Scaling behavior of dynamic hysteresis in Bi<Subscript>3.15</Subscript>Nd<Subscript>0.85</Subscript>Ti<Subscript>3</Subscript>O<Subscript>12</Subscript> ceramics

The scaling behavior of dynamic hysteresis was investigated in Bi_3.15Nd_0.85Ti₃O₁₂ bulk ceramics at a frequency of 1–1000 Hz and an external electric field amplitude of 79–221 kV/cm. The scaling behavior at low amplitude (E ₀ ≤ 114 kV/cm) takes the form of \(\langle A \rangle \propto f^{ - 0.013} E_{0}^{0.7}\) for low frequency (f ≤ 200 Hz) and \(\langle A \rangle \propto f^{ - 0.013} E_{0}^{0.22}\) for high frequency (f > 200 Hz), where \(\langle A \rangle\) is the area of hysteresis loop and f and E ₀ are frequency and amplitude of external electric field, respectively. At high amplitude (E ₀ > 114 kV/cm), we obtain \(\langle A \rangle \propto f^{0.011} E_{0}^{1.163}\) at low frequency and \(\langle A \rangle \propto f^{ - 0.015} E_{0}^{0.7}\) at high frequency. At low E ₀, the contribution to the scaling relation mainly results from reversible domain switching, while at high E ₀ reversible and irreversible domain switching concurrently contribute to the scaling relation.     

Superconducting Properties of NdO<Subscript>0.5</Subscript><Emphasis Type="Bold">F</Emphasis><Subscript>0.5</Subscript>BiS<Subscript>2</Subscript> Single Crystals

We report on superconducting properties of high-quality single crystals of F-substituted NdOBiS₂ using low-temperature magnetization and transport measurements. Using the mixture of CsCl and KCl as the flux, we have synthesized our single crystals. This compound exhibits bulk superconductivity with a transition temperature of about T _c～4.6 K. The critical current density J _c as a function of temperature has been derived and decreases with the increasing temperature. We construct the phase diagram H _c2(T). The zero-temperature value for \(H_{\mathrm {c2}}^{B\parallel c}\) for value for \(T_{c}^{90~\%}\) and \(T_{c}^{0~\%}\) is estimated to be approximately 2.17 and 1.72 T respectively by using Werthamer-Helfand-Hohenberg model.     

Temperature dependence of the lowest-direct-bandgap energy in the ternary chalcopyrite semiconductor AgInSe<Subscript>2</Subscript>

Photoreflectance spectra have been measured on the ternary chalcopyrite semiconductor AgInSe₂ at T = 15–300 K. The direct-bandgap energies, E _0A, E _0B, and E _0C, of AgInSe₂ show unusual temperature dependence at low temperatures. The resultant temperature coefficients \({\partial E_{0\alpha}/\partial T}\) \(({\alpha=\hbox{A, B, C}})\) are positive at T below ～100 K and negative above ～100 K. These results are successfully explained by taking into account the negative lattice thermal expansion at low temperatures. The spin–orbit and crystal-field parameters Δ_so and Δ_cf are also found to show small temperature variations.     

Inducement of Itinerant Electron Transport in Charge-Ordered Pr<Subscript>0.6</Subscript>Ca<Subscript>0.4</Subscript>MnO<Subscript>3</Subscript> by Ba Doping

