Spin-dependent extension of Calogero-Sutherland model through anyon-like representations of permutation operators

We consider a A_N−1 type of spin-dependent Calogero-Sutherland model, containing an arbitrary representation of the permutation operators on the combined internal space of all particles, and find that such a model can be solved as easily as its standard su(M) invariant counterpart through the diagonalisation of Dunkl operators. A class of novel representations of the permutation operator P_ij, which pick up non-trivial phase factors along with interchanging the spins of the ith and jth particles, are subsequently constructed. These ‘anyon-like’ representations interestingly lead to different variants of the spin Calogero-Sutherland model with highly non-local interactions. We also explicitly derive some exact eigenfunctions as well as energy eigenvalues of these models and observe that the related degeneracy factors crucially depend on the choice of a few discrete parameters which characterise such anyon-like representations.     

Replica symmetry breaking in a fermionic cluster spin glass model in a transverse field

We analyze a fermionic Ising spin glass model in the presence of a transverse magnetic field Γ within a cluster mean field theory. The model considers a Sherrington-Kirkpatrick type interaction between magnetic moments of clusters with a ferromagnetic intra-cluster coupling J₀. The spin site operators are written as a bilinear combination of fermionic operators. In these quantum spin glass model, the inter-cluster disorder is treated by using a framework of one-step replica symmetry breaking within the static approximation. The effective intra-cluster interaction is then computed by means of an exact diagonalization method. Results for several cluster size n_s, values of Γ and J₀ are presented. For instance, the specific heat shows a broad maximum (for n_s>1) at a temperature above the freezing temperature T_f, which is characterized by the inter-cluster replica symmetry breaking. Phase diagrams T versus Γ show that the critical temperature T_f(Γ) decreases for any value of n_s when Γ increases until it reaches a quantum critical point at some value of Γ_c.     

Fe2+ localized excitations in the random antiferromagnet with competing spin anisotropies, Fe(1−x)CoxBr2

The Fe²⁺ localized magnetic excitations observed in the Co-rich antiferromagnetic phase of the randomly mixed system with competing Ising and XY spin anisotropies, Fe(_1?x)Co_xBr₂ have been analyzed quantitatively. The calculated frequency-field diagram reproduces well the experiments. The expectation values of the Fe²⁺ spin components in the ground state are calculated. It is shown that even in the Co-rich antiferromagnetic phase Fe²⁺ spins make an angle with the c-plane of the crystal in which Co²⁺ spins are confined.     

Anderson Localization Triggered by Spin Disorder—With an Application to Eu<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Ca<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>B<Subscript>6</Subscript>

The phenomenon of Anderson localization is studied for a class of one-particle Schrödinger operators with random Zeeman interactions. These operators arise as follows: Static spins are placed randomly on the sites of a simple cubic lattice according to a site percolation process with density x and coupled to one another ferromagnetically. Scattering of an electron in a conduction band at these spins is described by a random Zeeman interaction term that originates from indirect exchange. It is shown rigorously that, for positive values of x below the percolation threshold, the spectrum of the one-electron Schrödinger operator near the band edges is dense pure-point, and the corresponding eigenfunctions are exponentially localized.Localization near the band edges persists in a weak external magnetic field, H, but disappears gradually, as H is increased. Our results lead us to predict the phenomenon of colossal (negative) magnetoresistance and the existence of a Mott transition, as H and/or x are increased.Our analysis is motivated directly by experimental results concerning the magnetic alloy Eu _x Ca_1?x B₆.     

n-Dimensional complex riemann-einstein spaces with O(n−1, C) as the symmetry group

Working with a complex Riemannian space V_n, we determine the most general form of the metric which admits O(n?1, C) as a symmetry subgroup. The conformal curvature tensor, which is of type D for the real cross-section of signature (+---) with n = 4, has a very similar structure for n > 4 and complex V_n. Solutions of the empty space Einstein equations with the λ-term are then studied. There are two different static solutions which, with n = 4 and real cross-section of signature (+---), reduce to Schwarzschild-de Sitter metric, or to the Nariai's solution. A proof of a slight generalization of Birkhoff's theorem that every time-dependent solution of G_μv = λg_μv is reducible, by a coordinate transformation, to one of these two solutions, is given. The complete symmetry groups of the solutions obtained are examined. The techniques of embedding in a higher-dimensional flat space and of Kruskal's variables which exhibit the spurious nature of Schwarzschild's singularity are generalized to the case of (complex) n dimensions. General properties of geodesic lines for both solutions are examined and various real cross-sections of Nariai's solution for n = 4 are discussed. The last section studies some contractions of the two solutions.     

