Onset Of Long-range Order Research Articles

Berezinskii—Kosterlitz—Thouless correlations in copper-based quasi-2D spin systems (Review Article)

We present an overview of selected copper-based quasi-2D square-lattice spin-1/2 materials with an easy-plane anisotropy, providing the possibility to study emergent Berezinskii-Kosterlitz-Thouless (BKT) correlations. In particular, in those materials with a comparatively small exchange coupling, the effective XY anisotropy of the low-temperature spin correlations can be controlled by an applied magnetic field, yielding a systematic evolution of the BKT correlations. In cases where the residual interlayer correlations are small enough, dynamical BKT correlations in the critical regime may be observed experimentally, whereas the completion of the genuine BKT transition is preempted by the onset of long-range order.

Spontaneous Formation of Exceptional Points at the Onset of Magnetism.

We reveal how symmetry-protected nodal points in topological semimetals may be promoted to pairs of generically stable exceptional points (EPs) by symmetry-breaking fluctuations at the onset of long-range order. This intriguing interplay between non-Hermitian (NH) topology and spontaneous symmetry breaking is exemplified by a magnetic NH Weyl phase spontaneously emerging at the surface of a strongly correlated three-dimensional topological insulator, when entering the ferromagnetic regime from a high-temperature paramagnetic phase. Here, electronic excitations with opposite spin acquire significantly different lifetimes, thus giving rise to an anti-Hermitian structure in spin that is incompatible with the chiral spin texture of the nodal surface states, and hence facilitate the spontaneous formation of EPs. We present numerical evidence of this phenomenon by solving a microscopic multiband Hubbard model nonperturbatively in the framework of dynamical mean-field theory.

Variational Quantum Simulation of Valence-Bond Solids

We introduce a hybrid quantum-classical variational algorithm to simulate ground-state phase diagrams of frustrated quantum spin models in the thermodynamic limit. The method is based on a cluster-Gutzwiller ansatz where the wave function of the cluster is provided by a parameterized quantum circuit whose key ingredient is a two-qubit real XY gate allowing to efficiently generate valence-bonds on nearest-neighbor qubits. Additional tunable single-qubit Z- and two-qubit ZZ-rotation gates allow the description of magnetically ordered and paramagnetic phases while restricting the variational optimization to the U(1) subspace. We benchmark the method against the J1−J2 Heisenberg model on the square lattice and uncover its phase diagram, which hosts long-range ordered Neel and columnar anti-ferromagnetic phases, as well as an intermediate valence-bond solid phase characterized by a periodic pattern of 2×2 strongly-correlated plaquettes. Our results show that the convergence of the algorithm is guided by the onset of long-range order, opening a promising route to synthetically realize frustrated quantum magnets and their quantum phase transition to paramagnetic valence-bond solids with currently developed superconducting circuit devices.

Split-and-Merge in Stationary Random Stirring on Lattice Torus

We show that in any dimension dge 1, the cycle-length process of stationary random stirring (or, random interchange) on the lattice torus converges to the canonical Markovian split-and-merge process with the invariant (and reversible) measure given by the Poisson–Dirichlet law mathsf {PD(1)}, as the size of the system grows to infinity. In the case of transient dimensions, dge 3, the problem is motivated by attempts to understand the onset of long range order in quantum Heisenberg models via random loop representations of the latter.

Magnetic behavior of Gd3Ru4Al12, a layered compound with distorted kagomé net

The magnetic behavior of the compound, Gd3Ru4Al12, which was reported about two decades ago to crystallize in a hexagonal structure (space group P63/mmc), has not been investigated in the past literature despite interesting structural features (that is, magnetic layers and triangular as well as kagomé-lattice features favoring frustrated magnetism) characterizing this compound. We report here the results of studies of magnetization, heat capacity and magnetoresistance in the temperature range T = 1.8–300 K. The results establish that there is a long-range magnetic order of antiferromagnetic type below (TN =) 18.5 K, despite a much larger value (~80 K) of paramagnetic Curie temperature with a positive sign characteristic of ferromagnetic interaction. We attribute this to geometric frustration. The most interesting finding is that there is an additional magnetic anomaly below ~55 K before the onset of long-range order in the magnetic susceptibility data. Concurrent with this observation, the sign of isothermal change in entropy, ΔS = S(0) − S(H), where H is the externally applied magnetic field, remains positive above TN, with a broad peak. This observation indicates the presence of ferromagnetic clusters before the onset of long-range magnetic order. Thus, this compound may serve as an example of a situation in which magnetic frustration due to geometrical reasons faces competition from such magnetic precursor effects. There is also a reversal of the sign of −ΔS in the curves for lower final fields (H < 30 kOe) on entering the magnetically ordered state consistent with the entrance to an antiferromagetic state. The magnetoresistance behavior is consistent with the above conclusions.

