Griffiths Phase Research Articles

Disorder, Low-Energy Excitations, and Topology in the Kitaev Spin Liquid.

The Kitaev model is a fascinating example of an exactly solvable model displaying a spin-liquid ground state in two dimensions. However, deviations from the original Kitaev model are expected to appear in real materials. In this Letter, we investigate the fate of Kitaev's spin liquid in the presence of disorder-bond defects or vacancies-for an extended version of the model. Considering static flux backgrounds, we observe a power-law divergence in the low-energy limit of the density of states with a nonuniversal exponent. We link this power-law distribution of energy scales to weakly coupled droplets inside the bulk, in an uncanny similarity to the Griffiths phase often present in the vicinity of disordered quantum phase transitions. If time-reversal symmetry is broken, we find that power-law singularities are tied to the destruction of the topological phase of the Kitaev model in the presence of bond disorder alone. However, there is a transition from this topologically trivial phase with power-law singularities to a topologically nontrivial one for weak to moderate site dilution. Therefore, diluted Kitaev materials are potential candidates to host Kitaev's chiral spin-liquid phase.

Unbiased identification of the Griffiths phase in intercalated transition metal dichalcogenides by using Lee-Yang zeros

The Griffiths phase, consisting of ordered magnetic clusters, may arise in a nominally paramagnetic state. However, univocal identification of this peculiar state in materials still remain elusive. Here, the authors show that the problem may be resolved by verification of a scaling law specific to the Griffiths phase. Analyzing magnetization data in intercalated titanium and the niobium dichalcogenides Fe${}_{x}$TiS${}_{2}$ and Cr${}_{x}$NbSe${}_{2}$ with the aid of the scaling law, the compounds with and without the Griffiths phase can be unambiguously identified.

Effect of chemical disorder on Griffiths phase in weak itinerant ferromagnetic Ni92−xCuxCr8 alloy

We report magnetic and thermal properties of Cu substituted Ni92−xCuxCr8 polycrystalline alloys close to their critical concentration (xc~18%), where ferromagnetic order disappears. From the detailed analysis of field and temperature dependent magnetization data weak itinerant ferromagnetic character has been identified for the compositions below xc. Spin-fluctuations theory using the Ginzburg–Landau formalism further revealed the contributions of spin fluctuations, which increase near xc. Specific heat data shows unusual low-temperature variation with an enhanced Sommerfeld coefficient and non Fermi-liquid behavior due to strong magnetic fluctuations near xc. The magnetization data and the linear term of the specific heat follow the theoretical predictions of a ferromagnetic quantum critical point within the experimental uncertainties. The exponent of the power-law M(H) ∝Hλ fits to low-temperature magnetic isotherms and its variation with composition indeed suggests a possibility of quantum Griffiths phase in these alloy compositions. Finally, this study shows that the Cu substituted Ni-Cr system shows Griffiths phase at critical point even after the reduction of disorder.

Origin of the Griffiths phase and correlation with the magnetic phase transition in the nanocrystalline manganiteLa0.4(Ca0.5Sr0.5)0.6MnO3

In this paper, a detailed comprehensive magnetic study on the origin of the Griffiths phase (GP) in the nanocrystalline ${\mathrm{La}}_{0.4}{({\mathrm{Ca}}_{0.5}{\mathrm{Sr}}_{0.5})}_{0.6}{\mathrm{MnO}}_{3}$ compound has been presented. The system exhibits a ferromagnetic (FM)-like transition around ${T}_{\mathrm{C}}\phantom{\rule{4pt}{0ex}}\ensuremath{\sim}$ 274 K. Interestingly, above ${T}_{\mathrm{C}}$, the state is not pure paramagnetic, but a short-range FM interaction or GP is observed and the interaction persists up to the Griffiths transition temperature, ${T}_{G}\phantom{\rule{4pt}{0ex}}\ensuremath{\sim}$ 350 K. The detailed investigation of isothermal magnetization and the magnetocaloric effect along with its theoretical analysis have been employed besides the conventional magnetic measurements to probe the GP. Disorder in the system is introduced via increasing an A-site cationic size mismatch along with an additional defect originated owing to the particle size reduction. The disorder-induced magnetic phase transition has also been analyzed by critical analysis. A correlation between the unusual critical parameters with the GP has been furnished.

