Antiferrodistortive Order Research Articles

Macroscopic Polarization from Nonlinear Gradient Couplings.

We show that a lattice mode of arbitrary symmetry induces a well-defined macroscopic polarization at first order in the momentum and second order in the amplitude. We identify a symmetric flexoelectric-like contribution, which is sensitive to both the electrical and mechanical boundary conditions, and an antisymmetric Dzialoshinskii-Moriya-like term, which is unaffected by either. We develop the first-principles methodology to compute the relevant coupling tensors in an arbitrary crystal, which we illustrate with the example of the antiferrodistortive order parameter in SrTiO_{3}.

Polar Morphologies from First Principles: PbTiO3 Films on SrTiO3 Substrates and the p(2×Λ) Surface Reconstruction

AbstractLow‐dimensional structures comprised of ferroelectric (FE) PbTiO3 (PTO) and quantum paraelectric SrTiO3 (STO) are hosts to complex polarization textures such as polar waves, flux‐closure domains, and polar skyrmion phases. Density functional theory (DFT) simulations can provide insight into this order, but are limited by the computational effort required. Within DFT, the novel multi‐site support function method is used to reduce the solution time for the electronic groundstate whilst preserving high accuracy. This allows for large‐scale simulations of PTO films on STO substrates with system sizes >2000 atoms. In the ultrathin limit, the polar wave texture with cylindrical chiral bubbles emerges as an intermediate phase between full‐flux‐closure domains and in‐plane polarization. This is driven by an internal bias field born of the compositionally broken inversion symmetry in the [001] direction. Manipulation of this built‐in field informs a new principle of design for control over chiral order on the nanoscale through the careful choice of substrate, surface termination, or use of overlayers. Antiferrodistortive (AFD) order locally interacts with these polar textures giving rise to strong FE/AFD coupling at the PbO terminated surface driving a surface reconstruction. This offers another pathway for the local control of ferroelectricity.

Intrinsic structural instabilities of domain walls driven by gradient coupling: Meandering antiferrodistortive-ferroelectric domain walls inBiFeO3

Using the Landau-Ginzburg-Devonshire approach, we predict the intrinsic instability of the ferroelectric-ferroelastic domain walls in the multiferroic $\mathrm{BiFe}{\mathrm{O}}_{3}$ emerging from the interplay between the gradient terms of the antiferrodistortive and ferroelectric order parameters at the walls. These instabilities are the interface analog of the structural instabilities in the vicinity of phase coexistence in the bulk, and so they do not stem from incomplete polarization screening in thin films or its spatial confinement, electrostrictive or flexoelectric coupling. The effect of $\mathrm{BiFe}{\mathrm{O}}_{3}$ material parameters on the ${71}^{\ensuremath{\circ}}$, ${109}^{\ensuremath{\circ}}$, and ${180}^{\ensuremath{\circ}}$ walls is explored, and it is shown that the meandering instability appears at ${109}^{\ensuremath{\circ}}$ and ${180}^{\ensuremath{\circ}}$ walls for small gradient energies, and the walls become straight and broaden for higher gradients. In contrast to the ${180}^{\ensuremath{\circ}}$ and ${109}^{\ensuremath{\circ}}$ domain walls, uncharged ${71}^{\ensuremath{\circ}}$ walls are always straight, and their width increases with increasing the tilt gradient coefficient. The wall instability and associated intrinsic meandering provide insight into the behavior of morphotropic and relaxor materials, wall pinning, and mechanisms of interactions between order parameter fields and local microstructure.

