Primary Order Parameter Research Articles

Universal dynamic magnetism in Yb pyrochlores with disparate ground states

The ytterbium pyrochlore magnets, Yb2B2O7 (B = Sn, Ti, Ge) are well described by S_eff = 1/2 quantum spins decorating a network of corner-sharing tetrahedra and interacting via anisotropic exchange. Structurally, only the non-magnetic B-site cation, and hence, primarily the lattice parameter, is changing across the series. Nonetheless, a range of magnetic behaviors are observed: the low temperature magnetism in Yb2Ti2O7 and Yb2Sn2O7 has ferromagnetic character, while Yb2Ge2O7 displays an antiferromagnetically ordered Neel state at low temperatures. While the static properties of the ytterbium pyrochlores are distinct, inelastic neutron scattering measurements reveal a common character to their exotic spin dynamics. All three ytterbium pyrochlores show a gapless continuum of spin excitations, resembling over-damped ferromagnetic spin waves at low Q. Furthermore, the specific heat of the series also follows a common form, with a broad, high-temperature anomaly followed by a sharp low-temperature anomaly at T_C or T_N. The novel spin dynamics we report correlate strongly with the broad specific heat anomaly only, remaining unchanged across the sharp anomaly. This result suggests that the primary order parameter in the ytterbium pyrochlores associated with the sharp anomaly is "hidden" and not simple magnetic dipole order.

Pressure and strain effects of hexagonal rare-earth manganites: a first-principles study

We have investigated the structural, electrical and magnetic properties as well as the phonon modes of hexagonal rare-earth manganites (RMnO3, R = Pr, Nd, Pm, Sm, Gd, Tb, Dy, Ho, Er, Tm and Lu) under chemical pressure, hydrostatic pressure and epitaxial strain by first-principles calculations. The magnetic ground state of RMnO3 is found to have magnetic configuration and to be stable under all considered external conditions. In contrast, the K3 phonon mode, which is the primary order parameter and responsible for the ‘improper ferroelectricity’, is greatly influenced by pressure and epitaxial strain. Consequently, the electric polarization is enhanced by 56.7% when the chemical pressure increases from R = Pr to R = Lu. The hydrostatic pressure can also improve the polarization to a certain degree, e.g. by 14.7% from 0 GPa to 40 GPa in LuMnO3. Finally, the dependence of polarization on the epitaxial strain is also given, revealing that the compressive strain could promote the ferroelectricity while tensile strain will suppress it.

Tetrahedral tilting and ferroelectricity in Bi2AO5 (A=Si, Ge) from first principles calculations

The properties of a tetrahedron containing Bi2AO5 (A=Si, Ge) are examined using Ab initio calculations and symmetry mode analysis. Stabilization of the polar phase is observed in both compounds with a monoclinic Cc phase. In the monoclinic ground state, the tilting angle (ϕ1) of tetrahedron is 7.21° and 21.94° for the Si and Ge compound, respectively. The relationship between a primary order parameter and the tetrahedral tilting is identified and an analytical formula between them is proposed by analyzing the structure. The detailed layer-by-layer polarization calculations shows that the main polarization component originates from the tetrahedron tilting of the AO4 unit, and the analytical relationship between the primary order parameter and spontaneous polarization is also calculated. This B3LYP hybrid functional calculation provides a band gap of 4.44eV and 4.18eV for Bi2SiO5 and Bi2GeO5, respectively. The main difference between the two compounds is also analyzed based on the electronic structure and electron localization function analysis.

Primary ferrotoroidicity in antiferromagnets

Antiferromagnetic ordering does not give rise to a measurable macroscopic symmetry-breaking order parameter such as the magnetization in a ferromagnet. An exception is the case of antiferromagnets with a vortexlike toroidal alignment of the magnetic moments in the unit cell because this gives rise to the formation of a spontaneous macroscopic toroidal moment which can be measured as a magnetoelectric effect. It is a long-standing question whether the toroidal moment is merely a side effect of the antiferromagnetic state or whether it can become the primary order parameter in a ferroic phase transition. Here we report the magnetoelectric properties of ${\mathrm{LiFeSi}}_{2}{\mathrm{O}}_{6}$ and show that they point to the role of the toroidal vector moment as the primary order parameter. Based on Landau theory we distinguish it from primary antiferromagnetic order. We thus justify the proposal that along with ferromagnets, ferroelectrics, and ferroelastics the ferrotoroidics constitute a new class of primary ferroics.

