Zero Temperature Phases of the Frustrated <Emphasis Type="Italic">J</Emphasis><Subscript>1</Subscript>–<Emphasis Type="Italic">J</Emphasis><Subscript>2</Subscript> Antiferromagnetic Spin-1/2 Heisenberg Model on a Simple Cubic Lattice

At zero temperature magnetic phases of the quantum spin-1/2 Heisenberg antiferromagnet on a simple cubic lattice with competing first and second neighbor exchanges (J ₁ and J ₂) is investigated using the non-linear spin wave theory. We find existence of two phases: a two sublattice Néel phase for small J ₂ (AF), and a collinear antiferromagnetic phase at large J ₂ (CAF). We obtain the sublattice magnetizations and ground state energies for the two phases and find that there exists a first order phase transition from the AF-phase to the CAF-phase at the critical transition point, p _c =0.56 or J ₂/J ₁=0.28. We also show that the quartic 1/S corrections due spin-wave interactions enhance the sublattice magnetization in both the phases which causes the intermediate paramagnetic phase predicted from linear spin wave theory to disappear.     

Magnetic properties of undoped YBa 2 Cu 3 O 6 + x system

In the present paper, we study the magnetic properties of bilayer cuprate antiferromagnets. In order to evaluate the expressions for spin-wave dispersion, sublattice magnetization, Néel temperature and the magnetic contribution to the specific heat, the double time Green's function technique has been employed in the random phase approximation (RPA). The spin wave dispersion curve for a bilayer antiferromagnetic system is found to consist of one acoustic and one optic branch. The “optical magnon gap” has been attributed solely to the intra-bilayer exchange coupling (J _⊥ ) as its magnitude does not change significantly with the inter-bilayer exchange coupling (J_z). However J_z is essential to obtain the acoustic mode contribution to the magnetization. The numerical calculations show that the Néel temperature (T _N ) of the bilayer antiferromagnetic system increases with the J_z and a small change in J_z gives rise to a large change in the Néel temperature of the system. The magnetic specific heat of the system follows a T² behaviour but in the presence of J_z it varies faster than T². Received 13 July 2000 and Received in final form 14 May 2001     

Coupled Cluster Method Calculations of Quantum Magnets with Spins of General Spin Quantum Number

We present a new high-order coupled cluster method (CCM) formalism for the ground states of lattice quantum spin systems for general spin quantum number, s. This new general-s formalism is found to be highly suitable for a computational implementation, and the technical details of this implementation are given. To illustrate our new formalism we perform high-order CCM calculations for the one-dimensional spin-half and spin-one antiferromagnetic XXZ models and for the one-dimensional spin-half/spin-one ferrimagnetic XXZ model. The results for the ground-state properties of the isotropic points of these systems are seen to be in excellent quantitative agreement with exact results for the special case of the spin-half antiferromagnet and results of density matrix renormalization group (DMRG) calculations for the other systems. Extrapolated CCM results for the sublattice magnetization of the spin-half antiferromagnet closely follow the exact Bethe Ansatz solution, which contains an infinite-order phase transition at =1. By contrast, extrapolated CCM results for the sublattice magnetization of the spin-one antiferromagnet using this same scheme are seen to go to zero at 1.2, which is in excellent agreement with the value for the onset of the Haldane phase for this model. Results for sublattice magnetizations of the ferrimagnet for both the spin-half and spin-one spins are non-zero and finite across a wide range of , up to and including the Heisenberg point at =1.     

Quantum Monte Carlo investigation of the 2D Heisenberg model with S=1/2

The two-dimensional (2D) Heisenberg model with anisotropic exchange (Δ = 1−J _x /J _z ) and S=1/2 is investigated by the quantum Monte Carlo method. The energy, susceptibility, specific heat, spin-spin correlation functions, and correlation radius are calculated. The sublattice magnetization (σ) and the Néel temperature of the anisotropic antiferromagnet are logarithmic functions of the exchange anisotropy: 1/σ+1+0.13(1)ln(1/Δ). Crossover of the static magnetic structural factor as a function of temperature from power-law to exponential occurs for T _c /J≈0.4. The correlation radius can be approximated by 1/ξ=2.05T ^1.0(6)/exp(1.0(4)/T). For La₂CuO₄ the sublattice magnetization is calculated as σ=0.45, the exchange is J=(1125–1305) K; for Er₂CuO₄ J∼625 K and the exchange anisotropy Δ∼0.003. The temperature dependence of the static structural magnetic factor and the correlation radius above the Néel temperature in these compounds can be explained by the formation of topological excitations (spinons). Fiz. Tverd. Tela (St. Petersburg) 41, 116–121 (January 1999)     

Magnetic-breakdown oscillations of the thermoelectric field in layered conductors

We consider the quasi-two-dimensional pseudo-spin-1/2 Kitaev–Heisenberg model proposed for A₂IrO₃ (A = Li, Na) compounds. The spin-wave excitation spectrum, the sublattice magnetization, and the transition temperatures are calculated in the random phase approximation for four different ordered phases observed in the parameter space of the model: antiferromagnetic, stripe, ferromagnetic, and zigzag phases. The Néel temperature and temperature dependence of the sublattice magnetization are compared with the experimental data on Na₂IrO₃.     

