Hall Effect In Mixed State Research Articles

Thermally activated flux flow, vortex-glass phase transition and the mixed-state Hall effect in 112-type iron pnictide superconductors

The transport properties in the mixed state of high-quality Ca0.8La0.2Fe0.98Co0.02As2 single crystal, a newly discovered 112-type iron pnictide superconductor, are comprehensively studied by magneto-resistivity measurement. The field-dependent activation energy, U0, is derived in the framework of thermally activated flux flow (TAFF) theory, yielding a power law dependence U0~Hα with a crossover at a magnetic field around 2 T in both H⊥ab and H//ab, which is ascribed to the different pinning mechanisms. Moreover, we have clearly observed the vortex phase transition from vortex-glass to vortex-liquid according to the vortex-glass model, and vortex phase diagrams are constructed for both H⊥ab and H//ab. Finally, the results of mixed-state Hall effect show that no sign reversal of transverse resistivity ρxy(H) is detected, indicating that the Hall component arising from the vortex flow is also negative based on the time dependent Ginzburg-Landau (TDGL) theory. Meanwhile, the transverse resistivity ρxy(H) and the longitudinal resistivity ρxx(H) follow the relation |ρxy(H)|=Aρxx(H)β well with an exponent β~2.0, which is in line with the results in theories or experiments previously reported on some high-Tc cuprates.

Anomalous scaling behavior in a mixed-state Hall effect of a cobalt-doped BaFe2As2epitaxial film with a high critical current density over 1 MA/cm2

The mixed-state Hall effect was examined in a Ba(Fe${}_{1\ensuremath{-}x}$Co${}_{x}$)${}_{2}$As${}_{2}$ epitaxial film with a high critical current density. The transverse resistivity ${\ensuremath{\rho}}_{xy}$ and the longitudinal resistivity ${\ensuremath{\rho}}_{xx}$ follow power law scaling ${\ensuremath{\rho}}_{xy}$ $=$ $A{\ensuremath{\rho}}_{xx}$${}^{\ensuremath{\beta}}$. In the temperature sweep with a fixed field ($T$ sweep), all of the \ensuremath{\beta} values are independent of magnetic field up to 9 T, and are lower than 2.0 (around 1.8). In contrast, the \ensuremath{\beta} values in the magnetic-field sweep with a fixed temperature ($H$ sweep) change from 1.8 to 2.0 as the temperature increases from 13 to 16 K even in the $T$/$H$ region that overlaps with the $T$ sweep measurements. These results indicate that the vortices introduced at low temperatures are trapped by strong pinning centers, but a portion of the vortices introduced at high temperatures are not strongly trapped by the pinning centers. The sign of ${\ensuremath{\rho}}_{xy}$ is negative, and a sign reversal is not detected. These distinct scaling behaviors, which sharply contrast cuprates and MgB${}_{2}$, are explained by high-density pinning centers in the Ba(Fe${}_{1\ensuremath{-}x}$Co${}_{x}$)${}_{2}$As${}_{2}$ epitaxial film and are consistent with a wider vortex liquid phase.

Doping effect on the anomalous behavior of the Hall effect in electron-doped superconductor Nd2−xCexCuO4+δ

Transport properties of Nd2−xCexCuO4+δ/SrTiO3 single crystal films (B‖c,J‖ab) are investigated in magnetic fields B up to 9T at T=(0.4–4.2)K. An analysis of normal state (at B>Bc2) Hall coefficient RHn dependence on Ce doping takes us to a conclusion about the existence both of electron-like and hole-like contributions to transport in nominally electron-doped system. In accordance with RHn(x) analysis an anomalous sign reversal of Hall effect in mixed state at B<Bc2 may be ascribed to a flux-flow regime for two types of carriers with opposite charges.

Scaling behavior of mixed-state hall effect in MgB2 thin films

The Hall resistivity (ρxy) and the longitudinal resistivity (ρxx) in c-axis-oriented superconducting MgB2 thin films have been investigated in extended fields up to 18T. We have observed a scaling behavior between the Hall resistivity and the longitudinal resistivity, ρxy=Aρxxβ, where the exponent (β) is observed to be independent of the temperatures and the magnetic fields. For a wide magnetic field region from 1 to 18T and a wide temperature region from 10 to 28K, a universal power law with β=2.0±0.1 was observed in c-axis-oriented MgB2 thin films. These results can be well interpreted by using recent models.

