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In a recent Letter (Phys. Rev. Lett. 81, p.5640 (1998), cond-mat/9808249 v3), it was suggested that nonlocal effects may prevent observation of the nonlinear Meissner effect in YBCO. We argue that this claim is incorrect with regards to measurements of the nonlinear transverse magnetic moment, and that the most likely reason for a null result lies elsewhere.
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We measure the local harmonic generation from superconducting thin films at microwave frequencies to investigate the intrinsic nonlinear Meissner effect near Tc in zero magnetic field. Both second and third harmonic generation are measured to identify time-reversal symmetry breaking (TRSB) and time-reversal symmetric (TRS) nonlinearities. We perform a systematic doping-dependent study of the nonlinear response and find that the TRS characteristic nonlinearity current density scale follows the doping dependence of the de-pairing critical current density. We also extract a spontaneous TRSB characteristic current density scale that onsets at Tc, grows with decreasing temperature, and systematically decreases in magnitude (at fixed T/Tc) with under-doping. The origin of this current scale could be Josephson circulating currents or the spontaneous magnetization associated with a TRSB order parameter.
A long-standing theoretical prediction is that in clean, nodal unconventional superconductors the magnetic penetration depth $lambda$, at zero temperature, varies linearly with magnetic field. This non-linear Meissner effect is an equally important manifestation of the nodal state as the well studied linear-in-$T$ dependence of $lambda$, but has never been convincingly experimentally observed. Here we present measurements of the nodal superconductors CeCoIn$_5$ and LaFePO which clearly show this non-linear Meissner effect. We further show how the effect of a small dc magnetic field on $lambda(T)$ can be used to distinguish gap nodes from non-nodal deep gap minima. Our measurements of KFe$_2$As$_2$ suggest that this material has such a non-nodal state.
An increase of the magnetic moment in superconductor/ferromagnet (S/F) bilayers V(40nm)/F [F$=$Fe(1,3nm), Co(3nm), Ni(3nm)] was observed using SQUID magnetometry upon cooling below the superconducting transition temperature Tc in magnetic fields of 10 Oe to 50 Oe applied parallel to the sample surface. A similar increase, often called the paramagnetic Meissner effect (PME), was observed before in various superconductors and superconductor/ferromagnet systems. To explain the PME effect in the presented S/F bilayers a model based on a row of vortices located at the S/F interface is proposed. According to the model the magnetic moment induced below Tc consists of the paramagnetic contribution of the vortex cores and the diamagnetic contribution of the vortex-free region of the S layer. Since the thickness of the S layer is found to be 3-4 times less than the magnetic field penetration depth, this latter diamagnetic contribution is negligible. The model correctly accounts for the sign, the approximate magnitude and the field dependence of the paramagnetic and the Meissner contributions of the induced magnetic moment upon passing the superconducting transition of a ferromagnet/superconductor bilayer.
Solving phenomenological macroscopic equations instead of microscopic Ginzburg-Landau equations for superconductors is much easier and can be advantageous in a variety of applications. However, till now, only Beans critical state model is available for the description of irreversible properties. Here we propose a plausible overall macroscopic model for both reversible and irreversible properties, combining London theory and Beans model together based on superposition principle. First, a simple case where there is no pinning is discussed, from which a microscopic basis for Beans model is explored. It is shown that a new concept of flux share is needed when the field is increased above the lower critical field. A portion of magnetic flux is completely shielded, named as Meissner share and the rest penetrates through vortices, named as vortices share. We argue that the flux shares are irreversible if there is pinning. It is shown that the irreversible flux shares can be the reason for observed peculiar reversible magnetization behavior near zero field. The overall macroscopic model seems to be valuable for the analysis of fundamental physical properties as well. As an example, it is shown the origin of paramagnetic Meissner effect can be explained by the phenomenological macroscopic model.
Paramagnetic Meissner Effect (PME) was observed in Co/Nb/Co trilayers and multilayers. Measurements of the response to perpendicular external field near the superconducting transition temperature were carried out for various Nb thicknesses. PME was found only when layer thickness is no smaller than penetration depth of Nb. A classical flux compression model [Koshelev and Larkin, Phys. Rev. B 52, 13559 (1995)] was used to explain our data. We inferred that the penetration depth was a critical length, below which superconducting current density became too small and the PME could not be achieved.
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