Local Energy Statistics in Spin Glasses

Recently, Bauke and Mertens conjectured that the local statistics of energies in random spin systems with discrete spin space should in most circumstances be the same as in the random energy model. We review some rigorous results confirming the validity of this conjecture. In the context of the SK models, we analyse the limits of the validity of the conjecture for energy levels growing with the volume of the system. In the case of the Generalised Random energy model, we give a complete analysis for the behaviour of the local energy statistics at all energy scales. In particular, we show that, in this case, the REM conjecture holds exactly up to energies E _N < β _c N, where β _c is the critical temperature. We also explain the more complex behaviour that sets in at higher energies. Research supported in part by the DFG in the Dutch-German Bilateral Research Group “Mathematics of Random Spatial Models from Physics and Biology” and by the European Science Foundation in the Programme RDSES.     

Theory of chemical bonds in metalloenzymes XX: magneto-structural correlations in the CaMn4O5 cluster in oxygen-evolving complex of photosystem II

ABSTRACT

Magneto-structural correlations in oxygen-evolving complex (OEC) of photosystem II (PSII) have been elucidated on the basis of theoretical and computational results in combination with available electron paramagnetic resonance (EPR) experimental results, and extended x-ray absorption fine structure (EXAFS) and x-ray diffraction (XRD) results. To this end, the computational methods based on broken-symmetry (BS) UB3LYP solutions have been developed to elucidate magnetic interactions in the active manganese catalyst for water oxidation by sunlight. The effective exchange interactions J for the CaMn(III)Mn(IV)₃O₅(H₂O)₃Y(Y = H₂O or OH^?) cluster (1) model of OEC of PSII have been calculated by the generalised approximate spin projection (GAP) method that eliminates the spin contamination errors of the BS UB3LYP solution. Full geometry optimisations followed by the zero-point energy (ZPE) correction have been performed for all the spin configurations of 1 to improve the J values that are compared with accumulated EPR in the S₂ state of Kok cycle and magnetic susceptibility results of Christou model complex Ca₂Mn(IV)₃O₄ (2). Using the calculated J values, exact diagonalisation of the spin Hamiltonian matrix has been carried out to obtain excitation energies and spin densities of the ground and lower excited states of 1. The calculated excitation energies are consistent with the available experimental results. The calculated spin densities (projection factors) are also compatible with those of the EPR results. The calculated spin densities have been used to calculate the isotropic hyperfine (A_iso) constants of ⁵⁵Mn ions revealed by the EPR experiments. Implications of the computational results are discussed in relation to the structural symmetry breaking (SSB) in the S₁, S₂ and S₃ states, spin crossover phenomenon induced by the near-infrared excitation and the right- and left-handed scenarios for the O–O bond formation for water oxidation.     

Instability of a system and its estimation in terms of the hybrid density functional theory method: a magnetic effective density functional (MEDF) approach

Potential curves and high and low spin energy gaps for radical clusters were calculated by spin polarized molecular orbital methods. Through-space effective exchange integrals (J _ab) and relative energies of spin projected low spin states by post-Hartree-Fock (HF) calculation were reproduced by the hybrid density functional theory (DFT) method. The hybrid parameters that could reproduce post-HF values such as UCCSD(T)'s for each model had close relations with the instabilities of those systems. Information entropy and related chemical indices were used to estimate the magnitude of the instabilities. A magnetic effective density functional (MEDF) scheme for spin clusters was proposed for practical computation of J _ab values in molecular magnetic materials.     

HighT c superconductivity in the itinerant Ising model II. Spin triplet pairing

We study the spin triplet pairing superconducting states of the itinerant Ising model. The spin and spatial symmetries of the states are explored. We find that only a restricted set of spin symmetry states are allowed, while an infinite number of spatial symmetry states exist. The spin triplet pairing states can either be gapless or have finite energy gaps, but all spin triplet pairing states have the sameT _c .The free energies of spin triplet and spin singlet pairing states are calculated and compared.     