Charge ordering geometries in uniaxially strainedNbSe2

Recent STM experiments reveal niobium diselenide to support domains of striped (1Q) charge order side-by-side with its better-known triangular (3Q) phase, suggesting that small variations in local strain may induce a quantum phase transition between the two. We use a theoretical model of the charge order in NbSe$_2$, based on a strong momentum- and orbital-dependent electron-phonon coupling, to study the effect of uniaxial strain. We find that as little as $0.1\%$ anisotropic shift in phonon energies breaks the threefold symmetry in favor of a 1Q state, in agreement with the experimental results. The altered symmetries change the transition into the ordered state from weakly-first-order in the 3Q case, to second order in the 1Q regime. Modeling the pseudogap phase of NbSe$_2$ as the range of temperatures above the onset of long-range order in which phase coherence is destroyed by local phonon fluctuations, we find a shortening of the local ordering wavevector with increasing temperature, complementing recent X-ray diffraction observations within the low-temperature phase.

Unconventional magnetism in the spin-orbit-driven Mott insulatorsBa3MIr2O9(M=Sc,Y)

We have carried out detailed bulk and local probe studies on the hexagonal oxides Ba3MIr2O9 (M=Sc,Y) where Ir is expected to have a fractional oxidation state of +4.5. In the structure, Ir-Ir dimers are arranged in an edge shared triangular network parallel to the ab plane. Whereas only weak anomalies are evident in the susceptibility data, clearer anomalies are present in the heat capacity data. Our 45Sc nuclear magnetic resonance (NMR) lineshape (first order quadrupole split) is symmetric at room temperature but becomes progressively asymmetric with decreasing temperatures. This is suggestive of distortions in the structure which could arise from progressive tilt/rotation of the IrO6 octahedra with a decrease in temperature T. The 45Sc NMR spectral weight shifts near the reference frequency with decreasing T indicating the development of magnetic singlet regions. Around 10K, a significant change in the spectrum takes place with a large intensity appearing near the reference frequency but with the spectrum remaining multi-peak. It appears from our 45Sc NMR data that in Ba3ScIr2O9 significant disorder is still present below 10K. In the case of Ba3YIr2O9, the 89Y NMR spectral lines are asymmetric at high temperatures but become nearly symmetric (single magnetic environment) below T~70K. Our 89Y spectra and T1 measurements confirm the onset of long range ordering (LRO) from a bulk of the sample at 4K in this compound. Our results suggest that Ba3YIr2O9 might be structurally distorted at room temperature (via, for example, tilt/rotations of the IrO6 octahedra) but becomes progressively a regular triangular lattice with decreasing T. The effective magnetic moments and magnetic entropy changes are strongly reduced in Ba3YIr2O9 as compared to those expected for a S=1/2 system. Similar effects have been found in other iridates which naturally have strong spin-orbit coupling (SOC).

Manifestation of long-range ordered state in layered VX2 (X = Cl, Br, I) systems

We report the first-principles based density functional investigation of correlated magnetic behavior for the layered VX2 (X = Cl, Br, I) system both in bulk and monolayer forms. The bulk system stabilizes in the Néel 120° spin structure with the onset of long-range order at a very low temperature. However, a monolayer of the same system results in a two-dimensional long-range ordered spin-gel configuration in the a–b plane. The occurrence of this two-dimensional non-collinear long-range order for such hexagonal systems with honeycomb topology may provide an additional feature for controlling the use of such materials in magnetic memory devices.

Jamming Behavior of Domains in a Spiral Antiferromagnetic System

Using resonant magnetic x-ray photon correlation spectroscopy, we show that the domains of a spiral antiferromagnet enter a jammed state at the onset of long-range order. We find that the slow thermal fluctuations of the domain walls exhibit a compressed exponential relaxation with an exponent of 1.5 found in a wide variety of solidlike jammed systems and can be qualitatively explained in terms of stress release in a stressed network. As the temperature decreases, the energy barrier for fluctuations becomes large enough to arrest further domain wall fluctuations, and the domains freeze into a spatial configuration within 10K of the Néel temperature. The relaxation times can be fitted with the Vogel-Fulcher law as observed in polymers, glasses, and colloids, thereby indicating that the dynamics of domain walls in an ordered antiferromagnet exhibit some of the universal features associated with jamming behavior.

