3D Spin Glass Research Articles

AC susceptibility of a novel 2D rare-earth boron-cluster spin glass system

The AC susceptibility of a novel rare-earth boron-cluster-containing spin glass was measured.REB17CN,REB22C2N,and REB28.5C4 (RE = Er,Ho)are a newly discovered class of crystalline, non-doped spin glass system in which the rare-earth atomshave a two-dimensional configuration. Well defined maxima in the in-phase linear AC susceptibilityof HoB22C2N were observed with corresponding behaviour of the out-of-phase susceptibility as expectedfor a spin glass. It was found that the dynamical scaling theory of a 3D system,τ/τ0 = [(T−T0)/T]−zν, could not describe the data well. More reasonable parameters could be extracted in termsof a generalized Arrhenius law which describes 2D spin glass systems. This result is in agreement with the previousstudies which indicate the two-dimensionality of this system.

Absence of an equilibrium ferromagnetic spin-glass phase in three dimensions.

Using ground state computations, we study the transition from a spin glass to a ferromagnet in 3D spin glasses when changing the mean value of the spin-spin interaction. We find good evidence for replica symmetry breaking up until the critical value where ferromagnetic ordering sets in, and no ferromagnetic spin glass phase. This phase diagram is in conflict with the droplet/scaling and mean field theories of spin glasses. We also find that the exponents of the second order ferromagnetic transition do not depend on the microscopic Hamiltonian, suggesting universality of this transition.

Critical slowing down in polynomial time algorithms.

Combinatorial optimization algorithms that compute exact ground states for disordered magnets are seen to exhibit critical slowing down at zero temperature phase transitions. Using the physical features of the models, such as vanishing stiffness on one side of the transition and the ground state degeneracy, the number of operations needed in the push-relabel algorithm for the random field Ising model and in the algorithm for the 2D spin glass is estimated. These results strengthen the connections between algorithms and the physical picture and may be used to improve the speed of computations.

Zero-temperature responses of a 3D spin glass in a magnetic field.

We probe the energy landscape of the 3D Edwards-Anderson spin glass in a magnetic field to test for a spin glass ordering. We find that the spin glass susceptibility is anomalously large on the lattice sizes we can reach. Our data suggest that a transition from the spin glass to the paramagnetic phase takes place at B(c) approximately 0.65, though the possibility B(c) = 0 cannot be excluded. We also discuss the question of the nature of the putative frozen phase.

Effects of a bulk perturbation on the ground state of 3D Ising spin glasses.

We compute and analyze couples of ground states of 3D spin glasses before and after applying a volume perturbation which adds to the Hamiltonian a repulsion from the true ground state. The physical picture based on replica symmetry breaking is in excellent agreement with the observed behavior.

Effects of changing the boundary conditions on the ground state of Ising spin glasses

We compute and analyze couples of ground states of 3D spin glass systems with the same quenched noise but periodic and anti-periodic boundary conditions for different lattice sizes. We discuss the possible different behaviors of the system, we analyze the average link overlap, the probability distribution of window overlaps (among ground states computed with different boundary conditions) and the spatial overlap and link overlap correlation functions. We establish that the picture based on Replica Symmetry Breaking correctly describes the behavior of 3D Spin Glasses.

Evidence against temperature chaos in mean-field and realistic spin glasses

We discuss temperature chaos in mean field and realistic 3D spin glasses. Our numerical simulations show no trace of a temperature chaotic behavior for the system sizes considered. We discuss the experimental and theoretical implications of these findings.

Frozen magnetic states in quasi-two-dimensional Cr1/3−x NixTaS2 compounds with competing exchange interactions

A study of the dynamic and static magnetic susceptibility of quasi-two-dimensional, doubly intercalated compounds Cr1/3−x NixTaS2 (0.08⩽x⩽0.23) is reported. It is shown that cooling from paramagnetic phase in this concentration range produces a spin-glass-type frozen magnetic state. In contrast to the classical 3D spin glasses, however, this state sets in within a broad temperature range rather than at a phase transition. A magnetic phase diagram of the studied compounds has been constructed.

Numerical evidence for spontaneously broken replica symmetry in 3D spin glasses.

By numerical simulations of the $3d$ Ising spin glass we find evidence that spontaneous replica symmetry breaking theory and not the droplet model describes with good accuracy the equilibrium behavior of the system.