Numerical results for ground states of spin glasses on Bethe lattices

The average ground state energy and entropy for ±J spin glasses on Bethe lattices of connectivities k + 1 = 3..., 26 at T = 0 are approximated numerically. To obtain sufficient accuracy for large system sizes (up to n = 2¹²), the Extremal Optimization heuristic is employed which provides high-quality results not only for the ground state energies per spin e_k+1 but also for their entropies s_k+1. The results indicate sizable differences between lattices of even and odd connectivities. The extrapolated ground state energies compare very well with recent one-step replica symmetry breaking calculations. These energies can be scaled for all even connectivities k + 1 to within a fraction of a percent onto a simple functional form, e _{k + 1} = E _SK - (2E _SK + )/, where E _SK = - 0.7633 is the ground state energy for the broken replica symmetry in the Sherrington-Kirkpatrick model. But this form is in conflict with perturbative calculations at large k + 1, which do not distinguish between even and odd connectivities. We also find non-zero entropies per spin s_k+1 at small connectivities. While s_k+1 seems to vanish asymptotically with 1/(k + 1) for even connectivities, it is numerically indistinguishable from zero already for odd k + 1 ≥ 9. Received 9 August 2002 Published online 27 January 2003 RID="a" ID="a"e-mail: sboettc@emory.edu www.physics.emory.edu/faculty/boettcher     

自旋为1/2的XY模型亚铁磁棱型链的物性和有序-无序竞争

利用不变本征算符法, 计算低温下自旋为1/2的XY模型一维亚铁磁棱型链系统的元激发谱, 讨论在此系统中不同的特殊情形下的元激发能量, 从而给出体系的三个临界磁场强度的解析解H_C1, H_C2, H_peak. 分析不同外磁场下 体系的磁化强度随温度的变化规律, 发现三个临界磁场强度的解析解H_C1, H_C2, H_peak是正确的, 并从三个元激发对磁化强度的贡献进行了说明. 低温下磁化强度随外磁场的变化呈现1/3磁化平台. 体系的磁化率随温度或者外磁场的变化都出现了双峰现象. 这说明双峰源于二聚体分子内电子自旋平行排列的铁磁交换作 用能和二聚体与单基体分子间电子自旋反平行排列的反铁磁交换作用能, 热无序能, 外磁场强度相关的自旋磁矩势能之间的竞争.     

Ferromagnetism in the Hubbard model: instability of the Nagaoka state on the square lattice

The instability of the fully polarized ferromagnetic ground state (Nagaoka state) of the Hubbard model on the square lattice is investigated. We use single spin flip variational wave functions including majority spin correlation effects and calculate spin flip energies in the thermodynamic limit. With very local wave functions and with moderate numbers of variational parameters we reproduce the best known estimate for the critical hole density δ_cr = 0.29 and we obtain an estimate of U_cr = 63 t for the critical coupling which is considerably better than the best estimate of U_cr = 42 t previously known. The simplicity of our wave functions makes the physical origin of the various aspects of the instability particularly transparent.     

Mössbauer study of Lu2Fe3O7: A two-dimensional antiferromagnet on a triangular lattice

Mössbauer studies reveal that there are two kinds of Fe³⁺ spins with completely different characteristics in Lu₂Fe₃O₇: one is an Ising-like property and the other is a Heisenberg-like property in a two-dimensional antiferromagnet on a triangular lattice. The former spin orders ferrimagnetically along thec-axis at around 220 K. The latter spin is lying in thec-plane and a corresponding hyperfine magnetic field is observed at temperatures below 50 K. At very low temperatures, however, the latter spin has a component parallel to thec-axis and couples with the former spin. This finding is consistent with the modulated profile of the magnetic scattering in neutron diffraction and the result of a magnetization measurement.     

