A renormalization-group study of an Ising spin-glass with annealed vacancies

Systems driven and characterized by fluctuations in density and magnetization can be realistically modeled using the Blume–Emery–Griffiths model; a spin-1 Ising model with bilinear, biquadratic, and crystal-field interactions. In this study, renormalization-group techniques are used on an exactly solvable system in which frustration is present due to competing ferromagnetic and antiferromagnetic interactions. Thus, this calculation models a spin-glass system with annealed vacancies. To determine the effects of these competing bilinear interactions, an exactly solvable frustrated hierarchical model has been constructed, similar to those introduced to study spin glasses [S.R. McKay, A.N. Berker, S. Kirkpatrick, Phys. Rev. Lett. 48 (1982) 767]. Phase diagrams have been calculated for a series of planes of constant biquadratic coupling while varying the temperature and concentration of annealed vacancies in the system. In addition, a phase diagram was produced for constant concentration of annealed vacancies as the biquadratic coupling (i.e. clustering bias) was varied. Each phase diagram reveals three qualitatively unique basins of attraction, each corresponding to a phase distinguished by a unique renormalization-group trajectory. The sink of each trajectory is interpreted to determine the nature of each phase: dense paramagnetic, dilute paramagnetic and spin-glass.     

On evaluation of transverse spin fluctuations in quantum magnets

A numerical method is described for evaluating transverse spin correlations in the random phase approximation. Quantum spin-fluctuation corrections to sublattice magnetization are evaluated for the antiferromagnetic ground state of the half-filled Hubbard model in two and three dimensions in the whole U/t range. Extension to the case of defects in the AF is also discussed for spin vacancies and low-U impurities. In the limit, the vacancy-induced enhancement in the spin fluctuation correction is obtained for the spin-vacancy problem in two dimensions, for vacancy concentration up to the percolation threshold. For low-U impurities, the overall spin fluctuation correction is found to be strongly suppressed, although surprisingly spin fluctuations are locally enhanced at the low-U sites. Received 27 April 1998 and Received in final form 13 August 1998     

Magnetism of Rare-Earth Compounds with Non-Magnetic Crystal-Field Ground Levels

Among rare-earth compounds, there are many materials having non-magnetic crystal-field （CF） ground levels. To understand their magnetic behaviour at low temperatures, we study the effects of the CF levels and the Heisenberg-like coupling on the magnetic process of such a crystalline with mean-field and CF theory. It is found that the material can be magnetically ordered if the Heisenberg exchange is sufficiently strong. Additionally we obtain a condition for initial magnetic ordering, and derive a formula for estimating the Curie temperature if the ordering occurs.     

A renormalization-group analysis of a spin-1 Ising ferromagnet with competing crystal-field and repulsive biquadratic interactions

Phase diagrams have been produced and critical exponents calculated for a Blume-Emery-Griffiths system with competing biquadratic and crystal-field interactions with uniform ferromagnetic bilinear interactions. This competition directly effects the clustering and density of nonmagnetic impurities. These results have been produced using renormalization-group methods with a hierarchical lattice. A series of planes of constant, repulsive biquadratic coupling have been probed while varying the temperature and concentration of annealed vacancies in the system. The sinks have been analyzed and interpreted, and critical exponents calculated for the higher order transitions.     

First principle study of the cation vacancy in anatase TiO2

Based on first principle FP‐LAPW calculations, we have studied the electronic and magnetic properties of anatase TiO₂ with Ti cation vacancy. We find that the Ti cation vacancy defect can induce a magnetic moment of about 4μ_B/supercell. The magnetic moment mainly comes from p‐orbitals of O atoms which surround the Ti vacancy. We also find that the two Ti vacancies in anatase always coupled ferromagnetically. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Oxygen vacancy induced ferromagnetism in rutile TiO2–x

First‐principles LDA + U calculations have been performed to study the effects of oxygen vacancies (V_O) on the electronic structure and magnetism in undoped rutile TiO_2–x . Instead of treated as an adjustive parameter, the value of U was determined by constrained‐density‐functional calculations. The calculated electronic structure reveals that the valence electrons released by V_O would occupy mainly the neighboring Ti:3d orbital which then becomes spin‐polarized due to intra‐atomic exchange interaction, thereby giving rise to the half‐metallic ferromagnetism. The magnetization induced by V_O in rutile TiO_2–x is almost proportional to the V_O concentration (x) for x > 0.0625, and becomes 0 for x ≤ 0.0417. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effects of topological defects and local curvature on the electronic properties of planar graphene

A formalism is proposed to study the electronic and transport properties of graphene sheets with corrugations as the one recently synthesized. The formalism is based on coupling the Dirac equation that models the low energy electronic excitations of clean flat graphene samples to a curved space. A cosmic string analogy allows to treat an arbitrary number of topological defects located at arbitrary positions on the graphene plane. The usual defects that will always be present in any graphene sample as pentagon–heptagon pairs and Stone–Wales defects are studied as an example. The local density of states around the defects acquires characteristic modulations that could be observed in scanning tunnel and transmission electron microscopy.     

