Polarization-flip transition under electric field in BCCD

Three-axes elastic neutron scattering measurements demonstrate that the five-fold modulated phase (phase 1/5) of BCCD exhibits under electric field a phase transition without change of superlattice periodicity. Through the monitoring of high-order satellite diffraction peaks as a function of electric field and temperature, the competition between this phase and neighboring polar phases with other periods has been characterized. At a threshold electric field of about 20 kV/cm, a rather abrupt redistribution of the satellite intensities of phase 1/5 is observed, without change of the corresponding primary modulation wave vector ( ⅕). A quantitative analysis of these intensity variations confirms the earlier conjecture based on dielectric experiments that the modulation essentially changes from a non-polar sequence 5up5down ( <5>) of polarized z-perpendicular layers of basic semicells, to a polar sequence 6up4down ( <64>). The transition is caused by the flip of the average polarization of one of the interface layers, and can then be described as a bounded discrete motion of the wall separating positive and negative microdomains within the five-fold unit cell. This type of polarization-flip phase transition had been detected and characterized in one-dimensional theoretical models as generalized Frenkel-Kontorova models or spin chains with elastic couplings, but had not been anticipated in theoretical analyses of BCCD, for which other phenomenological or microscopic models (as the ANNNI model) have been considered adequate. Only recently and in view of the experimental results reported here, we demonstrated, using a general phenomenological displacive model, the possibility of this type of transition in systems as BCCD [Phys. Rev. B 62, 11418 (2000)]. Phase diagrams with spin-flip phase transitions yield very peculiar phase diagrams with a checkerboard topological structure and self-similar features. In particular, they may present special critical points as the so-called upsilon points [J. Statistical Phys. 62, 45 (1991)]. BCCD may be then the first experimental system where they could be observed. Received 20 September 2001     

Exact ground state of a spin ladder with a quantum phase transition

We introduce a spin ladder with Ising interactions along the legs and intrinsically frustrated Heisenberg-like ferromagnetic interactions on the rungs. The model is solved exactly in the subspaces relevant for the ground state by mapping to the quantum Ising model, and we show that a first order quantum phase transition separates the classical from quantum regime, with the spin correlations on the rungs being either ferromagnetic or antiferromagnetic, and different spin excitations in both regimes. The present case resembles the quantum phase transition found in the compass model in one and two dimensions.     

Electron coherent and incoherent pairing instabilities in inhomogeneous bipartite and nonbipartite nanoclusters

Exact calculations of collective excitations and charge/spin (pseudo) gaps in an ensemble of bipartite and nonbipartite clusters yield level crossing degeneracies, spin-charge separation, condensation and recombination of electron charge and spin driven by interaction strength, inter-site couplings and temperature. Near crossing degeneracies, the electron configurations of the lowest energies control the physics of electronic pairing, phase separation and magnetic transitions. Rigorous conditions are found for the smooth and dramatic phase transitions with competing stable and unstable inhomogeneities. Condensation of electron charge and spin degrees at various temperatures offers a new mechanism of pairing and a possible route to superconductivity in inhomogeneous systems, different from the BCS scenario. Small bipartite and frustrated clusters exhibit charge and spin inhomogeneities in many respects typical for nano and heterostructured materials. The calculated phase diagrams in various geometries may be linked to atomic scale experiments in high Tc cuprates, manganites and other concentrated transition metal oxides.     

Model glasses coupled to two different heat baths

In a p-spin interaction spherical spin-glass model both the spins and the couplings are allowed to change with time. The spins are coupled to a heat bath with temperature T, while the coupling constants are coupled to a bath having temperature T_J. In an adiabatic limit (where relaxation time of the couplings is much larger that of the spins) we construct a generalized two-temperature thermodynamics. It involves entropies of the spins and the coupling constants. The application for spin-glass systems leads to a standard replica theory with a non-vanishing number of replicas, n=T/T _J . For p>2 there occur at low temperatures two different glassy phases, depending on the value of n. The obtained first-order transitions have positive latent heat, and positive discontinuity of the total entropy. This is an essentially non-equilibrium effect. The dynamical phase transition exists only for n<1. For p=2 correlation of the disorder (leading to a non-zero n) removes the known marginal stability of the spin glass phase. If the observation time is very large there occurs no finite-temperature spin glass phase. In this case there are analogies with the non-equilibrium (aging) dynamics. A generalized fluctuation-dissipation relation is derived. Received 12 July 1999 and Received in final form 8 December 1999     

