In order to study the phase diagram from a microscopic viewpoint, we have measured wTF- and ZF-$mu^+$SR spectra for the Sr$_{1-x}$Ca$_x$Co$_2$P$_2$ powder samples with $x=0$, 0.2, 0.4, 0.5, 0.6, 0.8, and 1. Due to a characteristic time window and spa
tial resolution of $mu^+$SR, the obtained phase diagram was found to be rather different from that determined by magnetization measurements. That is, as $x$ increases from 0, a Pauli-paramagnetic phase is observed even at the lowest $T$ measured (1.8~K) until $x=0.4$, then, a spin-glass like phase appears at $0.5leq xleq0.6$, and then, a phase with wide field distribution probably due to incommensurate AF order is detected for $x=0.8$, and finally, a commensurate $A$-type AF ordered phase (for $x=1$) is stabilized below $T_{rm N}sim80~$K. Such change is most likely reasonable and connected to the shrink of the $c$-axis length with $x$, which naturally enhances the magnetic interaction between the two adjacent Co planes.
A new analysis is performed in QCD sum rule for the lightest negative parity baryon Lambda (1405). Mixings of three-quark and five-quark Fock components are taken into account. Terms containing up to dimension 12 condensates are computed in the opera
tor product expansion. It is found that the sum rule gives much stronger coupling of Lambda* to the five-quark operator so that the five-quark components occupy about 90% of Lambda (1405).
The nature of the magnetic transition of the half-filled triangular antiferromagnet Ag$_{2}$NiO$_2$ with $T_{rm N}$=56K was studied with positive muon-spin-rotation and relaxation ($mu^+$SR) spectroscopy. Zero field $mu^+$SR measurements indicate the
existence of a static internal magnetic field at temperatures below $T_{rm N}$. Two components with slightly different precession frequencies and wide internal-field distributions suggest the formation of an incommensurate antiferromagnetic order below 56 K. This implies that the antifrerromagnetic interaction is predominant in the NiO$_2$ plane in contrast to the case of the related compound NaNiO$_2$. An additional transition was found at $sim$22 K by both $mu^+$SR and susceptibility measurements. It was also clarified that the transition at $sim$260 K observed in the susceptibility of Ag$_{2}$NiO$_{2}$ is induced by a purely structural transition.
By means of muon spin spectroscopy, we have found that K$_{0.49}$CoO$_2$ crystals undergo successive magnetic transitions from a high-T paramagnetic state to a magnetic ordered state below 60 K and then to a second ordered state below 16 K, even thou
gh K_{0.49}CoO_2 is metallic at least down to 4 K. An isotropic magnetic behavior and wide internal-field distributions suggest the formation of a commensurate helical spin density wave (SDW) state below 16 K, while a linear SDW state is likely to exist above 16 K. It was also found that K_{0.49}CoO_2 exhibits a further transition at 150 K presumably due to a change in the spin state of the Co ions. Since the T dependence of the internal-field below 60 K was similar to that for Na_{0.5}CoO_2, this suggests that magnetic order is more strongly affected by the Co valence than by the interlayer distance/interaction and/or the charge-ordering.
Magnetism of a misfit layered cobaltite [Ca$_2$Co$_{4/3}$Cu$_{2/3}$O$_4$]$_x^{rm RS}$[CoO$_2$] ($x sim$ 0.62, RS denotes a rocksalt-type block) was investigated by a positive muon spin rotation and relaxation ($mu^+$SR) experiment. A transition to an
incommensurate ({sf IC}) spin density wave ({sf SDW}) state was found below 180 K (= $T_{rm C}^{rm on}$); and a clear oscillation due to a static internal magnetic field was observed below 140 K (= $T_{rm C}$). Furthermore, an anisotropic behavior of the zero-field $mu^+$SR experiment indicated that the {sf IC-SDW} propagates in the $a$-$b$ plane, with oscillating moments directed along the c axis. These results were quite similar to those for the related compound [Ca$_2$CoO$_3$]$_{0.62}^{rm RS}$[CoO$_2$], {sl i.e.}, Ca$_3$Co$_4$O$_9$. Since the {sf IC-SDW} field in [Ca$_2$Co$_{4/3}$Cu$_{2/3}$O$_4$]$_{0.62}^{rm RS}$[CoO$_2$] was approximately same to those in pure and doped [Ca$_2$CoO$_3$]$_{0.62}^{rm RS}$[CoO$_2$], it was concluded that the {sf IC-SDW} exist in the [CoO$_2$] planes.
Magnetism of layered cobaltites Na$_x$CoO$_2$ with $x$ = 0.6 and 0.9 has been investigated by a positive muon spin rotation and relaxation ($mu^+$SR) spectroscopy together with magnetic susceptibility and specific heat measurements, using single crys
tal samples in the temperature range between 250 and 1.8 K. Zero-field (ZF-) $mu^+$SR measurements on Na$_{0.9}$CoO$_2$ indicates a transition from a paramagnetic to an incommensurate spin density wave state at 19 K(=$T_{sf SDW}$). The anisotropic ZF-$mu^+$SR spectra suggest that the oscillating moments of the {sf IC-SDW} directs along the c-axis. Since Na$_{0.6}$CoO$_2$ is paramagnetic down to 1.8 K, the magnitude of $T_{sf SDW}$ is found to strongly depend on $x$.This behavior is well explained using the Hubbard model within a mean field approximation on two-dimensional triangle lattice in the CoO$_2$ plane. Also, both the appearance of the {sf IC-SDW} state by the change in $x$ and the magnitude of the electronic specific heat parameter of Na$_{0.6}$CoO$_2$ indicate that Na$_x$CoO$_2$ is unlikely to be a typical strongly correlated electron system.
Using muon spin spectroscopy we have found that, for both Na$_x$CoO$_2$ (0.6 $leq x leq$ 0.9) and 3- and 4-layer cobaltites, a common low temperature magnetic state (which in some cases is manifest as an incommensurate spin density wave) forms in the
CoO$_2$ planes. Here we summarize those results and report a dome-shaped relation between the transition temperature into the low-$T$ magnetic state and the composition $x$ for Na$_x$CoO$_2$ and/or the high-temperature asymptotic limit of thermopower in the more complex 3- and 4-layer cobaltites. This behavior is explained using the Hubbard model on two-dimensional triangular lattice in the CoO$_2$ plane.
