Effect of chemical pressure, misfit strain and hydrostatic pressure on structural and magnetic behaviors of rare-earth orthochromates

First-principles calculations are performed to investigate structural and magnetic behaviors of rare-earth orthochromates as a function of 'chemical' pressure (that is, the rare-earth ionic radius), epitaxial misfit strain and hydrostatic pressure. From a structural point of view, (i) 'chemical' pressure significantly modifies antipolar displacements, Cr-O-Cr bond angles and the resulting oxygen octahedral tiltings; (ii) hydrostatic pressure mostly changes Cr-O bond lengths; and (iii) misfit strain affects all these quantities. The correlations between magnetic properties (Néel temperature and weak ferromagnetic moments) and unit cell volume are similar when varying the misfit strain or hydrostatic pressure, but differ from those associated with the 'chemical' pressure. Origins of such effects are also discussed.

Crafting the magnonic and spintronic response of BiFeO3 films by epitaxial strain

Multiferroics are compounds that show ferroelectricity and magnetism. BiFeO3, by far the most studied, has outstanding ferroelectric properties, a cycloidal magnetic order in the bulk, and many unexpected virtues such as conductive domain walls or a low bandgap of interest for photovoltaics. Although this flurry of properties makes BiFeO3 a paradigmatic multifunctional material, most are related to its ferroelectric character, and its other ferroic property--antiferromagnetism--has not been investigated extensively, especially in thin films. Here we bring insight into the rich spin physics of BiFeO3 in a detailed study of the static and dynamic magnetic response of strain-engineered films. Using Mössbauer and Raman spectroscopies combined with Landau-Ginzburg theory and effective Hamiltonian calculations, we show that the bulk-like cycloidal spin modulation that exists at low compressive strain is driven towards pseudo-collinear antiferromagnetism at high strain, both tensile and compressive. For moderate tensile strain we also predict and observe indications of a new cycloid. Accordingly, we find that the magnonic response is entirely modified, with low-energy magnon modes being suppressed as strain increases. Finally, we reveal that strain progressively drives the average spin angle from in-plane to out-of-plane, a property we use to tune the exchange bias and giant-magnetoresistive response of spin valves.

Effect of central mode on the dielectric tunability of ferroelectrics near room temperature: a first-principle-based study

First-principles-based effective Hamiltonian molecular dynamics simulations are performed to investigate GHz-THz dynamical properties of bulk and epitaxially strained film made of SrTiO3 near room temperature. Our simulations confirm the huge dielectric tunability recently observed in films. Moreover, universal phenomenological laws, with bulk-like parameters, are found to describe reasonably well the dielectric tunability-versus-dc electric field curves in both systems at low and high electric fields, except for the sole case of the STO film in the low-field regime. Such deviation originates from the presence of a central mode in this low-dimensional system. A revised equation, arising from an original analysis of the simulations, is proposed for modeling this latter situation.

Field-induced percolation of polar nanoregions in relaxor ferroelectrics

A first-principles-based effective Hamiltonian is used to investigate low-temperature properties of Ba(Zr,Ti)O(3) relaxor ferroelectrics under an increasing dc electric field. This system progressively develops an electric polarization that is highly nonlinear with the dc field. This development leads to a maximum of the static dielectric response at a critical field, E(th), and involves four different field regimes. Each of these regimes is associated with its own behavior of polar nanoregions, such as shrinking, flipping, and elongation of dipoles or change in morphology. The clusters propagating inside the whole sample, with dipoles being parallel to the field direction, begin to form at precisely the E(th) critical field. Such a result, and further analysis we perform, therefore, reveal that field-induced percolation of polar nanoregions is the driving mechanism for the transition from the relaxor to ferroelectric state.