Spinons in a crossed-chains model of a 2D spin liquid

Using the random phase approximation, we show that a crossed-chains model of spin-1/2 Heisenberg chains with frustrated interchain couplings has a nondimerized spin-liquid ground state in 2D, with deconfined spinons as the elementary excitations. The results are confirmed by a bosonization study, which shows that the system is an example of a "sliding Luttinger liquid." In an external field, the system develops an incommensurate field-induced long-range order with a finite transition temperature.     

The Ising model on random lattices in arbitrary dimensions

We study analytically the Ising model coupled to random lattices in dimension three and higher. The family of random lattices we use is generated by the large N limit of a colored tensor model generalizing the two-matrix model for Ising spins on random surfaces. We show that, in the continuum limit, the spin system does not exhibit a phase transition at finite temperature, in agreement with numerical investigations. Furthermore we outline a general method to study critical behavior in colored tensor models.     

Layered Ising models on triangular and honeycomb lattices

We study inhomogeneous Ising models on triangular and honeycomb lattices. The nearest neighbour couplings can have arbitrary strength and sign such that the coupling distribution is translationally invariant in the direction of one lattice axis, i.e. the models have a layered structure. By using a transfer matrix method we derive closed form expressions for the partition functions and free energies. The critical temperatures are calculated. Phase transitions at a finite critical temperature are universally of Ising type. Models with no phase transition may show different behaviour atT=0, which is explicitly shown for fully frustrated models on square, triangular and honeycomb lattices. Finally, generalizations to layered Ising models on more general lattices are discussed.Work performed within the research program of the Sonderforschungsbereich 125 Aachen-Jülich-Köln     

On the bethe approximation for the random bond Ising model

A random bond Ising model is considered in terms of the pair approximation, which is equivalent to the Bethe approximation, of the cluster variation method. On taking the configurational average over the random distribution of bonds ±J, we take into account the nearest neighbor correlations between effective fields and bonds. We investigate their effects to the phase transition temperature from the paramagnetic phase to the ferro- (or antiferro-) magnetic phase and to the spin glass phase for the Ising model on the square lattice. It turns out that the correlation effects act favorably to the spin glass phase and bend upward the line of transition temperature from the paramagnetic phase to the spin glass phase as the concentration being apart from 0.5. In the appendix, we derive the expression of free energy in the weak interaction limit.     

Spin glass behavior upon diluting frustrated magnets and spin liquids: a Bethe-Peierls treatment

A Bethe-Peierls treatment to dilution in frustrated magnets and spin liquids is given. A spin glass phase is present at low temperatures and close to the percolation point as soon as frustration takes a finite value in the dilute magnet model; the spin glass phase is reentrant inside the ferromagnetic phase. An extension of the model is given, in which the spin glass/ferromagnet phase boundary is shown not to reenter inside the ferromagnetic phase asymptotically close to the tricritical point whereas it has a turning point at lower temperatures. We conjecture similar phase diagrams to exist in finite dimensional models not constraint by a Nishimori's line. We increase frustration to study the effect of dilution in a spin liquid state. This provides a “minimal” ordering by disorder from an Ising paramagnet to an Ising spin glass. Received 9 April 1999 and Received in final form 27 September 1999     

Pressure-induced structural phase transition in ReO3

We have investigated the pressure-induced structural phase transition in ReO₃ by neutron diffraction on a single crystal. We collected neutron diffraction intensities from the ambient and high pressure phases at P=7 kbar and refined the crystal structures. We have determined the stability of the high pressure phase as a function temperature down to T=2 K and have constructed the (P-T) phase diagram. The critical pressure is P_c=5.2 kbar at T=300 K and decreases almost linearly with decreasing temperature to become P_c=2.5 kbar at T=50 K. The phase transition is driven by the softening of the M₃ phonon mode. The high pressure phase is formed by the rigid rotation of almost undistorted ReO₆ octahedra and the Re-O-Re angle deviates from 180°. We do not see any evidence for the existence of the tetragonal (P4/mbm) intermediate pressure phase reported earlier.     

