Spin-glass Transition Research Articles

Nanostructure-induced functional combination of vanishing magnetostriction and magnetic softness in ferromagnetic (GaNi)xCoCrFe (x = 0.4–1.6) high-entropy alloys

Searching for high-entropy alloys with functional properties that emerge from their multi-scale structure, we have investigated the (GaNi)xCoCrFe (x = 0.4–1.6) system. We have characterized structure, microstructure, nanostructure and chemical composition of the individual phases in the multi-phase alloys and determined their magnetic, magnetostrictive and electrical properties. We found that the alloys are ferromagnetic and exhibit functional combination of magnetic softness and vanishing magnetostriction, classifying them as energy-efficient “supersilent” materials (inaudible to a human ear) for alternating-current (AC) electromagnetic applications in the audio-frequency range. The alloys develop a two-phase structure, a face-centered cubic (fcc) and a body-centered cubic (bcc), where the fcc phase fraction decreases, while the bcc fraction increases with the increasing (GaNi)x content. Ferromagnetism of the alloys originates from the highly nanostructured bcc phase, with the ferromagnetic Curie temperatures in the range TC = 750–700 K, depending on x. The fcc phase is not nanostructured and is paramagnetic at room temperature, but undergoes a spin glass transition at Tf≈6.4 K. The magnetic softness and vanishing magnetostriction of the alloys are both nanomagnetic phenomena. The magnetic-softness and magnetostriction parameters of the x = 1.3 and 1.6 alloys make them relevant for supersilent AC applications at low frequencies.

Unusual spin dynamics in the van der Waals antiferromagnet FeGa2S4

Spin dynamics in the van der Waals antiferromagnet FeGa2S4with triangular lattices are investigated using magnetometry, neutron scattering, and muon spin relaxation measurements. The characteristic spin relaxation time is thoroughly clarified over thirteen orders of magnitude. Although the temperature dependence of DC and AC susceptibilities recalls a conventional spin-glass transition, nonlinear susceptibilities showing no divergences at the anomalous temperature,T∗=16.87(7) K, deny that and instead hint at other mechanisms. Elastic neutron scattering together with previously measured muon results depict a slowly fluctuated (∼10-5 s) spin state aboveT∗. In juxtaposing the underlying simplest structure among frustrated magnets with an intricate hierarchy of time scales, FeGa2S4can be a playground for studying temporal spin correlations in the two-dimensional limit.

Evidence for a Griffiths Phase to Cluster Spin Glass Transition in the La2/3Sr1/3(Mn1-3 xAl2 xTix)O3 System.

The presence of Griffiths phase to cluster spin glass transition has theoretically been predicted in both classical and quantum systems. However, its detection in a classical system has been lacking for decades, which hinders a complete understanding of the relationship between the Griffiths phase and cluster spin glass. Here, the experimental discovery of the Griffiths phase to cluster spin glass transition is reported in a classical magnetic system, diluted ferromagnets La2/3Sr1/3(Mn1-3 xAl2 xTix)O3 (0 ≤ x ≤ 0.12). The phase diagram of the system shows a transition from the Griffiths phase into a ferromagnetic state in the low disorder concentration range (0.01 < x ≤ 0.09). In the high disorder concentration range (0.09 < x ≤ 0.12), a Griffiths phase to cluster spin glass transition is identified, which nicely matches that of disordered quantum systems. Moreover, the Griffiths phase is essentially an unfrozen cluster spin glass with partially broken ergodicity is demonstrated experimentally. These findings serve as crucial experimental references for understanding the glassy phenomena in disordered magnets, facilitating future exploration of their unique properties and functionalities.