The effects of Ba ²⁺ doping on the electrical and magnetic properties of charge-ordered Pr_0.6Ca_0.4MnO₃ were investigated through electrical resistivity and AC susceptibility measurements. X-ray diffraction data analysis showed an increase in unit cell volume with increasing Ba ²⁺ content indicating the possibility of substituting Ba ²⁺ for the Ca-site. Electrical resistivity measurements showed insulating behavior and a resistivity anomaly at around 220 K. This anomaly is attributed to the existence of charge ordering transition temperature, \(T^{\mathrm {R}}_{\text {CO}}\) for the x = 0 sample. The Ba-substituted samples exhibited metallic to insulator transition (MI) behavior, with transition temperature, T _MI, increasing from ～98 K (x = 0.1) to ～122 K (x = 0.3). AC susceptibility measurements showed ferromagnetic to paramagnetic (FM-PM) transition for Ba-substituted samples with FM-PM transition temperature, T _c, increasing from ～121 K (x = 0.1) to ～170 K (x = 0.3), while for x = 0, an antiferromagnetic to paramagnetic transition behavior with transition temperature, T _N, ～170 K was observed. In addition, inverse susceptibility versus T plot showed a deviation from the Curie–Weiss behavior above T _c, indicating the existence of the Griffiths phase with deviation temperature, T _G, increasing from 160 K (x = 0.1) to 206 K (x = 0.3). Magnetoresistance, MR, behavior indicates intrinsic MR mechanism for x = 0.1 which changed to extrinsic MR for x > 0.2 as a result of Ba substitution. The weakening of charge ordering and inducement of ferromagnetic metallic (FMM) state as well as increase in both T _c and T _MI are suggested to be related to the increase of tolerance factor, τ, and increase of e _g ?electron bandwidth as average ionic radius at A-site, <r _A> increased with Ba substitution. The substitution may have reduced MnO₆ octahedral distortion and changed the Mn–O–Mn angle which, in turn, promotes itinerancy of charge carrier and enhanced double exchange mechanism. On the other hand, increase in A-site disorder, which is indicated by the increase in σ ² is suggested to be responsible for the widening of the difference between T _c and T _MI.     

Comparative Experimental and Density Functional Theory (<Emphasis Type="Italic">DFT</Emphasis>) Study of the Physical Properties of MgB<Subscript>2</Subscript> and AlB<Subscript>2</Subscript>

In the present study, we report an intercomparison of various physical and electronic properties of MgB₂ and AlB₂. In particular, the results of phase formation, resistivity ρ(T), thermoelectric power S(T), magnetization M(T), heat capacity (C _P ), and electronic band structure are reported. The original stretched hexagonal lattice with a=3.083 Å, and c=3.524 Å of MgB₂ shrinks in c-direction for AlB₂ with a=3.006 Å, and c=3.254 Å. The resistivity ρ(T), thermoelectric power S(T) and magnetization M(T) measurements exhibited superconductivity at 39 K for MgB₂. Superconductivity is not observed for AlB₂. Interestingly, the sign of S(T) is +ve for MgB₂ the same is ?ve for AlB₂. This is consistent with our band structure plots. We fitted the experimental specific heat of MgB₂ to Debye–Einstein model and estimated the value of Debye temperature (Θ _D) and Sommerfeld constant (γ) for electronic specific heat. Further, from γ, the electronic density of states (DOS) at Fermi level N(E _F) is calculated. From the ratio of experimental N(E _F) and the one being calculated from DFT, we obtained value of λ to be 1.84, thus placing MgB₂ in the strong coupling BCS category. The electronic specific heat of MgB₂ is also fitted below T _c using α-model and found that it is a two gap superconductor. The calculated values of two gaps are in good agreement with earlier reports. Our results clearly demonstrate that the superconductivity of MgB₂ is due to very large phonon contribution from its stretched lattice. The same two effects are obviously missing in AlB₂, and hence it is not superconducting. DFT calculations demonstrated that for MgB₂, the majority of states come from σ and π 2p states of boron on the other hand σ band at Fermi level for AlB₂ is absent. This leads to a weak electron phonon coupling and also to hole deficiency as π bands are known to be of electron type, and hence obviously the AlB₂ is not superconducting. The DFT calculations are consistent with the measured physical properties of the studied borides, i.e., MgB₂ and AlB₂.     

Compounds WAl<Subscript>4</Subscript>, WAl<Subscript>3</Subscript>, W<Subscript>3</Subscript>Al<Subscript>7</Subscript>, and WAl<Subscript>2</Subscript> and Al-W-N combustion products