Fermionic Ising glasses with BCS pairing interaction. Tricritical behaviour

We have examined the role of the BCS pairing mechanism in the formation of the magnetic moment and henceforth a spin glass (SG) phase by studying a fermionic Sherrington-Kirkpatrick model with a local BCS coupling between the fermions. This model is obtained by using perturbation theory to trace out the conduction electrons degrees of freedom in conventional superconducting alloys. The model is formulated in the path integral formalism where the spin operators are represented by bilinear combinations of Grassmann fields and it reduces to a single site problem that can be solved within the static approximation with a replica symmetric ansatz. We argue that this is a valid procedure for values of temperature above the de Almeida-Thouless instability line. The phase diagram in the T-g plane, where g is the strength of the pairing interaction, for fixed variance J ² /N of the random couplings J_ij, exhibits three regions: a normal paramagnetic (NP) phase, a spin glass (SG) phase and a pairing (PAIR) phase where there is formation of local pairs.The NP and PAIR phases are separated by a second order transition line g=g _c (T) that ends at a tricritical point T ₃ =0.9807J, g ₃ =5,8843J, from where it becomes a first order transition line that meets the line of second order transitions at T _c =0.9570J that separates the NP and the SG phases. For T<T _c the SG phase is separated from the PAIR phase by a line of first order transitions. These results agree qualitatively with experimental data in . Received 14 May 1998     

Frustration signatures in the anisotropic model of a nine-spin <Emphasis Type="Italic">s</Emphasis> = 3/2 ring with bond defect

Effects of magnetic frustration in the model of nine-membered antiferromagnetic s = 3/2 molecular spin ring are investigated. We use a Heisenberg spin model with nearest-neighbor interactions, single-ion anisotropy and with tunable bond defect leading to continuously varying topology: from closed to open ring. In order to identify a frustrated phase we calculate the full energy spectrum of the model and a number of thermodynamic quantities at low temperature. The calculations are performed by means of numerically exact methods: quantum transfer matrix and exact diagonalization. It is shown that total and local magnetizations, nearest-neighbor spin correlations and spin fluctuations can serve as consistent frustration signatures. Magnetizations and spin-spin correlations are reduced in the frustrated phase whereas fluctuations and correlations of fluctuations increase. The ground state in a frustrated phase is a m = 1/2 doublet and in the non-frustrated phase a m = 3/2 doublet. In the system studied bipartiteness is not opposite to frustration as there are regions in the parameter space for which the system is neither bipartite nor frustrated.     

Models of superfrustration

Earlier studies of the triangular lattice antiferromagnet and the fully frustrated model on the square lattice proved that in these models the pair correlation 〈S ₀ S _r 〉 decreases asymptotically asr ^?1/2 at zero temperature. In the present paper the existence of two and higher dimensional models is shown in which the frustration is so strong that it destroys the phase transition even atT=0: the correlation length remains finite. The influence of this “superfrustration” on the free energy and on the ground state properties is also discussed.     

Magnetic structure of geometrically frustrated compound Co2Cl(OH)3 determined by proton NMR

The magnetic structure of a geometrically frustrated system Co₂Cl(OH)₃ is determined by comparing the observed proton NMR spectrum with numerical calculations based on various magnetic models. The best fit is obtained with a model that the magnetic moments of Co²⁺ ions in the triangular plane are parallel to the principal axis of local crystal field and those of Co²⁺ ions in the kagome lattice plane are randomly disordered in the a-b plane, which nearly bisects the angle between the principal axis of the local field and a line pointing towards the body center of the tetrahedron. The coexistence of the ferromagnetic order in the triangular plane and the random disorder in the kagome plane is consistent with the results of measurements by Zheng et al. However, the magnetic moments of Co²⁺ ions are not directed towards the body center of the tetrahedron as characteristic in the “spin ice” magnetic structure. Furthermore, the Co²⁺ ions in the triangular plane have a smaller magnitude of magnetic moment than those in the kagome plane. Thus, our result suggests that the transition metal compound Co₂Cl(OH)₃ is different from the “spin ice” in magnetic structure, although it is similar to rare-earth pyrochlores in crystal structure.     

