Spin-glass Phase Transition Research Articles

Glassy behavior in a one-dimensional continuous-wave erbium-doped random fiber laser

The analogue of the paramagnetic to spin-glass phase transition in disordered magnetic systems, leading to the phenomenon of replica symmetry breaking, has been recently demonstrated in a two-dimensional random laser consisting of an organic-based amorphous solid-state thin film. We report here the first demonstration of replica symmetry breaking in a one-dimensional photonic system consisting of an erbium-doped random fiber laser operating in the continuous-wave regime based on a unique random fiber grating system, which plays the role of the random scatterers and operates in the Anderson localization regime. The clear transition from a photonic paramagnetic to a photonic spin glass phase, characterized by the probability distribution function of the Parisi overlap, was verified and characterized. In this unique system, the radiation field interacts only with the gain medium, and the fiber grating, which provides the disordered feedback mechanism, does not interfere with the pump.

Observation of photonic paramagnetic to spin-glass transition in a specially designed TiO2 particle-based dye-colloidal random laser.

Colloidal-based random lasers (RLs) are highly efficient and have been exploited in a wide range of geometries. However, in the particular case of ethanol solutions of rhodamines and TiO2 particles, the RL behavior is quite unstable due to the fast precipitation of the particles. In this Letter, specially designed amorphous TiO2 particles were synthesized by a sol-gel method, preventing the degradation of the RL for long operating lifetimes of over 105 shots. As a consequence, this modified colloidal RL allowed the observation of a clear replica-symmetry-breaking phase transition from the paramagnetic fluorescent to spin-glass RL behavior, which has not been observed in the system with nonfunctionalized TiO2 particles.

Spin-glass phase transition and behavior of nonlinear susceptibility in the Sherrington-Kirkpatrick model with random fields

The behavior of the nonlinear susceptibility $\chi_3$ and its relation to the spin-glass transition temperature $T_f$, in the presence of random fields, are investigated. To accomplish this task, the Sherrington-Kirkpatrick model is studied through the replica formalism, within a one-step replica-symmetry-breaking procedure. In addition, the dependence of the Almeida-Thouless eigenvalue $\lambda_{\rm AT}$ (replicon) on the random fields is analyzed. Particularly, in absence of random fields, the temperature $T_f$ can be traced by a divergence in the spin-glass susceptibility $\chi_{\rm SG}$, which presents a term inversely proportional to the replicon $\lambda_{\rm AT}$. As a result of a relation between $\chi_{\rm SG}$ and $\chi_3$, the latter also presents a divergence at $T_f$, which comes as a direct consequence of $\lambda_{\rm AT}=0$ at $T_f$. However, our results show that, in the presence of random fields, $\chi_3$ presents a rounded maximum at a temperature $T^{*}$, which does not coincide with the spin-glass transition temperature $T_f$ (i.e., $T^* > T_f$ for a given applied random field). Thus, the maximum value of $\chi_3$ at $T^*$ reflects the effects of the random fields in the paramagnetic phase, instead of the non-trivial ergodicity breaking associated with the spin-glass phase transition. It is also shown that $\chi_3$ still maintains a dependence on the replicon $\lambda_{\rm AT}$, although in a more complicated way, as compared with the case without random fields. These results are discussed in view of recent observations in the LiHo$_x$Y$_{1-x}$F$_4$ compound.

Chirality-driven intrinsic spin-glass ordering and field-induced ferromagnetism in Ni3Al nanoparticle aggregates