Intrinsic dynamics of the electric-field-induced phase switching in antiferroelectric PbZrO3 ultrathin films

Antiferroelectric ultrathin ${\mathrm{PbZrO}}_{3}$ films can exhibit both ferroelectric and antiferroelectric behavior depending on the thickness. We use first-principles-based nanoscopic simulations to investigate the intrinsic high-frequency dynamics of the electric-field-induced phase switching in such films which so far remains unknown. In this comprehensive study we report (i) the size and frequency evolution of the polarization response to the electric field; (ii) the intrinsic time for the phase switching; (iii) detailed comparison between the polarization reversal in the films with ferroelectric and antiferroelectric behavior; (iv) dynamics of the antiferroelectric and antiferrodistortive order parameters; (v) nanoscopic mechanism responsible for the phase switching. The nanoscopic insight leads to the prediction of the existence of two possible scenarios for the antipolar-polar phase switching depending on the mutual orientation of the antiferroelectric order parameter and the electric field. The two scenarios have different dynamical fingerprints. The polar-antipolar phase switching is found to be assisted by the formation of a nonpolar phase. Computational data indicate that the phase switching time is only fractions of nanoseconds for the polar-polar phase switching in ferroelectric films and polar-antipolar phase switching in antiferroelectric films. The antipolar-polar phase switching in antiferroelectric films is just a bit slower and takes the order of nanosecond. Under nonequilibrium conditions we find formation of antiferroelectric and antiferrodistortive nanodomains and coexistence of polar and antipolar order parameters.

The effect of chemical variations on the structural polarity of relaxor ferroelectrics studied by resonance Raman spectroscopy

Resonance Raman spectroscopy was applied to doped PbSc0.5Ta0.5O3 and PbSc0.5Nb0.5O3 relaxor ferroelectrics, to better understand the effect of composition disorder on the mesoscopic-scale polar order in complex perovskite-type (ABO3) ferroelectrics. The excitation photon energy used was 3.8 eV, which is slightly above the energy gap and corresponds to the maximum of the optical dielectric permittivity. Group-theory analysis reveals that the resonance Raman scattering (RRS) observed under these conditions is allowed only in polar crystal classes. Therefore, RRS is dominated by the atomic dynamics of nanoregions with coherent polar distortions, which considerably facilitates the comparison of polar order in various compounds. The results show that A-site doping (Ba2+, Sr2+, La3+, Bi3+) has significantly stronger effect on the structural polarity than the introduction of a third element at the B site (Nb5+ or Sn4+ doped in PbSc0.5Ta0.5O3). The A-site substitution by cations that in contrast to Pb2+ have isotropic outermost electron shells disturbs the system of lone-pair electrons, thus reducing the correlation length of coupled polar distortions and the strength of the electric field associated with the mean polarization of polar nanoregions. A-site doping with larger cations (Ba2+) augments the polar deformation of the individual BO6 octahedra due to local elastic fields. As a result, such A-site doping intensifies the initial structural polarity at high temperatures and prevails the enlargement of the polar fraction at low temperatures. A-site doping with smaller cations (Sr2+, La3+), regardless if they are isovalent or aliovalent to Pb2+, increases the correlation length of antiferrodistortive order (BO6 tilts), which in turn assists the development of double-perovskite structure with coherent local polar distortions. A-site doping with aliovalent cations (Bi3+) having the same outermost electron shell and ionic radius as the host A-site Pb2+ cations leads to stronger coupling along the –B–O–B– bond linkages due to enhanced random local electric fields.

Landau-Ginzburg description of anomalous properties of novel room temperature multiferroics Pb(Fe1/2Ta1/2)x(Zr0.53Ti0.47)1-xO3 and Pb(Fe1/2Nb1/2)x(Zr0.53Ti0.47)1−xO3