Multifunctional behaviour in B-site disordered double perovskite EuPrCoMnO6

We report magnetic, transport, dielectric, and complex impedance of polycrystalline double perovskite EuPrCoMnO6 which crystallizes in disordered orthorhombic phase with space group Pnma. The DC magnetization shows two successive ferromagnetic transitions around 146 K and 138 K. The temperature and magnetic field variation of DC-susceptibility suggest the existence of Griffith phase and spontaneous exchange bias. AC susceptibility measurement shows a glassy dynamic behaviour near ferromagnetic transition. Further, a re-entrant glassy dynamic state is seen at a low temperature around 40 K. Temperature-dependent resistivity shows semiconducting/insulating nature, which gets increased under the application of magnetic field, showing positive magnetoresistance. The dielectric study shows usual frequency-dependent step-like behaviour with a colossal dielectric constant near room temperature. The complex impedance study shows both grain and grain boundary contribute to the electrical properties. The observed properties suggest the material can be used for spintronic devices and high dielectric applications.

Nanostructure-driven complex magnetic behavior of Sm2CoMnO6 double perovskite

Magnetic double perovskite oxides have steadily emerged as an important class of functional materials. A clear understanding of the complex interactions that govern the magnetic behavior, and thereby, the functionality in these mixed valence compounds, however, remains elusive. In this study, we show that the complex nanostructure that forms in these compounds is at the root of their magnetic behavior. Using complementary experimental and micromagnetic simulation results, we have uncovered the complex nanostructure of polycrystalline Sm2CoMnO6, a typical double perovskite oxide, and established how the nanostructure drives its magnetic behavior. Our results show that Sm2CoMnO6 exhibits a Griffiths phase with the formation of ferromagnetic clusters above the ordering temperature. The isothermal magnetization curves show no sign of saturation, even at the highest measured field (9 T), and irreversibility in the entire magnetic field range. Despite a very clear indication of the presence of antiferromagnetic antisite defects, surprisingly, no antisite defect-induced exchange bias occurs. This is explained from the micromagnetic simulations that confirm the presence of ferromagnetic nanoclusters and nanosized, random, and uncorrelated antisite defects, resulting in no exchange bias. This work provides a clear understanding of the role of antisite defects, in particular, on how their structure can lead to the presence/absence of exchange bias. The fundamental insight offered in this work fills an important knowledge gap in the field and will be of immense value in realizing the true potential of double perovskite oxides for future technological applications.

Observation of Griffiths phase, critical exponent analysis and high magnetocaloric effect near room temperature at low magnetic field in V-doped La0.7Sr0.3MnO3

We report on observation of the Griffiths phase (GP), high magnetocaloric properties at low magnetic fields and temperature-dependent critical exponents of La0.7Sr0.3V x Mn1−x O3 (x = 0, 0.05 and 0.1) perovskite bulk materials. The Curie temperature (T C) of pure La0.7Sr0.3MnO3 (LMSO) is seen to be 368.7 K and decreases toward room temperature (RT) (342.2 K) by 10 mol% V doping at the Mn site. V doping leads to an enhancement in magnetic entropy change (−ΔS M) from 1 J kg−1 K−1to 1.41 J kg−1 K−1. V doping at a Mn site leads to the formation of GP, a magnetic disorder due to the coexistence of a paramagnetic (PM) matrix and short-range ferromagnetic (FM) clusters. X-ray photoelectron spectroscopy analysis confirms the presence of mixed-valence V4+/V5+along with Mn3+/Mn4+ ions contributing to various double exchange interactions. The natures of phase transitions and magnetic interactions are analyzed by evaluating critical exponents δ, β, and γ. All the samples show second-order FM to PM phase transition, confirmed from the modified Arrott plots and critical exponent analysis carried out using the Kouvel–Fisher method. The enhancement in magnetic entropy change along with the decrease in Curie temperature toward RT by V doping in the LMSO oxides indicates the possible application of these materials in magnetic refrigeration at low magnetic fields.