Intermediate-spin state of Co ions in magnetic and thermoelectric properties of double perovskite Ba2CoNbO6

Double perovskite Ba2CoNbO6, obtained by pyrolysis of nitrate-organic mixtures, was studied by XRD, XRF, DFT, AC/DC-magnetization, specific-heat, thermoelectric, and ESR methods. The sample has cubic symmetry space group Pm3m with a = b = c = 4.0074(11) Å. Deficiency in oxygen ions shows the presence of Co ions in both 3+ and 2+ valency. According to AC-magnetization and specific-heat data, Ba2CoNbO6 demonstrates spin-glass ordering at TSG = 30 K at external field value of 0.1 kOe. This temperature of spin glass transition drops with field power increase down to complete suppression at 10 kOe. The effective magnetic moment determined using the Curie-Weiss approximation is 4.29 μB, which is consistent with the theoretical estimation for Co ions in the intermediate-spin state. The peak at T = 90 K, observed in the temperature dependence of the specific heat and accompanied by a peak in the ESR linewidth, is possibly due to the structural transition at this temperature. The Seebeck coefficient of the compound is S = 4–6.5 μV/K and the band gap obtained within the small-polaron-jump conductivity model is ΔE = 0.284 eV in the temperature range of 350–550 K connected with DFT calculation. An intensity ESR line, related to Co2+ ions, was observed in ESR spectra.

A complex magnetic study: evidence of spin-glass transition below long-range magnetic ordering and its correlation with renormalization of phonon modes

In this paper, we report a complex magnetic behavior arising due to the interplay of three active magnetic cations (Nd/Sm, Co and Ir), forming 3d-5d-4f magnetic sublattices. The B-site ordered double perovskites Nd2CoIrO6and Sm2CoIrO6were successfully prepared by conventional solid-state method. Detailed structural analysis revealed that both samples crystallized in monoclinic structure with P21/n (No.-14) space group. X-ray photoelectron spectroscopy analysis confirms the presence of multiple oxidation states of Ir (i.e. Ir4+and Ir5+). Both samples show a paramagnetic-ferrimagnetic (TFiM) transition around 100 K, additionally, a low temperature transition is observed at around 10 K in the SCIO sample. This FM-like behavior of the samples is attributed to the antiparallel alignment of the Co2+and Ir4+spins, resulting in FiM ordering. The ac susceptibility analysis confirms a spin glass type transition just below the long-range ordering temperature in NCIO sample, The obtained characteristic flipping time of a single spin from both the law (Power law and Vogel-Fulcher law) and nonzero Vogel-Fulcher temperature (T0≃ 89.1 K) further verified the existence of cluster spin-glass behavior below the ordering temperature. The temperature evolution of phonon modes (up to 4 K) suggests that the phonon mode above the magnetic ordering temperature is mainly governed by the lattice degrees of freedom; notable renormalization of the mode frequency below the ordering temperature is due to the coupling of lattice with the underlying magnetic degrees of freedom.

Replica symmetry breaking in 1D Rayleigh scattering system: theory and validations

Spin glass theory, as a paradigm for describing disordered magnetic systems, constitutes a prominent subject of study within statistical physics. Replica symmetry breaking (RSB), as one of the pivotal concepts for the understanding of spin glass theory, means that under identical conditions, disordered systems can yield distinct states with nontrivial correlations. Random fiber laser (RFL) based on Rayleigh scattering (RS) is a complex disordered system, owing to the disorder and stochasticity of RS. In this work, for the first time, a precise theoretical model is elaborated for studying the photonic phase transition via the platform of RS-based RFL, in which we clearly reveal that, apart from the pump power, the photon phase variation in RFL is also an analogy to the temperature term in spin-glass phase transition, leading to a novel insight into the intrinsic mechanisms of photonic phase transition. In addition, based on this model and real-time high-fidelity detection spectral evolution, we theoretically predict and experimentally observe the mode-asymmetric characteristics of photonic phase transition in RS-based RFL. This finding contributes to a deeper understanding of the photonic RSB regime and the dynamics of RS-based RFL.

Interpenetrated Lattices of Quaternary Chalcogenides Displaying Magnetic Frustration, High Na-Ion Conductivity, and Cation Redox in Na-Ion Batteries.

