Magnetic polaron and Fermi surface effects in the spin-flip scattering ofEuB 6
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The spin-flip scattering (SFS) between conduction and $4{f}^{7}\phantom{\rule{0.3em}{0ex}}{\mathrm{Eu}}^{2+}$ $(^{8}S_{7∕2})$ electrons in the paramagnetic phase of $\mathrm{Eu}{\mathrm{B}}_{6}$ $(T\ensuremath{\geqslant}2{T}_{c}\ensuremath{\simeq}30\phantom{\rule{0.3em}{0ex}}\mathrm{K})$ is studied by means of electron spin resonance (ESR) at three frequencies. The single Dysonian resonance observed in all cases suggests a metallic environment for the ${\mathrm{Eu}}^{2+}$ ions. The ESR at high field, $H\ensuremath{\simeq}12.05\phantom{\rule{0.3em}{0ex}}\mathrm{kG}$ $(\ensuremath{\nu}\ensuremath{\simeq}33.9\phantom{\rule{0.3em}{0ex}}\mathrm{GHz})$, has an anisotropic linewidth with cubic symmetry. The low-field, $1.46\phantom{\rule{0.3em}{0ex}}\mathrm{kG}$ $(4.1\phantom{\rule{0.3em}{0ex}}\mathrm{Ghz})$ and $3.35\phantom{\rule{0.3em}{0ex}}\mathrm{kG}$ $(9.5\phantom{\rule{0.3em}{0ex}}\mathrm{GHz})$, ESR linewidths are unexpectedly broader and have a smaller anisotropy than at the higher field. The unconventional narrowing and anisotropy of the linewidth at higher fields are indicative of a homogeneous resonance and microscopic evidence for a strong reduction in spin-flip scattering between the spins of ${\mathrm{Eu}}^{2+}$ and the states in the electron and hole pockets at the $X$ points of the Brillouin zone by magnetic polarons.Measurements have been performed of the upper critical field Hc2 anisotropy in the magnetic heavy-fermion superconductor URu2Si2. The dHc2/dT value is constant within 5% when H is rotated in the basal plane, whereas ‖dHc2/dT‖ decreases by about 35% for H rotated by 20°–30° out of the basal plane. Contrary to CeCu2Si2 the Hc2 anisotropy in URu2Si2 is enhanced as temperature decreases below Tc. This disparity can be attributed to the different strengths of paramagnetic and spin-orbit effects responsible for the suppression of superconductivity by a magnetic field in CeCu2Si2 and URu2Si2.
Heavy fermion superconductor
Critical field
Basal plane
Type-II superconductor
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Paramagnetism describes a type of magnetism whereby a material is weakly attracted by an external magnetic field. The material forms induced magnetic fields in the direction of the external magnetic field. Pauli-paramagnetism is a weak form of paramagnetism. It arises in a conductor when a magnetic field is applied and its conduction band is split into a spin-up and a spin-down band due to the differences in magnetic potential energy for spin-up and spin-down electrons. As the Fermi level must be the same for each band, there is inevitably a surplus of the type of spin in the band that shifted downwards. In a regular (non-Pauli paramagnetic) superconductor, the superconductivity is destroyed due to the orbital supercurrents. However, in a Pauli-paramagnetic superconductor, the normal state is induced by the coupling of the magnetic field to the spin of the electrons (i.e. in materials with significant Pauli paramagnetism). The effects of the Pauliparamagnetism
are visible in the magnetic vortices of the superconductor as this is where the electron pairs have been “broken up”, and the nature of these vortices can be probed by small-angle neutron scattering.
Pauli exclusion principle
Magnetism
Critical field
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A possible mechanism of paramagnetic Meissner effect observed in some high-temperature superconductors is proposed. It is shown that a paramagnetic Meissner current flows if there exists a large quasi-particle density of states around zero energy in the energy gap. This suggests that the paramagnetic Meissner effect is associated with a zero-bias conductance peak which has often been observed in the tunneling experiments of high-temperature superconductors. The paramagnetic effect caused by the zero-energy excitations is consistent with the experiments.