Nontrivial order parameter inSr2IrO4

A thorough analysis of the ground state of the relativistic magnetic insulator ${\mathrm{Sr}}_{2}{\mathrm{IrO}}_{4}$ is performed. The results are in accordance with the small antiferromagnetic moment and gapped state found in experiment. The solution, obtained using the DFT+SO+$U$ methodology, is thoroughly analyzed in terms of Landau theory. We find that the ordered magnetic moment only forms a secondary order parameter while the primary order parameter is a higher order magnetic multipole of rank five. It is further observed that the electronic structure in the presence of this order parameter is related to the earlier proposed ${j}_{\mathrm{eff}}=1/2$ model, but in contrast to that model, the present picture can exactly explain the small magnitude of the ordered magnetic moments.

Distributed twofold ordering inURu2Si2

The identification of hidden order in URu${}_{2}$Si${}_{2}$ is currently a hot topic in condensed matter physics. By performing a much more detailed lineshape analysis of their own NMR data previously published in PRL, a strong argument is put forward that nematic/orthorhombic distortion is not the primary hidden order parameter and that this parameter may be sensitive to disorder. Many local defects were found, even in the best quality samples.

Multipole order and global/site symmetry in the hidden-order phase ofURu2Si2

On the basis of group theory and the first-principles calculations, we investigate high-rank multipole orderings in URu2Si2, which have been proposed as a genuine primary order parameter in the hidden order phase below 17.5K. We apply Shubnikov group theory to the multipole ordered states characterized by the wave vector Q = (0, 0, 1) and specify the global/site symmetry and the secondary order parameters, such as induced dipole moments and change in charge distribution. We find that such antiferroic magnetic multipole orderings have particularly advantageous to conceal the primary order parameter due to preserving high symmetry in charge distribution. Experimental observations of the inherent low-rank multipoles, which are explicitly classified in this paper, will be key pieces to understand the puzzling hidden order phase.

Observation of vortex domain structures in multiferroic hexagonal manganites RMnO3by transmission electron microscopy

Multiferroic hexagonal manganite RMnO3 (R = rare-earth elements) shows improper ferroelectricity accompanied by tilting of MnO5 hexahedra as the primary order parameter. The ferroelectricity is originated from displacements of rare-earth ions along c-axis triggered by the MnO5 hexahedra tilting. Although coupling between ferroelectric and antiferromagnetic domains below the magnetic transition temperature of ∼90 K has been reported from previous work[1], the relationship between the ferroelectric domains and structural domains due to the MnO5 hexahedra tilting has not been well-studied. In this talk, we will report our studies on unique patterns of ferroelectric antiphase domains with a vorticity in hexagonal RMnO3, obtained from the results of transmission electron microscopy [2].The electron diffraction patterns obtained at room temperature exhibit superlattice reflection spots due to the MnO5 hexahedra tilting and displacements of rare-earth ions along c-axis, in addition to the fundamental reflections associated with the high symmetry structure with the space group of P63/mmc. Unique antiphase/ferroelectric "cloverleaf-like" domain patterns are clearly observed in dark-field images taken using superlattice spots. The fundamental and superlattice dark-field imaging combined with high-resolution imaging clearly demonstrates that in the cloverleaf-like domain patterns the antiphase and ferroelectric domains arrange periodically with certain rotation direction. In addition, there exist two types of cloverleaf-like domain patterns with the opposite rotations next to each other in the superlattice dark-field images. These results indicate that the cloverleaf-like domain patterns can be considered as the aggregation of vortices and antivortices consisting of ferroelectric and antiphase domains.

Spherical neutron polarimetry in multiferroics under external stimuli

Study of multiferroics, materials simultaneously having more than one primary ferroic order parameter, is a hot topic of material sciences. The most extensively studied class of these compounds is the family of magnetoelectric multiferroics, where ferroelectricity can be induced by various types of magnetic orderings via the relativistic spin-orbit interaction. As a consequence of the cross coupling between spins and electric polarization, the spectacular control of the ferroelectric polarization by external magnetic field and the manipulation of the magnetic order via electric field can often be realized in these systems. Depending on the symmetry and microscopic mechanism of the multiferroicity the coupling energy between magnetic and electric ordering parameters can significantly vary. Classical neutron diffraction often fails in the precise determining of the complex magnetic structure in the multiferroics due to the presence of the statistically distributed domains in the macroscopic sample. Using spherical neutron polarimetry (SNP), known also as 3D polarization analysis, it is possible not only to precisely determine the complex magnetic structure, but also to investigate in-situ its evolution with external parameters and to control the magnetic domains distribution under the influence of the external electric or/and magnetic field. Here we will present some SNP results on few different multiferroic materials. In some of them, e.g. square lattice 2D antiferromagnet Ba2CoGe2O7, even strong electric field does not change the magnetic order. However rater week magnetic field is sufficient to create a mono-domain structure and to rotate spins in the plane. In other e.g. incommensurate (spiral) magnetic structure of the TbMnO3, solely electric field is sufficient to fully control the chirality of the magnetic structure. In the case of Cr2O3 both electric and magnetic fields should be applied in parallel in order to switch between the different antiferromagnetic domains.