Weak itinerant-electron ferromagnet Ni3Al is driven to magnetic instability (quantum critical point, QCP, where the long-range ferromagnetic order of the bulk ceases to exist) by reducing the average crystallite size to d=50nm. ‘Zero-field’ (H=0) linear and nonlinear ac-susceptibilities, measured on Ni3Al nanoparticle aggregates, with d=50nm (S1) and d=5nm (S2), provide strong evidence for two spin glass (SG)-like thermodynamic phase transitions: one at Ti(H=0)≃30K (Ti†(H=0)≃230K) and the other at a lower temperature Tp(H=0)≃8K (Th(H=0)≃52K) in S1 (S2). ‘In-field’ (H≠0) linear ac-susceptibility and dc magnetization demonstrate that the thermodynamic nature of these transitions is preserved in finite fields. The presently determined H–T phase diagrams for the samples S1 and S2 are compared with those predicted by the Kotliar–Sompolinsky and Gabay–Toulouse mean-field models and Monte Carlo simulations, based on the chirality-driven spin glass (SG) ordering scenario, for a three-dimensional nearest-neighbor Heisenberg SG system with or without weak random anisotropy. Such a detailed comparison permits us to unambiguously identify various ‘zero-field’ and ‘in-field’ SG phase transitions as: (i) the simultaneous paramagnetic (PM)-chiral glass (CG) and PM-SG phase transitions at Ti(H), (ii) the PM-CG transition at Ti†(H), (iii) the replica symmetry-breaking SG transition at Tp(H), and (iv) the continuous spin-rotation symmetry-breaking SG transition at Th(H). In the presence of random anisotropy, magnetization fails to saturate even at 90kOe in S1 whereas negligibly small anisotropy allows even fields as weak as 1kOe to saturate magnetization and induce ferromagnetism in S2. Due to the proximity to CG/SG-QCP, magnetization and susceptibility both exhibit non-Fermi liquid behavior over a wide range at low temperatures.

Universal dynamic scaling in three-dimensional Ising spin glasses

We use a nonequilibrium Monte Carlo simulation method and dynamical scaling to study the phase transition in three-dimensional Ising spin glasses. The transition point is repeatedly approached at finite velocity v (temperature change versus time) in Monte Carlo simulations starting at a high temperature. This approach has the advantage that the equilibrium limit does not have to be strictly reached for a scaling analysis to yield critical exponents. For the dynamic exponent we obtain z=5.85(9) for bimodal couplings distribution and z=6.00(10) for the Gaussian case. Assuming universal dynamic scaling, we combine the two results and obtain z=5.93±0.07 for generic 3D Ising spin glasses.

Collective magnetic behavior of biocompatible systems of maghemite particles coated with functional polymer shells

Abstract Three series of core–shell maghemite nanoparticles were prepared by a template synthesis using surface active oligoperoxides and further surface initiated grafting functional polymers, forming shell suitable for biomedical applications. Because the polymer shells prevent exchange coupling between maghemite particles, the overall magnetic properties of the samples studied are dominated by dipolar interparticle interactions. Only the sample with the highest polymer fraction displays superparamagnetic relaxation phenomena close to the room temperature. On cooling, the magnetostatic interactions lead to a disordered collective magnetic state that should be described in terms of a spin-glass phenomenology. This collective freezing cannot however be considered as a generic spin-glass phase transition at a well-defined temperature but rather as freezing to a metastable glass-like state of locally correlated structural domains (clusters) without a long-range order. A quasi static spin ordering is only achieved at temperatures much below the freezing temperature.

Spin-glass behavior in a giant unit cell compound Tb117Fe52Ge113.8(1)

In this paper we demonstrate evidence of a cluster spin glass in Tb117Fe52Ge113.8(1) (a compound with a giant cubic unit cell) via ac and dc magnetic susceptibility, magnetization, magnetic relaxation and heat capacity measurements. The results clearly show that Tb117Fe52Ge113.8(1) undergoes a spin glass phase transition at the freezing temperature, ~38 K. The good fit of the frequency dependence of the freezing temperature to the critical slowing down model and Vogel-Fulcher law strongly suggest the formation of cluster glass in the Tb117Fe52Ge113.8(1) system. The heat capacity data exhibit no evidence for long-range magnetic order, and yield a large value of Sommerfeld coefficient. The spin glass behavior of Tb117Fe52Ge113.8(1) may be understood by assuming the presence of competing interactions among multiple non-equivalent Tb sites present in the highly complex unit cell.