Transport, Magnetic, and Thermal Properties of La0.7Ca0.24Sr0.06MnO3Single Crystal

We report the transport, magnetic, and thermal properties of La0.7Ca0.24Sr0.06MnO3single crystal. It was prepared using floating zone technique used under oxygen pressure of 1 bar with a typical growth rate of 1 mm/hr. The resistivity data shows the metal to insulator transition (M-I) occuring atTMI=290 K along thec-axis and atTMI=280 K along theab-plane. It is observed that theTMIis higher along thec-axis as compared to that in theab-plane, thus indicating that more favorable hoping of electrons is along thec-axis. From bolometric application point of view, the temperature coefficient of resistance (TCR) is found to be ~28% K−1. Theac-susceptibility measurement shows that this material exhibits ferromagnetic to paramagnetic transition temperature (TC) 277 K. Sharp peak around this temperature in heat capacity data indicates the onset of long-range ordering. The entropy change associated with this transition is found to be 2.3 J/mol K.

Critical spin dynamics in the antiferromagnetLa4Ni3O8fromLa139nuclear magnetic resonance

We report $^{139}\mathrm{La}$ nuclear magnetic resonance data in ${\mathrm{La}}_{4}{\mathrm{Ni}}_{3}{\mathrm{O}}_{8}$ that reveal the presence of antiferromagnetic order below ${T}_{N}~105$ K. This remarkable compound contains two-dimensional (2D) layers of ${\mathrm{NiO}}_{2}$ with unusual Ni valences. ${\mathrm{La}}_{4}{\mathrm{Ni}}_{3}{\mathrm{O}}_{8}$, with antiferromagnetic order of $S=1/2 {\mathrm{Ni}}^{1+}$ spins, is analogous to the parent compounds of the cuprate superconductors. Our data clearly reveal dramatic spectral changes and low-energy antiferromagnetic correlations associated with the onset of long-range order below ${T}_{N}$. These critical spin fluctuations, however, do not diverge at the second-order phase transition but rather appear to be associated with a $T=0$ transition characteristic of 2D spin fluctuations.

Magnetoelasticity of Fe–Si single crystals

The tetragonal magnetostriction constant, (3/2)λ100, of Fe–Si single crystals was measured and was found to be structure dependent. Similar to that of Fe–Ge single crystals, (3/2)λ100 is positive in the single phase A2 regime, becomes negative in the single phase D03 regime, and changes from positive to negative between the two regimes. Short-range order in the A2 regime decreases the magnetostriction prior to the onset of long range order. In the single phase regions of both A2 and D03, thermal history does not show any obvious effect on the magnetostriction, contrary to that found for Fe–Ga alloys. However, in the regions of phase mixture involving A2, B2, and D03 phases, quenching pushes the change in magnetostriction from positive to negative to higher Si contents.

Ordering kinetics in bcc alloys with allowance for diffusion processes

The kinetics of inhomogeneous ordering in binary bcc substitution alloys of arbitrary stoichiometry is considered with the account for for diffusion processes. A system of kinetic equations describing the joint evolution of the occupancies of two sublattices of a bcc lattice is derived using a phenomenological approach. It is shown that, even within the mean-field approximation, this approach allows one to describe simultaneously the processes of establishment of the long-range order and diffusion of the alloy components. Numerical analysis of the obtained system of equations showed that quick onset of long-range order first occurs, which is followed by slow diffusion of the alloy components.

Kinetics of Polydomain Ordering at Second-Order Phase Transitions (by the Example of the AuCu3 Alloy)

Kinetics of polydomain spinodal ordering is studied in alloys of AuCu3 type. We introduce four non-conserved long-range order parameters whose sum, however, is conserved and, using the statistical approach, follow the temporal evolution of their random spatial distribution after a rapid temperature quench. A system of nonlinear differential equations for correlators of second and third order is derived. Asymptotical analysis of this system allows to investigate the scaling regime, which develops on the late stages of evolution and to extract additional information concerning the rate of decrease of the specific volume of disordered regions and the rate of decrease of the average thickness of antiphase boundaries. Comparison of these results to experimental data is given. The quench below the spinodal and the onset of long-range order may be separated by the incubation time, whose origin is different from that in first-order phase transitions. Numerical integration of equations for correlators shows also, that it is possible to prepare a sample in such a way that its further evolution will go with formation of transient kinetically slowed polydomain structures different from the final L12 structure.

Analysis of the conditions favoring the onset of long-range order in disordered relaxors of different types

The possibility of realizing a stable relaxor behavior in PbSc1/2Nb1/2O3 (PSN) compounds and the conditions favoring the formation of a phase with long-range order in PbZn1/3Nb2/3O3 (PZN) are studied using optical methods. It is found that the replacement of only 6% of Pb ions with Ba ions (PBSN-6) freezes the relaxor state in PSN compounds, while adding even 7% of PbTiO3 to the PZN relaxor (PZN-7PT) leads to the formation of a phase with long-range order and a phase transition occurring at Tmaxe through the percolation mechanism. Common features in the formation and destruction of the long-range order phase in relaxors of different types are revealed. The differences associated with the presence of spontaneously polarized ferroelectric regions in the cubic nonpolar matrix of PSN-type compounds are determined.

