Vogel-Fulcher Law Research Articles

Effect of spin glass frustration on exchange bias in NiMn/CoFeB bilayers.

Exchange bias in ferromagnetic/antiferromagnetic systems can be explained in terms of various interfacial phenomena. Among these, spin glass frustration can affect the magnetic properties in exchange bias systems. Here we have studied a NiMn/CoFeB exchange bias system in which spin glass frustration seems to play a crucial role. In order to account for the effect of spin glass frustration on magnetic properties, we have investigated the temperature and cooling field dependence of exchange bias. We have observed the decrease of exchange bias field (μ0HEB) with cooling field (μ0HFC) whereas there is a negligible effect on coercive field (μ0HC). Exponential decay of μ0HEB and μ0HC is found in this exchange bias system. Furthermore, training effect measurements have been performed to study the spin relaxation mechanism. We have fitted the training effect data with a frozen and rotatable spin relaxation model. We have determined the ratio of relaxation rates of interfacial rotatable and frozen spins in this study. The training effect data are also fitted with various other models. Furthermore, we have observed the shifting of the peak temperature towards higher temperature with frequency from the ac susceptibility data. The peak temperature vs. frequency data can be described by the Vogel-Fulcher law, which indicates the spin glass like state in the bilayer system.

Zn-Fe-oxide nanostructures of different iron concentrations for multifunctional applications: properties and precursor influence.

Zn-Fe-O nanoparticle systems (Z3F, Z20F and Z60F) were produced by changing the Zn:Fe ratio (0.97 : 0.03, 0.8 : 0.2 and 0.4 : 0.6 in at%, respectively) in Zn(ii)-Fe(iii)-carboxylate precursors. According to X-ray diffraction, Z60F is nearly single-phase ZnFe2O4 (5.9 nm crystallite size), Z20F is a ZnO/ZnFe2O4 nanocomposite consisting of 48.8% ZnFe2O4 (4.7 nm crystallite size), and Z3F is apparently pure ZnO (9.5 nm). We found evidence for a ZnFe2O4 spinel of high inversion degree (80-100%) and with superparamagnetic (SPM) behaviour at room temperature in all three samples by a remarkable correlation between HRTEM, FTIR, XPS, Mössbauer and magnetization analyses. Iron modifies the decomposition process of the precursor and enhances its viscosity, which appears to favour the separation of Zn- and Fe-rich phases. As a consequence, two-phase systems of individual nanocrystals/nanoparticles (ZnO and ZnFe2O4) are formed. The large anisotropy constant, 106-107 erg cm-3, of the ZnFe2O4 nanoparticles and the concentration dependence of their magnetic energy barrier are explained in terms of interparticle interactions interlinked with finite size effects and high inversion degree; these factors also control the other parameters of importance for applications, including the blocking temperature (13-111 K), saturation magnetization (1.08-17.7 emu g-1 at 300 K, 4.6-44.8 emu g-1 at 5 K) and coercivity (85.4-491 Oe at 5 K). Magnetic dynamic results, particularly modelled by the Néel-Brown and Vogel-Fulcher laws, yield fitting parameters which validate the presence of concentration-dependent dipole-like interactions between ZnFe2O4 nanoparticles. A fraction of iron was found in the Fe2+ state, presumably substituting for Zn2+ in zinc oxide; however, the samples behave like ZnFe2O4 SPM nanoclusters/nanoparticles dispersed in a nonmagnetic ZnO particle assembly, rather than Zn(Fe)O dilute magnetic semiconductors. The relevance of the properties of the investigated material for specific applications is highlighted throughout the manuscript.

Crossover of positive and negative magnetoconductance in composites of nanosilica glass containing dual transition metal oxides.

A facile sol–gel approach to prepare composites of nanosilica glass containing dual transition metal oxides with compositions xCoO·(20 − x)NiO·80SiO2 comprising x values 5 (NC-1), 10 (NC-2) and 15 (NC-3) within hexagonal pores of SBA-15 template has been demonstrated. The synergistic effect of dual transition metal oxide ions on MD properties and crossover of positive and negative magnetoconductance phenomena were observed in these nanocomposite systems. The physical origin of magnetoconductance switching is explained based on the factors: nanoconfinement effect, wave-function shrinkage and spin polarized electron hopping. DFT calculations were performed to understand the structural correlation of the nanoconfined system. The static (dc) and dynamic (ac) responses of magnetization revealed the spin-glass behaviour of the investigated samples. Both scaling law and Vogel–Fulcher law provide a satisfactory fit to our experimental results which are considered as a salient feature of the spin-glass system. Our studies indicate the possibilities of fabricating magnetically controlled multifunctional devices.