A series of quaternary selenides, NaxMGaSe4 (M = Mn, Fe, and mixed Zn/Fe), have been synthesized for the first time employing a high-temperature solid-state synthesis route through stochiometric or polychalcogenide flux reactions. Along with the selenides, a previously reported sulfide analogue, NaxFeGaS4, is also revisited with new findings. These compounds form an interpenetrated structure made up of a supertetrahedral unit. The electrochemical evaluations exhibit a reversible (de)intercalation of ∼0.6 and ∼0.45 Na-ions, respectively, from Na2.87FeGaS4 (1a) and Na2.5FeGaSe4 (2) involving Fe2+/Fe3+ redox when cycled between 1.5 and 2.5 V. Mössbauer spectroscopy of 1a shows the existence of a mixed oxidation state of Fe2+/3+ in the pristine compound and reversible oxidation of Fe2+ to Fe3+ during the electrochemical cycles. Na2.79Zn0.6Fe0.4GaSe4 possesses a reasonably high room temperature ionic conductivity of 0.077 ms/cm with an activation energy of 0.30 eV. The preliminary magnetic measurements show a bifurcation of FC-ZFC at 4.5 and 2.5 K, respectively, for 1a and Na3MnGaSe4 (4) arising most likely from a spin-glass like transition. The high negative values of the Weiss constants -368.15 and -308.43 K for 1a and 4, respectively, indicate strong antiferromagnetic interactions between the magnetic ions and also emphasize the presence of a high degree of magnetic frustration in these compounds.

Low-temperature cluster spin glass transition in the single-domain NiCr2O4 nanoparticles

NiCr2O4 nanoparticles with average particle size ∼15 nm, a single-domain size maintains the bulk canted antiferromagnetic ground state, were synthesized by a microwave combustion method. The magnetic behavior was carefully investigated by static and dynamic magnetic susceptibility measurements. In addition to a spin-glass-like behavior below paramagnetic-ferrimagnetic transition at T C, the NiCr2O4 nanoparticles demonstrate a low-temperature cluster spin glass transition below the spin canting transition T S, which manifests itself as a magnetic anomaly peak around ∼12 K (at 100 Oe) in the zero-field cooled magnetization with a relatively stronger field dependence in a ‘de Almeida-Thouless’ line for spin glasses. The AC susceptibility analyses in different approaches demonstrate a larger relative peak temperature variation per frequency decade and a longer characteristic relaxation time in the order of 0.04 and 10−7 s, against 0.01 and 10−9 s for the high-temperature blocking, indicating the slow spin dynamics for the low-temperature cluster glassy phase. A field-temperature magnetic phase diagram is proposed for the single-domain NiCr2O4 nanoparticles.

Exploring the critical behavior of the anomalous spin-glass transition in Ga1−xMnxS

Single-crystalline Ga1−xMnxS is a quasi-two-dimensional system that exhibits an anomalous spin-glass transition temperature compared with the other well-known spin-glass systems. In contrast to the other known spin-glasses that all have three-dimensional structures, our host chalcogenide GaS system is quasi-two-dimensional. Recent interest in utilizing spin-glass materials for applications in short-term, low-energy memory and processing power make this new 2-D system important for further exploration. We report on the critical behavior of the anomalous spin-glass transition in a single-crystalline Ga0.91Mn0.09S system. Using the scaling equation of state describing the spin-glass transition in Ga1−xMnxS, we obtained the relation χnl = C1H2/δ and extract the value δ = 5.5 ± 0.5 for this critical exponent as well as a value of ϕ = 4.8 for another critical exponent. We find this value of delta for the critical temperature Tc = 11.2 K, combined with the other critical exponents γ = 4.0 and β = 0.8 form a self-consistent description of the spin-glass transition in this unusual 2-D spin-glass system. Interestingly, these results represent convincing evidence that, despite Ga1−xMnxS having a quasi-two-dimensional structure, Ga1−xMnxS undergoes a true spin-glass transition and is related to the class of semiconducting spin-glass materials with short-range interactions. The spin-glass transition in Ga1−xMnxS is characterized by critical exponents similar to the three-dimensional spin-glass systems.

