Spontaneous Long-range Order Research Articles

Topological aspects of multi-k antiferromagnetism in cubic rare-earth compounds

We advertise rare-earth intermetallics with high-symmetry crystal structures and competing interactions as a possible materials platform hosting spin structures with non-trivial topological properties. Focusing on the series of cubic RCu compounds, where R = Ho, Er, Tm, the bulk properties of these systems display exceptionally rich magnetic phase diagrams hosting an abundance of different phase pockets characteristic of antiferromagnetic order in the presence of delicately balanced interactions. The electrical transport properties exhibit large anomalous contributions suggestive of topologically non-trivial winding in the electronic and magnetic structures. Neutron diffraction identifies spontaneous long-range magnetic order in terms of commensurate and incommensurate variations of (ππ0) antiferromagnetism with the possibility for various multi- k configurations. Motivated by general trends in these materials, we discuss the possible existence of topologically non-trivial winding in real and reciprocal space in the class of RCu compounds including antiferromagnetic skyrmion lattices. Putatively bringing together different limits of non-trivial topological winding in the same material, the combination of properties in RCu systems promises access to advanced functionalities.

Influence of a further-neighbour interaction on a rotating magnetoelectric effect in a coupled spin–electron model on a doubly decorated square lattice

Exact calculations are used to study the influence of a further-neighbour spin–spin interaction on a rotating magnetoelectric effect (RME) in a coupled spin–electron model (SEM) on a doubly-decorated square lattice. The special attention is focused on a ground-state analysis and a thermal behaviour at a half-filled case. It was found that the competition between the spin–spin interaction, electron hopping and electric field gives rise to novel spatially (an)isotropic magnetic states, whose frontiers are influenced by a spatial orientation of an applied electric field. It is shown that the thermal stability of spontaneous long-range order can be enhanced by RME, which may result in an enhancement of the critical temperature. The further-neighbour interaction may cause striking thermally-driven reentrant phase transitions.

On the failure of effective-field theory in predicting a spurious spontaneous ordering and phase transition of Ising nanoparticles, nanoislands, nanotubes and nanowires

The present work clarifies a failure of the effective-field theory in predicting a false spontaneous long-range order and phase transition of Ising nanoparticles, nanoislands, nanotubes and nanowires with either zero- or one-dimensional magnetic dimensionality. It is conjectured that the standard formulation of the effective-field theory due to Honmura and Kaneyoshi generally predicts for the Ising spin systems a spurious spontaneous long-range order with nonzero critical temperature regardless of their magnetic dimensionality whenever at least one Ising spin has coordination number greater than two. The failure of the effective-field theory is exemplified on a few paradigmatic exactly solved examples of zero- and one-dimensional Ising nanosystems: star, cube, decorated hexagon, star of David, branched chain, sawtooth chain, two-leg and hexagonal ladders. The presented exact solutions illustrate eligibility of a few rigorous analytical methods for exact treatment of the Ising nanosystems: exact enumeration, graph-theoretical approach, transfer-matrix method and decoration-iteration transformation. The paper also provides a substantial survey of the scientific literature, in which the effective-field theory led to a false prediction of the spontaneous long-range ordering and phase transition.

Spontaneous ferroelectric order in lead-free relaxor Na1/2Bi1/2TiO3 -based composites

Short-range ordered polar nanoregions are key to the giant electromechanical properties exhibited by relaxor ferroelectrics. Stabilization of the long-range ferroelectric order in relaxor systems has typically been achieved by applying external fields. In this work, spontaneous (zero-field) ferroelectric order is demonstrated in the composites constituting of nonergodic relaxor matrix phase $0.91\mathrm{N}{\mathrm{a}}_{1/2}\mathrm{B}{\mathrm{i}}_{1/2}\mathrm{Ti}{\mathrm{O}}_{3}\text{\ensuremath{-}}0.09\mathrm{BaTi}{\mathrm{O}}_{3}$ with ZnO inclusions. Direct structural evidence is provided for the long-range ferroelectric order in the composites using in situ electric-field-dependent synchrotron investigations and $^{23}\mathrm{Na}$ nuclear magnetic resonance spectroscopy. Thermodynamic analysis incorporating microelasticity reveals the role of spatial residual stress in stabilizing the ferroelectric order. The work provides a direct correlation between the stabilized ferroelectric order and enhanced thermal stability, which can be utilized to guide the design of spontaneous long-range order in other relaxor systems.