Magnetism and magnetic fluctuations in La 1 − xSr xCuO 4 for x = 0 (2D antiferromagnet), 0.04 (3D spin glass) and x = 0.15 (superconductor)

We review recent studies of the static and dynamic magnetic fluctuations in La 2 − x Sr x CuO 4. In La 2 CuO 4(T N = 325K) the instantaneous two-dimensional (2D) spin correlations have been studied over the temperature range 340 K < T ≤ 820 K. We find quantitative agreement for the correlation length over the complete temperature range with no adjustable parameters with predictions for the 2D quantum non-linear sigma model in the renormalized classical regime. We have carried out bulk magnetization measurements in La 1.96Sr 0.04CuO 4 which has neither antiferromagnetic long range order nor superconductivity. All of the features that characterize a canonical spin glass transition have been seen: irreversibility, remnant magnetization and scaling behavior. Finally, neutron inelastic scattering experiments have been performed on homogeneous single crystals of La 1.85Sr 0.15CuO 4 with T c = 37.3K (at onset), higher than any previously studied single crystals. The temperature dependence of the low energy incommensurate peak intensity at ( π(1 ± δ), π) and ( π, π(1 ± δ)) exhibits a pronounced maximum near 3T c . In contrast to the results reported on lower T c crystals, the intensity for energies below 3.5 meV dramatically decreases as the temperature decreases below T c , vanishing into the background below ~ 15K. The behavior is consistent with predictions based on a d x 2 − y 2 superconducting order parameter.

Magnetic phase diagram, static properties, and relaxation of the insulating spin glass CoCl2

The magnetic properties of ${\mathrm{CoCl}}_{2}$\ensuremath{\cdot}${\mathrm{H}}_{2}$O are examined by dc magnetization measurements as a function of temperature and field. This insulating system has both ferromagnetic and antiferromagnetic interactions, the distribution of which may be randomized to some degree by removal of one water from the parent system ${\mathrm{CoCl}}_{2}$\ensuremath{\cdot}${2\mathrm{H}}_{2}$O. It behaves as a reentrant spin glass. A field-induced transition is observed in the 4--6 kG range, a much smaller field than the 31.3-kG metamagnetic transition in ${\mathrm{CoCl}}_{2}$\ensuremath{\cdot}${2\mathrm{H}}_{2}$O. The nonlinear susceptibility displays an unusual variation with temperature, but does not scale in the conventional way. The thermoremanent magnetization (TRM) is examined as a function of cooling field and temperature. Its time development approximates a stretched exponential decay and the parameters characterizing this are analyzed. It is also found that the TRM scales well according to a T ${\mathrm{log}}_{10}$(t/${\mathrm{\ensuremath{\tau}}}_{0}$) form, for temperatures not much above \ensuremath{\sim}0.7${\mathit{T}}_{\mathit{g}}$, with ${\mathrm{\ensuremath{\tau}}}_{0}$\ensuremath{\sim}${10}^{\mathrm{\ensuremath{-}}10--}$${10}^{\mathrm{\ensuremath{-}}9}$ s. Irreversibility lines are derived from measurements of field-cooled and zero-field-cooled magnetizations. A weak irreversibility sets in at ${\mathit{T}}_{\mathit{g}}$(H=0)=9.0 K and displays no detectable field dependence up to 1 kG. A strong irreversibility sets in at ${\mathit{T}}_{\mathit{g}}$(H=0)=8.4 K and displays a strong field dependence. The results are analyzed using theories which consider anisotropy. The strong irreversibility line conforms much better to a (reduced) form ${\mathrm{\ensuremath{\tau}}}_{\mathit{g}}$\ensuremath{\propto}${\mathit{h}}^{0.53}$, recently proposed for the 3D Ising short-range spin glass, than to the usual De Almeida--Thouless mean-field form ${\mathrm{\ensuremath{\tau}}}_{\mathit{g}}$\ensuremath{\propto}${\mathit{h}}^{2/3}$.

Constrained Annealing for Spin Glasses

The quenched free energy of spin glasses is estimated by means of annealed averages where the frustration is constrained to its average value. We discuss the case of d-dimensional Ising models with random nearest neighbour coupling, and we introduce a new method to obtain constrained annealed averages without recurring to Lagrange multipliers. It requires to perform quenched averages either on small volumes in an analytic way, or on finite size strips via products of random transfer matrices. We thus give a sequence of converging lower bounds for the quenched free energy of 2d spin glasses.

Overlap length in a Cu-Mn spin glass probed by ac susceptibility.

An important theoretical concept in the ``droplet'' model of spin glasses is the existence of an overlap length. Experimentally this concept was verified by dc-magnetization measurements. However, recent ac-susceptibility measurements by Lefloch et al. [Europhys. Lett. 18, 647 (1992)] have been interpreted to contradict this result. In this paper, ac-susceptibility and dc-magnetization measurements on a Cu (2% Mn) spin glass are reported. The results of the ac-susceptibility measurements are consistent with dc measurements and provide evidence for the existence of an overlap length in 3d spin glasses at low temperatures.

