Quantum phase transitions of spin chiral nanotubes

Recently many interesting magnetic nanostructures have been fabricated and much attention is arising on the rich magnetic properties that originate in the quantum effects eminent in the nanoscale world. One of the peculiar aspects of the quantum effects is the spin excitation gap. In the spin-1/2 low-dimensional systems, the spin gap often appears when the lattice dimerization or the frustration in the spin–spin interaction are introduced. In the present study, we investigate the ground-state property of the spin-1/2 antiferromagnetic spin chiral nanotubes with the spatial modulation in the spin–spin interaction. The ground-state phase diagrams of them are determined by observing the behavior of the expectation value of the Lieb–Schultz–Mattis slow-twist operator calculated by the quantum Monte Carlo method with the continuous-time loop algorithm. We discuss the relation between the characteristic of the topology of the phase diagram and the chiral vector of the nanotubes.     

Electron spin transitions in quantum Hall systems

A system of two-dimensional electron gas in a strong magnetic field exhibits a remarkable phenomenon known as the fractional quantum Hall effect. Rapid advances in experimental techniques and intense theoretical work for well over a decade have significantly contributed to our understanding of the mechanism behind the effect. It is now a well established fact that electron correlations are largely responsible for the occurrence of this phenomenon. In recent years, theoretical and experimental investigations have revealed that those electron correlations, which are responsible for the quantum Hall effect, are also the reason for various spin transitions in the system. In this review, we systematically follow the theoretical studies of the role spin degree of freedom play in the quantum Hall effect regime and also describe several ingenious experiments reported in recent years which are in good agreement with the emerging theoretical picture.     

Phase transitions in anisotropic lattice spin systems

A general method for proving the existence of phase transitions is presented and applied to six nearest neighbor models, both classical and quantum mechanical, on the two dimensional square lattice. Included are some two dimensional Heisenberg models. All models are anisotropic in the sense that the groundstate is only finitely degenerate. Using our method which combines a Peierls argument with reflection positivity, i.e. chessboard estimates, and the principle of exponential localization we show that five of them have long range order at sufficiently low temperature. A possible exception is the quantum mechanical, anisotropic Heisenberg ferromagnet for which reflection positivity isnot proved, but for which the rest of the proof is valid.Work partially supported by U.S. National Science Foundation grant no. MPS 75-11864Work partially supported by U.S. National Science Foundation grant no. MCS 75-21684 A01     

Whither phase transitions in reentrant spin glasses !

The results of bulk magnetic response and⁵⁷Fe Mössbauer study in a new RSG system Fe₁.₄Ru₁.₆Si strongly discount the interpretation of data in terms of well defined phase transitions as per Gabay-Toulouse model. The reentrant behaviour is found to arise from small clusters constraining the dynamics of quasiferromagnetic bigger clusters.     

Characterisations of phase transitions in Ising spin systems

We construct aC*-algebraic formalism designed to provide a framework for the characterisation of phase transitions in a class of Ising spin systems: this class is large enough to include the rectangular lattice models, of arbitrary finite dimensionality, with nearest neighbour interactions. Using an extension of Onsager's transfer matrix formalism, we express properties of a Gibbs state of a system in terms of a contractive linear transformation, ₀, of a certain Hilbert space, the properties of ₀ being governed by the temperature as well as the interactions in the system. We obtain conditions on ₀ under which the system exhibits a phase transition characterised by (A) a thermodynamical singularity, (B) a change in symmetry, associated with theG-ergodic decomposition of Gibbs states, (C) a divergence of a correlation length (appropriately defined) at the critical point, and (D) scaling laws in the critical region. Applying our formalism to the rectangular two-dimensional Ising model with nearest neighbour interactions, we show that its phase transition possesses the properties (B) and (C), as well as (A).     