Quenching of spin-orbit coupling and signature of Griffiths Phase in nanocrystalline La0.6Ba0.4MnO3 perovskite manganite

The size-dependent structural and magnetic properties of nano and bulk samples of 40 ​mol% Ba2+-doped LaMnO3 (i.e., La0.6Ba0.4MnO3) manganite have been investigated in detail. The Rietveld refinement of X-ray diffraction data confirms that nano and bulk La0.6Ba0.4MnO3 manganites crystallize into ideal cubic perovskite structure with Pm3¯m space group. The refined unit cell parameters decrease with increasing calcinations temperature or particle size. The temperature dependent magnetization measurements reveal that both the bulk and nano samples exhibit paramagnetic (PM) to ferromagnetic (FM) phase transition at Curie temperature (TC). A distinct bifurcation between magnetization curves under zero-field cooled (MZFC) and field-cooled (MFC) measurements reveals the possible existence of frustrated magnetic ordering or spin glass clusters. For nano sample, a sharp downward deviation in inverse susceptibility from Curie-Weiss law is observed, which indicates the existence of Griffiths Phase. The analysis of the field dependent magnetization M(H) curves measured at 10 ​K, in terms of saturation moments, reveals that there is a coupling between spin and orbital magnetic moments, in bulk sample of La0.6Ba0.4MnO3 manganite, which can be quenched by reducing particle size of the manganite. According to the Banerjee's criterion, nano sample exhibits first-order magnetic transition and bulk sample shows second-order magnetic transition in the low magnetic field region.

Electronic Structure, Griffiths Phase, and Magnetocaloric Effect in La0.7Ca0.3Mn1−xCuxO3 (x = 0.1) showing first- and second-order characters

Electronic Structure, Griffiths Phase, and Magnetocaloric Effect in La0.7Ca0.3Mn1−xCuxO3 (x = 0.1) showing first- and second-order characters

Room-temperature magnetoresistive and magnetocaloric effect in La1−xBaxMnO3 compounds: Role of Griffiths phase with ferromagnetic metal cluster above Curie temperature

The evolution of the Griffiths phase (GP) with a ferromagnetic metal (FMM) cluster above the Curie temperature (TC) and its effect on the magnetic properties, electrical transport, magnetoresistance (MR), and magnetocaloric effect (MCE) is studied comprehensively, using bulk compounds of La1−xBaxMnO3 (0.15 ≤ x ≤ 0.25) with different lattice distortions but with the same structural symmetry and space group. These La1−xBaxMnO3 samples show ferromagnetic transition at TC increasing from 229 K for x = 0.15–300 K for x = 0.25, in addition to the presence of GP with FMM clusters in the paramagnetic (PM) region, which have been confirmed by the combination of magnetization (susceptibility) measurements, the GP theory, and electron paramagnetic resonance technology. With increasing the Ba2+ ion doping, GP temperature (TG) and TC of La1−xBaxMnO3 are increased, and the GP regime is strengthened. The GP ratio in the PM region reached 27.7% for the sample with x = 0.20. The resistivity decreases and the FMM phase increases with increasing x from 0.15 to 0.25, which can be explained by the decrease in the bandgap (Eg) and the enhancement of the double-exchange effect. Remarkably, large room-temperature MR (∼44.7%) can be observed in the sample with x = 0.25 under 60 kOe, which is related to the presence of the GP regime. Furthermore, the MCE is also affected by the GP regime, and it is deduced that the magnetic transition is of second order. The value of magnetic entropy change (|ΔSM|) reaches 3.04 J/kg K near room temperature for the sample with x = 0.25 under 50 kOe. This value is associated with a relative cooling power (RCP) of 248.1 J/kg. For the sample with x = 0.15, the value of RCP reaches 307.6 J/kg under 50 kOe. The discovery of the MR and MCE near room temperature is of great significance from the practical application of perovskite manganites in magnetic sensors and magnetic refrigerants.

Evidence of Griffith Phase in Quantum Critical Region of Dy2ti1.8mn0.2o7

Evidence of Griffith Phase in Quantum Critical Region of Dy2ti1.8mn0.2o7

Signatures of a Quantum Griffiths Phase Close to an Electronic Nematic Quantum Phase Transition.

In the vicinity of a quantum critical point, quenched disorder can lead to a quantum Griffiths phase, accompanied by an exotic power-law scaling with a continuously varying dynamical exponent that diverges in the zero-temperature limit. Here, we investigate a nematic quantum critical point in the iron-based superconductor FeSe_{0.89}S_{0.11} using applied hydrostatic pressure. We report an unusual crossing of the magnetoresistivity isotherms in the nonsuperconducting normal state that features a continuously varying dynamical exponent over a large temperature range. We interpret our results in terms of a quantum Griffiths phase caused by nematic islands that result from the local distribution of Se and S atoms. At low temperatures, the Griffiths phase is masked by the emergence of a Fermi liquid phase due to a strong nematoelastic coupling and a Lifshitz transition that changes the topology of the Fermi surface.

