Possible Pairing Symmetry of Three-dimensional Superconductor UPt3_3 -- Analysis Based on a Microscopic Calculation --

Stimulated by the anomalous superconducting properties of UPt$_3$, we investigate the pairing symmetry and the transition temperature in the two-dimensional(2D) and three-dimensional(3D) hexagonal Hubbard model. We solve the Eliashberg equation using the third order perturbation theory with respect to the on-site repulsion $U$. As results of the 2D calculation, we obtain distinct two types of stable spin-triplet pairing states. One is the $f$-wave(B$_1$) pairing around $n = 1.2$ and in a small $U$ region, which is caused by the ferromagnetic fluctuation. Then, the other is the $p_x$(or $p_y$)-wave(E$_1$) pairing in large $U$ region far from the half-filling ($n = 1$) which is caused by the vertex corrections only. However, we find that the former $f$-wave pairing is destroyed by introduced 3D dispersion. This is because the 3D dispersion breaks the favorable structures for the $f$-wave pairing such as the van Hove singularities and the small pocket structures. Thus, we conclude that the ferromagnetic fluctuation mediated spin-triplet state can not explain the superconductivity of UPt$_3$. We also study the case of the pairing symmetry with a polar gap. This $p_z$-wave(A$_1$) is stabilized by the large hopping integral along c-axis $t_z$. It is nearly degenerate with the suppressed $p_x$(or $p_y$)-wave(E$_1$) in the best fitting parameter region to UPt$_3$ ($1.3 \le t_z \le 1.5$). These two p-wave pairing states exist in the region far from the half-filling, in which the vertex correction terms play crucial roles like the case in Sr$_2$RuO$_4$.Comment: 15 pages, 12 figure

Antiferromagnetism and Superconductivity in UPt_3

The short ranged antiferromagnetism recently seen in UPt_3 is proved incompatible with two dimensional (2D) order parameter models that take the antiferromagnetism as a symmetry breaking field. To adjust to the local moment direction, the order parameter twists over very long length scales as per the Imry-Ma argument. A variational solution to the Ginzburg-Landau equations is used to study the nature of the short ranged order. Although there are still two transitions, the lower one is of first order -- in contradiction to experiments. It is shown that the latent heat predicted by the 2D models at the lower transition is too large not to have been seen. A simple periodic model is numerically studied to show that the lower transition can not be a crossover either.Comment: To appear in Journal of Physics: Condensed Matter. 9 pages, 2 figure

Reply to ``Comment on `Magnetic field effects on neutron diffraction in the antiferromagnetic phase of UPt3UPt_3'''

Fak, van Dijk and Wills (FDW) question our interpretation of elastic neutron-scattering experiments in the antiferromagnetic phase of UPt_3. They state that our analysis is incorrect because we average over magnetic structures that are disallowed by symmetry. We disagree with FDW and reply to their criticism. FDW also point out that we have mistaken the magnetic field direction in the experiment reported by N. H. van Dijk et al. [Phys. Rev. B 58, 3186 (1998)]. We correct this error and note that our previous conclusion is also valid for the correct field orientation.Comment: 3 page

Comment on "Magnetic field effects on neutron diffraction in the antiferromagnetic phase of UPt3"

Moreno and Sauls [Phys. Rev. B 63, 024419 (2000)] have recently tried to reanalyze earlier neutron scattering studies of the antiferromagnetic order in UPt3 with a magnetic field applied in the basal plane. In their calculation of the magnetic Bragg peak intensities, they perform an average over different magnetic structures belonging to distinct symmetry representations. This is incorrect. In addition, they have mistaken the magnetic field direction in one of the experiments, hence invalidating their conclusions concerning the experimental results.Comment: Revised 5 June 2001: Added group theory analysis and modified discussion of S and K domain

Transport and the Order Parameter of Superconducting UPt3

We calculate the ultrasonic absorption and the thermal conductivity in the superconducting state of UPt$_{3}$ as functions of temperature and direction of propagation and polarization. Two leading candidates for the superconducting order parameter are considered: the $E_{1g}$ and $E_{2u}$ representations. Both can fit the data except for the ultrasonic absorption in the $A$ phase. To do that, it is necessary to suppose that the system has only a single domain, and that must be chosen as the most favorable one. However, the $E_{2u}$ theory requires fine-tuning of parameters to fit the low temperature thermal conductivity. Thus, transport data favor the $E_{1g}$ theory. Measurements of the thermal conductivity as a function of pressure at low temperature could help to further distinguish the two theories.Comment: 7 pages, 4 figure

Identification of Non-unitary triplet pairing in a heavy Fermion superconductor UPt_3

A NMR experiment recently done by Tou et al. on a heavy Fermion superconductor UPt$_3$ is interpreted in terms of a non-unitary spin-triplet pairing state which we have been advocating. The proposed state successfully explains various aspects of the seemingly complicated Knight shift behaviors probed for major orientations, including a remarkable d-vector rotation under weak fields. This entitles UPt$_3$ as the first example that a charged many body system forms a spin-triplet odd-par ity pairing at low temperatures and demonstrates unambiguously that the putative spin-orbit coupling in UPt$_3$ is weak.Comment: 4 pages, 2 eps figures, to be published in J. Phys. Soc. Jpn. 67 (1998) No.

Nonmonotonous Magnetic Field Dependence and Scaling of the Thermal Conductivity for Superconductors with Nodes of the Order Parameter

We show that there is a new mechanism for nonmonotonous behavior of magnetic field dependence of the electronic thermal conductivity of clean superconductors with nodes of the order parameter on the Fermi surface. In particular, for unitary scatterers the nonmonotony of relaxation time takes place. Contribution from the intervortex space turns out to be essential for this effect even at low temperatures. Our results are in a qualitative agreement with recent experimental data for superconducting UPt_3. For E_{2u}-type of pairing we find approximately the scaling of the thermal conductivity in clean limit with a single parameter x=T/T_c\sqrt{B_{c2}/B} at low fields and low temperatures, as well as weak low-temperature dependence of the anisotropy ratio K_{zz}/K_{yy} in zero field. For E_{1g}-type of pairing deviations from the scaling are more noticeable and the anisotropy ratio is essentially temperature dependent.Comment: 37 pages, 8 Postscript figures, REVTE