Low-energy singlet sector in the spin-1/2 <Emphasis Type="Italic">J</Emphasis><Subscript>1</Subscript>–<Emphasis Type="Italic">J</Emphasis><Subscript>2</Subscript> Heisenberg model on a square lattice

Based on a special variant of the plaquette expansion, an operator is constructed whose eigenvalues give the low-energy singlet spectrum of a spin-\(\frac{1}{2}\) Heisenberg antiferromagnet on a square lattice with nearest-heighbor and frustrating next-nearest-neighbor exchange couplings J ₁ and J ₂. It is well known that a nonmagnetic phase arises in this model for 0.4 ? J ₂/J ₁ ? 0.6, sandwiched by two Néel ordered phases. In agreement with previous results, we observe a first-order quantum phase transition (QPT) at J ₂ ≈ 0.64 J ₁ from the non-magnetic phase to the Néel one. A large gap (? 0.4J ₁) is found in the singlet spectrum for J ₂ < 0.64J ₁, which excludes a gapless spin-liquid state for 0.4 ? J ₂/J ₁ ? 0.6 and the deconfined quantum criticality scenario for the QPT to another Néel phase. We observe a first-order QPT at J ₂ ≈ 0.55J ₁, presumably between two nonmagnetic phases.     

Influence of quantum fluctuations on the Néel temperature of a dilute two-dimensional anisotropic antiferromagnet

A quantum Monte Carlo procedure is used to calculate the energy, sublattice magnetization, Néel temperature, and the slopes of the S=[1/T _N(x=0)]dT _N(x)/dx curves as functions of the hole concentration and the exchange anisotropy Δ=1−J _x,y/J _z in the Heisenberg model with anisotropic negative interactions between nearest neighbors in a square lattice with dilution among the lattice sites. The slope diverges in the limit Δ→0: S∼ln(6.5/Δ). Fiz. Tverd. Tela (St. Petersburg) 39, 898–900 (May 1997)     

A frustrated quantum spin-s model on the Union Jack lattice with spins s > 1/2

The zero-temperature phase diagrams of a two-dimensional (2D) frustrated quantum antiferromagnetic system, namely the Union Jack model, are studied using the coupled cluster method (CCM) for the two cases when the lattice spins have spin quantum number s = 1 and s = \frac32\frac{3}{2}. The system is defined on a square lattice and the spins interact via isotropic Heisenberg interactions such that all nearest-neighbour (NN) exchange bonds are present with identical strength J ₁ > 0, and only half of the next-nearest-neighbour (NNN) exchange bonds are present with identical strength J ₂ ≡ κ J ₁ > 0. The bonds are arranged such that on the 2×2 unit cell they form the pattern of the Union Jack flag. Clearly, the NN bonds by themselves (viz., with J ₂ = 0) produce an antiferromagnetic Néel-ordered phase, but as the relative strength κ of the frustrating NNN bonds is increased a phase transition occurs in the classical case (s→ ∞) at κ _c ^cl = 0.5 to a canted ferrimagnetic phase. In the quantum cases considered here we also find strong evidence for a corresponding phase transition between a Néel-ordered phase and a quantum canted ferrimagnetic phase at a critical coupling κ _c1 = 0.580 ± 0.015 for s = 1 and κ _c1 = 0.545 ± 0.015 for s = \frac32\frac{3}{2}. In both cases the ground-state energy E and its first derivative dE/dκ seem continuous, thus providing a typical scenario of a second-order phase transition at κ = κ _c1. However, the order parameter for the transition (viz., the average ground-state on-site magnetization) does not go to zero there on either side of the transition. Thus, the phase transition at κ = κ _c1 between the Néel antiferromagnetic phase and the canted ferrimagnetic phase for both the s = 1 and s = \frac32\frac{3}{2} Union Jack models is similar in nature to that found previously for the s = \frac12\frac{1}{2} Union Jack model. It is thus also completely comparable to the transition in the s = \frac12\frac{1}{2} XXZ model on the 2D square lattice between two Néel antiferromagnetic phases, one aligned along the z-axis and the other along some perpendicular direction in the xy-plane.     