Revision of the freezing concept in relaxor ferroelectrics: the case of Na0.5Bi0.5TiO3-Sr0.7Bi0.2TiO3 solid solutions

Presence of a frequency-independent maximum and a frequency-dependent shoulder in temperature-frequency dependence of dielectric permittivity are characteristic features of NBT-based solid solutions, while interpretation of these features is insufficient. In the present work, dielectric dispersion is studied in a wide frequency range (20 mHz–30 GHz) in (1-x)NBT-xSr0.7Bi0.2TiO3 solid solutions, in which a continuous transfer from NBT-like to pure relaxor-like behaviour is observed upon increasing of Sr0.7Bi0.2TiO3 concentration. Temperature dependence of dielectric dispersion and static dielectric permittivity in different compositions of this solid solutions group is analysed. The observed behaviour of static dielectric permittivity upon increasing of x is interpreted as a diminishing of transition between the low and the high-temperature states, while the character of the dielectric dispersion remains the same in both sides of the transition. Upon increasing of x, the dielectric dispersion transforms from the behaviour characteristic to relaxor ferroelectrics into the behaviour resembling dipolar glass. Problems, arising from introducing of the concept of freezing, described by the Vogel-Fulcher law, are discussed.

Dynamic spin freezing and magnetic memory effect in ensembles of interacting anisotropic magnetic nanoparticles

We explore the influence of demagnetization interaction on magnetic memory effect by varying organization geometry of anisotropic ZnFe$_2$O$_4$ nanoparticles in an ensemble. The static and dynamic behaviour of two differently organized ensembles, compact ensemble (CE) and hollow core ensemble (HCE), are extensively studied by both dc and ac susceptibility, magnetic memory effect and spin relaxation. The frequency-dependence peak shifting of freezing temperature in both the systems is analyzed properly with the help of two dynamic scaling models: Vogel-Fulcher law and power law. Presence of cluster spin-glass phase is reflected from Vogel-Fulcher temperature $T_0$ $\simeq$ 142.58 K for CE, $\simeq$ 97 K for HCE and characteristic time constant $\tau_0$ $\simeq$ $8.85\times10^{-9}$ s for CE, $\simeq$ $3.8\times10^{-10}$ s for HCE; along with $\delta$T$_{Th}$ $\sim$ 0.1 for CE and 0.2 for HCE. The power law fitting with dynamic exponent $zv'$ = 6.2 $\pm$ 1.1 for CE, 6.3 $\pm$ 0.5 for HCE and single spin flip $\tau^*$ $\simeq$ $7.7\times10^{-11}$ s for CE, $\simeq$ $1.3\times10^{-10}$ s for HCE provide firm confirmation of cluster spin-glass phase. The progressive spin freezing across multiple metastable states with prominent memory effects is reflected in both the systems via nonequilibrium dynamics study. The hollow core geometry with anisotropic nanoparticles on surface with closer proximity leads to complex anisotropy energy landscape with enhanced demagnetizing field resulting highly frustrated surface spins. As a consequence, more prominent magnetic memory effect is observed in HCE with higher activation energy, reduced blocking temperature and enhanced coercivity than that of CE.

Understanding the relationship between the local crystal structure and the ferrimagnetic ordering of CoxMn3-xO4 (x = 0–0.5) solid solutions