Neutron diffraction study of magnetic structure in multiferroics under pressure

RMn2O5 (R = Y, Bi, rare-earth) is one of the prototypical multiferroic materials that exhibits a rich variety of magnetoelectric effects. Since the successive magnetic and ferroelectric phase transitions simultaneously take place, magnetic order has been thought to be a primary order parameter for the ferroelectricity in this system. We recently have found that in neutron diffraction study of 153EuMn2O5, magnetic phase transition is induced by applying hydrostatic pressure. As temperature decreases upon p = 1.4 GPa, the magnetic propagation wave vector changes from qM = (1/2, 0, 1/3) to (1/2, 0, 1/2), indicating that the period of magnetic unit cell as well as the magnetic structure change at the phase transition. We have also carried out the dielectric and polarization measurements under pressure and established magnetic and dielectric phase diagram as functions of temperature and pressure as shown in the figure. This study has revealed that the ferroelectric (FE1) – ferroelectric (FE2) phase transition concomitantly occurs at the magnetic phase transition, where the electric polarization is enhanced. To clarify the relevance between the ferroelectricity and the magnetic structure, we carried out single crystal magnetic structure analysis of 153EuMn2O5 upon ambient- and high-pressure. In the magnetic phase with qM = (1/2, 0, 1/3), cycloidal magnetic structure of manganese spins propagating along c-axis is realized. On the contrary in the magnetic phase with qM = (1/2, 0, 1/2), the spins arrange almost collinearly along c-axis. The result indicates that the presence of the cycloidal spin structure plays an important role for inducing (or reducing) the electric polarization in this compound. This study was supported by "KAKENHI"-programs of Scientific Research (B) (24340064), Scientific Research (A) (21244051), Challenging Exploratory Research (23654098) and of Scientific Research on Priority Areas "Novel States of Matter Induced by Frustration" (19052001).

Order-parameter symmetries of domain walls in ferroelectrics and ferroelastics

The symmetry of boundaries between ferroelectric, ferroelastic and antiphase domains is a key element for a theoretical understanding of their properties. Here, we derive this symmetry from their organic relation to the symmetry of the primary transition order parameters. The domain wall symmetries are shown to coincide with directions of the order-parameter n-dimensional vector space, corresponding to sum of the vectors associated with adjacent domain states. This property is illustrated by the determination of the domain wall maximal symmetries in BaTiO3, LaAlO3, SrTiO3 and Gd2(MoO4)3. Besides, the domain pattern in YMnO3 is interpreted as resulting from an annihilation-creation process, the annihilation of the antiphase domain walls creating six ferroelectric domain walls merging at a single point.

A high-resolution powder neutron diffraction study of the crystal structure of neighborite (NaMgF3) between 9 and 440 K

The temperature dependence of the unit-cell dimensions and the crystal structures of the fluorperovskite neighborite, NaMgF 3 (analyzed in the Pbnm setting of the space group), have been determined at 88 temperatures between 9 and 440 K from high-resolution, time-of-flight, powder neutron diffraction data. Lattice parameters exhibit saturation at low temperatures, before developing linear thermal expansion coefficients at temperatures above ~ 350 K. The temperature dependence of each axis has been analyzed, and fitted, using a two-term expression related to an Einstein internal energy function. The unit-cell parameters a and c behave in a conventional manner, however, an unexpected, and previously unobserved, region of negative linear thermal expansion has been found for the b axis in the temperature interval 20 ≤ T ≤ 90 K. Estimated, high-temperature axial thermal expansion coefficients derived from the lattice parameter fitting are in good agreement with those experimentally determined from an earlier synchrotron study, and indicate that high-temperature saturation has been achieved in neighborite by 440 K. The unit-cell volume varies smoothly and monotonically over the whole temperature interval, and the two-term Debye model of Barron has been successfully used to fit these data with characteristic temperatures of 369(2) and 1055(14) K. For the temperature interval 313.15-443.15 K, the thermodynamic Grüneisen constant has been determined using the Debye parameterization of the unit-cell volume, coupled with literature values of the isobaric molar heat capacity. The evolution of the crystal structure as a function of temperature is presented, and explained, in terms of the temperature dependence of the amplitudes of the seven symmetry-adapted basis-vectors of the aristotype phase that are consistent with the orthorhombic space group. The calculated temperature variations of the bond lengths are in excellent agreement with those experimentally determined. The primary order parameters for centrosymmetric, zone-boundary phase transitions in perovskite-structured compounds, i.e., the amplitudes of the basis vectors that transform as the irreducible representations R + 4 (anti-phase tilt) and M + 3 (in-phase tilt), have been fitted to a Landau free energy expansion that incorporates low-temperature saturation. Within the temperature range studied, the temperature dependence of the displacement corresponding to the anti-phase tilt is consistent with tricritical behavior. Experimental evidence is presented for a quadratic coupling of the in-phase tilt to the anti-phase tilt for temperatures greater than ~ 135 K, suggesting critical behavior at the orthorhombic-cubic transition is purely related to an instability at the R point of the pseudocubic Brillouin zone.