Criticality and Griffiths phases in random games with quenched disorder.

The perceived risk and reward for a given situation can vary depending on resource availability, accumulated wealth, and other extrinsic factors such as individual backgrounds. Based on this general aspect of everyday life, here we use evolutionary game theory to model a scenario with randomly perturbed payoffs in a prisoner's dilemma game. The perception diversity is modeled by adding a zero-average random noise in the payoff entries and a Monte Carlo simulation is used to obtain the population dynamics. This payoff heterogeneity can promote and maintain cooperation in a competitive scenario where only defectors would survive otherwise. In this work, we give a step further, understanding the role of heterogeneity by investigating the effects of quenched disorder in the critical properties of random games. We observe that payoff fluctuations induce a very slow dynamic, making the cooperation decay behave as power laws with varying exponents, instead of the usual exponential decay after the critical point, showing the emergence of a Griffiths phase. We also find a symmetric Griffiths phase near the defector's extinction point when fluctuations are present, indicating that Griffiths phases may be frequent in evolutionary game dynamics and play a role in the coexistence of different strategies.

Powerful method to evaluate the mass gaps of free-particle quantum critical systems

We present a numerical method for the evaluation of the mass gap, and the low-lying energy gaps, of a large family of free-fermionic and free-parafermionic quantum chains. The method is suitable for some generalizations of the quantum Ising and XY models with multispin interactions. We illustrate the method by considering the Ising quantum chains with uniform and random coupling constants. The mass gaps of these quantum chains are obtained from the largest root of a characteristic polynomial. We also show that the Laguerre bound, for the largest root of a polynomial, used as an initial guess for the largest root in the method, gives us estimates for the mass gaps sharing the same leading finite-size behavior as the exact results. This opens an interesting possibility of obtaining precise critical properties very efficiently which we explore by studying the critical point and the paramagnetic Griffiths phase of the quantum Ising chain with random couplings. In this last phase, we obtain the effective dynamical critical exponent as a function of the distance-to-criticality. Finally, we compare the mass gap estimates derived from the Laguerre bound and the strong-disorder renormalization-group method. Both estimates require comparable computational efforts, with the former having the advantage of being more accurate and also being applicable away from infinite-randomness fixed points. We believe this method is a relevant tool for tackling critical quantum chains with and without quenched disorder.

Effect of small cation occupancy and anomalous Griffiths phase disorder in nonstoichiometric magnetic perovskites

The structural, magnetic, magnetocaloric and Griffiths phase (GP) disorder of non-stoichiometric perovskite manganites La0.8−xSr0.2−yMn1+x+yO3 are reported here. Determination of valence states and structural phases evidenced that the smaller cations Mn2+ and Mn3+ will not occupy the A-site of a perovskite under atmospheric synthesis conditions. The same analysis also supports that the vacancy in the A-site of a perovskite induces a similar vacancy in the B-site. The La3+ and Sr2+ cation substitutions in the A-site with vacancy influences the magnetic phase transition temperature (TC) inversely, which is explained in terms of the electronic bandwidth change. An anomalous non-linear change of the GP has been observed in the Sr-substituted compounds. The agglomeration of Mn3+-Mn4+ pairs (denoted as dimerons), into small ferromagnetic clusters, has been identified as the reason for the occurrence of the GP. A threshold limit of the dimeron formation explains the observed non-linear behaviour of the GP formation. The Sr-substituted compounds show a relatively large value of isothermal entropy change (maximum 3.27 J/kgK at μ0H=2T) owing to its sharp magnetic transition, while the broad change of magnetization in the La-substituted compound enhances the relative cooling power (maximum 98 J/kg at μ0H=2T).

Structural and magnetic properties of La2Ni1−x Zn x MnO6 compounds

Compounds of a randomly diluted ferromagnetic system La2Ni1−x Zn x MnO6 (LNZ x MO) (x = 0.2, 0.4, 0.6, 0.8) have been synthesized by Sol-gel technique. These compounds possess monoclinic structure (P21/n, space group number 14) at room temperature. Below the Curie temperature (T C), LNZ x MO are soft ferromagnets with low values of remanent magnetization (M r ) and coercivity (H c ) for x less than equal to 0.6. The exchange interaction is of short range nature. Freezing of clusters is observed in LNZ0.8MO below T = 10 K. Although, LNZ x MO is a randomly diluted ferromagnetic system, no signature of Griffiths phase (GP) is found.

