Order-order transitions in spin systems with double electron exchange

Spin systems in the presence of isotropic single and double electron exchange are investigated at nonzero temperature. We use a generalized mean field approximation that allows for a variable local axis of quantization. This leads to the introduction of an angular parameter Θ giving the angle between nearest neighbor quantization axes. It is shown that order-order transitions can occur between phases of partially aligned spins (general Θ) and pure ferro- (Θ = 0) or antiferromagnetic (Θ = π) spin structures for physically reasonable values of the exchange ratio J₂/J₁ of double to single exchange when J₂ > 0. The order-order critical temperature τ₀ is determined as a function of J₂/J₁ for the particular cases of atomic spin $\text{s = 1,}\text{3}\text{2}\text{, 2,}\text{5}\text{2}$, and the corresponding phase diagrams are presented. Biquadratic and three-atom double electron exchange effects are considered separately. Expressions for the paramagnetic transition temperature and for the spontaneous magnetization M_s for general atomic spin s are given, and the discontinuous change in M_s at τ₀ is also found as a function of J₂/J₁.     

Ab initio determination of an extended Heisenberg Hamiltonian in CuO 2 layers

Accurate ab initio calculations on embedded Cu₄O₁₂ square clusters, fragments of the La₂CuO₄ lattice, confirm a value of the nearest neighbor antiferromagnetic coupling (J = 124 meV) previously obtained from ab initio calculations on bicentric clusters and in good agreement with experiment. These calculations predict non negligible antiferromagnetic second-neighbor interaction (J' = 6.5 meV) and four-spin cyclic exchange (K = 14 meV), which may affect the thermodynamic and spectroscopic properties of these materials. The dependence of the magnetic coupling on local lattice distortions has also been investigated. Among them the best candidate to induce a spin-phonon effect seems to be the movement of the Cu atoms, changing the Cu-Cu distance, for which the variation of the nearest neighbor magnetic coupling with the Cu-O distance is Δ J /Δ d _{Cu - O} ∼ 1700 cm^-1?^-1. Received 20 November 2000     

Islands of stability of the d-wave order parameter in s-wave anisotropic superconductors

In this paper we find and present on diagrams in the coordinates of η=2t₁/t₀ (the ratio of the second and the first nearest neighbor hopping integrals) and n (the carrier concentration) the areas of stability for the superconducting spin-singlet s- and d-wave and the spin-triplet p-wave order parameters hatching out during the phase transition from the normal to the superconducting phase. The diagrams are obtained for an anisotropic two-dimensional superconducting system with a relatively wide partially-filled conduction band. We study a tight-binding model with an attractive nearest neighbor interaction with the amplitude V₁, and the on-site interaction (with the amplitude V₀) taken either as repulsive or attractive. The problem of the coexistence of the s-, p- and d-wave order parameters is addressed and solved for chosen values of the ratio V₀/V₁. A possible island of stability of the d-wave order parameter in the s-wave order parameter environment for a relatively strong on-site interaction is revealed. The triple points, around which the s-, d-, and p-wave order parameters coexist, are localized on diagrams. It is shown that results of the calculations performed for the two-dimensional tight-binding band model are dissimilar with some obtained within the BCS-type approximation.     

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.     

Phase diagrams in an ultra-thin spin-1 transverse Ising film with bond or site dilution at surfaces

The phase diagrams of two nanoscaled thin films with bond and site dilutions at the surfaces, described by the spin-1 transverse Ising model, are investigated by the use of an effective field theory with correlations. A number of characteristic phenomena have been found in them, which are heavily dependent on the ratios (r = J₁/J and p = Ω_S/Ω, where J is the exchange interaction in the inner layer, J₁ is the exchange interaction between the surface and the next inner layer, Ω_S is the transverse field at the surfaces and Ω is the transverse field in the inner layer). Some of them have exhibited very similar behaviors found in the two spin-1/2 nanoscaled thin films with bond and site dilutions at the surfaces.     