Inhomogeneous Ising models with diagonal structure on a square lattice

We study inhomogeneous Ising models on a square lattice. The nearest neighbour couplings are allowed to be of arbitrary strength and sign such that the coupling distribution is translationally invariant in diagonal direction. We calculate the partition function and free energy for a random coupling distribution of finite period. The phase transition is universally of Ising type. The transition temperature is independent of specific details of the coupling distribution. In particular, unexpected results for the absence of a phase transition are derived. Special examples are considered in detail, phase diagrams and critical temperature are determined. We calculate ground state energy and ground state degeneracy or, equivalently, rest entropy for “pure” frustration models, i.e. models with couplings of fixed strength but arbitrary sign, which never show a phase transition at a finite temperature.     

The Berezinskii-Kosterlitz-Thouless transition and correlations in the XY kagomé antiferromagnet

The problem of the Berezinskii-Kosterlitz-Thouless transition in the highly frustrated XY kagomé antiferromagnet is solved. The transition temperature is found. It is shown that the spin correlation function exponentially decays with distance even in the low-temperature phase, in contrast to the order parameter correlation function, which decays algebraically with distance.     

Magnetoelastic coupling and symmetry breaking in the frustrated antiferromagnet alpha-NaMnO2

The magnetic and crystal structures of the alpha-NaMnO2 have been determined by high-resolution neutron powder diffraction. The system maps out a frustrated triangular spin lattice with anisotropic interactions that displays two-dimensional spin correlations below 200 K. Magnetic frustration is lifted through magneto-elastic coupling, evidenced by strong anisotropic broadening of the diffraction profiles at high temperature and ultimately by a structural phase transition at 45 K. In this low-temperature regime a three-dimensional antiferromagnetic state is observed with a propagation vector k=(1/2,1/2,0).     

Statics and kinetics at the nematic-isotropic interface in porous media

We extend the random anisotropy nematic spin model to study nematic-isotropic transitions in porous media. A complete phase diagram is obtained. In the limit of relative low randomness the existence of a triple point is predicted. For relatively large randomness we have found a depression in temperature at the transition, together with a first order transition which ends at a tricritical point, beyond which the transition becomes continuous. We use this model to investigate the motion of the nematic-isotropic interface. We assume the system to be isothermal and initially quenched into the metastable régime of the isotropic phase. Using an appropriate form of the free energy density we obtain the domain wall solutions of the time-dependent Ginzburg-Landau equation. We find that including a random field leads to smaller velocity of the interface and to larger interface width. Received 12 November 1998 and Received in final form 15 March 1999     

Decay of the remanent magnetization in the asymmetric spin chain

The dynamics of the one-dimensional spin glass with asymmetric interactions between neighboring spins is considered. We confine ourselves to discrete couplings with values ±J. We show that the algebraic decay of the remanent magnetization of the infinite ±J-spin chain at zero temperature is only valid for symmetric couplings. Our analytical investigations as well as computer simulations show stretched exponential decay for any finite concentration of antisymmetric bonds. Thus, the asymmetric ±J-spin chain shows an asymmetry-induced phase transition at zero temperature.     

Muon spin relaxation investigation of frustrated antiferromagnetic pyrochlores A2B2O7

In a system where magnetic ions occupy the vertices of edge or corner sharing triangular units, the natural antiferromagnetic coupling between ions is geometrically frustrated. A wide variety of interesting magnetic behaviour has been observed in pyrochlores, where magnetic ions form a network of corner sharing tetrahedra. The low temperature spin dynamics of a number of pyrochlores A₂B₂O₇ have been investigated using the technique of μ SR. For example, Y₂Mo₂O₇ shows a transition to a disordered magnetic state similar to a spin glass at T_F=22 K. However, unlike conventional metallic spin glasses, a non‐zero muon spin depolarization rate is observed to persist well below 0.1\ T_F. These results suggest that there is a finite density of states for magnetic excitations in this system near zero energy. This revised version was published online in July 2006 with corrections to the Cover Date.