57Fe Mössbauer studies of amorphous Pd40(NiFe)40P20 alloys

Zero-field 57Fe Mossbauer spectroscopy has been used to study the magnetic properties of an amorphous melt-spun Pd40Ni40−x FexP20 (x=5, 10, 17.5, 20) series. The alloys show quadrupole split doublets at room temperature indicating paramagnetic behaviour. At low temperatures the Mossbauer spectra are sextets due to the onset of long range order. The transition temperatures increase with Fe concentration from 12±2 K for Pd40Ni35Fe5P20 to 42.0±2.0 K for Pd40Ni20Fe20P20. The hyperfine field was found to follow Hf(0)(1−T/Tc)β over the critical region with the β exponent being close to 0.4.

Noise, coherent fluctuations, and the onset of order in an oscillated granular fluid.

We study fluctuations in a vertically oscillated layer of grains below the critical acceleration for the onset of ordered standing waves. As onset is approached, transient disordered waves with a characteristic length scale emerge and increase in power and coherence. The scaling behavior and the shift in the onset of order agrees with the Swift-Hohenberg theory for convection in fluids. However, the noise in the granular system is an order of magnitude larger than the thermal noise in the most sensitive convecting fluid experiments to date; the effect of the granular noise is observable 20% below the onset of order.

Spin liquid and spin ice under high pressure: a neutron study ofR2Ti2O7 (R = Tb,Ho)

The rare earth titanates show unusual types of short range magnetic order, known as spinliquid and spin ice states, which arise from the geometrical frustration of the pyrochlorelattice. We have investigated the effect of applied pressures on these magneticstates by means of powder neutron diffraction, up to 8 GPa. In the spin liquidTb2Ti2O7, pressureinduces a long range antiferromagnetic order, coexisting with the spin liquid state below the Néel temperature(TN = 2.1 K). The onset of long range order coincides with a strong decrease of the diffuse intensity,due to a gradual transfer from the liquid to the ordered state as the temperaturedecreases. The short range correlations are also modified under pressure, even aboveTN. Incontrast, in Ho2Ti2O7 the spin ice state remains stable under pressure, as was checked up to 6 GPa, and down to1.4 K. The short range correlations are unaffected here. The possible origins of thisbehaviour are discussed.

Low-temperature specific heat of the molecule-based magnet M[N(CN)2]2 (M=Co, Ni, Cu, Zn) series

We report the specific heat as a function of temperature in zero applied magnetic field for three magnetic systems (α-Co[N(CN)2]2, β-Co[N(CN)2]2, Ni[N(CN)2]2) and two nonmagnetic systems (Cu[N(CN)2]2, Zn[N(CN)2]2). The anomalies revealed by the magnetic contribution to the specific heat are associated with the onset of long-range order. The transition entropies imply that the magnetic ordering originates from a ground-state doublet (J=12) for the Co2+ systems and a ground-state triplet (J=1) for the Ni2+ system. In addition, we extract and compare the exchange couplings J using several theoretical models: interacting spin waves, high-temperature series expansions, total magnetic energy and mean field. The J-values and the Ising-like anisotropy obtained here, are in quantitative agreement with earlier magnetization and neutron diffraction results. The comparison of the zero-field and in-field (8T) specific heat of the Cu2+ system (J=12) demonstrates the previously unknown ferromagnetic order at very low temperature (⩽1.7K).

Site correlation and the determination of interactions between atoms situated on a 2-d triangular lattice

Site correlations are very sensitive to atomic interactions, especially for weak interactions far from the onset of long-range order. Therefore, they are especially suited for the determination of atomic interactions from STM measurements. In this paper, site correlations are given for dominant repulsive interaction between nearest and arbitrary (repulsive or attractive) interactions between next-nearest neighbors on a 2-d triangular lattice. This scheme simulates a fcc(111) or hexagonal (0001) surface: adatoms in atop sites, constituents of a substitutional alloy segregating or atoms forming a surface alloy there. Interactions considered are limited: J, the interaction between nearest neighbors, to | J/ kT|<1 and R, the ratio of next-nearest to nearest neighbor interactions, to | R|<1. Based on a Monte-Carlo calculation, graphs are given for various fixed surface concentrations ranging from 0.15 to 0.50, displaying J/ kT and R as functions of the correlations between nearest and next nearest neighbors, p nn/ c and p nnn/ c. The graphs shown are normalized so as to permit a simple interpolation between them.