The local crystal structure alterations in the tetrahedral positions of the hausmannite Mn3O4 structure by Co2+ ions and its consequence on the magnetic ordering are studied in detail. The cation composition, bond distance and bond angle of the CoxMn3-xO4 series (x = 0.0. 0.1, 0.3 and 0.5) is determined by XRD Rietveld refinement. The charge state of the elements Co, Mn and O are investigated using XPS measurements, which confirm the bivalent cobalt ion occupation in the tetrahedral lattice. Considerable reduction in tetrahedral and axial octahedral bonds with the introduction of Co2+ ions dramatically increased the Curie temperature (TC) from 43 K (Mn3O4) to 62 K (Co0.5Mn2.5O4). The Lotgering-Srinivasan-Seehra model is employed to study the canted spin arrangement and the exchange interactions of Co0.5Mn2.5O4. The presence of cluster glass transition at TP = 42 K in Co0.3Mn2.7O4 is well-established through the AC susceptibility measurements and it is further substantiated by Vogel-Fulcher law and dynamic scaling power law. The origin of the cluster glass state is confirmed by the calculated strong geometric frustration factor (f = 19.5), due to the inhomogeneous distribution of cobalt ions in the intermediate concentrations. Field cooled isothermal magnetic measurements corroborated the exchange bias phenomenon in the Co0.3Mn2.7O4 sample, because of the interaction between ferrimagnetic-cluster glass phases occurring below the spin freezing temperature TP.

Evolution of Relaxor Behavior in Multiferroic Pb(Fe2/3W1/3)O3-BiFeO3 Solid Solution of Complex Perovskite Structure

Mutiferroic materials like bismuth ferrite BiFeO3 have attracted much interest in the last decade due to their promising potential for such applications as spintronics and magnetoelectric data storage devices. On the other hand, relaxor ferroelectrics have been intensively studied for their complex structures with quenched disorder and polar nanoregions which play an important role in their outstanding piezoelectric performance. Much less studied are the single-phase multiferroics that exhibit ferroelectric and/or magnetic relaxor behavior and the correlation between their structure and intricate magneto-electric interactions. In this work, we investigate the evolution of the structure and relaxor behavior in the solid solution between the complex perovskite multirelaxor Pb(Fe2/3W1/3)O3 [PFW] and canonical multiferroic BiFeO3 [BFO], (1-x)PFW-xBFO (with a solubility limit of x = 0.30). The temperature dependences of the dielectric permittivity and loss tangent measured in the frequency range from 100 Hz to 1 MHz indicate characteristic relaxor ferroelectric properties for compositions of x ≤ 0.15, with a frequency-dependent dielectric permittivity peak and its temperature, Tm, satisfying the Vogel-Fulcher law. Detailed studies of the evolution of the relaxor behavior with composition reveal that Tm decreases firstly with a small amount (x = 0.05) of BFO substitution and then increases with further increase of BFO concentration. The degree of relaxor character, as defined by ΔTm [Tm (1 MHz) - Tm (100 Hz)], increases monotonously with increasing BFO content, signifying an enhancement of relaxor behavior with BFO substitution, which is confirmed by the Lorenz-type quadratic variation of the static permittivity. A temperature - composition phase diagram is constructed in terms of the characteristic Burns temperature (TB) and freezing temperature (Tf), which delimits a paraelectric state (PE) above TB, a non-ergotic relaxor state (NR) below Tf, and an ergotic relaxor state (ER) in between. The observed enhancement of relaxor behavior is explained by an increase in the number and size distribution of polar nanoregions in the ER phase, resulting from increased compositional and charge disorders as a result of BFO substitution. The evolution of relaxor behavior and its microscopic mechanisms studied in this work are insightful for a better understanding the multirelaxor properties in multiferroics. Moreover, further substitution of BFO (x ≥ 0.2) flattens the permittivity curves and leads to a temperature-stable variation of high dielectric constant (≈ 103) in a wide temperature range, making the PFW-BFO solid solution attractive for such applications as high energy density capacitors.

Avoided quantum criticality and cluster-glass formation in itinerant ferromagnet Sr1−x(La0.5K0.5)xRuO3

We demonstrate that the cluster-glass state emerges as ferromagnetic quantum criticality is avoided in itinerant ferromagnet Sr1-x(La0.5K0.5)xRuO3. In this compound, the ferromagnetic order is suppressed by increasing x, and then disappears at the critical concentration: x=0.5. In this x range, the present study reveals that no prominent feature is ascribed to the quantum critical fluctuations in specific heat. Instead, ac magnetic susceptibility exhibits a broad peak due to spontaneous spin freezing, and the peak temperature depends significantly on the frequency of the applied ac magnetic field. Furthermore, specific heat is enhanced within a wide temperature range, whereas specific heat shows no salient anomaly associated with spin freezing. These features are characteristics of the formation of cluster-glass; in particular, the observed frequency variations in ac magnetic susceptibility are well described by the Vogel-Fulcher law. We compare the features concerning the suppression of the ferromagnetic order in this doped compound with those in isostructural Ca- and La-doped SrRuO3, and suggest that a local correlated disorder effect and the very small coherence of itinerant Ru 4d electrons are responsible for the cluster-glass formation instead of the quantum phase transition in Sr1-x(La0.5K0.5)xRuO3.