X-ray diffraction data are presented for combustion products in the Al-W-N system. New, nonequilibrium intermetallic compounds have been identified, their diffraction patterns have been indexed, and their unit-cell parameters have been determined. The phases α-and β-WAl₄ are shown to exist in three isomorphous forms, differing in unit-cell centering. The phases α′-, α″-, and α?-WAl₄ are monoclinic, with a ₀ = 5.272 Å, b ₀ = 17.770 Å, c ₀ = 5.218 Å, β = 100.10°; point groups C12/c1, A12/n1, I12/a1, respectively. The phases β′-, β″-, and β?-WAl₄ are monoclinic, with a ₀ = 5.465 Å, b ₀ = 12.814 Å, c ₀ = 5.428 Å, β = 105.92°; point groups A112/m, B112/m, I112/m, respectively. The compounds WAl₂ and W₃Al₇, identified each in two isomorphous forms, differ in cell metrics (doubling) but possess the same point group: P222. WAl ₂ ^′ : orthorhombic, a ₀ = 5.793 Å, b ₀ = 3.740 Å, c ₀ = 6.852 Å. WAl ₂ ^″ : orthorhombic, a ₀ = 11.586 Å, b ₀ = 3.740 Å, c ₀ = 6.852 Å. W₃Al ₇ ^′ : orthorhombic, Pmm2, a ₀ = 6.225 Å, b ₀ = 4.806 Å, c ₀ = 4.437 Å. W₃Al ₇ ^″ : orthorhombic, Pmm2, a ₀ = 12.500 Å, b ₀ = 4.806 Å, c ₀ = 8.874 Å. The new phase WAl₃: triclinic, P1, a ₀ = 8.642 Å, b ₀ = 10.872 Å, c ₀ = 5.478 Å, α = 104.02°, β = 64.90°, γ = 107.15°.     

Magnetic Entropy Change by Mean-Field Theory for the Second-Order Phase Transition Manganite Nd<Subscript>0.6</Subscript>Sr<Subscript>0.3</Subscript>Ca<Subscript>0.1</Subscript>Mn<Subscript>0.975</Subscript>Fe<Subscript>0.025</Subscript>O<Subscript>3</Subscript>

In this work, we are going to show the method based on mean-field scaling for the Nd_0.6Sr_0.3Ca_0.1Mn_0.975Fe_0.025 O₃ sample, where from scaling of experimental magnetization data, the mean-field exchange parameter λ and the f function of the equation of state \(M(T,H)=B_{S} [\frac {\left ({H+H_{\text {ex}}} \right )}{T}]\) are directly determined. The scaling approach allows finding the dependence of H _ex on T or higher powers of M, which determine the order of the phase transition. Quantum spin number has been determined. In this study, we use \(\left | {\Delta S_{M} (T)} \right |\) obtained from isothermal magnetization measurements; we compare this result to mean-field theory fittings from a novel scaling method through the use of theoretical results S, g, and λ. The obtained results by mean-field theory are suitable and in good agreement with the classical Maxwell relation.     

Anomalous Impact of Hydrostatic Pressure on Superconductivity of Polycrystalline LaO<Subscript>0.5</Subscript>F<Subscript>0.5</Subscript>BiSe<Subscript>2</Subscript>

We report bulk superconductivity at 2.5 K in LaO_0.5F_0.5BiSe₂ compound through the DC magnetic susceptibility and electrical resistivity measurements. The synthesized LaO_0.5F_0.5BiSe₂ compound is crystallized in tetragonal structure with space group P4/nmm and Reitveld refined lattice parameters are a = 4.15(1) Å and c = 14.02(2) Å. The lower critical field of H _c1 = 40 Oe, at temperature 2 K is estimated through the low field magnetization measurements. The LaO_0.5F_0.5BiSe₂ compound showed metallic normal state electrical resistivity with residual resistivity value of 1.35 m Ω cm. The compound is a type-II superconductor, and the estimated H _c2(0) value obtained by WHH formula is above 20 kOe for 90 % ρ _n criteria. The superconducting transition temperature decreases with applied pressure till around 1.68 GPa and with further higher pressures a high- T _c phase emerges with possible onset T _c of above 5 K for 2.5 GPa.     

The H-T and P-T Phase Diagram of the Superconducting Phase in Pd:Bi<Subscript>2</Subscript>Te<Subscript>3</Subscript>

We study the magnetic field vs. temperature (H – T) and pressure vs. temperature (P – T) phase diagrams of the T _c ≈ 5.5 K superconducting phase in Pd _x Bi₂Te₃ (x ≈ 1) using electrical resistivity versus temperature measurements at various applied magnetic fields (H) and magnetic susceptibility versus temperature measurements at various applied magnetic fields (H) and pressure (P). The H – T phase diagram has an initial upward curvature as observed in some unconventional superconductors. The critical field extrapolated to T = 0 K is H _c (0) ≈ 6–10 kOe. The T _c is suppressed approximately linearly with pressure at a rate d T _c /d P ≈ ?0.28 K/GPa.     