Effect of the transverse field on the site-diluted Ising model in a longitudinal random field

Phase diagrams and magnetization curves of a diluted spin-3/2 transverse Ising model in a random field on honeycomb lattices are investigated by the use of an effective-field theory with correlations. The tricritical point is found in the system, in contrast to the corresponding spin-1/2 Ising counterpart. The possible reentrant phenomena displayed by the system due to the competition effects that occur for appropriate ranges of the random and transverse fields are investigated.     

Exact results of a mixed spin-1/2 and spin-1 Ising chain with both longitude and transverse single-ion anisotropies

The mixed spin-1/2 and spin-1 Ising chain with both longitude and transverse single-ion anisotropies Dz and Dx is solved exactly by means of a mapping to the spin-1/2 Ising chain with the alternating transverse fields and the Jordan-Wigner transformation. The analytical expressions of the quasi-particles' spectra Λk, the minimal energy gap Δ₀ for exciting a fermion quasi-particle, the minimal energy gap Δh for exciting a hole, and the ground state energy are obtained. The phase diagram of the ground state is also given. The results show that when Dz?0 for any finite value of Dx, there is no quantum critical point and the ground state is always in a spin ordered phase disregard of the boundary condition in the present system.     

Gauge vortices on a square lattice

The effective interaction between gauge vortices on a square lattice is revealed to be attractive at short distance and oscillate between repulsion and attraction at long distance. It is analyzed that the strong attraction at short distance makes the gauge vortices cluster at a given flux concentration; while the oscillatory nature in the interaction potential is the consequence of the existence of the electron Fermi surface in the nonuniform flux phases states.     

Specific heat and magnetic ordering of NdNi2B2C

In this work, the specific heat of NdNi₂B₂C was computed with the three sets of crystal-field parameters proposed by previous authors. All curves of the heat capacity plotted with the calculated results exhibit sharp peaks around the magnetic transition temperature TN as experimentally observed. To understand the mechanism of its magnetic ordering, we also calculated the magnetization of the material in low temperature region with the ground crystal-field (CF) level, the two lowest CF levels, and the full CF levels of J=9/2 multiplet respectively for comparison. Using the two eigenstates of the ground CF level, we derived a formula for 〈Jx〉 with mean-field approach for theoretical analysis. Both our numeric and theoretical results suggest that the two lowest CF levels play dominant roles in the magnetic process of the material below TN. It is also very interesting to notice that the ground CF level itself results in a larger TN, but the inclusion of the first excited CF doublet in calculations instead hinders the magnetic ordering, leading to a weakly reduced transition temperature.     

Magnetoelastic instability in Ising-like models

The magnetoelastic instability in nanostructured ring-shaped Ising-like spin 1/2 model has been investigated by using the exact diagonalization method. It is found that there exists two critical anisotropy parameters and () in the phase diagram. As the anisotropy parameter , the magnetoelastic transition from dimerized phase to uniform phase is a first order transition with an increase of the lattice spring constant. While for , the transition is continuous. Another critical value divides the different lattice distortion behavior as the anisotropy is strengthened.     

Thermodynamics of the anisotropic spin-1/2 Heisenberg chain and related quantum chains

The free energy and correlation lengths of the spin-1/2XYZ chain are studied at finite temperature. We use the quantum transfer matrix approach and derive non-linear integral equations for all eigenvalues. Analytic results are presented for the low-temperature asymptotics, in particular for the criticalXXZ chain in an external magnetic field. These results are compared to predictions by conformal field theory. The integral equations are solved numerically for the non-criticalXXZ chain and the related spin-1 biquadratic chain at arbitrary temperature.Work performed within the research program of the Sonderforschungsbereich 341, Köln-Aachen-Jülich     

Magnetic properties of a mixed spin- 1/2 and spin- 3/2 transverse Ising model in a longitudinal magnetic field

The mixed spin- 1/2 and spin- 3/2 transverse Ising model in a longitudinal magnetic field is studied within the framework of the effective-field theory with correlations. In this approach the effective-field equations are derived by using a probability distribution method based on the generalized but approximated van der Waerden identities. The total longitudinal and transverse magnetizations, the transverse susceptibility and longitudinal susceptibility and the critical temperatures are obtained. We find a number of interesting phenomena in these quantities, due to the applied transverse field and the longitudinal field.     