Structural stability and magnetic properties of Mn2FeAl alloy with a β-Mn structure

The synthesized Mn2FeAl alloys crystallize in a geometrically frustrated cubic β-Mn structure (space group: P4132) with an antiferromagnetic ordering whereas the previous theoretical findings suggest for a Heusler structure (L21: regular and X: inverse). The experimental stability of the structure is verified by electronic structure calculations performed for various arrangements of Mn, Fe and Al atoms in the β-Mn-type crystal structure. When compared the energy of the β-Mn structure with the energy of L21 and X type structures, it is found that for an expansion of the lattice volume β-Mn structure becomes more preferable in total energy than L21 and X-type structures. The calculated theoretical equilibrium lattice parameter value for the β-Mn2FeAl is within the accuracy of the experimental value obtained in this work. Additional DFT + U calculations for the optimized crystal structure of the β-Mn2FeAl revealed that the electronic correlations in the Mn ions result in the increased total magnetic moment. In the X type structure, Mn2FeAl is a half metal, whereas the disordered arrangement of atoms in the β-Mn structure leads to the closure of the semiconductor gap. The β- Mn2FeAl alloys exhibit antiferromagnetic ordering (TN ≈ 42 K), which is in excellent agreement with our electronic structure calculations. The detailed analysis of the magnetic and heat capacity measurements suggests a short-range magnetic ordering in the Mn2FeAl alloys. Owing to the strong antiferromagnetic spin fluctuation caused by the geometric frustration in β-Mn, a large enhancement in the electronic heat capacity is noticed. Mn2FeAl shows the characteristic features of spin glass as verified from the frequency dependent AC susceptibility analysis using critical power law and Vogel-Fulcher law. To the best of our knowledge, this is the first ever report on the theoretically predicted lowest ground state configuration for Mn2FeAl with a β-Mn structure and the experimental realization of spin glass features in this geometrically frustrated antiferromagnet.

Cluster glass transition in the ternary Dy2AgIn3 system determined by neutron diffraction and Ac–Dc magnetization measurements

The crystallographic and magnetic properties of the polycrystalline intermetallic compound Dy2AgIn3 are presented. The compound crystallizes in the hexagonal CaIn2- type structure (space groupP63/mmc). The magnetic susceptibility data reveals a Curie–Weiss (CW) law behavior above120K, with a calculated effective magnetic moment μeff=10.63±0.29μB/Dy3+and a Curie paramagnetic temperatureθp=17.5K±0.5K, demonstrating the dominance of ferromagnetic (FM) couplings in the sample. In the temperature range of 60-120Kit exhibits a Griffith’s phase like behavior. The dc field cooled (FC) and zero field cooled (ZFC) susceptibility, show field dependent irreversible phenomena belowTr~43K, and the ZFC plots present a cusp glass like maxima at31K. The irreversibility temperatureTradopts aH2/3, field dependence of de Almeida–Thouless type line which defines the stability limits in the H-T plane withTr(0)=44.5±0.5K. The ac susceptibility data shows a relative shift in freezing temperature δTf~0.048±0.004, while near the freezing temperature it exhibits a Power- Vogel-Fulcher law dependency characterized by the dynamic exponentszν=7.4, single flip time τ0=10-6sandTg=24.5±0.65K. These values suggest the formation of cluster spin-glass states (CSG). At low angles the neutron diffraction (ND) profiles display diffuse scattering of antiferromagnetic (AFM) origin which is triggered by the ~5nm- magnetic spin clusters.

Direct estimation of the activation energy and relaxation times from the anomalies observed in the dielectric, AC and DC resistivity data using modified Lorentz equation

In the present study, we have investigated the dielectric, AC and DC resistivity properties of [Ba(Nd0.1Ti0.8Nb0.1)O3](1−y)[Na0.5Bi0.5TiO3]y ceramics with y = 0.60, 0.65 and 0.70. These ceramic materials were prepared through a solid-state double sintering route. It is shown in this paper, the other possible way to estimate the activation energy and relaxation times using modified Lorentz equations as proposed by us instead of well-known Arrhenius, modified Arrhenius and Vogel–Fulcher laws.