Specific Heat Jump at T<Emphasis Type="Italic">c</Emphasis> of High T<Emphasis Type="Italic">c</Emphasis> Superconductors: Effect of Van Hove Singularity

In the BCS framework, exact expressions for the ratio between the jump in the specific heat at T _c and the normal phase specific heat are derived within the Van Hove singularity scenario. Analytical results are obtained for an isotropic s-wave and anisotropic d-wave pairing symmetries. Graphical solutions of the ratio as functions of ω _D /T _c and E _F /T _c , where ω _D is the cutoff energy and E _F is the Fermi energy, show significant deviations from the BCS value of 1.43.     

Crystal structure of [CH<Subscript>3</Subscript>NH<Subscript>3</Subscript>][(UO<Subscript>2</Subscript>)(H<Subscript>2</Subscript>AsO<Subscript>4</Subscript>)<Subscript>3</Subscript>]

The crystal structure of a previously unknown compound [CH₃NH₃][(UO₂)(H₂AsO₄)₃] was solved by direct methods and refined to R ₁ = 0.038 for 3041 reflections with |F _hkl | >-4σ |F _hkl |. The compound crystallizes in the monoclinic system, space group P2₁/c, a = 8.980(1), b = 21.767(2), c = 7.867(1) Å, β = 115.919(5)°, V = 1383.1(3) ų, Z = 4. In the structure of the compound, pentagonal bipyramids of uranyl ions, sharing bridging atoms with tetrahedral [H₂AsO₄]^? anions, form strongly corrugated layered complexes [(UO₂)(H₂AsO₄)₃]^? arranged parallel to the (100) plane. The protonated methylamine molecules [CH₃NH₃]⁺ form unidimensional tapelike packings parallel to the c axis and linked by hydrophilic-hydro-phobic interactions. The topology of the layered uranyl arsenate complex [(UO₂)(H₂AsO₄)₃]^? is unusual for uranyl compounds and was not observed previously. A specific feature of this topology is the presence of monodentate arsenate “branches” arranged within the layer.     

Magnetocaloric-Transport Properties Correlation in La<Subscript>0.8</Subscript> Ca<Subscript>0.2</Subscript>MnO<Subscript>3</Subscript>-Doped Manganites

This investigation is interested in studying the relation between magnetocaloric effect and transport properties i La_0.8Ca_0.2MnO₃ manganite compound. The value of the magnetocaloric effect has been determined from the calculation of magnetization as a function of temperature under different external magnetic fields. This study also provides an alternative method to determine the magnetocaloric properties such as magnetic entropy change and heat capacity change on the basis of M(T, H) measurements. On the other hand, based on magnetic and resistivity measurements, the magnetocaloric properties of this compound were investigated using an equation of the form \({\Delta } S \,=\, - \alpha {\int \limits _{0}^{H}} {\left [ {\frac {\delta Ln\left (\rho \right )}{\delta T}} \right ]}_{H} dH\), which relates magnetic order to transport behavior of the compounds. As an important result, the values of MCE and the results of calculation are in good agreement with the experimental ones, which indicates the strong correlation between the electric and magnetic properties in manganites.     

Superconductivity in Ca<Subscript>0.5</Subscript>La<Subscript>0.5</Subscript>FBiSe<Subscript>2</Subscript>

Through the measurement of resistivity, magnetic susceptibility, and Hall effect, we discovered a novel BiSe₂-based superconductor Ca_0.5La_0.5FBiSe₂ with T _c of 3.9 K. A strong diamagnetic signal below T _c in susceptibility χ(T) is observed indicating the bulk superconductivity. The negative Hall coefficient throughout the whole temperature regime implies the dominant electron-type carriers in the sample. Different to most of BiS₂-based compounds where superconductivity develops from a semiconducting-like normal state, its resistivity in the present compound exhibits a metallic behavior down to T _c . Together with the enhanced T _c , the metallic character of the normal state implies that the electronic structure of Ca_0.5La_0.5FBiSe₂ may be different to those in the other BiS₂-based compounds.     

