Abstract

A material becomes a superconductor when it is cooled and, as a result, loses resistance to the flow of electric current. Practical applications of superconductors include the development of superconducting magnets for fusion reactors, particle accelerators, and magnetic energy storage devices. Muon-spin-resonance (mSR) vortex data of underdoped ceramic single-phase Tl₂Ba₂Ca₂Cu₃O_y (Tl2223; T_c = 105K) are analyzed to search for antiferromagnetism in and near its vortex cores. Using the Maximum-Entropy (ME) technique, the obtained ME transforms reflect the magnetic field distributions in the vortex states. We fit the temperature-dependent ME-mSR transforms by means of expected Gaussians. Below T_c, the grain-boundary signal near the external field (5 kOe) is well represented by a narrow Gaussian. Below 0.5 T_c, the vortex signal is better fitted by a Lorentzian on its high-field side. This indicates additional magnetic fields in the high-field regions of the Tl2223 field distributions below 0.5 T_c. These fields occur in and near the vortex cores; thus, extra magnetism is associated with the vortex core. Our ME-mSR vortex-core results are consistent with those of RBCO. Zero-field (ZF) mSR data of Tl2223 flux-trapping have been recorded at 10 K. After field cooling in an applied 5-kOe field, flux trapping in Tl2223 was studied in zero field. ME-mSR analysis suggests evidence of three ZF-mSR frequency signals, corresponding to 70 Oe, 0.7 kOe, and 1.8 kOe, as expected below 5 kOe. We suggest that the 70-Oe fields correspond to apparent magnetism in the original vortex cores.

Introduction

Antiferromagnetism is a type of magnetism in solids whereby adjacent ions that behave as tiny magnets spontaneously align themselves at relatively low temperatures into opposite directions throughout the material, resulting in almost no net external magnetism. In antiferromagnetic materials, which include certain metals and alloys in addition to some ionic solids, the magnetism from magnetic atoms or ions oriented in one direction is canceled out by the set of magnetic atoms or ions that are aligned in the reverse direction. In general, the vortex core of a superconductor is a cylinder of normal material (non-superconducting material) whose radius is the Ginzburg-Landau coherence length.

The prospect of antiferromagnetism (AF) in and around the vortex cores of
cuprate (copper oxide) superconductors holds important implications for cuprate
superconductivity (Arovas et al. 1997). An applied magnetic field penetrates a superconductor at the vortices, returning these cores to a normal, metallic state. If these vortex cores show magnetism, a magnetic origin to cuprate superconductivity is likely, as predicted by theory (Zhang 1997; Yeh and Chen 2003).

Experiments

The high quality ceramic sample of Tl2223 is single phase and was prepared at Los Alamos National Laboratory (Santiago et al. 2000). The mSR technique, like NMR and the Mössbauer Effect, is a magnetic resonance method. The applied transverse field is 5 kOe and the cuprate samples are field-cooled through T_c. Since muons precess in response to magnetic fields that are transverse to their spin, they act as magnetic probes measuring the vortex state. At various temperatures, the mSR time histograms were recorded (Santiago et al. 2001).

Applying the ME technique to the mSR time histograms, we obtained magnetic field distributions in the vortex states. If extra alternating fields are present in and near the vortex cores, a Lorentzian should fit the vortex signal better than a Gaussian. This is especially true for the high-field side of the field distribution. Finding these magnetism indicators is complicated due to the overlap of the vortex and grain-boundary (GB) signals.

The ME-mSR analysis is performed over a 66 - 69 MHz frequency interval, using a Gaussian filter function. ME-mSR transforms are generated with filter time T_f of 2.2 ms. This T_f reduces the long-lived GB signal effect and Poisson noise sufficiently and covers the entire vortex signal. The ME-mSR transforms are fitted with Gaussians assigned to the GB signals, while the vortex signals are fitted either with Gaussians or Lorentzians, beside a constant background term. Results from Lorentzian (vortex) - Gaussian (GB) fittings (LG) are compared to those of two Gaussian fittings (GG). A lower goodness of fit (c₂) indicates a better fit result. Thus, smaller c₂ values for LG than GG are indications that (antiferro)magnetism occurs in and near the vortex core.

To study flux trapping, we cooled the Tl2223 sample to 10 K in an applied field of 5 kOe. Then, the external field was shut down to zero and zero-field (ZF) mSR data were recorded to measure the field distribution in the trapped flux state. For ME analysis, a Gaussian T_f of 1.1 ms is optimal.

Results

The character of the ME-mSR field distribution shows a substantial change at 50 K for the Tl2223 vortex state. LG fits for ME-mSR transforms at T < 50 K are substantially better than GG fits. Figure 1 shows ME-mSR transforms of Tl2223 at 40 K and 5 kOe. The top transform is fitted with a Lorentzian representing the vortex signal and a GB Gaussian. The bottom one is fitted with two Gaussians. Here, the c₂(GG) is a factor of two larger than c₂(LG); thus, strongly favoring LG fitting. For T > 50 K, GG fits are slightly better than LG for Tl2223. Figure 2 shows a ME-mSR transform of Tl2223 at 60 K and 5 kOe.

Despite the substantial overlap of the GB signal with the vortex signal, magnetic effects on the vortex signal are nevertheless observed below 50 K. For Tl2223 below 0.4 T_c, the c₂ values for LG fits are lower than those of GG fits, and point toward magnetism in these cuprate vortex states. Since the Lorentzian character is not limited to the high-field side (i.e., the vortex core), extra magnetism extending outside the core cannot be excluded.

In the ZF-mSR flux-trapping experiment, we observed strong hints of three frequency signals corresponding to ~ 70 Oe, ~ 0.7 kOe, and ~ 1.8 kOe. These trapped fields are below 5 kOe, as expected. We suggest the 70-Oe fields may correspond to the magnetism in and around the initial vortex core. The 0.7-kOe fields can be associated with the first critical field. The 1.8-kOe fields may be remnants of the initial main mixed state.

Discussion

Our observed magnetic effects related to the vortex core occur at low magnetic fields, compared to the high fields used in NMR vortex studies (Kumagai et al. 2003; Mitrovic et al. 2003) and the YBCO-mSR experiment (Miller et al. 2002). This means that the core volume for our mSR vortex states is much smaller than that for their high field vortex states. Our result strongly argues that extra magnetism is not only present in the vortex core, but also found around the core. This result is consistent with the neutron study by Lake et al. (2002), who also found AF outside the core. Furthermore, the SO(5) theory of Zhang et al. (1997) indicates that the AF coherence length is a factor of five larger than the superconductivity coherence length. This strongly suggests the volume associated with AF order should be a factor of 100 larger than that of just the vortex core volume.

Our Tl2223 results are consistent with RBa2Cu3O7-d (RBCO; R = Eu, Ho & Y) studies (Miller et al. 2002; Lake et al. 2002). For EuBCO and HoBCO vortex states, recent ME-mSR evidence (Boekema et al. 2003) revealed that magnetic effects appear to be present near and in the vortex cores below 0.5 T_c. These findings extend the time-fitting results for underdoped YBCO (Miller et al. 2002). This and our earlier study (Boekema et al. 2003) do not exclude extra magnetism outside the vortex core.

Conclusion

ME-mSR analysis of Tl2223 vortex data indicates antiferromagnetism, or some sort of Cu-spin ordering, that is associated with the cuprate vortex cores. This magnetism in and around the cores appears below 0.4 T_c. Several studies with different time scales indicate the appearance of induced magnetism in the cuprate vortex state. These findings support theories that predict a magnetic origin to cuprate superconductors.