Reentrant spin-glass behaviour in highly frustrated Mn-rich spinel zinc manganate

The present work offers an insight into the magnetic properties of Mn-rich spinel zinc manganate. Rietveld refinement reveals the formation of Zn0.67Mn2.33O4, where Zn2+ and Mn2+ ions are randomly distributed in the tetrahedral sublattice. DC and AC susceptibility measurement of Zn0.67Mn2.33O4 infers the occurrence of two kinds of transition below 11 K. Paramagnetic to ferrimagnetic transition occur at 10.7 K and ferrimagnetic to spin glass-like transition occurs at 5.8 K. The long-range canted ferrimagnetic ordering is corroborated using modified Lotgering model and calculated the exchange interaction values (JAA = 5.2 K,JAB = 5.3 K, JBB = 14.8 K). Further, the observed shift in freezing temperature with DC magnetic field obeys Almeida–Thouless behaviour and frequency dependence of AC susceptibility follows Vogel–Fulcher law. However, the complete establishment of the canonical spin glass state is denied since the manganese ions occupied at the tetrahedral site is equal to the percolation threshold (=33%). Subsequently, the observed spin glass-like behaviour (5.8 K) below Curie temperature (10.7 K) evidences the reentrant spin glass nature. Similarly, the strong frustration in Zn0.67Mn2.33O4 lattice is observed through the substantial negative value of Curie–Weiss temperature (∼−599 K) and very high frustration factor (f = 56). Overall, the chosen Zn0.67Mn2.33O4 is a highly frustrated magnetic system revealing re-entrant spin-glass behaviour.

Low-temperature magnetic properties of MgFe1.2Ga0.8O4 spinel nanoparticles

A detailed study has been carried out of the static and dynamic magnetic properties of ferrimagnetic spinel MgFe1.2Ga0.8O4 nanoparticles (NPs), including the measurements of low-field dc-magnetization M(T) under zero-field-cooled (ZFC) and field-cooled (FC) conditions and ac-susceptibility χac(T) at different frequencies (f) and amplitudes of the ac-field (Hac). Below, a Curie temperature (TC), a clear magnetic irreversibility (MZFC(T) ≠ MFC(T)), as well as a broad peak in both MZFC(T)–MFC(T) magnetizations have been observed. At T ≪ TC, the two distinct, frequency-dependent peaks at Tp1 ≈ 9 K and Tp2 ≈ 14 K in the imaginary part of the ac-susceptibility χac''(T) have been found. Their positions have been consistent with those of the anomalies detected on the temperature dependence of the magnetic contribution to the heat capacity Cmag(T), and a sharp decrease of the MZFC(T) magnetization near ≈ 10–20 K. It was revealed that the fitting of the frequency dependence of the peaks’ positions (Tp1(f) and Tp2(f)) in the imaginary part of ac-susceptibility χac''(T) using the Neel-Arrhenius law yields unphysical values of the relaxation time (τ0) and, therefore, these results ruled out a possibility of an existence of superparamagnetic (SPM) clusters in the system. On the other hand, the Tp1(f) and Tp2(f) dependences followed both the Vogel-Fulcher law and the power law. These observations indicate that, a complex magnetic state in MgFe1.2Ga0.8O4, realized in the low temperature region, may likely be related to a progressive freezing of magnetic clusters.

Cluster glass behavior of the frustrated birnessites AxMnO2·yH2O(A=Na,K)

We report on the synthesis and magnetic properties of frustrated Na0.22MnO2*0.39H2O and K0.6MnO2*0.48H2O with the birnessite structure. The structure, static and dynamic magnetic properties of the compounds are investigated in detail. A combination of DC and AC magnetic susceptibility measurements and magnetization decay measurements reveal cluster glass behavior below the freezing temperature of 4 K for Na-birnessite and 6 K for K-birnessite. The frequency dependence of the freezing temperature is analyzed on the basis of dynamic scaling laws including the critical slowing down formula and the Vogel-Fulcher law, which further confirm cluster glass formation in both compounds.