Investigation of Magnetic,Magnetocaloric, and Critical Properties of La<Subscript>0.5</Subscript>Ba<Subscript>0.5</Subscript>MnO<Subscript>3</Subscript> Manganite

We present an extensive study of the magnetic properties of a novel La_0.5Ba_0.5MnO₃ perovskite material prepared by the hydrothermal method. The explored sample was structurally studied by the x-ray diffraction (XRD) method which confirms the formation of a pure cubic phase of a perovskite structure with Pm3m space group. The magnetic properties were probed by employing temperature M (T) and external magnetic field M (μ_oH) dependence of magnetization measurements. A magnetic phase transition from ferromagnetic to paramagnetic phase occurs at 339 K in this sample. The maximum magnetic entropy change (\(\left | {{\Delta } S}_{M}^{\max } \right |\)) took a value of 1.4 J kg^??1 K^??1 at the applied magnetic field of 4.0 T for the explored sample and has also been found to occur at Curie temperature (T_C). This large entropy change might be instigated from the abrupt reduction of magnetization at T_C. The magnetocaloric effect (MCE) is maximum at T_C as represented by M (μ_oH) isotherms. The relative cooling power (RCP) is 243.2 J kg^??1 at μ_oH =?4.0 T. Moreover, the critical properties near T_C have been probed from magnetic data. The critical exponents δ, β, and γ with values 3.82, 0.42, and 1.2 are close to the values predicted by the 3D Ising model. Additionally, the authenticity of the critical exponents has been confirmed by the scaling equation of state and all data fall on two separate branches, one for T < T_C and the other for T > T_C, signifying that the critical exponents obtained in this work are accurate.     

X-ray Photoelectron Spectroscopy,Magnetotransport and Magnetisation Study of Nb<Subscript>2</Subscript>PdS<Subscript>5</Subscript> Superconductor

In the present report, we investigate various properties of the Nb₂PdS₅ superconductor. Scanning electron microscopy displayed slabs like laminar growth of Nb₂PdS₅ while X-ray photoelectron spectroscopy exhibited the hybridisation of sulphur (2p) with both palladium (3d) and niobium (3d). High-field (140 kOe) magneto-transport measurements revealed that superconductivity (\(T_{c}^{\text {onset}} =?7\) K and T cρ=?0 = 6.2 K) of the studied Nb₂PdS₅ material is quite robust against magnetic field with the upper critical field (H _c2) outside the Pauli paramagnetic limit. Thermally activated flux flow (TAFF) of the compound showed that resistivity curves follow Arrhenius behaviour. The activation energy for Nb₂PdS₅ is found to decrease from 15.15 meV at 10 kOe to 2.35 meV at 140 kOe. Seemingly, the single vortex pinning is dominant in low-field regions, while collective pinning is dominant in high-field region. The temperature dependence of AC susceptibility confirmed the T _c at 6 K, further varying amplitude and frequency, showed well-coupled granular nature of superconductivity. The lower critical field (H _c1) is extracted from DC magnetisation measurements at various T below T _c. It is found that H _c1(T) of Nb₂PdS₅ material seemingly follows the multiband nature of superconductivity.     

High-<Emphasis Type="Italic">T</Emphasis><Subscript>c</Subscript> Hydrides: Interplay of Optical and Acoustic Modes and Comments Regarding the Upper Limit of <Emphasis Type="Italic">T</Emphasis><Subscript>c</Subscript>

The phonon spectrum of many superconducting compounds and, especially, high-T_c hydrides, is broad and rather complicated, because of the presence of high-frequency optical modes. In order to analyze an interplay of optical and acoustic phonon branches, it is convenient to introduce two coupling constants, \(\lambda _{\text {opt.}}\) and \(\lambda _{\text {ac.}}\), along with characteristic frequencies. The correlation between the value of T_c and this interplay is demonstrated for the family of tantal hydrides (TaH₂/TaH₄/TaH₆). The problem of the upper limit of T_c is discussed. The phenomenon of room temperature superconductivity can be provided by the electron-phonon interaction and is described by the strong coupling theory.     