Nature of Griffiths phase and ferromagnetic 3d-4f interaction in double-perovskite Dy2CoMnO6

Double perovskites Dy2CoMnO6 (DCMO) was synthesized by a sol-gel method and the structure and magnetic properties were systematically investigated. Both X-ray diffraction and Raman spectrum indicate that double pervoskite DCMO has a monoclinic structure with a space group P21/n. A Griffiths phase is confirmed to be existing in DCMO by the magnetic behaviors, which is significantly different from the behaviors of the non-Griffiths phase of Gd2CoMnO6 (GCMO) recently reported in reference. It is suggested that the origins of the different short-range magnetic orders of them can be attributed to the different 3d-4f exchange interactions in DCMO and GCMO, besides the effect of the unavoidable anti-site disorder, interrupting the long-range ferromagnetic (FM) order of Co2+-O-Mn4+, resulting in the formation of short-range FM order. The effects of A-site rare-earth Re3+ ions on the magnetism of double perovskite Re2Co(Ni)MnO6 are dominated by the combining and competing functions of the radius and the moments of rare earth ions (or the 3d-4f exchange interactions). The FM/AFM coupling is not only related to the most outer 4f electrons of the rare earth ions, but also to the inner 5d/6s orbital electrons.

Observation of In-Plane Quantum Griffiths Singularity in Two-Dimensional Crystalline Superconductors.

Quantum Griffiths singularity (QGS) reveals the profound influence of quenched disorder on the quantum phase transitions, characterized by the divergence of the dynamical critical exponent at the boundary of the vortex glasslike phase, named as quantum Griffiths phase. However, in the absence of vortices, whether the QGS can exist under a parallel magnetic field remains a puzzle. Here, we study the magnetic field induced superconductor-metal transition in ultrathin crystalline PdTe_{2} films grown by molecular beam epitaxy. Remarkably, the QGS emerges under both perpendicular and parallel magnetic field in four-monolayer PdTe_{2} films. The direct activated scaling analysis with a new irrelevant correction has been proposed, providing important evidence of QGS. With increasing film thickness to six monolayers, the QGS disappears under perpendicular field but persists under parallel field, and this discordance may originate from the differences in microscopic processes. Our work demonstrates the universality of parallel field induced QGS and can stimulate further investigations on novel quantum phase transitions under parallel magnetic field.

Controlling extended criticality via modular connectivity

Criticality has been conjectured as an integral part of neuronal network dynamics. Operating at a critical threshold requires precise parameter tuning and a corresponding mechanism remains an open question. Recent studies have suggested that topological features observed in brain networks give rise to a Griffiths phase, leading to power-law scaling in brain activity dynamics and the operational benefits of criticality in an extended parameter region. Motivated by growing evidence of neural correlates of different states of consciousness, we investigate how topological changes affect the expression of a Griffiths phase. We analyze the activity decay in modular networks using a susceptible-infected-susceptible propagation model and find that we can control the extension of the Griffiths phase by altering intra- and intermodular connectivity. We find that by adjusting system parameters, we can counteract changes in critical behavior and maintain a stable critical region despite changes in network topology. Our results give insight into how structural network properties affect the emergence of a Griffiths phase and how its features are linked to established topological network metrics. We discuss how those findings could contribute to an understanding of the changes in functional brain networks.

Tunable magnetization reversal and exchange bias in NiCr2O4 ceramics doped with non-magnetic ions

The magnetization reversal and exchange bias (EB) effects were systematically investigated for nanocrystalline samples of NiCr2-xGaxO4 (x = 0–1.0). The intrinsic temperature-induced magnetization reversal (TIMR) effect could be modulated by doping with Ga ions and controlling the particle size. The TIMR effect was closely related to the Griffiths phase observed in this system. Both the zero-field-cooling and field-cooling EB effects could be observed simultaneously within the doping range x = 0.1–0.5. Upon doping with non-magnetic ions, the magnetic interactions of Ni–Cr and Cr–Cr were significantly diluted, which were further confirmed by specific heat measurements. Overall, the results highlight the potential to control the TIMR and EB phenomena by doping and controlling the particle size.