terms of current-assisted thermal activation., Comment: 3 pages, 3 figures

We study current-driven magnetization switching in nanofabricated Ni84Fe16/Cu/Ni84Fe16 trilayers at 295 K and 4.2 K. The shape of the hysteretic switching diagram at low magnetic field changes from 295 K to 4.2 K. The reversible behavior at higher field involves two phenomena, a threshold current for magnetic excitations closely correlated with the switching current, and a peak in differential resistance characterized by telegraph noise, with average period that decreases exponentially with current and shifts with temperature. We interpret both static and dynamic results at 295 K and 4.2 K in terms of thermal activation over a potential barrier, with a current dependent effective magnetic temperature., Comment: 4 pages, 4 Figures

Scanning tunneling spectroscopy images of Bi$_2$Se$_3$ doped with excess Bi reveal electronic defect states with a striking shape resembling clover leaves. With a simple tight-binding model we show that the geometry of the defect states in Bi$_2$Se$_3$ can be directly related to the position of the originating impurities. Only the Bi defects at the Se sites five atomic layers below the surface are experimentally observed. We show that this effect can be explained by the interplay of defect and surface electronic structure., Comment: 4 pages, 4 figures

Recently discovered fine structure of the morphotropic phase boundaries in highly piezoelectric mixture compounds PZT, PMN-PT, and PZN-PT demonstrates the importance of highly non-linear interactions in these systems. We show that an adequate Landau-type description of the ferroelectric phase transitions in these compounds is achieved by the use of a twelfth-order expansion of the Landau potential in terms of the phenomenological order parameter. Group-theoretical and catastrophe-theory methods are used in constructing the appropriate Landau potential. A complete phase diagram is calculated in phenomenological parameter space. The theory describes both PZT and PZN-PT types of phase diagrams, including the newly found monoclinic and orthorhombic phases. Anomalously large piezoelectric coefficients are predicted in the vicinity of the phase transition lines., Comment: RevTex4, 8 pages, 2 figures. Dramatically changed after referees' Comments, to appear in Phys. Rev. B, 1 April 2002