Mössbauer study of magnetic ordering in K2FeF4

The sublattice magnetization of the quadratic-layer basal-plane antiferromagnet K₂FeF₄ has been studied by use of Mössbauer spectroscopy. A distribution of Néel temperatures with a width ～3 K is found at a mean T_N = 67.2±0.3 K. For 0.3 < T/T_N < 0.99 the sublattice magnetization is described by a power law with critical exponent β = 0.17±0.01.     

Domain wall energy in ErCrO3

Domain structure in ErCrO₃ was studied from 10 K up to the Néel temperature by means of Faraday effect. Experimental temperature dependence of domain wall energy was obtained. Using a two-sublattice molecular-field model, the expression for the domain wall energy density was derived. It was shown that domain walls in ErCrO₃ have a Bloch wall character with the rotation of the sublattice magnetization in (ac) plane.     

Antiferromagnetism in Mn0.27Co0.73Cl2·6H2O

The specific heat of Mn_0.27Co_0.73Cl₂·6H₂O has been measured in the temperature range 1.4 K to 4.4 K. A λ-type anomaly was observed at 2.10 K, corresponding to an antiferromagnetic-paramagnetic transition. Approximately 50% of the entropy is recovered above the Néel temperature. Using the specific heat data, a calculated sublattice magnetization was obtained and compared to several statistical models.     

Ground state properties of a spin-3/2 model on a decorated square lattice

We present the construction of an optimum ground state for a quantum spin-3/2 antiferromagnet. The spins reside on a decorated square lattice, in which the basis consists of a plaquette of four sites. By using the vertex state model approach we generate the ground state from the same vertices as those used for the corresponding ground state on the hexagonal lattice. The properties of these two ground states are very similar. Particularly there is also a parameter-controlled phase transition from a disordered to a Néel ordered phase. In the regime of this transition, ground state properties can be obtained from an integrable classical vertex model. Received 28 June 1999     

Strong short-range magnetic order in a frustrated FCC lattice and its possible role in the iron structural transformation

The magnetic properties of a frustrated Heisenberg antiferromagnet with the fcc lattice and exchange interaction between the nearest (J ₁) and next-to-nearest (J ₂) neighbors are studied in this work. For the collinear phase with the wave vector Q= (π,π,π), the equations of the self-consistent spin-wave theory are obtained and solved numerically for the sublattice magnetization and the averaged short-range order parameter. The dependence of the Néel temperatureT _N on the ratio J ₂/J ₁ is found. It is shown that, in the case of a sufficiently strong frustration, strong short-range magnetic order persists over a wide temperature range above T _N. The possible application of this result to the mechanism of structural phase transition from α-Fe to γ-Fe is considered.     

An investigation of the quantum J 1 - J 2 - J 3 model on the honeycomb lattice

We have investigated the quantum J ₁ - J ₂ - J ₃ model on the honeycomb lattice with exact diagonalizations and linear spin-wave calculations for selected values of J ₂ / J ₁ , J ₃ / J ₁ and antiferromagnetic (J ₁ > 0) or ferromagnetic (J ₁ < 0) nearest neighbor interactions. We found a variety of quantum effects: “order by disorder" selection of a Néel ordered ground-state, good candidates for non-classical ground-states with dimer long range order or spin-liquid like. The purely antiferromagnetic Heisenberg model is confirmed to be Néel ordered. Comparing these results with those observed on the square and triangular lattices, we enumerate some conjectures on the nature of the quantum phases in the isotropic models. Received 17 November 2000 and Received in final form 21 January 2001     

Theoretical studies on intervalley splittings in Si/SiO<Subscript>2</Subscript> quantum dot structures