Landau-Ginzburg thermodynamic formalism is used for the description of the anomalous ferroelectric, ferromagnetic, and magnetoelectric properties of Pb(Fe1/2Ta1/2)x(Zr0.53Ti0.47)1−xO3 and Pb(Fe1/2Nb1/2)x(Zr0.53Ti0.47)1−xO3 micro-ceramics. We calculated temperature, composition, and external field dependences of ferroelectric, ferromagnetic, and antiferromagnetic phases transition temperatures, remanent polarization, magnetization, hysteresis loops, dielectric permittivity, and magnetoelectric coupling. Special attention was paid to the comparison of developed theory with experiments. It appeared possible to describe adequately main experimental results including a reasonable agreement between the shape of calculated and measured hysteresis loops and remnant polarization. Since Landau-Ginzburg thermodynamic formalism appertains to single domain properties of a ferroic, we did not aim to describe quantitatively the coercive field under the presence of realistic poly-domain switching. Information about linear and nonlinear magnetoelectric coupling coefficients was extracted from the experimental data. From the fitting of experimental data with theoretical formula, we obtained the composition dependence of Curie-Weiss constant that is known to be inversely proportional to harmonic (linear) dielectric stiffness, as well as the strong nonlinear dependence of anharmonic parameters in free energy. Keeping in mind the essential influence of these parameters on multiferroic properties, the obtained results open the way to govern practically all the material properties with the help of suitable composition choice. A forecast of the strong enough influence of antiferrodistortive order parameter on the transition temperatures and so on the phase diagrams and properties of multiferroics are made on the basis of the developed theory.

Separate Kinetics of the Polar and Antiferrodistortive Order Parameters in the Antiferroelectric Transition of PbZr1-xTixO3 and the Influence of Defects

Abstract The transition from the rhombohedral-ferroelectric to the lower temperature orthorhombic-antiferroelectric phase in Zr-rich PZT involves two order parameters (OPs): 1) the polar OP for the displacements of the cations with respect to the O octahedra; 2) an antiferrodistortive OP responsible for tilting of the octahedra. It is shown that at Ti compositions near the morphotropic boundary with the FE phase (0.046 ≤ x ≤ 0.054), the two OPs may be almost independent of each other at cooling rates of 0.5 K/min or faster, depending on the sample history. This fact gives rise to a great variety of shapes of the curves of the elastic compliance s(T), but all of them can be fitted very well as superpositions of variously broadened steps for each of the modes involved in the transitions, including the tilt transition occurring in the untransformed FE fraction. The evolution of the s(T) curves includes enhancements up to a factor of four during aging for weeks in the region of the AFE/FE coexistence. Restiffening and reduction of the thermal hysteresis of the AFE/FE transition are recovered by heating up to 800-900 K. It is proposed that ageing is due to the clustering of relatively mobile defects, most likely O vacancies, at the domain walls in the coexisting AFE/FE phases. Such defect structures are probably at the origin of intense thermally activated relaxation processes observed above TC in the dielectric and anelastic spectra, and can be annealed out above 800 K, allowing the AFE transition to recover a fast kinetics.

Pressure-induced structural transformations in advanced ferroelectrics with relaxor behaviour

A series of model perovskite-type relaxor ferroelectrics (pure and A-/B-site doped PbSc1/2Ta1/2O3 and PbSc1/2Nb1/2O3 as well as of 0.9PbZn1/3Nb2/3O3−0.1PbTiO3) were studied by high pressure diffraction and inelastic light scattering in order to elucidate the mesoscopic-scale ferroic atomic arrangements responsible for the superb macroscopic properties of these materials. The combined analysis of the pressure-enhanced phonon anomalies observed by Raman spectroscopy and the pressure-induced long-range order detected by synchrotron X-ray and neutron diffraction revealed that at ambient conditions antiferrodistortive order coexists with the ferroelectric order on the mesoscopic scale. This suggests that the locally polarized spatial nanoregions known as polar nanoregions are ferrielectric in nature and their abundance and mean size depend on both the antiferrodistortive and ferroelectric coupling, which in turn can be tuned by appropriate chemical variations.