Effect of coupling with strain in multiferroics on phase diagrams and elastic anomalies

The Landau theory was applied to treat the phase diagrams for a multiferroic with two second order phase transitions taking into account the coupling of the primary order parameters with strain. Two order parameters are coupled biquadratically which corresponds to the magnetoelectric materials. The coupling with strain is assumed to be linear in strain and quadratic in order parameters. Three ordered phases are discussed. Analytic relationships were obtained for the phase transition temperatures and for elastic modulus changes through the phase transitions. Strong influence of the coupling with strain on the phase diagrams was shown.

Erratum: Domain walls in a perovskite oxide with two primary structural order parameters: First-principles study ofBiFeO3[Phys. Rev. B87, 024102 (2013)

Received 22 January 2014DOI:https://doi.org/10.1103/PhysRevB.89.059901©2014 American Physical Society

Magneto-thermal conduction and phonon anomalies across magnetic transitions in multiferroic (poly and nanocrystalline) bismuth ferrite

Bismuth ferric oxide (BFO) or bismuth ferrite is a multiferroic material with perovskite structure in which ferroelectric and antiferromagnetic orderings coexist. The magneto-electric coupling in this material makes it interesting from fundamental physics and applications points of view. As a result of complex magneto-elastic coupling and spin-glass behavior at low temperatures, the material exhibits a number of phase transitions driven by magnetic ordering. Earlier reports indicate that the primary order parameter in these transitions is not polarization but are related to magnon mode softening. In order to throw more light on the magneto-elastic and phonon related properties of this material, we measured the thermal transport properties, thermal conductivity and specific heat capacity, in the presence of an external magnetic field and compared the results with the zero field case. Results are reported for polycrystalline as well as nanocrystalline samples of BFO between 140K and 250K. A photopyroelectric thermal wave technique has been employed for the measurements. Anomalies in thermal properties observed at 140K, 200K and 240K in polycrystalline samples as well as their changes with applied field are explained in terms of magneto-elastic and spin–phonon couplings. It is found that the transitions get less well defined and one of the transition temperatures get shifted upwards considerably as the particle sizes are reduced to nanometer scales. Particle size dependences of phonon and magnon–phonon scattering are invoked to explain these results.

Spontaneous polarization analysis in hydrogen bonded ferroelectric liquid crystals

Characterization of a novel series of linear ferroelectric double hydrogen bonded liquid crystals has been elucidated. The phases exhibited are cholesteric, smectic C*, smectic F* and smectic G*. A new smectic ordering referred to as smectic X* has been characterized by various techniques, which is sandwiched between cholesteric and traditional smectic C* phases. Spontaneous polarization and response times are measured in smectic X* and smectic C* phases, and are fitted to a power law. Primary order parameters, viz., tilt angle measurements in smectic C* phase have been carried out and fitted to a power law. Thermal stability and order of transition of all the phases are deduced.

Measurement of the elastoresistivity coefficients of the underdoped iron arsenide Ba(Fe0.975Co0.025)2As2

A new method is presented for measuring terms in the elastoresistivity tensor ${m}_{ij}$ of single crystal samples with tetragonal symmetry. The technique is applied to a representative underdoped Fe-arsenide, Ba(Fe${}_{0.975}$Co${}_{0.025}$)${}_{2}$As${}_{2}$, revealing an anomalously large and anisotropic elastoresistance in comparison to simple metals. The ${m}_{66}$ coefficient follows a Curie-Weiss temperature dependence, providing direct evidence that the tetragonal-to-orthorhombic structural phase transition that occurs at ${T}_{s}=97.5$ K in this material is not the result of a true-proper ferroelastic transition. Rather, the material suffers a pseudoproper transition for which the lattice strain is not the primary order parameter.