Using the coupled cluster method we investigatespin-s J ₁-J′ ₂ Heisenberg antiferromagnets (HAFs) on an infinite, anisotropic, two-dimensional triangular lattice for the two cases where the spin quantum number s = 1 and s = $\frac{3} {2}$\frac{3} {2}. With respect to an underlying square-lattice geometry the model has antiferromagnetic (J ₁ > 0) bonds between nearest neighbours and competing (J′ ₂ > 0) bonds between next-nearest neighbours across only one of the diagonals of each square plaquette, the same diagonal in each square. In a topologically equivalent triangular-lattice geometry, the model has two types of nearest-neighbour bonds: namely the J′ ₂ ≡ κJ ₁ bonds along parallel chains and the J ₁ bonds producing an interchain coupling. The model thus interpolates between an isotropic HAF on the square lattice at one limit (κ = 0) and a set of decoupled chains at the other limit (κ → ∞), with the isotropic HAF on the triangular lattice in between at κ = 1. For both the spin-1 model and the spin-$\frac{3} {2}$\frac{3} {2} model we find a second-order type of quantum phase transition at κ _c = 0.615 ± 0.010 and κ _c = 0.575 ± 0.005 respectively, between a Néel antiferromagnetic state and a helically ordered state. In both cases the ground-state energy E and its first derivative dE/dκ are continuous at κ = κ _c , while the order parameter for the transition (viz., the average ground-state on-site magnetization) does not go to zero there on either side of the transition. The phase transition at κ = κ _c between the Néel antiferromagnetic phase and the helical phase for both the s = 1 and s = $\frac{3} {2}$\frac{3} {2} cases is analogous to that also observed in our previous work for the s = $\frac{1} {2}$\frac{1} {2} case at a value κ _c = 0.80 ± 0.01. However, for the higher spin values the transition appears to be of continuous (second-order) type, exactly as in the classical case, whereas for the s = $\frac{1} {2}$\frac{1} {2} case it appears to be weakly first-order in nature (although a second-order transition could not be ruled out entirely).     

Errata

The Mössbauer effect has been used to study the behavior of the sublattice magnetization of the antiferromagnet RbFeF₄ near the Néel temperature T_N = 133.6 K. In the asymptotic critical region (1 ? T/T_N < 10^-2), a critical exponent β = 0.316 ± 0.005 was found, indicating a three-dimensional critical behavior.     

Negative evidence of any history dependence of the néel temperature of a Dy crystal from neutron scattering and ultrasonic measurements

A simultaneous measurement of the sublattice magnetization of helical ordered Dy with neutrons and of the C₁₁, C₃₃ and C₄₄ elastic constants, indicate a Néel temperature of (177.3±0.2) K. This value is not noticeably changed by repeated cycling of the specimen through T_N, in contrast to a previous observation of a large change in T_N for a Dy crystal (Palmer and Greenough, 1976).     

Neutron diffraction study of Ho(Rh0.3Ir0.7)4B4

Using powder neutron diffraction techniques, we have examined the magnetic order of the pseudoternary compound Ho(Rh_0.3Ir_0.7)₄B₄ below the Néel temperature T_N=2.7K. The magnetic structure consists of stacked antiferromagnetic basal plane sheets forming a body centered tetragonal unit cell, with a sublattice magnetization corresponding to 9.6±0.6μ_B per Ho³⁺ion at 1.5 K. Magnetic intensity versus temperature measurements indicate that the transition is second order and reveal no anomalous effects when the compound becomes superconducting at T_c=1.34K.     

Heavy electron YBNi2B2C and giant exchange YbNiBC: 170Yb Mössbauer spectroscopy and magnetization studies

We present magnetic properties of the three-band Hubbard model in the para- and antiferromagnetic phase on a hypercubic lattice calculated with the Dynamical Mean-Field Theory (DMFT). To allow for solutions with broken spin-symmetry we extended the approach to lattices with AB-like structure. Above a critical sublattice magnetization one can observe rich structures in the spectral-functions similar to the t-J model which can be related to the well known bound states for one hole in the Neél-background. In addition to the one-particle properties we discuss the static spin-susceptibility in the paramagnetic state at the points and for different dopings . The -T-phase-diagram exhibits an enhanced stability of the antiferromagnetic state for electron-doped systems in comparison to hole-doped. This asymmetry in the phase diagram is in qualitative agreement with experiments for high-T_c materials. Received: 28 May 1998 / Revised and Accepted: 14 September 1998     

Die magnetischen Eigenschaften der Europium-Chalkogenide unter hydrostatischem Druck

The magnetic ordering temperatures and the magnetization curves of the europium chalcogenides have been measured in compressed helium. Under the application of hydrostatic pressures up to 4 kbar the Curie temperatures increase, the Néel temperatures remain constant and the ferrimagnetic transition temperature of EuSe decreases. Magnetization curves of Eu(Se, S) mixed crystals are similar to those of EuSe under pressure. The results are analysed within the molecular field approximation with exchange interactionsJ ₁ andJ ₂ between nearest and next nearest neighbours, respectively.J ₁ increases with pressure in EuO and EuS but is not changed in EuSe.J ₂ decreases under pressure in EuSe but remains constant in EuTe. The results are compared with different theoretical models for the exchange interactions in these compounds.