In situ high-temperature high-pressure Raman spectroscopy on single-crystal relaxor ferroelectrics PbSc1/2Ta1/2O3 and PbSc1/2Nb1/2O3

The effect of temperature on the pressure-induced structural changes in perovskite-type (ABO3) relaxor ferroelectrics is studied by in situ high-temperature high-pressure Raman spectroscopy on single crystals of PbSc1/2Ta1/2O3 (PST) and PbSc1/2Nb1/2O3 (PSN), which allowed us to elucidate the interplay between the polar and antiferrodistortive order coexisting on the mesoscopic scale at ambient conditions. High-pressure experiments were carried out at elevated temperatures below and above the characteristic intermediate temperature T*. The results were compared with those obtained at room temperature, which for PST is just above the paraelectric–ferroelectric phase transition TC, whereas for PSN is below TC. It is shown that the first critical pressure pc1, at which a transition from a relaxor to a non-polar rhombohedral state with antiphase octahedral tilt ordering occurs, decreases at elevated temperatures due to the weakening of the polar coupling, which in turn facilitates the evolution of the preexisting medium-range antiferrodistortive order into a long-range order. The critical pressure pc2 of the second phase transition, involving a change in the type of the antiferrodistortive order, is not affected by temperature, i.e. it is independent of the state of polar coupling and is mainly related to the initial correlation length of antiferrodistortive order. The strong influence of temperature on pc1, which occurs only when the mesoscopic polar order is suppressed, emphasizes the importance of coexisting ferroelectric and antiferrodistortive coupling for the occurrence of the relaxor states.

Structural investigation of strontium titanate nanoparticles and the core-shell model

Nanoparticles of strontium titanate (SrTiO${}_{3}$) have been synthesized in the 15 nm to 1 \ensuremath{\mu}m size range and studied using a combination of dielectric, Raman, x-ray, and neutron measurements. When diminishing the grain size, a strong reduction of dielectric permittivity, an enhancement of (normally forbidden) Raman polar modes and a progressive decoupling (or nonlinear coupling) between the antiferrodistortive (AFD) order parameter and the spontaneous strain, is observed. A qualitative explanation of all these effects could be achieved using the Petzelt core-shell model of SrTiO${}_{3}$ nanoparticles, with a core constituted of nonferroelectric AFD phase and a shell with frozen polarization. Depending on the route of synthesis, a strong increase of the AFD ferroelastic critical temperature ${T}_{c}$ is observed. This behavior cannot be explained by considering only pure size or external strain effects, and a more complicated mechanism involving defects induced by the synthesis process should probably be considered. Interestingly, those are able to strongly affect the core grain structure, modifying thereby the macroscopic physical properties of SrTiO${}_{3}$ nanoparticle-based-materials.

New multiferroics based on EuxSr1−xTiO3 nanotubes and nanowires

Using Landau-Ginzburg-Devonshire theory, we have addressed the complex interplay between structural antiferrodistortive order parameter (oxygen octahedron rotations), polarization and magnetization in EuxSr1−xTiO3 nanosystems. We have calculated the phase diagrams of EuxSr1−xTiO3 bulk, nanotubes and nanowires, which include the antiferrodistortive, ferroelectric, ferromagnetic, and antiferromagnetic phases. For EuxSr1−xTiO3 nanosystems, our calculations show the presence of antiferrodistortive-ferroelectric-ferromagnetic phase or the triple phase at low temperatures (≤10 K). The polarization and magnetization values in the triple phase are calculated to be relatively high (∼50 μC/cm2 and ∼0.5 MA/m). Therefore, the strong coupling between structural distortions, polarization, and magnetization suggests the EuxSr1−xTiO3 nanosystems as strong candidates for possible multiferroic applications.

Emergent Superstructural Dynamic Order due to Competing Antiferroelectric and Antiferrodistortive Instabilities in BulkEuTiO3

Microscopic structural instabilities of EuTiO3 single crystal were investigated by synchrotron x-ray diffraction. Antiferrodistortive (AFD) oxygen octahedral rotational order was observed alongside Ti derived antiferroelectric (AFE) distortions. The competition between the two instabilities is reconciled through a cooperatively modulated structure allowing both to coexist. The electric and magnetic field effect on the modulated AFD order shows that the origin of large magnetoelectric coupling is based upon the dynamic equilibrium between the AFD - antiferromagnetic interactions versus the electric polarization - ferromagnetic interactions.