Phase transition in an Ising-spinglass-model including next-nearest-neighbor-interaction?

The Transfermatrix-Method [1, 2] is applied to an Ising-spinglass-model on the square lattice with nearest neighbor interactionsJ ₁ positive and next nearest neighbor interactionsJ ₂ negative, when a fraction 1-x of the spins is removed at random. An example for this model is Eu _x Sr_1-x S [3, 4]. The question concerning the existence of a springlass-phase is not yet clarified. Investigation of the correlation function s ₀s_R² (correlation between two spins with distanceR), which is related to the Edwards-Anderson-orderparameter shows in the present work evidence against a spinglass-phase at finiteT. Analogous to the more common ±J-model (competing nearest neighbor interactions at random) a phase transition should only occur atT=0.     

Effect of single-ion uniaxial anisotropy on the phase diagrams of magnetic system in the presence of internal spin fluctuation

Basing on the two-spin-per-site Heisenberg model, the effect of single-ion uniaxial anisotropy on the phase diagrams of magnetic system in the presence of internal spin fluctuation has been investigated by use of the mean field theory. It was found that single-ion uniaxial anisotropy has important effect on the phase digrams. In the ferromagnetic case (J₃>0) the positive single-ion uniaxial anisotropies (D) suppress the internal spin fluctuation and raise the phase trasition temperature, and negative single-ion uniaxial anisotropies (D) increase the internal spin fluctuation and reduce the phase trasition temperature. In the antiferromagnetic case (J₃<0), there exist two critical values J_c1 and J_c2 (|J_c2|<|J_c1|) in the positive D values. In the |J₃|<|J_c2| range intra-spin exchange coupling prevails inter-spin exchange coupling, the positive D values suppress the internal spin fluctuation and raise the phase transition temperature. In the |J₃|>|J_c1| range the two sub-spins behave as a rigid spin and the positive D values make the reduction of the phase transition temperature. We also observe that the larger D values make the range of internal spin fluctuation to move towards the larger |J₃| range.     

Monte Carlo study of entropy for face-centered cubic Ising antiferromagnets

A face-centered cubic Ising model with nearest neighbor antiferromagnetic exchangeJ _nn in the presence of a magnetic fieldH is investigated by Monte Carlo methods. Free energy and entropy of the model are obtained by integrating the equation of state along various paths, starting at suitable reference states. It is shown that at low temperatures first-order phase transitions can be located with very good precision. At the two critical fieldsH _c1/|J _nn |=4,H _c2/|J _nn |=12 a residual ground-state entropyS(0) is found, which is estimated as aboutS(0)/k _B (ln 2)/3 in both cases.In the presence of a ferromagnetic next-nearest neighbor exchange there is no longer a nonzero entropy at the critical fields, however. ForR+J _nnn /J _nn +–1 we find the same structure of the phase diagram as qualitatively predicted by Domany et al., where lines of 3-state and 4-state Potts model-like transitions meet at a multicritical point atH=0. Some consequences of our results for interpreting the ordering of face-centered cubic binary alloys are also discussed.     

Entanglement in the Extended XY Spin Model with Three Spin Interaction and External Field

We investigate the pairwise thermal entanglement of the extended XY model with three spin interactions and external filed on zig-zag lattice. The influences of three spin interactions J ₂ and external field λ on the thermal entanglement of the nearest neighbor (NN) and next nearest neighbor (NNN) spins are considered. It is found that J ₂ and λ suppress both the maximal value and the critical temperature of the NN entanglement C ₁₂. However, when it comes to the NNN entanglement C ₁₃, there exists a critical value of J ₂ above which both the maximal entanglement and the critical temperature can be enhanced by J ₂ for a fixed external field. With J ₂ fixed, the effect of λ on C ₁₃ are different for different values of J ₂. For J ₂<1, λ suppresses both T _C and the maximal values of C ₁₃. For J ₂≥1, λ enhances the maximal values of C ₁₃ while decreases the critical temperature. These results show that one is able to get the entanglement wanted by properly controlling the values of the three spin interactions J ₂ and the external field λ.     