Quantum registers based on single NV + <Emphasis Type="Italic">n</Emphasis><Superscript>13</Superscript>C centers in diamond: II. Spin characteristics of registers and spectra of optically detected magnetic resonance

The spin Hamiltonian method in combination with ab initio calculations of the spin characteristics of quantum registers that include an electron spin S = 1 of a single NV center in the ground electronic state and nuclear spins I = 1/2 of several atoms ¹³C located at different lattice sites near the vacancy of the NV center is applied to find eigenvalues and eigenfunctions of spin systems NV + n ¹³C for cases where the lattice sites nearest to the vacancy of the NV center contain one, two, or three ¹³C nuclear spins, as well as for cases where ¹³C atoms are located at sites more distant from the vacancy. For these single spin NV + n ¹³C systems, the spectra of optically detected magnetic resonance (ODMR) are calculated, which agree well with available experimental data.     

Nonadiabatic interaction of acoustic phonons with spins <Emphasis Type="Italic">S</Emphasis>=1/2 in the two-dimensional Heisenberg model

The ground state of a two-dimensional antiferromagnet having spins S=1/2 and interacting with acoustic phonons is investigated in the nonadiabatic approximation using the quantum-mechanical Monte Carlo method. The critical parameters of the spin-phonon coupling, corresponding to the formation of bound spin-phonon excitations, crystal symmetry lowering, and the emergence of a gap in the spin excitation spectrum, as well as the antiferromagnet-quantum spin liquid transition, are determined. The orthorhombicity parameter, the sublattice magnetization, the violation of the spherical symmetry of spin-spin correlation functions, and the magnetic moment in Gd₂CuO₄ and Eu₂CuO₄ are calculated.     

Paramagnetische Resonanz von Zentren mit den Symmetrienn,\bar n undn/mundn/m

The consequences of applying the spin-Hamiltonians ofAbragam andPryce to paramagnetic centers with the low symmetriesn,\(\bar n\) andn/m(C _n ,C _nh ,S _n ) are examined. The asymmetry of theg- and the hfs-tensors, described in an earlier paper, is considered in this context. The point is that for the symmetries under consideration the coordinate systems are not determined by the symmetry elements. For this reason it is possible to introduce separate coordinate systems for the magnetic field, the electron spin and the spins of the nuclei and this allows the symmetrisation of the tensors under certain conditions. This procedure also leeds to an understanding of the independent parameters found in the Hamiltonians. Ambiguities between the spin-Hamiltonians and the esr-spectra indicate the limits of theAbragam andPryce formalism. The application of the theory to paramagnetic centers under the influence of external, electrical fields is discussed and reveals interesting aspects.     

Planar nano-block structures Tin+1Al0.5Cn and Tin+1Cn (n = 1, and 2) from MAX phases: Structural,electronic properties and relative stability from first principles calculations

Structural, electronic properties and relative stability of quasi-two-dimensional (2D) free-standing planar nano-block (NBs) structures Ti_n+1Al_0.5C_n and Ti_n+1C_n (n = 1 and 2), which can be prepared using the recently developed procedure of exfoliation of corresponding NBs from MAX phases, were examined within first principles calculations in comparison with parent MAX phases Ti₃AlC₂ and Ti₂AlC. We found that in general Ti_n+1C_n and Ti_n+1Al_0.5C_n NBs retain the atomic geometries of the corresponding blocks of the MAX phases, but some structural distortions for the NBs occur owing to the lowering of the coordination number for atoms in the external Ti sheets of the nano-block structures. Our analysis based on their cohesive and formation energies reveals that the stability of the nano-block structures increases with index n (or, in other words, with a growth of the number of Ti–C bonds), the Al-containing NBs becoming more stable than the “pure” Ti–C NBs. Our data show that the magnetization of the simulated planar nano-block structures can be expected; so, for the Ti₃C₂ nano-block the most stable will be the spin configuration, where within each external Ti sheet the spins are coupled ferromagnetically together with antiferromagnetic ordering between opposite external titanium sheets of this nano-block.     