Reentrant spin glass transition and partial substitution induced superconductivity in magnetocaloric Mn5Sn3 alloys

Reentrant spin glass transition and partial substitution induced superconductivity in magnetocaloric Mn5Sn3 alloys

Gauge theory for quantum XYZ spin glasses

Nishimori’s gauge theory is extended to the quantum XYZ p-spin glass model in finite dimensions. This enables us to obtain useful correlation equalities, which show also that Duhamel correlation functions at an arbitrary temperature are bounded by those in the corresponding classical model on the Nishimori line. These bounds give that the spontaneous magnetization vanishes in any low temperature even if the model enters the Z2 -symmetry broken spin glass phase. This theory explains well-known fact from experiments and numerical calculations that the magnetic susceptibility does not diverge in the spin glass transition. The new gauge theory together with the known phase diagram of the Edwards–Anderson model can specify the spin glass region in the coupling constant space of the quantum Heisenberg XYZ spin glass model.

High-pressure synthesis of A-site ordered perovskite PbMn3(CrMn3)O12 with long-range antiferromagnetic ordering and a spin glass transition.

An AA'3B4O12-type perovskite oxide PbMn3(CrMn3)O12 was synthesized by high-pressure solid-state reactions at 8 GPa and 1373 K. Synchrotron X-ray diffraction shows a cubic crystal structure with the space group Im3̄. The charge states are verified by X-ray photoelectron spectroscopy to be PbMn3+3(Cr3+Mn3+2Mn4+)O12, where the Pb2+ and Mn3+ are 1 : 3 ordered respectively at A and A' sites, while the Cr3+, Mn3+ and Mn4+ are disorderly distributed at the B site. PbMn3(CrMn3)O12 features a long-range antiferromagnetic order of A'-site Mn3+ spins at about 66 K and a subsequent spin glass transition around 36 K due to the randomly distributed Cr3+, Mn3+, and Mn4+ cations at the B site. This unique stepwise order of A' and B-site spins indicates weak A'-B site spin interactions, which are dominated by the difference in the B-site Mn3+/Ni2+ and Mn4+ number in the quadruple perovskites AMn3B4O12.

Phase transitions and slow spin dynamics of slightly inverted A-site spinel CoAl2−x Ga x O4

We report the properties of an A-site spinel magnet, CoAl2−x Ga x O4, and analyze its anomalous, low-temperature magnetic behavior, which is derived from inherent, magnetically frustrated interactions. Rietveld analysis of the x-ray diffraction profile for CoAl2−x Ga x O4 revealed that the metallic ions were randomly distributed in the tetrahedral (A-) and octahedral (B-) sites in the cubic spinel structure. The inversion parameter η could be controlled by varying the gallium (Ga) composition in the range 0.055 ⩽ η ⩽ 0.664. The composition-induced Néel-to-spin-glass (NSG) transition occurred between 0.05 ⩽ η ⩽ 0.08 and was verified by measurements of DC-AC susceptibilities χ and thermoremanent magnetization (TRM) below the Néel transition temperature T N. The relaxation rate and derivative with respect to temperature of TRM increased at both T N and the spin glass (SG) transition temperature T SG. The TRM decayed rapidly above and below these transitions. TRM was highly sensitive to macroscopic magnetic transitions that occurred in both the Néel and SG phases of CoAl2−x Ga x O4. In the vicinity of the NSG boundary, there was a maximum of the TRM relaxation rate at T max < T N. With increasing inversion η(x), the anomaly at T max merged with that of the Néel transition at a tricritical point (η tc, T tc) = (0.08, 4.0 K), where the paramagnetic, Néel, and SG states met. We successfully extracted the relaxation time τ and other characteristic parameters from the TRM isothermal temporal evolution based on the Weron function derived for a purely stochastic process. To distinguish the magnetic states, we compared our results with previously studied inversion-free A-site spinel, CoRh2O4, and CoGa2O4 cluster glass. We generated an inversion-temperature phase diagram based on the comprehensive measurements of DC and AC susceptibilities, TRM, and specific heat in the range 0.055 ⩽ η ⩽ 0.664 for CoAl2−x Ga x O4. Based on this phase diagram, we speculate that a NSG quantum critical phase transition occurred at η = 0.050(6). Our findings are consistent with suppression of the long-range order antiferromagnetic state in CoAl2O4 revealed through neutron diffraction studies, even at T << T N.