Dynamic phase transitions and dynamic phase diagrams of the Blume–Emery–Griffiths model in an oscillating field: the effective-field theory based on the Glauber-type stochastic dynamics

Using the effective-field theory based on the Glauber-type stochastic dynamics (DEFT), we investigate dynamic phase transitions and dynamic phase diagrams of the Blume–Emery–Griffiths model under an oscillating magnetic field. We presented the dynamic phase diagrams in (T/J, h₀/J), (D/J, T/J) and (K/J, T/J) planes, where T, h₀, D, K and z are the temperature, magnetic field amplitude, crystal–field interaction, biquadratic interaction and the coordination number. The dynamic phase diagrams exhibit several ordered phases, coexistence phase regions and special critical points, as well as re-entrant behavior depending on interaction parameters. We also compare and discuss the results with the results of the same system within the mean-field theory based on the Glauber-type stochastic dynamics and find that some of the dynamic first-order phase lines and special dynamic critical points disappeared in the DEFT calculation.     

Magnetic phase diagram of spinel spin-glasses

The article by Villain [Z. Phys. B — Condensed Matter33, 31 (1979)] is discussed and a modified magnetic phase diagram is suggested for the spinel system (AB₂O₄) in which theA andB sites are partially (or completely) occupied by magnetic atoms. This diagram takes into account the antiferromagnetic exchange interactionsJ _AA,J _BB andJ _AB between nearest neighbor cations of various types. Regions of paramagnetic, antiferromagnetic, ferrimagnetic and possible spin glass behaviour are indicated on the diagram.Supported by the National Science Foundation under Grant ISP-80-11451     

Spin Dynamics and Dirac Nodes in a Kagome Lattice

Herein, the spin dynamics for various magnetic configurations arranged on a Kagome lattice is investigated. Using a Holstein–Primakoff expansion of the isotropic Heisenberg Hamiltonian with multiple exchange parameters, the development and evolution of magnetic Dirac nodes with both anisotropy and magnetic field are examined. From the classical energies, the phase diagrams for the ferromagnetic (FM), antiferrimagnetic (AfM), and the 120°  phases are shown as functions of J₁, J₂, J₃, and anisotropy. Furthermore, the production of bosonic Dirac and Weyl nodes in the spin-wave spectra is shown. Through frustration of the magnetic geometry, a connection to the asymmetric properties of the Kagome lattice and the various antiferromagnetic configurations is discerned. Most interesting is the 120°  phase, which does not have Dirac nodes when considering only J₁ due to the formation of an analogous antiferromagnetic honeycomb lattice, but gains Dirac symmetry with next-nearest neighbor interactions. Additionally, the presence of flat modes that are characteristic of cluster excitations is shown. Further study of external frustrations from a magnetic field and anisotropy reveals a tunability of the exchange interactions and nodal points.     

Nuclear-induced time evolution of entanglement of two-electron spins in anisotropically coupled quantum dot

We study the time evolution of entanglement of two spins in an anisotropically coupled quantum dot interacting with the unpolarised nuclear spins environment. We assume that the exchange coupling strength in the z direction J _z is different from the lateral one J _l . We observe that the entanglement decays as a result of the coupling to the nuclear environment and reaches a saturation value, which depends on the value of the exchange interaction difference J = ‖J _l ? J _z ‖ between the two spins and the strength of the applied external magnetic field. We find that the entanglement exhibits a critical behaviour controlled by the competition between the exchange interaction J and the external magnetic field. The entanglement shows a quasi-symmetric behaviour above and below a critical value of the exchange interaction. It becomes more symmetric as the external magnetic field increases. The entanglement reaches a large saturation value, close to unity, when the exchange interaction is far above or below its critical value and a small one as it closely approaches the critical value. Furthermore, we find that the decay rate profile of entanglement is linear when the exchange interaction is much higher or lower than the critical value but converts to a power law and finally to a Gaussian as the critical value is approached from both directions. The dynamics of entanglement is found to be independent of the exchange interaction for an isotropically coupled quantum dot.     

