The electron paramagnetic resonance (EPR) signal in the mixed valence perovskite ${\mathrm{La}}_{1-x}{\mathrm{Ca}}_x{\mathrm{MnO}}_{3+y}$ was investigated in the paramagnetic regime for ${}^{16}$O and ${}^{18}$O isotope substituted compounds. The characteristic differences observed in EPR intensity and linewidth for the two isotope samples can be explained by a model in which a bottlenecked spin relaxation takes place from the exchange-coupled constituent ${\mathrm{Mn}}^{4+}$ ions via the ${\mathrm{Mn}}^{3+}$ Jahn-Teller ions to the lattice. For $x=0.2\mathrm{}$ the ferromagnetic exchange energy $J$ exhibits a ${}^{16}\mathrm{O}{/}^{18}\mathrm{O}$ oxygen isotope effect of $\sim -10\mathrm{}\%$. The observed isotope effects suggest the presence of Jahn-Teller polarons in these materials.

In its orthorhombic T_d polymorph, MoTe₂ is a type-II Weyl semimetal, where the Weyl fermions emerge at the boundary between electron and hole pockets. Non-saturating magnetoresistance and superconductivity were also observed in T_d-MoTe₂. Understanding the superconductivity in T_d-MoTe₂, which was proposed to be topologically non-trivial, is of eminent interest. Here, we report high-pressure muon-spin rotation experiments probing the temperature-dependent magnetic penetration depth in T_d-MoTe₂. A substantial increase of the superfluid density and a linear scaling with the superconducting critical temperature T_c is observed under pressure. Moreover, the superconducting order parameter in T_d-MoTe₂ is determined to have 2-gap s-wave symmetry. We also exclude time-reversal symmetry breaking in the superconducting state with zero-field μSR experiments. Considering the strong suppression of T_c in MoTe₂ by disorder, we suggest that topologically non-trivial s⁺⁻ state is more likely to be realized in MoTe₂ than the topologically trivial s⁺⁺ state.

The in-plane magnetic field penetration depth (${\lambda }_{\mathrm{ab}}$) in single-crystal ${\mathrm{La}}_{1.83}{\mathrm{Sr}}_{0.17}{\mathrm{CuO}}_4$ was investigated by muon-spin rotation ($\mu \mathrm{SR}$). The temperature dependence of ${\lambda }_{\mathrm{ab}}^{-2}$ has an inflection point around 10–15 K, suggesting the presence of two superconducting gaps: a large gap (${\Delta }_1^d$) with $d$-wave and a small gap (${\Delta }_2^s$) with $s$-wave symmetry. The zero-temperature values of the gaps at ${\mu }_{0}H=0.02\mathrm{T}$ were found to be ${\Delta }_1^d(0)=8.2(1)\mathrm{meV}$ and ${\Delta }_2^s(0)=1.57(8)\mathrm{meV}$.

Our experiments unambiguously establish 2H-MoTe ₂ and 2H-MoSe ₂ as magnetic, moderate bandgap semiconductors.

Recent EPR and susceptibility measurements in ${\mathrm{La}}_{1-x}{\mathrm{Ca}}_x{\mathrm{MnO}}_3$ support the existence of a bottleneck EPR regime up to 1000 K quantitatively. The EPR linewidth and electrical conductivity follow the same temperature dependence in the range of 250 to 650 K predicted by the small polaron hopping model. This indicates that spin-lattice relaxation in manganates is due to the relaxation of spins of $e_g$ Jahn-Teller polarons to the lattice.

The in-plane magnetic penetration depth ${\lambda }_{ab}$ of the iron selenide superconductor with the nominal composition ${\text{FeSe}}_{0.85}$ was studied by means of muon-spin rotation. The measurements of ${\lambda }_{ab}^{-2}\left(T\right)$ are inconsistent with a simple isotropic $s$-wave type of the order parameter but are rather in favor of two-gap $\left(s+s\right)$ and anisotropic $s$-wave order parameter symmetries, thus implying that the superconducting energy gap in ${\text{FeSe}}_{0.85}$ contains no nodes.