Inhomogeneous Ferromagnetism and Spin-Glass-Like Behavior in <inline-formula> <tex-math notation="TeX">$({\rm Nd}_{1-x}{\rm Y}_{x})_{0.7}{\rm Sr}_{0.3}{\rm MnO}_{3}$ </tex-math></inline-formula> With <inline-formula> <tex-math notation="TeX">$x=0.21{-}0.35$ </tex-math></inline-formula>

The magnetic properties of polycrystalline ceramic samples $({\rm Nd}_{1-x}{\rm Y}_{x})_{0.7}{\rm Sr}_{0.3}{\rm MnO}_{3}$ with $x=0.21-0.35$ were studied by means of dc magnetization and ac susceptibility measurements. Experimental results reveal a strong decrease of the ferromagnetic (FM)-paramagnetic phase-transition temperature $(T_{C})$ from 97 to 65 K as increasing $x$ from 0.21 to 0.35, respectively. There is magnetic inhomogeneity associated with short-range FM order. Particularly, the samples undergo a spin-glass (SG) phase transition at the so-called blocking temperature $(T_{B})$ below $T_{C}$ , which shifts toward lower temperatures with increasing the applied field, $H_{\rm ex}$ ; $T_{B}\to T_{g}$ (the SG phase-transition temperature) as $H_{\rm ex}\to 0$ . The existence of the SG behavior in these samples was also confirmed by frequency $(f)$ dependences of the ac susceptibility. For the in-phase/real component, $\chi^{\prime}(T)$ , it shows a frequency-dependent peak at the SG freezing temperature $(T_{f})$ ; $T_{f}\to T_{g}$ as $f\to 0$ . Dynamics of this process were analyzed by means of the slowing down scaling law, $\tau/\tau_{0}\propto (T_{f}/T_{g}-1)^{-zv}$ , where $\tau_{0}$ and $zv$ are the characteristic time and critical exponent, respectively. Fitting the experimental $T\!_{f}(f)$ data to the scaling law gave the results of $zv=10.1{-}12.3$ and $\tau_{0}=10^{-21}{-}10^{-15}~{\rm s}$ . These values are different from those expected for canonical SG systems with $zv={10}$ and $\tau_{0}=10^{-13}~{\rm s}$ , revealing the cluster-SG behavior of $({\rm Nd}_{1-x}{\rm Y}_{x})_{0.7}{\rm Sr}_{0.3}{\rm MnO}_{3}$ samples. Notably, the increase in Y content leads to the shift of $\tau_{0}$ and $zv$ values toward those of canonical SG systems, which is ascribed to an expansion of SG clusters.

Phase transition in three-dimensional Heisenberg spin glasses with strong random anisotropies through a multi-GPU parallelization

We characterize the phase diagram of anisotropic Heisenberg spin glasses, finding both the spin and the chiral glass transition. We remark the presence of strong finite-size effects on the chiral sector. We find a unique phase transition for the chiral and spin glass sector, in the Universality class of Ising spin glasses. We focus on keeping finite-size effects under control, and we stress that they are important to understand experiments. Thanks to large GPU clusters we have been able to thermalize cubic lattices with up to 64x64x64 spins, over a vast range of temperatures.

Coexistence of considerable inter-particle interactions and spin-glass behavior in La0.7Ca0.3MnO3 nanoparticles

We have studied the magnetic and spin-glass (SG) properties of La0.7Ca0.3MnO3 single-crystalline nanoparticles, which were prepared by the mechanical milling method with different milling times (tm). Analyzing the susceptibility data in the paramagnetic region indicates both ferromagnetic (FM) and anti-FM interactions coexisting in nanoparticles. Additionally, there is a peak associated with the freezing temperature (Tf) appearing on the real part curve of the ac susceptibility, χ′(T). The Tf value increases with increasing frequency as expected for SG systems. The SG behavior was also checked by using the criterion parameter c = ΔTf/TfΔ(log10f), and the power law τ = τ0(T/Tg − 1)−zν. The obtained values of c ≈ 5 × 10−2, τ0 ≈ 10−5 s and zν ≈ 2–3 are consistent with those expected for SG-like systems, suggesting an existence of a SG phase transition at Tg below Tf, which decreases with decreasing ⟨D⟩. Basing on ln(f) versus Tf data, and the Néel-Arrhenius model [ln(f) = ln(f0) - Ea/kBT] and Vogel–Fulcher law [ln(f) = ln(f0) - Ea/kB(T - T0)], the Larmor frequency (f0), activation energy (Ea) and effective temperature (T0) for the samples with different ⟨D⟩ were determined. Obtained results indicate the existence a strong interaction between nanoparticles.