Phase transition in the Blume-Capel model with second neighbour interaction

A two dimensional antiferromagnetic spin-1 Ising model with negative next- nearest neighbour interaction (J ₂ <0) and under an external magnetic field is investigated by two methods: The mean-field theory and Finite-Size-Scaling based on transfer matrix (TMFSS) calculations. The ground state diagrams exhibit several new phases including frustrated ones. At finite temperature we obtain by these two methods quite rich phase diagrams, with several multicritical points. While Mean field approximation yields phase diagrams which are sometimes even qualitatively incorrect, accurate results are obtained from transfer matrix finite size scaling calculations. For a certain range of interaction parameters, the model is shown to violate the ordinary universality hypothesis. Received: 3 November 1997 / Revised: 31 March 1998 / Accepted: 7 April 1998     

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.     

交换弹簧磁性多层膜的磁矩取向及磁滞回线的解析研究

本文以界面交换耦合常数Jⁱ和软磁相厚度L^s为主要参变量,研究了易轴与膜面平行情况下的Nd₂Fe₁₄B/α-Fe磁性多层膜的磁矩随外场变化的取向及磁滞回线,并得到了成核场的解析公式.分析发现,Jⁱ对磁矩取向、钉扎场和矫顽力机理有着较大的影响.当L^s较小时,钉扎场等于成核场,随着Jⁱ的减小 关键词： 成核场 钉扎场 矫顽力 磁滞回线     

Mixed spin- and spin- Ising models with random nearest-neighbour interactions

Using the effective field theory with correlations, we study mixed spin?3/2 and spin?1/2 Ising models with random bonds and crystal-field interactions on the honeycomb lattice. The nearest-neighbour couplings J_ij are taken as random variables with distribution P(J_ij) = pδ(J_ij ? J)+(1 ? p)δ(J_ij ? αJ), where J > 0 and |α| ≤ 1. In a certain range of negative values of α, the phase diagrams exhibit re-entrant behaviour. In detail, we investigate separately two kinds of disorder: Bond dilution (α = 0) and random ±J interactions (α = ?1). In both cases, the influence of the an-isotropy on the phase diagrams shows some new outstanding features.     

Effect of the block-spin configuration on the location of βc in two-dimensional Ising modelsin two-dimensional Ising models

We consider the nearest neighbor Ising model on the 2D square lattice and divide the lattice into 2 by 2 blocks. Each block is assigned one spin value (1 or –1) and these block spin values are kept fixed. We then impose the majority rule and look at the effect on the phase transition that was present in the original unconstrained spin system. We find that for the checkerboard block-spin configuration, Monte Carlo simulations show that _c is close to 1, which, compared to the original nearest neighbor Ising _c = 0.44..., shows that the critical temperature has been reduced by more than one half. For none of the other 11 block-spin configurations that we have considered is there any indication of a phase transition in the constrained system of original spins.     

Dimensionality Effects on the Mixed Spin-1/2 and Spin-2 Blume-Capel Model: Renormalization Group Theory

We have used the real-space Migdal-Kadanoff renormalization group technique on d-dimensional hypercubic lattice to study the mixed spin-1/2 and spin-2 Blume-Capel model. First, we indicate a critical dimension d_C ≈?2.05, above and below which different topologies of phase diagrams occur. The phase diagrams have been plotted in the (crystal field, temperature) plane around d_C, in which there is a second-order phase transition. Moreover, using the variation of the free energy at low temperatures, we have established the ground-state phase diagrams in the (?/J, C/J) plane for d?<?d_C and d?≥?d_C. In particular, we have seen the appearance of two first-order transitions at very low temperatures by the use of the free energy and its isotherm derivative. A detailed analysis of fixed points and flow diagrams indicates that there is no tricritical point.