A microscopic theory for the spin triplet Cooper pairing in non-centrosymmetric superconductors like CePt_3Si and CeTSi_3 (T=Rh, Ir) is presented. The lack of inversion symmetry leads to new anomalous spin fluctuations which stabilize the triplet par
t in addition to the singlet part originating from the centrosymmetric spin fluctuations. It is shown that both parts have similar nontrivial momentum dependence of A_1 type. Therefore the mixed singlet-triplet gap function has accidental line nodes on both Fermi surface sheets which are stable as function of temperature. This gap function explains the salient features of CePt_3Si and CeTSi_3 superconductors.
Low frequency spin fluctuation dynamics in paramagnetic spinel LiV$_2$O$_4$, a rare 3$d$-electron heavy fermion system, is investigated. A parametrized self-consistent renormalization (SCR) theory of the dominant AFM spin fluctuations is developed an
d applied to describe temperature and pressure dependences of the low-$T$ nuclear spin-lattice relaxation rate $1/T_1$ in this material. The experimental data for $1/T_1$ available down to $sim 1$K are well reproduced by the SCR theory, showing the development of AFM spin fluctuations as the paramagnetic metal approaches a magnetic instability under the applied pressure. The low-$T$ upturn of $1/T_1T$ detected below 0.6 K under the highest applied pressure of 4.74 GPa is explained as the nuclear spin relaxation effect due to the spin freezing of magnetic defects unavoidably present in the measured sample of LiV$_2$O$_4$.
We examine static spin susceptibilities $chi_{alphabeta}({bf q})$ of spin components $S_{alpha}$ and $S_{beta}$ in the non-centrosymmetric tetragonal system. These show anomalous momentum dependences like $chi_{xx}({bf q})-chi_{yy}({bf q})sim q_x^2-q
_y^2$ and $chi_{xy}({bf q})+chi_{yx}({bf q})sim q_x q_y$, which vanish in centrosymmetric systems. The magnitudes of the anomalous spin susceptibilities are enhanced by the on-site Coulomb interaction, especially, around an ordering wave vector. The significant and anomalous momentum dependences of these susceptibilities are explained by a group theoretical analysis. As the direct probe of the anomalous spin susceptibility, we propose a polarized neutron scattering experiment.
A phenomenological description for the dynamical spin susceptibility $chi({bf q},omega;T)$ observed in inelastic neutron scattering measurements on powder samples of LiV$_2$O$_4$ is developed in terms of the parametrized self-consistent renormalizati
on (SCR) theory of spin fluctuations. Compatible with previous studies at $Tto 0$, a peculiar distribution in ${bf q}$-space of strongly enhanced and slow spin fluctuations at $q sim Q_c simeq$ 0.6 $AA^{-1}$ in LiV$_2$O$_4$ is involved to derive the mode-mode coupling term entering the basic equation of the SCR theory. The equation is solved self-consistently with the parameter values found from a fit of theoretical results to experimental data. For low temperatures, $T lesssim 30$K, where the SCR theory is more reliable, the observed temperature variations of the static spin susceptibility $chi(Q_c;T)$ and the relaxation rate $Gamma_Q(T)$ at $qsim Q_c$ are well reproduced by those suggested by the theory. For $Tgtrsim 30$K, the present SCR is capable in predicting only main trends in $T$-dependences of $chi(Q_c;T)$ and $Gamma_Q(T)$. The discussion is focused on a marked evolution (from $q sim Q_c$ at $Tto 0$ towards low $q$ values at higher temperatures) of the dominant low-$omega$ integrated neutron scattering intensity $I(q; T)$.
The tetragonal compound YbRu$_{2}$Ge$_{2}$ exhibits a non-magnetic transition at $T_0$=10.2K and a magnetic transition at $T_1$=6.5K in zero magnetic field. We present a model for this material based on a quasi-quartet of Yb$^{3+}$ crystalline electr
ic field (CEF) states and discuss its mean field solution. Taking into account the broadening of the specific heat jump at $T_0$ for magnetic field perpendicular to [001] and the decrease of $T_0$ with magnetic field parallel to [001], it is shown that ferro-quadrupole order of either O$_{2}^{2}$ or O$_{rm xy}$ - type are prime candidates for the non-magnetic transition. Considering the matrix element of these quadrupole moments, we show that the lower CEF states of the level scheme consist of a $Gamma_{6}$ and a $Gamma_{7}$ doublet. This leads to induced type of O$_{2}^{2}$ and O$_{rm xy}$ quadrupolar order parameters. The quadrupolar order introduces exchange anisotropy for planar magnetic moments. This causes a spin flop transition at low fields perpendicular [001] which explains the observed metamagnetism. We also obtain a good explanation for the temperature dependence of magnetic susceptibility and specific heat for fields both parallel and perpendicular to the [001] direction.