Overlap length in two-dimensional Cu(Mn) spin-glass films.

Time-dependent dc-magnetization measurements on two-dimensional (2D) Cu(Mn) spin-glass films are reported. Results from the wait-time dependence of the relaxation of the zero-field-cooled magnetization combined with particular effects of temperature cyclings prior to the field application provide evidence for the existence of an overlap length in 2D spin glasses.

Multicanonical simulations of 2D and 3D ising spin glasses

We present a recursive procedure to calculate the parameters of the recently proposed multicanonical ensemble and explore the approach for spin glasses. We carried out lengthy simulations of 2D and 3D Edwards-Anderson spin glass model. Replica on lattices up to 48 2 in 2D and up to 12 3 in 3D are investigated. Temperature dependence of the energy, the entropy and other physical quantities are easily calculable at all temperatures. We studied their finite size scaling and the zero temperature limit to explore the ground state properties. The increase of the ergodicity time with lattice is reduced to an approximately V 3 power law. Our results shows that the multicanonical ensemble may open new horizons for simulations of spin glasses and other systems with conflicting constraints.

Aging in a two-dimensional CuMn spin glass

Utilizing zero-field cooled magnetization measurements the nonequilibrium dynamics in a 2D spin glass film is investigated. The experiments show that aging is an inherent property of 2D spin glass systems with qualitatively similar features as in 3D systems.

Nonlinear susceptibility of 2D spin glass films

A careful study of the nonlinear susceptibility of multilayered two-dimensional Cu(14 at% Mn) spin glass layers separated by thick interlayers of Cu is reported. The experiments were performed in SQUID magnetometers using an ac susceptibility technique in the field range 0–0.5 kG and dc magnetization measurements in the field range 0–10 kG. The static 2D critical exponents have been determined from scaling analysis.

AC susceptibilities in spin glasses and dynamics in an ultrametric space

The authors show that the temperature and frequency dependence of the AC susceptibilities chi ( omega ) in the 2D and 3D+or-J Ising spin glasses (SGs) can be reproduced by a model based on the picture of motion in phase space as thermally activated hopping in an ultrametric space. The characteristic difference in the frequency dependence of Im chi ( omega ) in the 2D and 3D SGs, previously found by the Monte Carlo (MC) simulation, is reduced to a difference in a scaling of free-energy barriers with ultrametric distance. One assumption is needed to combine dynamics in an ultrametric space with a correlation function of the magnetization in the SGs. chi ( omega )-values that were obtained previously by the MC simulation are reproduced based on the authors' assumption with better results than those of Sibani (1987). Further the relation obtained by the Lundgren et al. (1981) lm chi =-( pi /2)(d(Re chi )/d(In omega )) holds without taking a special limit z to 1, where z is a branching ratio of the hierarchical structure.

AC susceptibilities and relaxation time distributions for the two-dimensional and three-dimensional +or-J Ising spin glasses

By means of two different methods in a Monte Carlo simulation, the authors calculate the AC susceptibilities chi ( omega ) and relaxation time distributions g( tau ) in the +or-J Ising two-dimensional (2D) and three-dimensional (3D) spin glasses. The data obtained by the two methods separately are confirmed to be consistent with each other through the fluctuation dissipation theorem chi ( omega )=(1/T) integral d tau g( tau )/(1-i omega tau ). The imaginary parts Im chi of the AC susceptibilities show a characteristic difference in the 2D and 3D spin glasses; as the frequency of the AC field is decreased, the height of the peak of Im chi becomes higher in the 2D spin glass, and lower in the 3D spin glass. They can also see a difference between the g( tau ) distributions in the 2D and 3D spin glasses, reflected by the difference in the chi ( omega )-values. In the 3D spin glass, Im chi has no frequency dependence at low temperatures, suggesting that the fluctuation spectrum of the magnetization shows 1/f-noise behaviour in the spin-glass phase.

Magnetic phase transitions in spin glasses

The nature of a phase transition in spin glasses remains unsettled. Its characterization lies in experimentation on materials which closely mimic the theoretical models. Here I consider the “ideal” (2D-Ising) spin glass Rb 2 Cu 1− x Co x F 4 . The complex ac-susceptibility is measured as a function of temperature and frequency. The results are analyzed to determine the median relaxation time which diverges towards T c = 0K according to activated dynamics. Far above T c the relaxation time leaves the experimentally available window. Consequently an equilibrium phase transition cannot be studied as T → T c + . A similar situation is expected for model 3D spin glasses where T c is finite.