Evidence for temperature-dependent spin diffusion as a mechanism of intrinsic flux noise in SQUIDs

The intrinsic flux noise observed in superconducting quantum interference devices (SQUIDs) is thought to be due to the fluctuation of electron-spin impurities, but the frequency and temperature dependence observed in experiments do not agree with the usual $1/f$ models. We present theoretical calculations and experimental measurements of flux noise in rf SQUID flux qubits that show how these observations, and previous reported measurements, can be interpreted in terms of a spin-diffusion constant that increases with temperature. We fit measurements of flux noise in 16 devices, taken in the $20\text{--}80$ mK temperature range, to the spin-diffusion model. This allows us to extract the spin-diffusion constant and its temperature dependence, suggesting that the spin system is close to a spin-glass phase transition.

Phase transition in a super superspin glass

We here confirm the occurrence of spin glass phase transition and extract estimates of associated critical exponents of a highly monodisperse and densely compacted system of bare maghemite nanoparticles. This system has earlier been found to behave like an archetypal spin glass, with, e.g., a sharp transition from paramagnetic to non-equilibrium behavior, suggesting that this system undergoes a spin glass phase transition at a relatively high temperature, Tg ∼ 140 K.

Highq-state clock spin glasses in three dimensions and the Lyapunov exponents of chaotic phases and chaotic phase boundaries

Spin-glass phases and phase transitions for $q$-state clock models and their $q\ensuremath{\rightarrow}\ensuremath{\infty}$ limit the $XY$ model, in spatial dimension $d=3$, are studied by a detailed renormalization-group study that is exact for the $d=3$ hierarchical lattice and approximate for the cubic lattice. In addition to the now well-established chaotic rescaling behavior of the spin-glass phase, each of the two types of spin-glass phase boundaries displays, under renormalization-group trajectories, their own distinctive chaotic behavior. These chaotic renormalization-group trajectories subdivide into two categories, namely as strong-coupling chaos (in the spin-glass phase and, distinctly, on the spin-glass--ferromagnetic phase boundary) and as intermediate-coupling chaos (on the spin-glass--paramagnetic phase boundary). We thus characterize each different phase and phase boundary exhibiting chaos by its distinct Lyapunov exponent, which we calculate. We show that, under renormalization group, chaotic trajectories and fixed distributions are mechanistically and quantitatively equivalent. The phase diagrams of arbitrary even $q$-state clock spin-glass models in $d=3$ are calculated. These models, for all non-infinite $q$, have a finite-temperature spin-glass phase. Furthermore, the spin-glass phases exhibit a universal ordering behavior, independent of $q$. The spin-glass phases and the spin-glass--paramagnetic phase boundaries exhibit universal fixed distributions, chaotic trajectories and Lyapunov exponents. In the $XY$ model limit, our calculations indicate a zero-temperature spin-glass phase.

Spin glass and glass-like lattice behaviour in HoB66 at low temperatures

The low-temperature specific heat, magnetic susceptibility, and thermal expansion are studied experimentally in the fcc boride HoB66 and compared to similar quantities in non-magnetic LuB66. The anomalous behaviour observed in HoB66 is explained within a glass-like picture together with magnetic subsystem ordering processes. The character of the observed anomalies suggests the existence of a spin-glass phase transition in HoB66 below a characteristic temperature of T s ≈ 0.98 K.

Spin-glass behavior and magnetic splitting in molecular magnetic materials {[N(n-C4H9)4][MIIFeIII(C2O4)3]}n (M = Co, Mn)

The mixed valence character and the antiferromagnetic coupling in the molecular magnetic materials {[N(n-C4H9)4][MIIFeIII(C2O4)3]}n (M = Co, Mn) were investigated by Mossbauer spectroscopy and magnetic measurements. In the material {[N(n-C4H9)4][CoFe(C2O4)3]}n, the appearence of the spin-glass phase transition temperature and the magnetic phase transition under zero-field-cooled AC magnetic measurements were studied in the temperature range 5–100 K. In the Mossbauer spectra of {[N(n-C4H9)4][MnFe(C2O4)3]} a magnetic splitting was observed below 30 K. The appearance of the magnetic splitting indicates the occurrence of magnetic ordering in this complex. The hyperfine parameters show that the electronic state of iron is high-spin Fe3+.