Ferroelectric domains in multiferroic BiFeO3 films under epitaxial strains

First-principles calculations are performed to investigate energetic and atomistic characteristics of ferroelectric domains walls (DWs) of BiFeO(3) (BFO) films subject to compressive strain. Significantly lower DW energies than those previously reported, and a different energetic hierarchy between the various DW types, are found for small strains. In all investigated cases (corresponding to ideal angles of 71°, 109°, and 180° formed by the domain polarizations), the DW energy reaches its maximum value for misfit strains that are around the critical strain at which the transition between the R-like and T-like phases occurs in single-domain BFO. Near these strains, several quantities depend strongly on the type of domain wall; such distinct behavior is associated with an elastic difference and a large out-of-plane polarization at the DW in the 180° case. A further increase of the magnitude of the strain leads to (i) a change of hierarchy of the DW energies, (ii) large out-of-plane polarizations inside each up and down domain, and (iii) novel atomic arrangements at the domain walls. Our study can thus initiate a new research direction, namely strain engineering of domain-wall functionalities.

Predicted coupling of the electromagnetic angular momentum density with magnetic moments

Analytical derivations are developed to demonstrate that (i) the angular moment density associated with an electromagnetic field can directly couple with magnetic moments to produce a physical energy, (ii) this direct coupling explains known, subtle phenomena, including some recently predicted in magnetoelectric materials, and (iii) this coupling also results in novel effects, such as the occurrence of a magnetic anisotropy that is driven by antiferroelectricity.

Thickness-dependent polarization of strained BiFeO3 films with constant tetragonality

We measure the ferroelectric polarization of BiFeO3 films down to 3.6 nm using low energy electron and photoelectron emission microscopy. The measured polarization decays strongly below a critical thickness of 5-7 nm predicted by continuous medium theory whereas the tetragonal distortion does not change. We resolve this apparent contradiction using first-principles-based effective Hamiltonian calculations. In ultrathin films, the energetics of near open circuit electrical boundary conditions, i.e., an unscreened depolarizing field, drive the system through a phase transition from single out-of-plane polarization to nanoscale stripe domains. It gives rise to an average polarization close to zero as measured by the electron microscopy while maintaining the relatively large tetragonal distortion imposed by the nonzero polarization state of each individual domain.

Understanding and revisiting properties of EuTiO3 bulk material and films from first principles

Ab initio computations are performed to investigate properties of bulk material and epitaxial films made of EuTiO3 (ETO). A whole family of nanoscale twinned phases, that present complex oxygen octahedra tilting (OOT) and unusual antiferroelectricity, is found to be degenerate in energy with simpler phases (all possessing typical OOT) in bulk ETO. Such degeneracy provides a successful explanation of recently observed anomalous phenomena. The calculations also lead to revisiting the (rich) phase diagram of ETO films.

Novel complex phenomena in ferroelectric nanocomposites

A first-principles-based effective Hamiltonian is used to investigate finite-temperature properties of ferroelectric nanocomposites made of periodic arrays of ferroelectric nanowires embedded in a matrix formed by another ferroelectric material. Novel transitions and features related to flux-closure configurations are found. Examples include (i) a vortex core transition, that is characterized by the change of the vortex cores from being axisymmetric to exhibiting a 'broken symmetry'; (ii) translational mode of the vortex cores; (iii) striking zigzag dipolar chains along the vortex core axis; and (iv) phase-locking of ferroelectric vortices accompanied by ferroelectric antivortices. These complex phenomena are all found to coexist with a spontaneous electrical polarization aligned along the normal of the plane containing the vortices.

Atomistic molecular dynamic simulations of multiferroics

A first-principles-based approach is developed to simulate dynamical properties, including complex permittivity and permeability in the GHz-THz range, of multiferroics at finite temperatures. It includes both structural degrees of freedom and magnetic moments as dynamic variables in Newtonian and Landau-Lifshitz-Gilbert (LLG) equations within molecular dynamics, respectively, with the couplings between these variables being incorporated. The use of a damping coefficient and of the fluctuation field in the LLG equations is required to obtain equilibrated magnetic properties at any temperature. No electromagnon is found in the spin-canted structure of BiFeO3. On the other hand, two magnons with very different frequencies are predicted via the use of this method. The smallest-in-frequency magnon corresponds to oscillations of the weak ferromagnetic vector in the basal plane being perpendicular to the polarization while the second magnon corresponds to magnetic dipoles going in and out of this basal plane. The large value of the frequency of this second magnon is caused by static couplings between magnetic dipoles with electric dipoles and oxygen octahedra tiltings.