Spin liquid in an almost ferromagnetic Kondo lattice

A theory of stabilization of a spin liquid in a Kondo lattice at temperatures close to the temperature of antiferromagnetic instability has been developed. Kondo exchange scattering of conduction electrons leads to emergence of a state of the spin liquid of the resonating valence bonds (RVB) type at T>T _K. Owing to this stabilization, low-energy processes of Kondo scattering with energies below T _K are frozen so that the “singlet” state of the Kondo lattice is not realized; instead a strongly correlated spin liquid with developed antiferromagnetic fluctuations occurs. A new version of the Feynman diagram technique has been developed to describe interaction between spin fluctuations and resonant valence bonds in a self-consistent manner. Emergence of a strongly anisotropic RVB spin liquid is discussed. Zh. éksp. Teor. Fiz. 112, 729–759 (August 1997)     

Independent magnon states on magnetic polytopes

For many spin systems with constant isotropic antiferromagnetic next-neighbour Heisenberg coupling the minimal energies E _min(S) form a rotational band, i.e. depend approximately quadratically on the total spin quantum number S, a property which is also known as Landé interval rule. However, we find that for certain coupling topologies, including recently synthesised icosidodecahedral structures this rule is violated for high total spins. Instead the minimal energies are a linear function of total spin. This anomaly results in a corresponding jump of the magnetisation curve which otherwise would be a regular staircase. Received 27 August 2001 and Received in final form 18 October 2001     

Proton spectra according to the diffraction excitation model

Inclusive proton spectra arising from pp collisions are calculated from the diffraction excitation model. Comparison with the data shows that diffraction dissociation cannot account for a major part of σ_inel at low energies (s ? 50 GeV²), but that it could be the dominant mechanism at ISR energies.     

Quantum-critical theory of the spin-fermion model and its application to cuprates: Normal state analysis

We present the full analysis of the normal state properties of the spin-fermion model near the antiferromagnetic instability in two dimensions. The model describes low-energy fermions interacting with their own collective spin fluctuations, which soften at the antiferromagnetic transition. We argue that in 2D, the system has two typical energies—an effective spin-fermion interaction g¯ and an energy ω_sf below which the system behaves as a Fermi liquid. The ratio of the two determines the dimensionless coupling constant for spin-fermion interaction λ² ∝ g¯/ω_sf. We show that λ scales with the spin correlation length and diverges at criticality. This divergence implies that the conventional perturbative expansion breaks down. We develop a novel approach to the problem—the expansion in either the inverse number of hot spots in the Brillouin zone, or the inverse number of fermionic flavours—which allows us to explicitly account for all terms which diverge as powers of λ, and treat the remaining, O(log λ) terms in the RG formalism. We apply this technique to study the properties of the spin-fermion model in various frequency and temperature regimes. We present the results for the fermionic spectral function, spin susceptibility, optical conductivity and other observables. We compare our results in detail with the normal state data for the cuprates, and argue that the spin-fermion model is capable of explaining the anomalous normal state properties of the high T _c materials. We also show that the conventional {⁴ theory of the quantum-critical behaviour is inapplicable in 2D due to the singularity of the {⁴ vertex.     

Structural, electronic, and magnetic properties of Co-doped ZnO

Density functional theory based calculations have been carried out to study structural, electronic, and magnetic properties of Zn1-xCoxO (x = 0, 0.25, 0.50, 0.75) in the zinc-blende phase, and the generalized gradient approximation proposed by Wu and Cohen has been used. Our calculated lattice constants decrease while the bulk moduli increase with the increase of Co 2+ concentration. The calculated spin polarized band structures show the metallic behavior of Co-doped ZnO for both the up and the down spin cases with various doping concentrations. Moreover, the electron population is found to shift from the Zn-O bond to the Co-O bond with the increase of Co 2+ concentration. The total magnetic moment, the interstitial magnetic moment, the valence and the conduction band edge spin splitting energies, and the exchange constants decrease, while the local magnetic moments of Zn, Co, O, the exchange spin splitting energies, and crystal field splitting energies increase with the increase of dopant concentration.     

The bulk twist action on the single local monodomains of the smectic C liquid crystal

The angular dependence of the surface anchoring energies of the smectic C with temperature independent tilt angle (type C₁) on two surfaces, SiO _x /ITO/glass and holographic diffraction grating, were measured using a twist-cell method. The smectic C monodomains rotation, starting at a critical imposed bulk twist, revealed a surface anchoring breaking. The surface anchoring strengths of the SiO _x /ITO/glass and holographic grating were evaluated. A model for the bulk twist influence on the smectic C monodomain growth was suggested.     