LiZn2V3O8: a new geometrically frustrated cluster spin-glass

We have investigated the structural and magnetic properties of a new cubic spinel LiZn2V3O8 (LZVO) through x-ray diffraction, dc and ac susceptibility, magnetic relaxation, aging, memory effect, heat capacity and 7Li nuclear magnetic resonance (NMR) measurements. A Curie–Weiss fit of the dc susceptibility () yields a Curie–Weiss temperature K. This suggests strong antiferromagnetic (AFM) interactions among the magnetic vanadium ions. The dc and ac susceptibility data indicate the spin-glass behavior below a freezing temperature Tf 3 K. The frequency dependence of the Tf is characterized by the Vogel–Fulcher law and critical dynamic scaling behavior or power law. From both fitting, we obtained the value of the characteristic angular frequency 3.56 106 Hz, the dynamic exponent 2.65, and the critical time constant 1.82 10−6 s, which falls in the conventional range for typical cluster spin-glass (CSG) systems. The value of relative shift in freezing temperature 0.039 supports a CSG ground states. We also found aging phenomena and memory effects in LZVO. The asymmetric response of the magnetic relaxation below Tf supports the hierarchical model. Heat capacity data show no long-range or short-range ordering down to 2 K. Only about 25% magnetic entropy change signifies the presence of strong frustration in the system. The 7Li NMR spectra show a shift and broadening with decreasing temperature. The spin-lattice and spin–spin relaxation rates show anomalies due to spin freezing around 3 K as the bulk magnetization.

Distributions of relaxation times in relaxor ferroelectric Ba(Ti0.8 Ce0.2)O3

The dielectric behavior of the Ba(Ti0.8Ce0.2)O3 ceramics was studied by broadband dielectric spectroscopy in a temperature interval 140–500 K. The broad dielectric relaxation was analyzed by the Havriliak–Negami relationship and the distribution of relaxation times formalism. It was found that the Havriliak–Negami average relaxation time, longest and most probable relaxation times from the distribution of relaxation times follow the Vogel–Fulcher law. The freezing temperature of the longest relaxation time is substantially higher than the freezing temperature of the most probable relaxation time, indicating the distribution of freezing temperatures. The dielectric dispersion has all features inherent to relaxor ferroelectrics and the relaxation is assigned to the dynamics of polar nanoregions.

Dielectric and ferroelectric properties of Gd3+ doped (K0.5Na0.5)0.96Li0.04(Nb0.8Ta0.20)O3 piezoelectric ceramics

We report the structural, dielectric, ferroelectric and piezoelectric properties of Gd3+ doped lead-free (K0.5Na0.5)0.96Li0.04(Nb0.8Ta0.20)O3 (KNLNT) ceramics. The transition temperature (TT-C and TO-T) shifted towards the lower temperature (281 °C and 110 °C) for (K0.5Na0.5)0.92Li0.04Gd0.04(Nb0.8Ta0.20)O3 (KNLGNT) ceramics. Frequency dispersion of TT-C or TO-T suggests that KNLGNT ceramics exhibit a relaxor behavior supported by the Vogel-Fulcher law and modified Curie Weiss law. Temperature-dependent resistivity analysis shows that the conduction mechanism follows Mott’s variable range hopping with an average hopping length of 7.23 nm, hopping energy 0.46 eV and density of states near the Fermi level [N(EF)] = 129 × 1016 eV−1 cm−3 for KNLGNT ceramics. Reduction in leakage current and enhancement in dielectric (εr = 1025, tanδ = 0.061 at 1 MHz), ferroelectric properties (Pr = 23.14 μC/cm2,EC = 8.70 kV/cm at 1 Hz) and piezoelectric properties (kp (53%) and d33 (128 pC/N)) were observed for KNLGNT ceramics, which are promising for high-frequency piezoelectric devices.