Spin glass behavior and dielectric properties of Sm2CuMnO6 perovskites

Monoclinic Sm2CuMnO6 is a fascinating material that exhibits intriguing magnetic and dielectric properties. In this study, we investigated the magnetic transition, conduction mechanism, and dielectric behavior of the material. Mott's variable range hopping of polarons is proposed as a satisfactory explanation for the conduction process, shedding light on the underlying charge transport mechanism. Furthermore, the material displays a spin glass transition at a freezing temperature of Tf = 18 K, suggesting the presence of competing magnetic interactions. Dielectric measurements reveal intriguing temperature and frequency dependence of the dielectric constant (ε) in Monoclinic Sm2CuMnO6. Below 100 K, the dielectric constant remains unchanged with variations in both temperature and frequency, indicating a stable dielectric response. However, above 100 K, ε exhibits an increasing trend with rising temperature and also displays frequency dependence. This behavior suggests the contribution of both deformational and relaxation polarizations, emphasizing the complex nature of the dielectric response.

Evolution of magnetic surfboards and spin glass behavior in (Fe1−p Ga p )2TiO5

The unusual anisotropy of the spin glass (SG) transition in the pseudobrookite system Fe2TiO5 has been interpreted as arising from an induced, van der Waals-like, interaction among magnetic clusters. Here we present susceptibility () and specific heat data () for Fe2TiO5 diluted with non-magnetic Ga, (Fe1−p Ga p )2TiO5, for disorder parameter = 0, 0.11, and 0.42, and elastic neutron scattering data for = 0.20. A uniform suppression of is observed upon increasing , along with a value of that increases as decreases, i.e. We also observe in the low temperature limit. The observed behavior places (Fe1−p Ga p )2TiO5 in the category of a strongly geometrically frustrated SG.

Structural and magnetic properties of nanoparticles of La3Ni2NbO9 double perovskite

The nanoparticles of La3Ni2NbO9 (LNNO) have been produced via the glycine-nitrate combustion technique followed by a process of calcination with an average crystallite size of ∼ 25 nm. The powder X-ray diffraction (XRD) pattern was analyzed for structure analysis by Rietveld structure refinement. Study on the XRD pattern reveals that LNNO crystallizes in the single phase of monoclinic crystal structure with P21/n space group. Analysis of temperature-dependent magnetization reveals that nanoparticles of LNNO undergo paramagnetic to antiferromagnetic phase transition at Neel temperature TN ∼ 43 K and antiferromagnetic to spin glass transition at Tg ∼ 31.45 K. Analysis of magnetic ac-susceptibility reveals that the LNNO nanoparticles follow Vogel-Fulcher and dynamic scaling power laws in the low-temperature region.

Dynamical Scaling Analysis for ±J Ising Model in Three Dimensions

The ±J Ising model in three dimensions is investigated using dynamical scaling analysis for a nonequilibrium relaxation process. The spin-glass (SG) transition is analyzed under an assumed dynamical exponent z proposed for the scaling analysis of the SG transition. To estimate dynamical exponent z precisely, we introduce an extrapolation scheme for the asymptotic value of the logarithmic derivative of the dynamical Binder parameter. We obtain the phase diagram in the temperature–concentration (p–T) space, as well as the p-dependence of critical exponents γ, ν, and z. For the static exponents of the SG transition, the universality is strongly indicated numerically along the whole region of the paramagnetic (PM)–SG phase boundary. A remarkable crossover behavior is observed for estimations of critical exponents at the boundary close to the multicritical point (MCP) of PM–ferromagnetic (FM)–SG phases. In addition, the dynamical assumption for z resulting from the slow relaxation in the SG region disappears in the FM region, and the crossover between them occurs around the Nishimori Line.