Two-Dimensional Coulomb Glass as a Model for Vortex Pinning in Superconducting Films

A glass model of vortex pinning in highly disordered thin superconducting films in magnetic fields B ≪ H_c2 at low temperatures is proposed. Strong collective pinning of a vortex system realized in disordered superconductors that are close to the quantum phase transition to the insulating phase, such as InO_x, NbN, TiN, MoGe, and nanogranular aluminum, is considered theoretically for the first time. Utilizing the replica trick developed for the spin glass theory, we demonstrate that such vortex system is in non-ergodic state of glass type with a large kinetic inductance per square L_K. The distribution function of local pinning energies is calculated, and it is shown that it possesses a wide gap; i.e., the probability to find a weakly pinned vortex is extremely low.

     

High energy spin dynamics of La2CuO4 and La1.9Sr0.1CuO4

The magnetic excitations in La₂CuO₄ and La_1.9Sr_0.1CuO₄ were studied by inelastic neutron scattering up to energies of 76 meV. For the pure sample, the results forE15 meV can be well described by conventional spin wave theory with a spin wave velocity c=0.89±0.07 eVÅ. For lower energies, the observed intensities were somewhat higher than expected from spin wave theory and did not follow the Bose-Einstein factor. For the doped sample, the linewidth in constant-E scans at smallE shows a very short correlation length of =7.5 Å only, which is considerably below the value expected from the concentration dependence reported by other authors. An increase of the linewidth for largeE indicates a reduced spin-wave stiffness when compared to the undoped material. However, the use of a spin-wave picture may not be appropriate as the standard expression for damped spin waves in a paramagnetic material is in serious conflict with experiment.     

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.     

Measurements of the two and three spin-index observables inn p elastic scattering between 0.80 and 1.10 GeV

We present data of several rescattering observables measured inn p elastic scattering between 0.80 and 1.10 GeV. The SATURNE II polarized beam of free neutrons obtained from the break-up of polarized deuterons was scattered on the Saclay polarized frozen-spin proton target. Three different configurations of beam and target polarization directions were used: the observablesD _onon andK _onno were measured with the normal-normal spin configuration at eight energies;N _onkk ,D _os″ok andK _os″ko were determined with the longitudinal-longitudinal configuration at six energies;N _onsk ,D _os″ok andK _os″so with the sideway-longitudinal configuration at six energies. Part of the data was obtained with an unpolarized CH₂ target where only the two spin-index polarization transfer parametersK _os″ko andK _os″so were determined. Data are compared with phase shift analyses predictions and with the LAMPF results at 0.788 GeV. Present results are the first measurements of rescattering observables above 0.80 GeV. They provide an important contribution to any future theoretical or phenomenological analysis.

     

μSR study of the S=1/2 triangular lattice antiferromagnet AgNiO2

AgNiO₂, a model compound of an S=1/2 triangular lattice, was studied by muon spin relaxation in addition to ac, dc susceptibility, electrical resistivity and neutron diffraction. The relaxation rate shows a sharp peak at around T_N=28 K followed by a sudden decrease of initial asymmetry indicating a magnetic ordering. Three internal fields ranging from 0.2 to 0.3 T were obtained from the muon precession period. However, a neutron diffraction experiment failed to detect any magnetic order at low temperatures. From these results, it was concluded that magnetic coherence is confined to small domain compared with the coherence length of neutron diffraction due to spin frustration. This revised version was published online in August 2006 with corrections to the Cover Date.     

Spin-wave renormalization by mobile holes in a two-dimensional quantum antiferromagnet

The coupling of antiferromagnetic spin excitations and propagating holes has been studied theoretically on a square lattice in order to investigate the dependence of antiferromagnetic order on hole doping, being of relevance, e.g., for the Cu–3 d⁹ system in antiferromagnetic CuO₂-planes of high-T_c superconductors. An effective Hamiltonian has been used, which results from a 2D Hubbard model (hopping integral t) with holes and with strong on-site Coulomb repulsion U. Bare antiferromagnetic excitations and holes with energies of the same order of magnitude t²/U are interacting via a coupling term being proportional to t and allowing holes to hop by emitting and absorbing spinwaves. In terms of a self-consistent one-loop approximation the renormalization of the spectral function both of holes and antiferromagnetic spin excitations are calculated.