Domain walls in a perovskite oxide with two primary structural order parameters: First-principles study of BiFeO3

We present a first-principles study of ferroelectric domain walls (FE-DWs) in multiferroic BiFeO$_3$ (BFO), a material in which the FE order parameter coexists with anti-ferrodistortive (AFD) modes involving rotations of the O$_6$ octahedra. We find that the energetics of the DWs are dominated by the capability of the domains to match their O$_6$ octahedra rotation patterns at the plane of the wall, so that the distortion of the oxygen groups is minimized. Our results thus indicate that, in essence, it is the discontinuity in the AFD order parameter, and not the change in the electric polarization, what decides which crystallographic planes are most likely to host BFO's FE-DWs. Such a result clearly suggests that the O$_6$ rotational patterns play a primary role in the FE phase of this compound, in contrast with the usual (implicit) assumption that they are subordinated to the FE order parameter. Our calculations show that, for the most favorable cases in BFO, the DW energy amounts to a several tens of mJ/m$^2$, which is higher than what was computed for other ferroelectric perovskites with no O$_6$ rotations. Interestingly, we find that the structure of BFO at the most stable DWs resembles the atomic arrangements that are characteristic of low-lying (meta)stable phases of the material. Further, we argue that our results for the DWs of bulk BFO are related with the nanoscale-twinned structures that Prosandeev et al. [Adv. Funct. Mats. (2012), doi: 10.1002/adfm.201201467] have recently predicted to occur in this compound, and suggest that BFO can be viewed as a polytypic material. Our work thus contributes to shape a coherent picture of the structural variants that BFO can present and the way in which they are related.

Structural phase transitions in Ruddlesden-Popper phases of strontium titanate:Ab initioand modulated Ginzburg-Landau approaches

We present the first systematic {\em ab initio} study of anti-ferrodistortive (AFD) order in Ruddlesden-Popper (RP) phases of strontium titanate, Sr$_{1+n}$Ti$_n$O$_{3n+1}$, as a function of both compressive epitaxial strain and phase number $n$. We find all RP phases to exhibit AFD order under a significant range of strains, recovering the bulk AFD order as $\sim 1/n^2$. A Ginzburg-Landau Hamiltonian generalized to include inter-octahedral interactions reproduces our {\em ab initio} results well, opening a pathway to understanding other nanostructured perovskite systems.

ChemInform Abstract: Crystal and Magnetic Structures of NaMnF4.

An X-ray single crystal structure determination (monoclinic, space group P2₁/c, a = 573.6(2), b = 489.2(1), c = 574.8(2) pm, β = 108.07(2), Z = 2; wR = 0.038 for 380 reflections) shows that NaMnF₄ crystallizes in the same layered structure type as LiMnF₄. In the quadratic layers the Mn-F-Mn bridges are strongly asymmetric, due to the Jahn-Teller effect, leading to an antiferrodistortive order of elongated octahedra. The bridging angle is 138.4°. The Na⁺ ions are 6-coordinated as well. The common structural arrangement of both [MnF₆] and [NaF₆] octahedra shows topological relation to the rutile structure. In the magnetic measurements performed on powder samples NaMnF₄ behaves as an antiferromagnet with a weak ferromagnetic component below 13 K. By neutron diffraction on powder (4-70 K) a magnetic cell doubled along the α-axis is found and below a Neel temperature of TN = 13 K the magnetic structure shows colinear antiferromagnetic arrangement of the spins pointing slightly (16) out of the layer plane. The resulting magnetic moment is 3.52 μΒ.

Synthesis of Double-Layer Perovskite Fluoride K3Cu2F7 with Spin Gap and Orbital Order

We synthesized a single-phase polycrystalline sample of a double-layer perovskite fluoride K 3 Cu 2 F 7 . This compound is the new member of the potassium copper fluoride family, which has an antiferrodistortive orbital order (AFDOO). Magnetic susceptibility measurements revealed that K 3 Cu 2 F 7 is a rare experimental realization of antiferromagnetically isolated spin dimers on a simple double-square lattice with no frustration, and that AFDOO causes ferromagnetic interactions in respective layers. The coexistence of spin gap and AFDOO is an exotic phenomenon both in quantum spin systems and strongly correlated electron systems.