Normal and mixed state Hall effect in (Hg 0.9Re 0.1)Ba 2CaCu 2O 6+ δ fully textured HTSC thin films

Temperature and magnetic field dependence of the Hall effect in the normal and mixed state of fully textured (Hg 0.9Re 0.1)Ba 2CaCu 2O 6+ δ (HgRe-1212) HTSC thin films prepared by laser ablation deposition have been studied. The longitudinal resistivity ρ xx and Hall resistivity ρ yx of HgRe-1212 superconductor thin films were measured for a wide range of magnetic fields from 125 mT to 12 T with the field perpendicular to the ab plane and the current in the ab plane. A sign change of the Hall resistivity is observed in fields below 3 T in the region close to the superconducting onset temperature. The temperature dependencies ρ xx ∝ T and ρ yx ∝ 1/ T have been observed for HgRe-1212 thin films. The Hall angle θ H relation cot θ H = αT 2 + β, remains valid for temperatures T between T c and 200 K. In the mixed state a power-law behavior is observed, where ρ yx scales to a power-law function of ρ xx : ρ yx = A ρ xx β , with β increasing from 1.0 to 1.7 as the field increases from 1 to 12 T.

Mixed state Hall effect in the multiphase superconductors

Hall effect below T c in multiphase superconductors has been studied on Bi-based superconductors. Samples with different relative content of 2212 and 2223 phase have been prepared. The phase content has been verified by X-ray diffraction. Results show that while resistance and ac susceptibility is almost insensitive to the content of 2212 phase, the qualitative behavior of the Hall resistance is strongly influenced by the presence of both phases. Theoretical calculation of Hall resistance has been made based on effective medium approximation and compared with experimental results.

Hall effect inc-axis-orientedMgB2thin films

We have measured the longitudinal resistivity and the Hall resistivity in the ab-plane of highly c-axis-oriented MgB2 thin films. In the normal state, the Hall coefficient (R_H) behaves as R_H ~ T with increasing temperature (T) up to 130 K and then deviates from that linear T-dependence at higher temperatures. The T^2 dependence of the cotangent of the Hall angle is only observed above 130 K. The mixed-state Hall effect reveals no sign anomaly over a wide range of current densities from 10^2 to 10^4 A/cm^2 and for magnetic fields up to 5 T.

Mixed-state hall effect in Hg- and Tl-based superconducting thin films containing columnar defects

We have investigated the mixed-state Hall resistivity ρ xy and longitudinal resistivity ρ xx in HgBa 2CaCu 2O 6, HgBa 2Ca 2Cu 3O 8, and Tl 2Ba 2CaCu 2O 8 thin films for various parameters, such as densities of columnar defects, number of CuO 2 planes, and anisotropy ratios, as a function of the magnetic field up to 18 T. The scaling exponent β in ρ xy = Aρ xx β is 1.9 ± 0.1 in the clean limit (CL) at high fields and low T whereas β is 1 ± 0.1 in the moderately clean limit (MCL) at low fields and high T. We also find the triple sign reversal in the HgBa 2CaCu 2O 6 films containing high-density columnar defects. These results can be interpreted within the context of a recent theory based on the midgap states in the vortex core.

Mixed-state Hall effect in high-temperature superconductors in small and large magnetic fields

In many high-temperature superconductors, the Hall effect in the mixed superconducting state has a sign opposite to that in the normal state. Some highly anisotropic materials exhibit even a double sign reversal of the mixed-state Hall effect. We investigate this anomaly in precisely-patterned thin films of YBa 2Cu 3O 7−δ (YBCO) in a large range of magnetic fields from 32 mT to 13 T. The Hall conductivity appears to decompose into two contributions of different sign. The positive (hole-like) part increases steeply below the critical temperature and indicates that the scattering rate of the quasiparticles in the superconducting state is drastically reduced. The negative contribution is present around the critical temperature and becomes important in low fields only. The delicate interplay between these two contributions, together with the cutoff of the experimental window by pinning, leads to the various experimental observations, and eventually to a double sign change in fields below 0.25 T that has not been observed previously in YBCO.