A simple law governing coupled magnetic orders in perovskites

An energetic expression containing four different macroscopic terms is proposed to explain and understand coupled magnetic orders (and the directions of the simultaneously occurring ferromagnetic and/or antiferromagnetic vectors) in terms of anti-phase and/or in-phase tilting of oxygen octahedra in magnetic and multiferroic perovskites. This expression is derived from a suggested simple microscopic formula, and has its roots in the Dzyaloshinsky-Moriya interaction. Comparison with data available in the literature and with first-principles calculations we conduct here confirms the validity of such a simple and general law for any tested structural paraelectric and even ferroelectric phase, and for any chosen direction of any selected primary magnetic vector.

Revisiting properties of ferroelectric and multiferroic thin films under tensile strain from first principles

First-principles calculations are performed to revisit properties of (001) epitaxial BiFeO(3) (BFO) and PbTiO(3) thin films under tensile strain. While these two films possess different ground states when experiencing no misfit strain, they both exhibit the same, previously unknown phase for tensile strains above ≃5% at T = 0 K. This novel state is of orthorhombic Pmc2(1) symmetry and is macroscopically characterized by a large in-plane polarization coexisting with oxygen octahedra tilting in-phase about the out-of-plane direction. On a microscopic point of view, this Pmc2(1) state exhibits short atomic bonds and zigzag cation displacement patterns, unlike conventional ferroelectric phases and typical domains. Such unusual inhomogeneous patterns originate from the coexistence of polar and antiferroelectric distortions having the same magnitude and lead BFO films to be the first known material for which orbital ordering coexists with a large polarization. Furthermore, this Pmc2(1) state is also found in other perovskite films under tensile strain, which emphasizes its generality.

Magnetic cycloid of BiFeO3 from atomistic simulations

An effective Hamiltonian is developed to investigate the magnetic cycloid of the BiFeO3 (BFO) multiferroic. This approach reproduces many complex features of this cycloid, such as its plane of rotation containing the polarization and the newly discovered spin density waves resulting from the canting of magnetic dipoles out of this cycloidal plane. It also suggests that the energetic origin of the cycloid can be thought of in terms of the converse spin-current model, and reveals the mechanisms responsible for the spin density waves. Finally, this atomistic scheme resolves an ongoing controversy about the cycloid anharmonicity, and revisits a recent misconception about the relationship between out-of-plane spin-density waves and the weak magnetization associated with the spin-canted structure of BFO.

Finite-temperature properties of Ba(Zr,Ti)O3 relaxors from first principles

A first-principles-based technique is developed to investigate the properties of Ba(Zr,Ti)O(3) relaxor ferroelectrics as a function of temperature. The use of this scheme provides answers to important, unresolved and/or controversial questions such as the following. What do the different critical temperatures usually found in relaxors correspond to? Do polar nanoregions really exist in relaxors? If yes, do they only form inside chemically ordered regions? Is it necessary that antiferroelectricity develop in order for the relaxor behavior to occur? Are random fields and random strains really the mechanisms responsible for relaxor behavior? If not, what are these mechanisms? These ab initio based calculations also lead to deep microscopic insight into relaxors.

Strain dependence of polarization and piezoelectric response in epitaxial BiFeO3 thin films

Epitaxial strain has recently emerged as a powerful means to engineer the properties of ferroelectric thin films, for instance to enhance the ferroelectric Curie temperature (T(C)) in BaTiO(3). However, in multiferroic BiFeO(3) thin films an unanticipated strain-driven decrease of T(C) was reported and ascribed to the peculiar competition between polar and antiferrodistortive instabilities. Here, we report a systematic characterization of the room-temperature ferroelectric and piezoelectric properties for strain levels ranging between -2.5% and +1%. We find that polarization and the piezoelectric coefficient increase by about 20% and 250%, respectively, in this strain range. These trends are well reproduced by first-principles-based techniques.

