A factorization of a super-conformal map

A super-conformal map and a minimal surface are factored into a product of two maps by modeling the Euclidean four-space and the complex Euclidean plane on the set of all quaternions. One of these two maps is a holomorphic map or a meromorphic map. These conformal maps adopt properties of a holomorphic function or a meromorphic function. Analogs of the Liouville theorem, the Schwarz lemma, the Schwarz-Pick theorem, the Weierstrass factorization theorem, the Abel-Jacobi theorem, and a relation between zeros of a minimal surface and branch points of a super-conformal map are obtained.Comment: 21 page

Current-induced magnetization reversal in a (Ga,Mn)As-based magnetic tunnel junction

We report current-induced magnetization reversal in a ferromagnetic semiconductor-based magnetic tunnel junction (Ga,Mn)As/AlAs/(Ga,Mn)As prepared by molecular beam epitaxy on a p-GaAs(001) substrate. A change in magneto-resistance that is asymmetric with respect to the current direction is found with the excitation current of 10^6 A/cm^2. Contributions of both unpolarized and spin-polarized components are examined, and we conclude that the partial magnetization reversal occurs in the (Ga,Mn)As layer of smaller magnetization with the spin-polarized tunneling current of 10^5 A/cm^2.Comment: 13 pages, 3 figure

Quantum Valence Criticality as Origin of Unconventional Critical Phenomena

It is shown that unconventional critical phenomena commonly observed in paramagnetic metals YbRh2Si2, YbRh2(Si0.95Ge0.05)2, and beta-YbAlB4 is naturally explained by the quantum criticality of Yb-valence fluctuations. We construct the mode coupling theory taking account of local correlation effects of f electrons and find that unconventional criticality is caused by the locality of the valence fluctuation mode. We show that measured low-temperature anomalies such as divergence of uniform spin susceptibility \chi T^{-\zeta) with $\zeta~0.6$ giving rise to a huge enhancement of the Wilson ratio and the emergence of T-linear resistivity are explained in a unified way.Comment: 5 pages, 3 figures, to be published in Physical Review Letter

Superconductivity and Pseudogap in Quasi-Two-Dimensional Metals around the Antiferromagnetic Quantum Critical Point

Spin fluctuations (SF) and SF-mediated superconductivity (SC) in quasi-two-dimensional metals around the antiferrromagnetic (AF) quantum critical point (QCP) are investigated by using the self-consistent renormalization theory for SF and the strong coupling theory for SC. We introduce a parameter y0 as a measure for the distance from the AFQCP which is approximately proportional to (x-xc), x being the electron (e) or hole (h) doping concentration to the half-filled band and xc being the value at the AFQCP. We present phase diagrams in the T-y0 plane including contour maps of the AF correlation length and AF and SC transition temperatures TN and Tc, respectively. The Tc curve is dome-shaped with a maximum at around the AFQCP. The calculated one-electron spectral density shows a pseudogap in the high-density-of-states region near (pi,0) below around a certain temperature T* and gives a contour map at the Fermi energy reminiscent of the Fermi arc. These results are discussed in comparison with e- and h-doped high-Tc cuprates.Comment: 5 pages, 3 figure

Ferromagnetism in one-dimensional metals: breakdown of the Hartree-Fock approximation and possible first order phase transition

We calculate the Gibbs potential Gamma (M) of a one-dimensional metal at constant magnetization M to second order in the screened electron-electron interaction U. At zero temperature we find that Gamma (M) contains non-analytic corrections proportional to M^2 \ln | M| and | M |^3, implying that a possible paramagnetic-ferromagnetic quantum phase transition in one-dimensional metals must be first order.Comment: 8 pages, 7 figures; we have changed our choice of the ultraviolet cutoff, as suggested by a referee. Phase transition occurs now for Stoner factor smaller than unity. Fig 5 and Fig.7 are have been redraw

Ferromagnetic Quantum Critical Fluctuations and Anomalous Coexistence of Ferromagnetism and Superconductivity in UCoGe Revealed by Co-NMR and NQR Studies

Co nuclear magnetic resonance (NMR) and nuclear quadrupole resonance (NQR) studies were performed in the recently discovered UCoGe, in which the ferromagnetic and superconducting (SC) transitions were reported to occur at $T_{\rm Curie} \sim 3$ K and $T_S \sim 0.8$ K (N. T. Huy {\it et al.}, Phys. Rev. Lett. {\bf 99} (2007) 067006), in order to investigate the coexistence of ferromagnetism and superconductivity as well as the normal-state and SC properties from a microscopic point of view. From the nuclear spin-lattice relaxation rate $1/T_1$ and Knight-shift measurements, we confirmed that ferromagnetic fluctuations which possess a quantum critical character are present above $T_{\rm Curie}$ and the occurrence of ferromagnetic transition at 2.5 K in our polycrystalline sample. The magnetic fluctuations in the normal state show that UCoGe is an itinerant ferromagnet similar to ZrZn$_2$ and YCo$_2$. The onset SC transition was identified at $T_S \sim 0.7$ K, below which $1/T_1$ of 30 % of the volume fraction starts to decrease due to the opening of the SC gap. This component of $1/T_1$, which follows a $T^3$ dependence in the temperature range of $0.3 - 0.1$ K, coexists with the magnetic components of $1/T_1$ showing a $\sqrt{T}$ dependence below $T_S$. From the NQR measurements in the SC state, we suggest that the self-induced vortex state is realized in UCoGe.Comment: 5 pages, 7 figures. submitted to J. Phys. Soc. Jpn. To appear in J. Phys. Soc. Jp

Metamagnetic Quantum Criticality Revealed by 17O-NMR in the Itinerant Metamagnet Sr3Ru2O7

We have investigated the spin dynamics in the bilayered perovskite Sr3Ru2O7 as a function of magnetic field and temperature using 17O-NMR. This system sits close to a metamagnetic quantum critical point (MMQCP) for the field perpendicular to the ruthenium oxide planes. We confirm Fermi-liquid behavior at low temperatures except for a narrow field region close to the MMQCP. The nuclear spin-lattice relaxation rate divided by temperature 1/T1T is enhanced on approaching the metamagnetic critical field of 7.9 T and at the critical field 1/T1T continues to increase and does not show Fermi- liquid behavior down to 0.3 K. The temperature dependence of T1T in this region suggests the critical temperature Theta to be 0 K, which is a strong evidence that the spin dynamics possesses a quantum critical character. Comparison between uniform susceptibility and 1/T1T reveals that antiferromagnetic fluctuations instead of two-dimensional ferromagnetic fluctuations dominate the spin fluctuation spectrum at the critical field, which is unexpected for itinerant metamagnetism.Comment: 5 pages, 4 figures, Accepted by Phys. Rev. Let