We report on a novel spin-charge fluctuation in the all-in-all-out pyrochlore magnet Cd$_2$Os$_2$O$_7$, where the spin fluctuation is driven by the conduction of thermally excited electrons/holes and associated fluctuation of Os valence. The fluctuat
ion exhibits an activation energy significantly greater than the spin-charge excitation gap and a peculiar frequency range of $10^{6}$--$10^{10}$ s$^{-1}$. These features are attributed to the hopping motion of carriers as small polarons in the insulating phase, where the polaron state is presumably induced by the magnetoelastic coupling via the strong spin-orbit interaction. Such a coupled spin-charge-phonon fluctuation manifests as a part of the metal-insulator transition that is extended over a wide temperature range due to the modest electron correlation comparable with other interactions characteristic for 5$d$-subshell systems.
The hyperfine features and thermal stability of a muonium (Mu)-related paramagnetic center were investigated in the SrTiO$_3$ perovskite titanate via muon spin rotation spectroscopy. The hyperfine coupling tensor of the paramagnetic center was found
to have prominent dipolar characteristics, indicating that the electron spin density is dominantly distributed on a Ti site to form a small polaron near an ionized Mu$^+$ donor. Based on a hydrogen-Mu analogy, interstitial hydrogen is also expected to form such a polaronic center in the dilute doping limit. The small activation energy of 30(3) meV found for the thermal dissociation of the Mu$^+$-polaron complex suggests that the strain energy required to distort the lattice is comparable to the electronic energy gained by localizing the electron.
Excited configurations of hydrogen in the oxyhydride BaTiO$_{3-x}$H$_x$ ($x=0.1-0.5$), which are considered to be involved in its hydrogen transport and exchange processes, were investigated by positive muon spin relaxation ($mu^+$SR) spectroscopy us
ing muonium (Mu) as a pseudoisotope of hydrogen. Muons implanted into the BaTiO$_{3-x}$H$_x$ perovskite lattice were mainly found in two qualitatively different metastable states. One was assigned to a highly mobile interstitial protonic state, which is commonly observed in perovskite oxides. The other was found to form an entangled two spin-$frac{1}{2}$ system with the nuclear spin of an H$^-$ ion at the anion site. The structure of the (H,Mu) complex agrees well with that of a neutralized center containing two H$^-$ ions at a doubly charged oxygen vacancy, which was predicted to form in the SrTiO$_{3-delta}$ perovskite lattice by a computational study [Y. Iwazaki $et$ $al$., APL Materials 2, 012103 (2014)]. Above 100 K, interstitial Mu$^+$ diffusion and retrapping to a deep defect were observed, which could be a rate-limiting step of macroscopic Mu/H transport in the BaTiO$_{3-x}$H$_x$ lattice.
The hyperfine structure of the interstitial muonium (Mu) in rutile (TiO$_2$, weakly $n$-type) has been identified by means of a muon spin rotation technique. The angle-resolved hyperfine parameters exhibit a tetragonal anisotropy within the $ab$ plan
e and axial anisotropy with respect to the $langle 001rangle$ ($hat{c}$) axis. This strongly suggests that the Mu is bound to O (forming an OH bond) at an off-center site within a channel along the $hat{c}$ axis, while the unpaired Mu electron is localized around the neighboring Ti site. The hyperfine parameters are quantitatively explained by a model that considers spin polarization of the unpaired electron at both the Ti and O sites, providing evidence for the formation of Mu as a Ti-O-Mu complex paramagnetic state. The disappearance of the Mu signal above $sim$10 K suggests that the energy necessary for the promotion of the unpaired electron to the conduction band by thermal activation is of the order of $10^1$ meV. These observations suggest that, while the electronic structure of Mu (and hence H) differs considerably from that of the conventional shallow level donor described by the effective mass model, Mu supplies a loosely bound electron, and thus, serves as a donor in rutile.
The hyperfine structure of the interstitial muonium (Mu) center in rutile (TiO$_2$, weakly $n$-type) has been identified by means of muon spin rotation technique. The angle-resolved hyperfine parameter has a tetragonal anisotropy within the $ab$ plan
e and axial anisotropy along the $c$ axis, strongly suggesting that Mu simulates the known local structure of interstitial hydrogen (H) located at an off-center position within a channel along $c$ axis, and the electron wave function bound to Mu is highly delocalized (~1.5 nm along $c$ axis, ~0.8 nm for $a$ axis). The ionization energy of Mu ($rightarrow mu^+ + e^-$) due to thermal activation is deduced to be 1.2(4) meV, as is directly inferred from the disappearance of Mu signal above ~8 K. These observations suggest that electronic level associated with Mu (as well as H) is situated near the bottom of the conduction band, serving as a shallow donor state in rutile.
The internal magnetic field distribution in a mixed state of a cuprate superconductor, Ca$_{2-x}$Na$_x$CuO$_2$Cl$_2$ ($T_{rm c}simeq28.5$ K, near the optimal doping), was measured by muon spin rotation ($mu$SR) technique up to 60 kOe. The $mu$SR line
width $Lambda(B)$ which exhibits excess broadening at higher fields ($B>5$ kOe) due to field-induced magnetism (FIM), is described by a relation, $Lambda(B)proptosqrt{B}$. This suggests that the orbital current and associated quasiparticle excitation plays predominant roles in stabilizing the quasistatic correlation. Moreover, a slowing down of the vortex fluctuation sets in well above $T_{rm c}$, as inferred from the trace of FIM observed up to $sim80$ K, and develops continuously without a singularity at $T_{rm c}$ as the temperature decreases.
The response of vortex state to the magnetic field in Nb3Sn is probed using muon spin rotation and small-angle neutron scattering. A transformation of vortex structure between hexagonal and squared lattice is observed over a relatively low field rang
e of 2-3 Tesla. The gradual increase of the magnetic penetration depth with increasing field provides microscopic evidence for anisotropic (or multi-gapped) s-wave pairing suggested by the Raman scattering experiment. This result renders need for careful examination on the difference of electronic properties between Nb3Sn and V3Si.