Spin current in quantum XXZ spin chain

The spin current in the one-dimensional quantum XXZ spin chain is studied based on the exact solutions. It is found that the spin voltage controlled by the unparallel boundary magnetic fields can induce the pure longitudinal spin current in the system. By using Wiener–Hopf and generalized algebraic Bethe ansatz methods, the analytic expressions for the spin current and the spin conductance are obtained. The spin current is proportional to the inverse of the length of the spin chain. The magnitude of spin current can be manipulated by the strength and the twist angle of two boundary magnetic fields. The exact analysis also shows that there exist an Ohm law or London equation type relation between the spin current and the spin conductance.     

Ground-state phases and quantum phase transitions in a two-dimensional spin-1/2 XY model with four-spin interactions

We discuss the ground state phase transition between an antiferromagnet and a valence-bond solid in a two-dimensional spin-1/2 XY model with a four-spin interaction. This transition has been proposed as a candidate for a deconfined quantum-critical point. We analyze quantum Monte Carlo data in order to accurately characterize the transition. The central question that remains to be answered is whether the transition really is continuous, or whether it is actually weakly first-order. We present the current status of both ground state and finite-temperature calculations. Based on the results, we discuss possible scenarios for the transition, none of which is consistent with deconfined quantum-criticality. However, we argue that a deconfined quantum-critical point may be located nearby in an extended parameter space.We also discuss the staggered Ising phase obtaining in the limit of strong four-spin coupling.     

Effect of magnon-phonon interaction on phonon damping of two-dimensional Heisenberg ferromagnetic system at finite temperature

A magnon-phonon interaction model is developed on the basis of a two-dimensional square Heisenberg ferromagnetic system. By using Matsubara Green function theory we studied the transverse and longitudinal acoustic phonon dampings and calculated the transverse and longitudinal acoustic phonon damping curves on the main symmetric point and line in the first Brillouin zone. It is found that on the line Δ there is no damping for transverse acoustic phonon and on the line Z there is no damping for longitudinal acoustic phonon. In the first Brillouin zone the damping of transverse acoustic phonons is at least one order larger than that of longitudinal acoustic phonons. The influences of various parameters on transverse and longitudinal acoustic phonon dampings are discussed and the lifetime and the density of state of transverse and longitudinal acoustic phonons are explored as well according to the relation of the phonon damping and its lifetime and the relation of the phonon damping and its density of state.     

Theoretical estimates for proton-NMR spin–lattice relaxation rates of heterometallic spin rings

Heterometallic molecular chromium wheels are fascinating new magnetic materials. We reexamine the available experimental susceptibility data on MCr₇ wheels in terms of a simple isotropic Heisenberg Hamiltonian for M=Fe, Ni, Cu, and Zn and find in that FeCr₇ needs to be described with an iron–chromium exchange that is different from all other cases. In a second step we model the behavior of the proton spin lattice relaxation rate as a function of applied magnetic field for low temperatures as it is measured in nuclear magnetic resonance (NMR) experiments. It appears that CuCr₇ and NiCr₇ show an unexpectedly reduced relaxation rate at certain level crossings.     

Dynamics of the one-dimensional random transverse Ising model with next-nearest-neighbor interactions

The dynamics of the one-dimensional random transverse Ising model with both nearest-neighbor (NN) and next-nearest-neighbor (NNN) interactions is studied in the high-temperature limit by the method of recurrence relations. Both the time-dependent transverse correlation function and the corresponding spectral density are calculated for two typical disordered states. We find that for the case of bimodal disorder the dynamics of the system undergoes a crossover from a collective-mode behavior to a central-peak one and for the case of Gaussian disorder the dynamics is complex. For both cases, it is found that the central-peak behavior becomes more obvious and the collective-mode behavior becomes weaker as K_i increase, especially when K_i>J_i/2 (J_i and K_i are the exchange couplings of the NN and NNN interactions, respectively). However, the effects are small when the NNN interactions are weak (K_i<J_i/2).     

Ground-state properties of a supersolid in RPA

We investigate the newly discovered supersolid phase by solving in random-phase approximation the anisotropic Heisenberg model of the hard-core boson ⁴He lattice at zero temperature. We include nearest and next-nearest neighbor interactions and calculate exactly all pair correlation functions in a cumulant decoupling scheme. We demonstrate the importance of vacancies and interstitials in the formation of the supersolid phase. The supersolid phase is characterised by strong quantum fluctuations which are taken into account rigorously. Furthermore we confirm that the superfluid to supersolid transition is triggered by a collapsing roton minimum however is stable against spontaneously induced superflow, i.e. vortex creation.