Multiferroic phase transition near room temperature in BiFeO3 films

In multiferroic BiFeO(3) thin films grown on highly mismatched LaAlO(3) substrates, we reveal the coexistence of two differently distorted polymorphs that leads to striking features in the temperature dependence of the structural and multiferroic properties. Notably, the highly distorted phase quasiconcomitantly presents an abrupt structural change, transforms from a standard to a nonconventional ferroelectric, and transitions from antiferromagnetic to paramagnetic at 360±20 K. These coupled ferroic transitions just above room temperature hold promises of giant piezoelectric, magnetoelectric, and piezomagnetic responses, with potential in many applications fields.

Fermi resonance involving nonlinear dynamical couplings in Pb(Zr,Ti)O3 solid solutions

We have used first-principles-based simulations and Raman scattering techniques to reveal a novel dynamical phenomenon in Pb(Zr,Ti)O(3) solid solutions: a Fermi resonance (FR) emerging from the nonlinear coupling between ferroelectric (FE) motions and tiltings of oxygen octahedra. This FR manifests itself as the doubling of a nominally single FE mode in a purely FE phase, when the resonant frequency of the FE mode is close to the first overtone of the tiltings. We show that the FR is the result of a nonlinear coupling that is proportional to the spontaneous polarization of the material and derive an analytical model that captures the essence of the effect.

Prediction of the magnetotoroidic effect from atomistic simulations

An effective Hamiltonian technique is used to investigate the effect of applying curled electric fields on physical properties of stress-free BiFeO(3) dots being under open-circuit electrical boundary conditions. It is discovered that such fields can lead to a control of not only the magnitude but also the direction of the magnetization. Such control originates from the field-induced transformation or switching of electrical vortices and their couplings with oxygen octahedral tilts and magnetic dipoles. This control involves striking intermediate states and constitutes a novel phenomenon that can be termed a "magnetotoroidic" effect.

Phase transitions in epitaxial (-110) BiFeO3 films from first principles

The effect of misfit strain on properties of epitaxial BiFeO3 films that are grown along the pseudocubic [110] direction, rather than along the usual [001] direction, is predicted from density-functional theory. These films adopt the monoclinic Cc space group for compressive misfit strains smaller in magnitude than ≃1.6% and for any investigated tensile strain. In this Cc phase, both polarization and the axis about which antiphase oxygen octahedra tilt rotate within the epitaxial plane as the strain varies. Surprisingly and unlike in (001) films, for compressive strain larger in magnitude than ≃1.6%, the polarization vanishes and two orthorhombic phases of Pnma and P2(1)2(1)2(1) symmetry successively emerge via strain-induced transitions. The Pnma-to-P2(1)2(1)2(1) transition is a rare example of a so-called pure gyrotropic phase transition, and the P2(1)2(1)2(1) phase exhibits original interpenetrated arrays of ferroelectric vortices and antivortices.

BiFeO3 films under tensile epitaxial strain from first principles

Density-functional calculations are performed to predict structural and magnetic properties of (001) BiFeO(3) films under tensile epitaxial strain. These films remain monoclinic (Cc space group) for misfit strains between 0% and ≈8%, with the polarization, tilt axis and magnetization all rotating when varying the strain. At a tensile strain ≈8%, these films undergo a first-order phase transition towards an orthorhombic phase (Ima2 space group). In this novel phase, the polarization and tilt axis lie in the epitaxial plane, while the magnetization is along the out-of-plane direction and the direction of the antiferromagnetic vector is unchanged by the phase transition. An unexpected additional degree of freedom, namely, an antiphase arrangement of Bi atoms, is also found for all tensile strains.