Meissner effect
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Diamagnetism
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The 1964 reports of Fulde, Ferrell, Larkin, and Ovchinnikov (FFLO or LOFF) on paramagnetic enhancement of superconductivity suggested that superconductivity can persist at applied magnetic fields above both its orbital and paramagnetic limits. By forming spatially alternating superconducting and paramagnetic regions, the increase in local magnetic field in the paramagnetic region allows a reduction in field inside the superconductor. We present an FFLO phase diagram model for layered organic superconductors and confirm it with high magnetic field data from four materials. Our work suggests that paramagnetic and superconducting regions form as radially alternating rings about each vortex rather than plane waves, as FFLO is usually described.
Critical field
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The magnetic field and temperature dependence of the magnetic susceptibility is studied for the ferromagnetic layered manganites SrO(La1−xSrxMnO3)2 in the composition range x=0.32–0.40. In the paramagnetic phase, the susceptibility exhibits an anomalous maximum at an intermediate magnetic field value. The size of this field-induced susceptibility enhancement increases dramatically with x from 10% for x=0.32 to 160% for x=0.40. The temperature dependence of the effect shows a maximum at T≈1.1 TC for all x. Quantitative analysis in terms of the Landau theory of phase transitions enables us to identify a distortion of the free energy F in the paramagnetic phase that is associated with the susceptibility anomaly. This free energy distortion corresponds to a magnetic system that approaches a first order magnetic phase transition as the temperature is lowered toward TC. Such a behavior is indicative of a second, competing order parameter, which is identified as the recently observed charge density wave. In the immediate vicinity of TC, the anomaly disappears and the system seems to undergo a more conventional second order paramagnetic–ferromagnetic phase transition.
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We have studied the temperature and magnetic field dependence of the electrical resistivity of GdCu(6) and have co-related the results with the temperature dependence of heat capacity and magnetization. The magnetoresistance of GdCu(6) is found to be positive both in the paramagnetic and antiferromagnetic regimes. Within the antiferromagnetic regime, the magnetoresistance is very high and increases to still higher values both with increasing field and decreasing temperature. In the paramagnetic regime the magnetoresistance continues to exhibit a finite positive value up to temperatures much higher than that corresponding to the antiferromagnetic to paramagnetic phase transition. We have shown through quantitative analysis that both the temperature dependences of resistivity and heat capacity indicate the presence of spin fluctuations within the paramagnetic regime of GdCu(6). The field dependence of electrical resistivity indicates that the positive magnetoresistance in the paramagnetic phase is not related to the orbital motion of the conduction electrons in a magnetic field (the Kohler rule). In contrast, our analysis indicates that these spin fluctuations are responsible for the positive magnetoresistance observed within this paramagnetic regime. The nature of the field dependence of electrical resistivity is found to be qualitatively similar both in the antiferromagnetic and paramagnetic regimes, which probably indicates that spin fluctuations in the paramagnetic regime are of the antiferromagnetic type.
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The current transport in polycrystalline MgB2 is strongly influenced by the intrinsic anisotropy of this superconductor. Untextured bulks and wires are macroscopically isotropic, but the grains retain their anisotropic properties and the field dependence of the critical currents is much stronger than in isotropic superconductors. Weakly or partially textured tapes are macroscopically anisotropic, but the anisotropy of the zero resistivity (or irreversibility) field is smaller than the intrinsic upper critical field anisotropy, γ. The Jc-anisotropy is field and temperature dependent and can be much larger than γ. The most suitable parameter for the quantification of the macroscopic anisotropy is, therefore, the anisotropy of the zero resistivity field. It is difficult to distinguish between a higher degree of texture at a lower intrinsic anisotropy and a weaker texture at higher anisotropy and hardly possible on the basis of the field dependence of the critical current anisotropy alone. The knowledge of the upper critical field is crucial and angularly resolved measurements of either the critical currents or, better, the resistive in-field transitions are favorable for this purpose.
Texture (cosmology)
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The contribution of spin fluctuations to the temperature and field dependence of the low-temperature spin susceptibility of exchange-enhanced paramagnets in finite magnetic fields is studied on the basis of the Fermi-liquid approach.
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Specific heat
Superconducting transition temperature
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