Structure and electrical properties of MnO doped (Ba<Subscript>0.96</Subscript>Ca<Subscript>0.04</Subscript>)(Ti<Subscript>0.92</Subscript>Sn<Subscript>0.08</Subscript>)O<Subscript>3</Subscript> lead free ceramics

In this work, (Ba_0.96Ca_0.04)(Ti_0.92Sn_0.08)O₃–xmol MnO (BCTS–xMn) lead-free piezoelectric ceramics were fabricated by the conventional solid-state technique. The composition dependence (0 ≤ x ≤ 3.0 %) of the microstructure, phase structure, and electrical properties was systematically investigated. An O–T phase structure was obtained in all ceramics, and the sintering behavior of the BCTS ceramics was gradually improved by doping MnO content. In addition, the relationship between poling temperature and piezoelectric activity was discussed. The ceramics with x = 1.5 % sintering at temperature of 1330 °C demonstrated an optimum electrical behavior: d ₃₃ ~ 475 pC/N, k _p ~ 50 %, ε _r ~ 4060, tanδ ~ 0.4 %, P _r ~ 10.3 μC/cm², E _c ~ 1.35 kV/mm, T _C ~ 82 °C, strain ~0.114 % and \(d_{33}^{*}\) ~ 525 pm/V. As a result, we achieved a preferable electric performance in BaTiO₃-based ceramics with lower sintering temperature, suggesting that the BCTS–xMn material system is a promising candidate for lead-free piezoelectric ceramics.     

Crystal structures of Ln<Subscript>2</Subscript>TiO<Subscript>5</Subscript> (Ln = Gd,Dy) polymorphs

Single crystals of four Ln₂TiO₅ polymorphs have been grown, and their structures have been determined: orthorhombic (Gd₂TiO₅, a = 10.460(5), b = 11.317(6), c = 3.750(3) Å, Pnam, Z = 4), hexagonal (Gd_1.8Lu_0.2TiO₅, a = 3.663(3), c = 11.98(1) Å, P6₃/mmc, Z = 1.2), cubic (Dy₂TiO₅, a = 10.28(1) Å, Fd3m, Z = 10.4), and monoclinic (Dy₂TiO₅, a = 10.33(1), b = 3.653(5), c = 7.306(6) Å, β = 90.00(7)°, B2/m, Z = 2.4). The last polymorph has been identified for the first time.     

Synthesis and Superconductivity of Layered Compounds with Orthogonal [Zr<Subscript>2</Subscript>N<Subscript>2</Subscript>] Network

Layered α-form ZrNX (X: Cl and Br) compounds with high quality were prepared by chemical vapor transport. The intercalation of alkali metal A (A: Li, Na, K, Rb) was carried out to realize electron doping into the orthogonal [Zr₂N₂] layers. The Rietveld refinement analysis reveals that the [Zr₂N₂] crystalline layers in the intercalation compounds shift mutually in the ab plane when compared with the hosts. Magnetic measurements show that the intercalation compounds A _x ZrNX are changed into superconductors with transition temperature T _c of up to 12 K. Upon the cointercalation of solvent molecules such as THF, T _c decreases to as low as 6.1 K with increasing the interlayer spacing d up to 14 Å, which is similar to the d dependence of T _c recently found in electron-doped α-form TiNX series. We also succeeded in synthesizing another new polymorph of α-Zr₂N₂S by the topochemical reaction between α-form ZrNX and Na₂S. α-Zr₂N₂S (space group: Immm, a = 4.1375(1) Å, b = 3.5422(1) Å, and c = 11.5204(3) Å) has the same α-[Zr₂N₂] layers, whereas the interlayer spacing between two adjacent [Zr₂N₂] layers is effectively decreased by 1/3 when compared with the parent compounds of ZrNX.     

Methods of Extracting Current Density Dependence of the Effective Activation Energy <Emphasis Type="Italic">U</Emphasis><Subscript>eff</Subscript>(J) in High <Emphasis Type="Italic">T</Emphasis><Subscript>c</Subscript> Superconductors

We have reviewed the methods of extracting current density dependence of the effective activation energy U_eff(J) from experimental data, including transport measurements and magnetic relaxations. Then we applied the method proposed by Maley etc. on our single-phase HgBaCaCuO-1223 sample to obtain the effective activation energy. The effective activation energy U_eff(J, H = 1~T) is extracted from the magnetization relaxation data. On the other hand, U_eff(J) can be theoretically estimated for the model of a sinusoidal washboard potential in superconductors. By comparing the two results we believe that the single curve obtained in the former way can be seen as real current density dependence of effective activation energy U_eff(J). In addition, we have analyzed the reasons why the magnetic decay data at various temperatures can be scaled onto a single curve. The pinning mechanism in the measured temperature range does not change, and the activation energy depends separately on the three variables: T, B, and J are thought as two important factors for this. In the temperature close to zero and near T_c, thermally assisted flux motion would no longer valid since other processes predominate.