Biaxial order parameter in the homologous series of orthogonal bent-core smectic liquid crystals

The fundamental parameter of the uniaxial liquid crystalline state that governs nearly all of its physical properties is the primary orientational order parameter (S) for the long axes of molecules with respect to the director. The biaxial liquid crystals (LCs) possess biaxial order parameters depending on the phase symmetry of the system. In this paper we show that in the first approximation a biaxial orthogonal smectic phase can be described by two primary order parameters: S for the long axes and C for the ordering of the short axes of molecules. The temperature dependencies of S and C are obtained by the Haller's extrapolation technique through measurements of the optical birefringence and biaxiality on a nontilted polar antiferroelectric (Sm-AP(A)) phase of a homologous series of LCs built from the bent-core achiral molecules. For such a biaxial smectic phase both S and C, particularly the temperature dependency of the latter, are being experimentally determined. Results show that S in the orthogonal smectic phase composed of bent cores is higher than in Sm-A calamatic LCs and C is also significantly large.

Thermoelastic and structural properties of ionically conducting cerate perovskites: (I) BaCeO3 at low temperature in the Pbnm phase

The thermoelastic and structural properties of BaCeO3 perovskite in the Pbnm phase field have been studied using high resolution neutron diffractometry at 37 temperatures between 2K and 350K. From a simultaneous fit of the isochoric heat capacity and unit cell volume, the vibrational density of states in the Pbnm phase is shown to be approximated by a two-term modified Debye model with characteristic temperatures 176(1)K and 543(2)K. Vibrational Debye temperatures, determined from the temperature-variation of the atomic displacement parameters, suggest the cations to be more associated with the lower characteristic temperature, whilst those for the anions, are closer to the higher characteristic temperature. The weighted average of the Grüneisen constants associated with the two characteristic temperatures is in good agreement with the experimentally determined thermodynamic Grüneisen parameter. Structural parameters are presented as the amplitudes of the seven symmetry-adapted basis-vectors of the aristotype phase, and a structural basis for the temperature-dependence of the bond lengths is outlined. The critical exponent associated with the temperature variation of the primary order parameter in the phase transition from Pbnm to Ibnn at 563K is consistent with this transition being tricritical in nature.

Second-order P6c2-P31c transition and structural crystallography of the cyclosilicate benitoite, BaTiSi3O9, at high pressure

Experimental high-pressure investigations on benitoite in the diamond-anvil cell reveal a second-order phase transition at a critical transition pressure P c = 4.24(3) GPa, as determined from synchrotron powder diffraction, single-crystal X-ray diffraction, and Raman spectroscopy. Diffraction experiments indicate a non-isomorphous transition from P 6 c 2 to P 31 c space-group symmetry with a ′ = a √3 and c ′ = c relative to the P 62 c subcell below P c . The high-pressure polymorph is characterized by a larger compressibility compared to the compressional behavior of benitoite below P c . Fitting second-order Birch-Murnaghan equations of state to the experimental data sets, the parameters obtained are V 0 = 372.34(4) A 3 , K 0 = 117.9(7) GPa, with a 0 = 6.6387(3) A, K a = 108.1(7) GPa, and c 0 = 9.7554(4) A, K c = 143.3(1.1) GPa for the low-pressure form ( P P c ), and V 0 = 376.1(4) A 3 , K 0 = 88.9(1.6) GPa, with a 0 = 11.516(4) A, K a = 95.4(1.8) GPa, and c 0 = 9.826(4) A, K c = 77.2(1.6) GPa for the high-pressure form ( P > P c ). One of the most significant structural changes is related to the coordination of Ba atoms, changing from an irregular [6+6] coordination to a more regular ninefold. Simultaneously, the Si 3 O 9 rings are distorted due to no longer being constrained by mirror-plane symmetry, and the Si atoms occupy three independent sites. The higher compressibility along the c-axis direction is explained by the relative displacement of the Ba position to the Si 3 O 9 rings, which is coupled to the lateral displacement of the non-bridging O2-type atoms of the ring unit. A symmetry mode analysis revealed that the transition is induced by the onset of a primary order parameter transforming according to the K 6 irreducible representation of P 6 c 2.