Triple sign reversal of the Hall effect inHgBa2CaCu2O6thin films after heavy-ion irradiation

The triple sign reversal in the mixed-state Hall effect has been observed in ion-irradiated ${\mathrm{HgBa}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{6}$ thin films. The negative dip at the third sign reversal is more pronounced for higher fields, which is opposite to the case of the first sign reversal near ${T}_{c}$ in most high-${T}_{c}$ superconductors. These observations can be explained by a recent prediction in which the third sign reversal is attributed to the energy derivative of the density of states and to a temperature-dependent function related to the superconducting energy gap. These contributions prominently appear in cases where the mean free path is significantly decreased, such as our case of ion-irradiated thin films.

Magnetic field and current density dependence of the mixed-state Hall effect in Bi 2Sr 2CaCu 2O x

We report on measurements of the mixed-state Hall effect in Bi 2Sr 2CaCu 2O x thin films in magnetic fields ranging from B=60 mT to B=1 T and current densities j up to 3 MA cm −2. To reduce the problem of sample heating, we employed a pulsed current technique and developed a new heating correction procedure. We observe a double sign reversal of the Hall resistivity ρ yx in the mixed state, resulting in two peaks which both depend on B and j. The position of the sign changes only varies with B, but is found to be independent of j. The Hall conductivity σ xy turns positive again in the superconducting regime and dramatically increases towards lower temperatures and current densities, as the pinning is reduced by intense currents.

Effect of anion doping on Hall sign anomaly in the mixed-state of Tl2Ba2CuO6+delta thin films

The mixed-state Hall effect has been studied in Tl2Ba2CuO6-delta thin films with oxygen content tuned from underdoped to overdoped. Two sign reversals observed both in the underdoped and optimally doped samples disappear simultaneously when the sample is slightly overdoped. These results contradict the prediction of the time-dependent Ginzberg-Landau and microscopic theories but confirm that both Hall sign reversals are determined by electronic band structure. Unlike the previous experiment, our results show that the Hall sign in the underdoped region may be either hole-like or electron-like in the superconducting state.

Decomposition of the Hall angle in the mixed state of superconductors

Much work has gone into the study of the mixed-state Hall effect in high-temperature superconductors (HTS). One of the intriguing features is the reversal of the sign of the Hall angle upon entry into the superconducting state. A common observation for some of the HTS materials, is an empirical decomposition of the measured Hall angle into two terms, one proportional to field (like a normal metal) and the other weakly dependent on field. This observed decomposition can be explained in terms of the Hall effect within the normal vortex cores, combined with the hydrodynamic Magnus force on the body of the vortex. The problem has been treated in the framework of the time-dependent Ginzburg–Landau (TDGL) theory by Kopnin, Ivlev, and Kalatsky [J. Low Temp. Phys. 90 (1993) 1]. We show that the TDGL approach qualitatively explains the observed decomposition, and upon comparing with our data and several other published data, we find rough quantitative agreement as well.

Mixed-State Hall Effect in HgBa 2 CaCu 2 O 6+δ Thin Films with Columnar Defects

The mixed state Hall effect has been studied in high quality HgBa2CaCu2O6+δ thin films while the pinning strength is modified by the irraddition of columnar defects. It has been shown that the pinning strength can be significantly improved by columnar defects. The sign reversal in Hall resistivity is found to be nearly independent of pinning while the scaling behavior between Hall resistivity (ρxy) and longitudinal resistivity (ρxx) is influenced by pinning. The exponent β in the scaling law βxy ∼ βxyβ decrease from 1.8 ± 0.1 to 1.5 ± 0.1 as pinning is enhanced. This results suggest that the sign reversal and the scaling are unrelated, and pinning is not the mechanism of the sign reversal.

Comment on “Pinning Strength Dependence of Mixed-State Hall Effect inYBa2Cu3O7Crystals with Columnar Defects”

A comment on the Letter by W. N. Kang et al., Phys. Rev. Lett. 76, 2993 (1996). The authors of the Letter offer a Reply.