Jahn-Teller-type phase transitions in oxide ceramics and other solids with Cu(II) — from the viewpoint of a solid state chemist

After a short outline of the vibronic features of the local Jahn-Teller effect (Eg ⊗ eg coupling) the cooperative aspects — in particular the various order patterns of the elongated octahedra in Cu(II) solids — are reviewed. While the elastic interactions can be described by energy terms of Qe symmetry, the local Jahn-Teller effect has Qθ symmetry (ϕ = 0). Phase transitions in dependence on the Cu(II) concentration are analysed in detail for oxidic ordered perovskites Ba(Sr)2Zn(Ni)1-xCuxW(Te)O6, which exhibit ferrodistortive order patterns connected with first order phase transitions at high x-values. At lower x-values at the short-range order scale elastic Qe-type strains prevail as in the cases of antiferrodistortive order, leading to continuous phase transitions. Here, the cluster distribution has been successfully analysed by EPR spectroscopy.

Observation of Pressure-Induced Structural Transition in K2CuF4by Phonon-Raman Scattering Experiments: Change of the Orbital Ordering by Pressure

Since the ferromagnetic intralayer exchange interaction in K 2 CuF 4 is due to the antiferrodistortive (AFD) orbital ordering of the 3d holes of Cu 2+ ions, we expect that the ferromagnetism of this compound to disappear when the AFD order of the distortion of CuF 6 octahedra collapses. Recent magnetic susceptibility measurements performed at high pressures on this compound actually confirmed the disappearance of the ferromagnetism above approximately 9 GPa [M. Ishizuka et al. : J. Phys. Soc. Jpn. 65 (1996) 1927]. To obtain evidence of the pressure-induced structural change which corresponds to the magnetic change mentioned above, we measured the pressure dependence of the phonon-Raman spectra of this compound. As a result, we found that the scattering lines relevant to the vibrational modes of CuF 6 octahedra ordered in the AFD fashion disappeared above 9∼10 GPa. This result is consistent with the structure above 9 GPa revealed by recent X-ray diffraction experiments that we performed.

Pressure Effects in Ferromagnetism of Orbital Ordering Ferromagnet

We have studied pressure effects on layered Perovskite-type orbital ordering ferromagnet K 2 CuF 4 , particularly the pressure-induced transition from ferromagnetic (F) to antiferromagnetic (AF) state. First the magnetic phase diagram of simple one-dimensional multi-band Hubbard Hamiltonian with antiferrodistortive order is constructed with exact diagonalization procedure. It is found that AF and helical (HI) states can be stable in a region of large transfer energy even with keeping antiferrodistortive order. For more realistic two-dimensional models relevant to CuF 2 plane in K 2 CuF 4 the magnetic phase diagram is derived by perturbational procedure. Judging from the parameter values estimated by FLAPW band calculations for K 2 CuF 4 under high pressure as well as at ambient pressure, it is concluded that the pressure-induced F-AF transition may be realized in K 2 CuF 4 without structural transition from antiferrodistortive to ferrodistortive phase. Further the observed pressure dependence of T C of K ...

Antiferrodistortive Order in the New Solid Solution CrZr0.75Nb0.25F6

The new compound CrZr0.75Nb0.25F6has been synthesized. Structural determination by the Rietveld full-profile technique has been carried out on powdered samples. This compound crystallizes in the orthorhombic system, space groupPnma, witha=11.5728(4)Å,b=7.9671(2)Å, andc=5.8203(2)Å. The structure displays an antiferrodistortive order of elongated CrF6octahedra induced by a cooperative Jahn–Teller effect. This result is compared with ferrodistortive order of CrF6octahedra in the HT CrNbF6form. The magnetic behavior of both CrNbF6and CrZr0.75Nb0.25F6at low temperature is described.