A study of cluster spin-glass behaviour at the critical composition [formula omitted]NiGe

The solid solution Mn1-xFexNiGe with x~0.27 has been investigated via powder ray diffraction, dc magnetization, ac susceptibility, heat capacity, and magnetic relaxation measurements. The alloy Mn0.73Fe0.27NiGe crystallizes in a Ni2In-type hexagonal structure at room temperature. A coexistence of hexagonal and orthorhombic phases with a phase fraction of nearly 88:12 was found below 80 K. The dc susceptibility measurements reveal a paramagnetic to ferromagnetic transition at around Tt≃80 K and a thermal hysteresis observed during field-cooled-cooling and field-cooled-warming suggests the first order nature of the magnetic transition. The splitting between zero-field-cooled and field-cooled dc susceptibilities and the appearance of a frequency dependent peak in ac susceptibility indicate the onset of a spin-glass transition at Tg≃58 K. The relative shift in freezing temperature (δTf) is calculated to be ~0.03 and ~0.09, respectively from the real and imaginary parts of ac susceptibility indicating the formation of cluster spin-glass state. The analysis of frequency dependent Tf using power law yields a characteristic time for a single spin flip τ*≃1.5×10-10 s and critical exponent zν′≃5.5. Similarly, the analysis using the Vogel-Fulcher law results a characteristic time for a single spin flip τ0≃1.2×10-8 s, Vogel-Fulcher temperature T0≃54.8 K, and an activation energy Ea/kB≃72.8 K. The magnitude of τ* and τ0 together with a non-zero value of T0 add further evidence for the formation of cluster spin-glass. The magnetic relaxation and memory effect measurements also demonstrate the low temperature cluster spin-glass behaviour. The reason for the cluster spin-glass behaviour could be the difference in local environment of Mn atoms in the coexisting Mn-rich antiferromagnetic and Fe-rich ferromagnetic phases. Furthermore, Mn0.73Fe0.27NiGe shows the asymmetric response of magnetic relaxation with a change in temperature, belowTf, which can be explained by the hierarchical model. The low temperature heat capacity gives a large electronic coefficient γ≃25 mJ/mol K2 and the Debye temperature θD≃300 K. This value of θD is in close agreement with that calculated from the temperature variation of unit cell volume.

Dielectric behaviors and relaxor characteristics in Bi0.5Na0.5TiO3-BaTiO3 ceramics

Microstructure and dielectric behaviors of heating/cooling and bias-field were investigated in lead-free ceramics ([Formula: see text])[Formula: see text][Formula: see text][Formula: see text]BaTiO3 (BNT[Formula: see text]BT, [Formula: see text], 0.02, 0.04, 0.06, 0.08 and 0.10). The relaxor characters and the Vogel–Fulcher law of frequency-dependent dielectric properties were analyzed. Three dielectric anomalies with pronounced frequency dispersion at [Formula: see text], a maximum dielectric with variable frequency-dispersion at [Formula: see text] and a third Maxwell–Wagner-type relaxation over a wide temperature range in high-temperature region were observed. The significant dielectric thermal hysteresis, low barrier energy, high freezing temperature in heating process and the maximum dielectric tunability appeared in [Formula: see text] ceramic.

Dielectric Properties of Epoxy-Matrix Composites with Tungsten Disulfide Nanotubes

Addition of conductive nanotubes to an insulating polymer matrix has been proven as an efficient strategy that can improve the electromagnetic shielding performance, due to the high aspect ratio of nanotubes. Herein, a set of epoxy-matrix composites filled with 0.15-1.6 vol% of tungsten disulfide (WS2) nanotubes being of 30-120 nm in diameter and 5-20 μm in length has been produced. Electromagnetic properties of the prepared composites were probed in the frequency range from 20 Hz to 1 MHz in a temperature range from 250 K to 500 K. Broadband properties of these materials are controlled by the dynamics of epoxy resin molecules, and no electrical percolation was observed up to the highest concentration (1.6 vol%) of WS2 nanotubes. The value of dielectric permittivity for all composites is not bigger than 6 at room temperature and 1 kHz frequency, and the electrical conductivity of composites is about 10-6 S/m at 500 K, which demonstrate that the composites are suitable for antistatic applications at higher temperatures. The relaxation time follows the Vogel-Fulcher law, and the Vogel temperature T0 has the minimum for the WS2 nanotube concentration 0.15 vol%. Above 410 K, the electrical conductivity determines the properties of the investigated composites due to nonzero electrical conductivity of epoxy resin. The value of DC electrical conductivity for pure epoxy at T=450 K is 0.3 μS/m, while the DC conductivity of the composites slightly increases with the WS2 concentration. Therefore, the electrical contacts between WS2 nanotubes and polymer matrix are rather ohmic. Additionally, the activation energy is almost independent on the concentration of WS2. However, it is higher in composites than in pure epoxy resin.