Spin alignment of yrast levels populated by pre-equilibrium (α, xnγ) reactions

Angular momenta of yrast levels following pre-equilibrium (α, xnγ) reactions at E_α, = 110 MeV were found to be aligned as well as those following the equilibrium (compound) (α, xnγ) reactions at E_α = 20–50 MeV. They are uniform against the neutron multiplicity x. The degrees of the spin (angular momentum) alignment with rank 2 for the yrast levels with spins 8–12 average about α₂ ≈ 0.87 ± 0.05. The good spin alignment indicates that both the neutron emission and the γ-emission are stretched in angular momentum space. This supports the pre-equilibrium neutron emission process, where the momenta carried away by the neutrons are not in random directions but rather in the beam direction. The result is well reproduced by the pre-equilibrium neutron emission process followed by neutron evaporation and the K-band γ-deexcitation process.     

Geometrical, electronic, and magnetic properties of small AunSc (n=1-8) clusters

Geometrical, electronic, and magnetic properties of the Sc-doped gold clusters, Au_nSc (n=1-8), have been studied using the density-functional theory within the generalized gradient approximation. An extensive structural search shows that the Sc atom in low-energy Au_nSc isomers tends to occupy the most highly coordinated position. The substitution of a Sc atom for an Au atom in the Au_n+1 cluster markedly changes the structure of the host cluster. Moreover, we confirm that the ground-state Au₆Sc cluster has a distortion to a lower D_2h symmetry. The relative stabilities and electronic properties of the lowest-energy Au_nSc clusters are analyzed based on the averaged binding energies, second-order energy differences, fragmentation energies, chemical hardnesses, and HOMO-LUMO gaps. It is found that the magic Au₃Sc cluster can be perceived as a superatom with high chemical stability and its HOMO-LUMO gap is larger than that of the closed-shell Zr@Au₁₄ cluster. The high symmetry and spin multiplicity of the Au₃Sc and Au₆Sc clusters are responsible for their large vertical ionization potential and electron affinity. The magnetism calculations indicate that the magnetic moment of the Sc atom in the ground-state Au_nSc (n=2-8) clusters gradually decreases for even n and is completely quenched for odd n.     

EPR Investigation of Exchange Interactions Between Neodymium Ions in {[Nd2(α-C4H3OCOO)6(H2O)2]} n

Electron paramagnetic resonance (EPR) of a new compound {[Nd₂(α-C₄H₃OCOO)₆(H₂O)₂]} _n composed of Nd³⁺–Nd³⁺ dimers is reported. The anisotropy parameters of the spin–spin interaction are determined by fitting experimental and simulated spectra in X- and Q-bands. It is shown that the anisotropy of the exchange interaction gives the main contribution to the anisotropy of the spin–spin interaction. The observed anisotropy disagrees with the expected in the model of the isotropic exchange interaction between real spins. A feature of the EPR spectrum not described by the model of the isolated Nd–Nd dimers and reflecting the magnetization transfer between dimers is detected. The magnetization transfer due to both the relaxation transitions and the interdimer interaction is considered.     

Magnetic contribution to heat capacity and entropy of nickel ferrite (NiFe2O4)

The heat capacity of nickel ferrite was measured as a function of temperature from 50 to 1200 °C using a differential scanning calorimeter. A thermal anomaly was observed at 584.9 °C, the expected Curie temperature, T_C. The observed behavior was interpreted by recognizing the sum of three contributions: (1) lattice (vibrational), (2) a spin wave (magnetic) component and (3) a λ-transition (antiferromagnetic-paramagnetic transition) at the Curie temperature. The first was modeled using vibrational frequencies derived from an experimentally-based IR absorption spectrum, while the second was modeled using a spin wave analysis that provided a T^3/2 dependency in the low-temperature limit, but incorporated an exchange interaction between cation spins in the octahedral and tetrahedral sites at elevated temperatures, as first suggested by Grimes [15]. The λ-transition was fitted to an Inden-type model which consisted of two truncated power law series in dimensionless temperature (T/T_C). Exponential equality (m=n=7) was observed below and above T_C, indicating symmetry about the Curie temperature. Application of the methodology to existing heat capacity data for other transition metal ferrites (AFe₂O₄, A=Fe, Co) revealed nearly the same exponential equality, i.e., m=n=5.     