Cluster spin glass in off-stoichiometric Ni2.01Mn1.58Sn0.41 alloy

The Ni2.01Mn1.58Sn0.41 alloy is a member of the Heusler material family which undergoes diffusionless structural transition from cubic austenite to orthorhombic martensite during its cooling. The transition was observed at temperature 398 K from paramagnetic austenite to martensite with complex magnetic structure. The measurement of AC magnetic susceptibility of the alloy confirmed spin-glass state at temperatures below 155 K and from the frequency dependence of the cups in AC susceptibility, a presence of clusters (11 nm3 in size) with strong interaction is deduced. The alloy shows anomalous Hall effect (AHE) of the order of 0.051 μΩ cm at 2 K in the spin-glass state of the alloy and its sign changes at around 140 K. The ordinary Hall coefficient of the metallic alloy is strikingly positive in the whole studied temperature region, and it points to complex magnetic and electronic structure of the alloy. The electrical resistance of the sample shows a flat maximum of 220 μΩ cm at spin-glass transition temperature. The magnetoresistance is of the order of 1% and is negative in the whole temperature region which points to a standard scattering of charge carriers on magnetic fluctuations. Quantum-mechanical calculations of supercells with compositions Ni32Mn25Sn7, Ni32Mn26Sn6 and Ni32Mn24Sn8 simulated different arrangement of Mn and Sn atoms. Ni32Mn25Sn7 composition is thermodynamically the most stable, although its magnetic moment is 1.67 μB/f.u., twice higher than the measured value. The combination of the latter two states, with additional Mn–Sn swaps, provides the magnetic moments matching the experimental value at a very small energy cost. Theoretical results then indicate that a scenario of local chemical variations and clustering is likely in the studied alloy.

Structural and spin-glass properties of single crystal J eff = ½ pyrochlore antiferromagnet NaCdCo2F7: correlating T f with magnetic-bond-disorder

Weak bond disorder disrupts the expected spin-liquid ground-state of the ideal S = 1/2 Heisenberg pyrochlore antiferromagnet. Here we introduce a single crystal study of the structural and magnetic properties of the bond-disordered pyrochlore NaCdCo2F7. The magnetic susceptibility appears isotropic, with a large negative Curie-Weiss temperature (θCW = −108(1) K), however no magnetic order is observed on cooling until a spin-glass transition at T f = 4.0 K. AC-susceptibility measurements show a frequency-dependent shift of the associated cusp in χ’ at T f, that can be fitted well by the empirical Vogel-Fulcher law. The magnetic moment of μ eff = 5.4(1) μ B/Co2+ indicates a significant orbital contribution and heat capacity measurements show that down to 1.8 K, well below T f, only S mag ∼ Rln(2) of the magnetic entropy is recovered, suggestive of residual continued dynamics. Structural and magnetism comparisons are made with the other known members of the NaA’’Co2F7 family (A″ = Ca2+, Sr2+), confirming the expected relationship between spin-glass freezing temperature, and extent of magnetic bond disorder brought about by the size mismatch between A-site ions.

Mg-Doped CoCr2O4 Nanoparticles: Implications for Magnetic Memory and Magnetocaloric Effect

Using the co-precipitate method, Mg-doped CoCr2O4 nanoparticles (NPs) with a particle size ranging from 11 to 22 nm were synthesized, and their structural, surface, vibrational, and magnetic properties were examined through experimental and theoretical approaches. The inherent magnetic inhomogeneity of the NPs was found to be the cause of the observed exchange bias effect. The magnetic memory effect was studied below the spin glass-transition temperature using time- and temperature-dependent magnetization measurements, and the magnetocaloric effect was investigated across the Curie temperature. These NPs show promising potential for magnetic memory and magnetocaloric effect fields.