Correlation Dynamics of Dipolar Bosons in 1D Triple Well Optical Lattice

The concept of spontaneous symmetry breaking and off-diagonal long-range order (ODLRO) are associated with Bose–Einstein condensation. However, as in the system of reduced dimension the effect of quantum fluctuation is dominating, the concept of ODLRO becomes more interesting, especially for the long-range interaction. In the present manuscript, we study the correlation dynamics triggered by lattice depth quench in a system of three dipolar bosons in a 1D triple-well optical lattice from the first principle using the multiconfigurational time-dependent Hartree method for bosons (MCTDHB). Our main motivation is to explore how ODLRO develops and decays with time when the system is brought out-of-equilibrium by a sudden change in the lattice depth. We compare results of dipolar bosons with contact interaction. For forward quench ( V f > V i ) , the system exhibits the collapse–revival dynamics in the time evolution of normalized first- and second-order Glauber’s correlation function, time evolution of Shannon information entropy both for the contact as well as for the dipolar interaction which is reminiscent of the one observed in Greiner’s experiment [Nature, 415 (2002)]. We define the collapse and revival time ratio as the figure of merit ( τ ) which can uniquely distinguish the timescale of dynamics for dipolar interaction from that of contact interaction. In the reverse quench process ( V i > V f ) , for dipolar interaction, the dynamics is complex and the system does not exhibit any definite time scale of evolution, whereas the system with contact interaction exhibits collapse–revival dynamics with a definite time-scale. The long-range repulsive tail in the dipolar interaction inhibits the spreading of correlation across the lattice sites.

Absence of a spontaneous long-range order in a mixed spin-(1/2, 3/2) Ising model on a decorated square lattice due to anomalous spin frustration driven by a magnetoelastic coupling

The mixed spin-(1/2, 3/2) Ising model on a decorated square lattice, which takes into account lattice vibrations of the spin-3/2 decorating magnetic ions at a quantum-mechanical level under the assumption of a perfect lattice rigidity of the spin-1/2 nodal magnetic ions, is examined via an exact mapping correspondence with the effective spin-1/2 Ising model on a square lattice. Although the considered magnetic structure is in principle unfrustrated due to bipartite nature of a decorated square lattice, the model under investigation may display anomalous spin frustration driven by a magnetoelastic coupling. It turns out that the magnetoelastic coupling is a primary cause for existence of the frustrated antiferromagnetic phases, which exhibit a peculiar coexistence of antiferromagnetic long-range order of the nodal spins with a partial disorder of the decorating spins with possible reentrant critical behavior. Under certain conditions, the anomalous spin frustration caused by the magnetoelastic coupling is responsible for unprecedented absence of spontaneous long-range order in the mixed-spin Ising model composed from half-odd-integer spins only.

Topochemical nitridation of Sr2FeMoO6.

The topotactic nitridation of cation ordered, tetragonal Sr2FeMoO6 in NH3 at moderate temperatures leads to cubic, Fm3[combining macron]m double perovskite oxynitride Sr2FeMoO4.9N1.1 where double-exchange interactions determine ferromagnetic order with TC ≈ 100 K. Substitution of oxide by nitride induces bond asymmetries and local electronically driven structural distortions, which combined with Fermi level lowering restricts charge itinerancy to confined regions and preclude spontaneous long-range magnetic order. Under a magnetic field, ferromagnetic correlations expand, favoring charge delocalization and a negative magnetoresistance is observed.

Polariton Chimeras: Bose-Einstein Condensates with Intrinsic Chaoticity and Spontaneous Long-Range Ordering.