Comment on “Pinning Strength Dependence of Mixed-State Hall Effect inYBa2Cu3O7Crystals with Columnar Defects”

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Effect of Zn impurities on the mixed state Hall effect in Bi-2212 single crystal

The ab plane Hall resistivity in the vortex state of undoped, Zn=0.6% and 0.98% doped Bi 2Sr 2Ca(Cu 1−x Zn x) 2O 8 has been measured in magnetic field H parallel to the c axis of the crystal. Three Hall sign reversals were observed for Zn=0.6% doped sample with crystal defect. It is expected that the crystal defect in Zn=0.6% doped sample causes the change of the electronic state density at the Fermi level and leads to the third Hall sign reversal in low temperature.

Mixed-state Hall effect of YBa2Cu3O7 thin films at high current densities

Measurements of the mixed-state Hall effect in YBa2Cu3O7 thin film microbridges in high current densities up to 2.7 MA/cm2 are reported. Sample heating was greatly reduced by applying a pulsed-current measurement method. We found that the vortex pinning is significantly suppressed in high current densities resulting in an enhancement of the anomalous negative peak of the mixed-state Hall effect. The Hall conductivity, however, increases monotonically below Tc. The results suggest that the sign change of the Hall effect is not related to pinning and that the sharp negative peak results from a competition between the rapidly increasing negative Hall conductivity and the vortex pinning.

Scaling behavior and mixed-state Hall effect in epitaxialHgBa2CaCu2O6+δsthin films

We have measured the mixed-state Hall effect in superconducting ${\mathrm{HgBa}}_{2}$ ${\mathrm{CaCu}}_{2}$ ${\mathrm{O}}_{6+\mathrm{\ensuremath{\delta}}}$ thin films. We found that the Hall resistivity ${\mathrm{\ensuremath{\rho}}}_{\mathrm{xy}}$ shows a double sign reversal in low fields, then shifts to positive without changing the general shape in higher fields. At the higher field region, the Hall conductivity ${\mathrm{\ensuremath{\rho}}}_{\mathrm{xy}}$ is observed to be the sum of two terms, ${\mathrm{C}}_{1}$ /H and ${\mathrm{C}}_{2}$ H, where ${\mathrm{C}}_{1}$ and ${\mathrm{C}}_{2}$ are field independent. The scaling behavior between ${\mathrm{\ensuremath{\sigma}}}_{\mathrm{xy}}$ and ${\mathrm{\ensuremath{\rho}}}_{\mathrm{xx}}$ (longitudinal resistivity) shows a strong dependence on fields. The scaling exponent \ensuremath{\mathrm{B}} in ${\mathrm{\ensuremath{\rho}}}_{\mathrm{xy}}$ =A${\mathrm{\ensuremath{\rho}}}_{\mathrm{xx}}^{\mathrm{\ensuremath{\mathrm{B}}}g}$ increases from 1.5\ifmmode\pm\else\textpm\fi{}0.1 to 1.9\ifmmode\pm\else\textpm\fi{}0.1 as field increases from 1 to 5.5 T. The field dependence of tangent of the Hall angle is linear only in the flux-flow regime, different from Bi- and Tl-based cuprates.

The Pinning Force and the Flux Velocity in the Mixed-State Hall Effect

Using the single flux motion model of Wang, Dong, and Ting (WDT) and taking into account both the pinning and thermal fluctuation, we perform a numerical study to investigate the dependence between the average pinning force F-p and the flux velocity vL in different temperature regions in the mixed-state of high-Tc superconductors. The numerical simulation shows that there does not exist a unified scaling relation between F-p and vL in the whole flux flow temperature region, but F-p and vL keep a linear dependence in the lower temperature region of the negative Hall effect. The variations of the magnetic field or the pinning concentration do not change this linear relation. Employing this linear relation and WDT's theory, we naturally give the scaling law of ρxy ∝ ρβxx with β ≈︂ 2. We also make a power fit for the data of F-p and vL in the high-temperature region of both the negative and the whole positive Hall effect. Finally, we obtain F-p ∼ v—νL with ν ≈︂ 1.5 to 2.0 for different magnetic fields and pinning concentrations.