Monte Carlo Simulation of 2D Ising Spin Glass with Power Law Decaying Interactions

We study the distance dependent interaction coupling in 2D in order to show how a spin glass phase transition occurs when couplings between far away spins are permitted by considering the Edwards–Anderson Ising spin glass model. The interaction coupling is a quenched random variable whose probability of being non-zero decays with distance between two spin sites $(p(J_{ij})\propto r_{ij}^{-\rho })$ . We study the model by changing ρ in three different regimes (ρ>2D, $\frac{4}{3} D < \rho < 2D$ , $\rho <\frac{4}{3} D$ ). We obtain a phase transition temperature for ρ=2,3,4.

Fluctuation theorems on the Nishimori line

The distribution of the performed work for spin glasses with gauge symmetry is considered. With the aid of gauge symmetry, which leads to exact (rigorous) results in spin glasses, we find a fascinating relation of the performed work to the fluctuation theorem. The integral form of the resultant relation reproduces the Jarzynski-type equation for spin glasses that we have obtained. We show that similar relations can be established not only for the distribution of the performed work but also for that of the free energy of spin glasses with gauge symmetry, which provides another interpretation of the phase transition in spin glasses.

Spin-glass in the spinel-type CuCrTiS4

It is difficult to find a typical compound to understand the spin-glass (SG). Only a few model compounds for the SG have been investigated; Fe0.50Mn0.50TiO3 as a short-range interacting three-dimensional (3D) Ising SG, Dy0.103Y0.897Ru2Si2 as a long-range 3D Ising SG, and AgMn as a long-range 3D Heisenberg SG. A spinel-type compound CuCrTiS4 will be provided in this study as a realistic candidate for a short-range interacting 3D Heisenberg SG. This CuCrTiS4 can cause a SG phase below T g = 7.91 K, which is obtained by a random non-magnetic 50% substitution of Ti for Cr on B-sites in the ferromagnetic mother spinel CuCr2S4. The localized magnetic moment of CuCrTiS4 comes from Cr3+ with S = 3/2, where a valence state of Cu+Cr3+Ti4+S4 2− is built up. Experimental data will be focused only on the static properties of dc magnetization M(T) under various magnetic fields, without any dynamical magnetic feature. The spin-glass phase transition T g is well defined at low field, nevertheless hardly in higher fields than approximately 40 Oe. An appearance of the field dependence of M(T) of CuCrTiS4 is similar to that of Fe0.50Mn0.50TiO3 with the short-range Ising SG, and also these of AgMn and CuMn with the long-range interacting Heisenberg SGs. This general nature in M(T) seems to originate from the common mechanism under magnetic fields for all the spin-glasses.

Magnetic ordering in Ni–Cd ferrite

A series of Ni1−xCdxFe2O4 (0.0≤x≤0.8) were prepared by conventional double sintering ceramic method and sintered at 1200°C for 6h. X-ray diffraction results confirmed the single-phase spinel structures of all the samples. The Curie temperature decreases linearly with increasing Cd content, which is explained due to the weakening of the A–B exchange interaction. The sample with x=0.7 shows re-entrant type of spin glass phase transitions. The magnetic moment and saturation magnetization at 20K are found to increase with Cd content up to x=0.5 and then tends to decrease for x>0.5. The increase in magnetic moment with cadmium is attributed to Neel's two sublattice (A- and B-sublattice) collinear models according to which the magnetic moment is the vector sum of the lattice magnetic moment. The decrease in magnetization for x>0.5 obeys the Yafet–Kittel (Y–K) model. The increase in Y–K angles for x>0.3 indicates the increased tendency for triangular spin arrangements on B-sites. This suggests the existence of a canted spin structure in the ferrite system with higher content of Cd.

Field dependence of the transverse spin glass phase transition: Quantitative agreement between Monte Carlo simulations and experiments

The field dependence of the transverse spin glass phase transition temperature, Txy(B), has been determined both for a – FexZr100−x (x = 90, 91, 92, and 93) using muon spin relaxation and for the bond-frustrated nearest neighbor ±J Heisenberg spin glass using Monte Carlo simulations. In both cases, we find Txy(B) ∝ 1/B, providing direct, quantitative agreement between experiments and simulations.