The system of cavity polaritons driven by a plane electromagnetic wave is found to undergo the spontaneous breaking of spatial symmetry, which results in a lifted phase locking with respect to the driving field and, consequently, in the possibility of internal ordering. In particular, periodic spin and intensity patterns arise in polariton wires; they exhibit strong long-range order and can serve as media for signal transmission. Such patterns have the properties of dynamical chimeras: they are formed spontaneously in perfectly homogeneous media and can be partially chaotic. The reported new mechanism of chimera formation requires neither time-delayed feedback loops nor nonlocal interactions.

Quantum phase transitions in the HeisenbergJ1−J2triangular antiferromagnet in a magnetic field

We present the zero temperature phase diagram of a Heisenberg antiferromagnet on a frustrated triangular lattice with nearest neighbor ($J_1$) and next nearest neighbor ($J_2$) interactions, in a magnetic field. We show that the classical model has an accidental degeneracy for all $J_2/J_1$ and all fields, but the degeneracy is lifted by quantum fluctuations. We show that at large $S$, for $J_2/J_1 <1/8$, quantum fluctuations select the same sequence of three sublattice co-planar states in a field as for $J_2 =0$, and for $1/8<J_2/J_1 <1$ they select the canted stripe state for all non-zero fields. The transition between the two states is first order in all fields, with the hysteresis width set by quantum fluctuations. We study the model with arbitrary $S$, including $S=1/2$, near the saturation field by exploring the fact that near saturation the density of bosons is small for all $S$. We show that for $S >1$, the transition remains first order, with a finite hysteresis width, but for $S=1/2$ and, possibly, $S=1$, there appears a new intermediate phase, likely without a spontaneous long-range order.

Reversible 2D Phase Transition Driven By an Electric Field: Visualization and Control on the Atomic Scale.

We report on a reversible structural phase transition of a two-dimensional system that can be locally induced by an external electric field. Two different structural configurations may coexist within a CO monolayer on Cu(111). The balance between the two phases can be shifted by an external electric field, causing the domain boundaries to move, increasing the area of the favored phase controllable both in location and size. If the field is further enhanced new domains nucleate. The arrangement of the CO molecules on the Cu surface is observed in real time and real space with atomic resolution while the electric field driving the phase transition is easily varied over a broad range. Together with the well-known molecular manipulation of CO adlayers, our findings open exciting prospects for combining spontaneous long-range order with man-made CO structures such as "molecule cascades" or "molecular graphene". Our new manipulation mode permits us to bridge the gap between fundamental concepts and the fabrication of arbitrary atomic patterns in large scale, by providing unprecedented insight into the physics of structural phase transitions on the atomic scale.

Spherulitic assembly of peptide nanowires via spontaneous crystallization.

In this work, the hierarchal arrangement of peptide nanowires was achieved via the spontaneous crystallization of peptide molecules. Peptide molecules, which are structural motifs associated with Alzheimer's disease, assembled into one-dimensional nanowires and spontaneously formed two-dimensional peptide spherulites during crystallization of the peptide melt. The assembly behavior of the peptides could be directed by physically confining the soft mold. Furthermore, a hybrid assembly of small functional molecules, such as photoluminescent Alq3, was also achieved. Our approach offers a simple method for achieving spontaneous long-range crystalline order of building blocks approaching macroscopic dimensions and also a facile hybridization strategy to conjugate biomolecules and functional small molecules.

Order-from-disorder effect in the exactly solved mixed spin-(1/2, 1) Ising model on fully frustrated triangles-in-triangles lattices

The mixed spin-(1/2, 1) Ising model on two fully frustrated triangles-in-triangles lattices is exactly solved with the help of the generalized star-triangle transformation, which establishes a rigorous mapping correspondence with the equivalent spin- 1/2 Ising model on a triangular lattice. It is shown that the mutual interplay between the spin frustration and single-ion anisotropy gives rise to various spontaneously ordered and disordered ground states, which differ mainly in an occurrence probability of the non-magnetic spin state of the integer-valued decorating spins. We have convincingly evidenced a possible coexistence of the spontaneous long-range order with a partial disorder within the striking ordered–disordered ground state, which manifests itself through a non-trivial criticality at finite temperatures as well. A rather rich critical behavior including the order-from-disorder effect and reentrant phase transitions with either two or three successive critical points is also found.