Monte Carlo study of low/high spin transitions

We study the finite temperature property of a model on two dimensional square lattices with two Ising spins at each lattice site by Monte Carlo simulations. When those Ising spins at a lattice site are parallel the site is said to be in the high-spin state (HS), while when they are antiparallel the site is said to be in the low-spin state (LS). Throughout the study, the energy of HS is presumed to be higher than that of LS. Two Ising spins at each site are added to form a total spin, which interacts with its nearest neighbour total spins via spin-spin couplings. The spin-phonon coupling also is introduced via harmonic springs between nearest neighbour sites with spring constants and equilibrium distances depending on the spin states of the sites involved. In this system, we investigate the feature of transitions between LS and HS (to be called low/high spin transition (LHST)) by varying the temperature. As for the ferromagnetic interaction between total spins, the second order phase transition: pure HSmixed state of HS and LS is possible to occur in a pure spin system, as is expected from mean field calculations. The role of lattice distortions by the change of lattice spacings is shown to be essential for LHST: pure LS(pure)HS. In the model investigated, there appears an indication of the strong first order phase transition which reveals a conspicuous hysteresis.     

Localization transitions for nuclear spin waves in ferromagnetic alloys

We investigate the possible localization of nuclear spin waves associated with the minority constituent of a binary ferromagnetic alloy. NMR methods for observing the transition and the time scale of propagating spin waves are suggested.     

Surface spin dynamics of magnets near spin-orientational phase transitions

The sufficient conditions for the formation of a dipole-exchange generalized surface spin wave which softens near a volume spin-orientational phase transition are found for a definite form of the high-frequency magnetic susceptibility tensor. Fiz. Tverd. Tela (St. Petersburg) 40, 1532–1536 (August 1998)     

Vortices and phase transitions in two-dimensional non-abelian spin models

We modify O(n) models (n>2) in two dimensions so as to comparedifferent thoeries with identical local properties and different global ones. Our O′ (3) model with a particular interaction has vortex-like configuration (π₁(P₂) = Z₂) though it is locally equivalent to an O (3) model (π₁(S₂) = 0). Our results have been obtained by means of strong coupling methods. The Padé extrapolants show a critical value x_c = 11.8.     

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.     

Phase transitions far from thermal equilibrium in spin systems

The nonlinear effects in the spin resonance due to the negative differential r.f. magnetic susceptibility are considered. The r.f. magnetization is shown to exhibite a kind of first order phase transition. A set of scaling relations, valid near the appropriate critical point, is obtained.     

Isotopic selection using nuclear spin induced electric dipole transitions

The nuclear spin induced electric dipole transitions $\text{6p}{}^2\text{(}\text{1}\text{2}\text{,}\text{1}\text{2}{}_0\text{?6p}\text{n}\text{s(}\text{1}\text{2}\text{,}\text{1}\text{2}\text{)}{}^0{}_0$ and $\text{6p}{}^2\text{(}\text{1}\text{2}\text{,}\text{1}\text{2}\text{)}{}_0\text{?6p}\text{n}\text{d}\text{1}\text{2}\text{[}\text{3}\text{2}\text{]}{}^0{}_2$ in ²⁰⁷Pb have been observed in the vacuum ultraviolet absorption spectrum of lead. Utilization of such transitions as a step in the laser isotope separation of ²⁰⁷Pb has the advantage that the selective pumping step involves levels which are separated by the relatively large fine structure spacing rather than the relatively small electronic isotopic and/or hyperfine spacings. The possibility of the separation of other odd mass numbered isotopes in the sixth and seventh periods by similar techniques is discussed briefly.     

Multiple transitions of the spin configuration in quantum dots

Single electron tunneling is studied in a many electron quantum dot in high magnetic fields. For such a system multiple transitions of the spin configuration are theoretically predicted. With a combination of spin blockade and Kondo effect we are able to detect five regions with different spin configurations. Transitions are induced with changing electron numbers.     

Homogeneous-inhomogeneous transitions in a Landau level with spin splitting

The homogeneous-inhomogeneous transitions of a two-dimensional electron gas in a strong perpendicular magnetic field are studied in the particular case when half of the states in a spin splitted Landau level are occupied. To this end the dielectric susceptibility in the homogeneous states as well as the free energy in the modulated states are calculated. Unless theg factor dos not exceed a certain value the charge-density waves are stable in an interval of finite temperatures.