Algebraic realization of the quantum rotor — odd-A nuclei

An algebraic realization of the quantum rotor for non-zero spin values (integer as well as half-integer) is established by constructing a model Hamiltonian out of rotationally invariant functions of the generators ofSU(3). The eigenvalues of this Hamiltonian in the leading normal-SU(3) symmetry for²⁵Mg and the so-called leading pseudo-SU(3) symmetries for¹⁵⁹Dy and¹⁶⁵Er are compared with the corresponding rotor results. For spinfree systems the internal symmetry group of the rotor and itsSU(3) realization are known to be D₂, the Vierergruppe. This symmetry extends to integral spin values, while for half-integer spins the rotor and itsSU (3) realization are shown to display an internal quaternion group symmetry. The theory points to a microscopic (many-particle shell-model) picture of nuclear rotational motion with spin degrees of freedom taken fully into account. An algebraic realization of the many-particle Nilsson model for odd-A nuclei, with the orbit-orbit and spin-orbit terms included, is given and applied to²³Na.     

Critical behaviour of SU(n) quantum chains and topological non-linear σ-models

The critical behaviour of SU(n) quantum “spin” chains, Wess-Zumino-Witten σ-models and grassmanian σ-models at topological angle θ = π (of possible relevance to the quantum Hall effect) is reexamined. It is argued that an additional Z_n symmetry is generally necessary to stabilize the massless phase. This symmetry is not present for the σ-models for n > 2 and is only present for certain representations of “spin” chains.     

Magnetische struktur von columbiten MnTa2O6 und CoNb2O6

By means of neutron diffraction we found for MnTa₂O₆S₁S₂ S₃S₄ with a magnetic unit which is the same as the chemical. Whereas the chemical unit of CoNb₂O₆ is doubled in c-direction; all spins in the chemical unit are parallel. Therefore the orthorhombic symmetry of the crystal structure cannot be maintained. In both compositions are the spins parallel to the a-axis.     

Spectral Artifacts Resulting from Multiple-Quantum Coherence Transfers by Spin Decoupling during Acquisition

Off-resonance coherent decoupling of spin X in a heteronuclear SX_N spin system can result in a multiplet with overlapping lines of spin Sand an overall shape similar to that of a doublet. Such lineshape distortions occur if certain multiple-spin coherences are present when the decoupler is switched on. The distortion could cause an apparent change in the multiplicity of an M + 1 multiplet of an SX_NY_M spin system when a selective decoupling of spins X is applied after a polarization transfer from spins X to spin S by INEPT or DEPT. Possibilities for suppressing the distortions are discussed.     

Spin glass and ferromagnetism in Kondo lattice compounds

The Kondo lattice model has been analyzed in the presence of a random inter-site interaction among localized spins with non zero mean J₀ and standard deviation J. Following the same framework previously introduced by us, the problem is formulated in the path integral formalism where the spin operators are expressed as bilinear combinations of Grassmann fields. The static approximation and the replica symmetry ansatz have allowed us to solve the problem at a mean field level. The resulting phase diagram displays several phase transitions among a ferromagnetically ordered region,a spin glass one, a mixed phase and a Kondo state depending on J₀, J and its relation with the Kondo interaction coupling J_K. These results could be used to address part of the experimental data for the CeNi _{1 - x} Cu _x compound, when x ⩽ 0.8. Received 24 June 2002 Published online 31 December 2002     

Gauge symmetry and the EMC spin effect

We emphasise the EMC spin effect as a problem of symmetry and discuss the renormalisation of theC=+1 axial tensor operators. This involves the generalisation of the Adler-Bell-Jackiw anomaly to each of these operators. We find that the contribution of the axial anomaly to the spin dependent structure functiong ₁(x, Q ²) scales at O(α_s). This means that the anomaly can be a largex effect ing ₁. Finally we discuss the jet signature of the anomaly.