Long-range order instead of phase separation in large lattice-mismatch isovalentAX−BXsystems

Large atomic size mismatch between compounds discourages their binding into a common lattice because of the ensuing cost in strain energy. This central paradigm in the theory of isovalent alloys long used to disqualify alloys with highly mismatched components from technological use is clearly broken by the occurrence of stable spontaneous long-range order in mixtures of alkali halides with as much as 40% size mismatch (e.g., LiF-CsF). Our theoretical analysis of these failures uncovered a different design principle for stable alloys: very large atomic size mismatch can lead to spontaneous ordering if the large (small) components have the ability to raise (lower) their coordination number (CN) within the mixed phase. This heuristic design principle has led us to explore via first-principles structure search a few very largely mismatched binary systems whose components have a propensity for CN disproportionation. We find ordered structures for BeO-BaO (37% size mismatch) and BeO-SrO (30%), and ordering in LiCl-KCl (20%), whereas BN-InN (33%) is found to lower its positive formation enthalpy by ∼60% when CN disproportionation is allowed. This new design principle could be used to explore phases unsuspected to order by the common paradigm of strain instability. © 2009 The American Physical Society.

Temperature and Size Dependence of Antiferromagnetism in Mn Nanostructures

We report on variable-temperature STM investigations of the spontaneous long-range magnetic order of Mn monolayer nanostructures epitaxially grown on stepped W(110). The measurements reveal that the onset of the antiferromagnetic order is closely related to the Mn nanostructure width along the [001] direction, with a decreasing Néel temperature as we move from a 2D toward a quasi-1D system. In contrast, lateral confinement along the [110] direction seems to play a less important role. The results are discussed in terms of anisotropic exchange coupling and of boundary effects, both potentially stabilizing long-range magnetic order in nanostructures confined in the [110] direction.

Hidden symmetries and their consequences int2gcubic perovskites

The five-band Hubbard model for a d band with one electron per site is a model which has very interesting properties when the relevant ions are located at sites with high (e.g., cubic) symmetry. In that case, if the crystal-field splitting is large, one may consider excitations confined to the lowest threefold-degenerate ${t}_{2g}$ orbital states. When the electron hopping matrix element (t) is much smaller than the on-site Coulomb interaction energy $(U),$ the Hubbard model can be mapped onto the well-known effective Hamiltonian (at order ${t}^{2}/U)$ derived by Kugel and Khomskii (KK). Recently we have shown that the KK Hamiltonian does not support long-range spin order at any nonzero temperature due to several novel hidden symmetries that it possesses. Here we extend our theory to show that these symmetries also apply to the underlying three-band Hubbard model. Using these symmetries we develop a rigorous Mermin-Wagner construction, which shows that the three-band Hubbard model does not support spontaneous long-range spin order at any nonzero temperature and at any order in $t/U$---despite the three-dimensional lattice structure. The introduction of spin-orbit coupling does allow spin ordering, but even then the excitation spectrum is gapless due to a subtle continuous symmetry. Finally we show that these hidden symmetries dramatically simplify the numerical exact diagonalization studies of finite clusters.

Controlled synthesis and magnetic properties of 2D and 3D iron azide networks infinity2[Fe(N3)2(4,4'-bpy)] and infinity3[Fe(N3)2(4,4'-bpy)

Controlled synthesis of transition metal complexes with mixed ligands has led to two new compounds with the same empirical formula [Fe(N3)2(4,4'-bpy)] (4,4'-bpy=4,4'- bipyridine). The compound 2D-[Fe(N3)2(4,4'-bpy)] (I) contains end-on (EO) bridging azido ligands. It crystallizes in the orthorhombic crystal system, space group Cmmm (No. 65): a=11.444(2) A, b=15.181(3) A, c=3.458(1) A, V=600.8(2) A(3), and Z=2. The compound 3D-[Fe(N3)2(4,4'-bpy)] (II) contains end-to-end (EE) azido bridges. It belongs to the tetragonal crystal system, space group P4(1)2(1)2 (No. 92): a=8.132(1) A, b=8.132(1) A, c=16.708(3) A, V=1104.9(5) A(3), and Z=4. Crystals of I and II have been grown by the diffusion method. Phase-pure samples of both compounds have been obtained by means of an optimal solution synthesis. Spontaneous long-range magnetic ordering was found in both I and II, with I being a metamagnet, and II being a ferromagnet. For I, in the low-field region, multiple transitions at TN1=20 K and TN2=5 K were observed, and these indicated the existence of Fe moment reorientation. Heat capacity measurements on II confirmed ferromagnetic transition at TC=20 K.