Epitaxial Pb(Zr,Ti)O3 ultrathin films under open-circuit electrical boundary conditions

The temperature-versus-misfit-strain phase diagram of Pb(Zr,Ti)O3 ultrathin films under open-circuit electrical boundary conditions is simulated via the use of an effective Hamiltonian. Two novel phases, both exhibiting dipolar nanodomains and oxygen octahedral tilting, are discovered. The interplay between dipolar, antiferrodistortive, alloying, and strain degrees of freedom induces several striking features in these two phases, such as the chemical pinning of domain walls, the enhancement of oxygen octahedral tilting near the domain walls, and the existence of dipolar waves and cylindrical dipolar chiral bubbles.

Descriptive epidemiology of mechanical hip pathology in adults under 50 years of age. Prospective series of 292 cases: Clinical and radiological aspects and physiopathological review

Two hundred and ninety-two patients, aged between 16 and 50 years and presenting with mechanical hip pathology, were included in a prospective multicenter study. The descriptive study concerned the clinical examination and analysis of three X-ray views (AP pelvic, Lequesne false profile and lateral axial view). The series comprised 62% males, mean age 35 years, with 53% right side and 22% bilateral involvement. Initial trauma was reported in 19% of cases, and direct familial history of hip pathology in 20%. Seventy percent of the patients played sports, 30% were high-level athletes, and 17% played combat sports. The physical impingement sign was present in 18% to 65% of cases depending on the variant studied. On imaging (n=241), 62% of hips showed osteoarthritis, with 25% at the evolved stage. In the series, as a whole, there was a 35% rate of dysplasia, 63% of impingement and 5% of normal X-ray results. The radiologic impingement aspects were 58% cam-type, 19% pincer-type and 23% mixed. Twenty-two percent of dysplasia cases showed signs of associated impingement. Pain experienced exclusively in flexion/internal rotation/adduction on examination showed little sensitivity (20%) but considerable specificity (86%) for the main diagnosis of impingement. The links between impingement and dysplasia are discussed, and an integrative schema of all risk factors is put forward.

Kittel law in BiFeO₃ ultrathin films: a first-principles-based study

A first-principles-based effective Hamiltonian is used to investigate the thickness dependency of the size of straight-walled domains in ultrathin films made of the multiferroic BiFeO₃ (BFO) material. It is found that the Kittel law is followed, as in ferroelectric or ferromagnetic films. However, an original real-space decomposition of the different energetic terms of this effective Hamiltonian allows the discovery that the microscopic origins of such a law in BFO films dramatically differ from those in ferroelectric or ferromagnetic films. In particular, interactions between tilting of oxygen octahedra around the domain walls and magnetoelectric couplings near the surface (and away from the domain walls) play an important role in the observance of the Kittel law in the studied BFO films.

Bridging multiferroic phase transitions by epitaxial strain in BiFeO3

We report the influence of epitaxial strain on the multiferroic phase transitions of BiFeO3 films. Using advanced characterization techniques and calculations we show that while the magnetic Néel temperature hardly varies, the ferroelectric Curie temperature TC decreases dramatically with strain. This is in contrast with the behavior of standard ferroelectrics where strain enhances the polar cation shifts and thus TC. We argue that this is caused by an interplay of polar and oxygen tilting instabilities and that strain can drive both transitions close together to yield increased magnetoelectric responses.

Chiral patterns of tilting of oxygen octahedra in zero-dimensional ferroelectrics and multiferroics: a first principle-based study

First-principles-based Monte Carlo approaches are developed to investigate finite-temperature properties of stress-free nanodots made of the ferroelectric Pb(Zr,Ti)O3 system and of the multiferroic BiFeO3 compound. These zero-dimensional materials both exhibit various, novel chiral patterns for the tilting of the oxygen octahedra. Such exotic patterns originate from the coupling between the tiltings of the oxygen octahedra and the electric dipole vortices, and require original order parameters to quantify them.