Effect of Oxygen Content and Oxygen Vacancy Ordering on the Properties of TbBaCo2O6?? Perovskites

Using IR-spectroscopy, heat capacity experiments, neutron and X-ray diffraction, as well as magnetization and resistivity measurements, TbBaCo2O6—δ samples with different oxygen content and different thermal history are studied. It is shown that the structural, magnetic and electrical properties are strongly sensitive to oxygen content and oxygen vacancy ordering. We submit that the first order semiconductor-to-metal phase transition at 340 to 345 K in this compound is accompanied by oxygen vacancy ordering and short-range magnetic ordering, and only at 285 K spontaneous long-range ferrimagnetic ordering occurs.

Growth temperature dependence of long-range alloy order and magnetic properties of epitaxial FexPt1−x (x≂0.5) films

The structural and magnetic properties of 1000-Å-thick epitaxial FexPt1−x(001) alloy films, grown by molecular beam epitaxy with x≂0.5, have been studied as a function of growth temperature. X-ray diffraction analysis showed that the long-range order parameter increased from near zero for films grown at 100 °C to a maximum of 0.93 in films grown at 500 °C. Over this range the magnetic easy axis changed from in-plane to perpendicular and the polar Kerr rotation increased strongly. Spontaneous long-range ordering in these films has an activation energy ∼0.2 eV, consistent with an energy barrier for surface and step down diffusion.

Self-Assembled Smectic Phases in Rod-Coil Block Copolymers

Rod-coil block copolymers are self-assembling polymers that combine the physics of orientational ordering of rodlike polymers and the microphase separation of coil-coil block copolymers. Several new solid-state morphologies were observed in a series of anionically synthesized model poly(hexyl isocyanate-b-styrene) rod-coil diblock copolymers examined by transmission electron microscopy and selected-area electron diffraction. The rod-coils formed smectic C-like and O-like morphologies with domain sizes ranging from tens of nanometers to almost 1 micrometer. Both structural and orientational changes were found for increasing rod volume fractions. In addition, some morphologies exhibited spontaneous long-range orientational order over many tens of micrometers.

Direct optical transitions in indirect-gap (Al0.5Ga0.5)0.51In0.49P by atomic ordering.

(${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${)}_{\mathit{y}}$${\mathrm{In}}_{1\mathrm{\ensuremath{-}}\mathit{y}}$P alloys naturally constitute monolayer superlattices on GaAs(001) substrates by atomic ordering when they are grown by organometallic vapor-phase epitaxy. The spontaneous long-range ordering causes the band-gap reduction and band splitting at the valence-band maximum. When the Al composition in a (${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${)}_{0.5}$${\mathrm{In}}_{0.5}$P-random alloy is larger than \ensuremath{\sim}0.4, the optical transition is indirect, and the conduction-band minimum is at ${\mathit{X}}_{6\mathit{c}}$. From electroreflectance and photoluminescence measurements, we have found for long-range ordered (${\mathrm{Al}}_{0.5}$${\mathrm{Ga}}_{0.5}$${)}_{0.51}$${\mathrm{In}}_{0.49}$P that the ${\mathrm{\ensuremath{\Gamma}}}_{6\mathit{c}}$ valley crosses the ${\mathit{X}}_{6\mathit{c}}$ by the band-gap reduction. The emission from the strongly ordered alloy is optically direct. The temperature dependence of photoluminescence intensity shows that statistical potential fluctuations and localized states in the low-energy part of the exciton resonance play an important role in the direct luminescence of the long-range ordered (${\mathrm{Al}}_{0.5}$${\mathrm{Ga}}_{0.5}$${)}_{0.51}$${\mathrm{In}}_{0.49}$P. \textcopyright{} 1996 The American Physical Society.