The correlation between the charge density wave (CDW) and $f$ local moments is observed in ${\mathrm{GdNiC}}_2$ by means of x-ray diffraction in a magnetic field. Various kinds of electronic states exist in the magnetic field. The intensity of the CDW peak changes in the successive transitions and the commensurate-incommensurate transition of the CDW takes place as well. The successive transitions are explained in terms of a cooperative effect of the Peierls instability and the spin Friedel oscillation, in which the antiferromagnetic order of the $f$ local moments is coupled to the spin density wave coexisting with the CDW of the conduction electron.

In the spinel titanate ${\mathrm{MgTi}}_2{\mathrm{O}}_4$, the tetragonal phase collapses upon substitution of a tiny amount of Mg ions at the Ti site, and the cubic phase with the geometrical frustration is resurrected. The atomic pair distribution function (PDF) and the extended x-ray absorption fine structure (EXAFS) reveal the nanoscale structural fluctuation, in which the Ti atomic displacement has the two-in two-out configuration in the cubic phase. We argue that the geometrical frustration plays an essential role in the collapse of the tetragonal phase and the resultant nanoscale ice-type structural fluctuation.

The magnetic field dependence of electronic transport, magnetic, and elastic properties in single crystals of PbTe were investigated in high magnetic fields up to 55 T. The magnetoresistance, magnetization, ultrasonic attenuation, and sound velocity showed clear quantum oscillations with pronounced Zeeman splitting, which causes a large second harmonic in the frequency spectra. The ratio of the Zeeman to the cyclotron energy, which is regarded as an index of “Diracness” [H. Hayasaka and Y. Fuseya, J. Phys.: Condens. Matter 28, 31LT01 (2016)], was determined to be 0.52 and 0.57 in samples with different carrier densities. We also pointed out that the effect of Zeeman splitting seriously affects the Landau-level fan diagram analysis, which is widely used to extract the nontrivial Berry's phase from the quantum oscillations.

We studied the effect of the localized spin concentration on the giant magnetoresistance (GMR) and the charge order (CO) in the phthalocyanine (Pc) molecular conductors TPP[FexCo1−x(Pc)(CN)2]2 (TPP = tetraphenylphosphonium), in which the localized spin concentration can be controlled by adjusting the Fe concentration x. Resistivity studies indicated that the CO state was stabilized by localized spins. The negative magnetoresistance was observed even in the region of a localized spin concentration of as low as about 5%. In the high-concentration region, the negative magnetoresistance changed into a positive one at low temperatures. This result shows that a magnetic field stabilizes the CO state, unless the magnetic field is sufficiently strong to break the antiferromagnetic order of the localized spins.

We have experimentally studied the Landau levels near the quantum limit in the magnetic Dirac material ($\mathrm{Eu},\mathrm{Gd}){\mathrm{MnBi}}_2$. In this series of materials, the Fermi level is systematically controlled by substituting ${\mathrm{Eu}}^{2+}$ with ${\mathrm{Gd}}^{3+}$ while keeping high mobility. We measured the Shubnikov–de Haas (SdH) oscillation for a single crystal with the lowest hole concentration at tilted magnetic fields up to 20–50 T and clarified the dependence of the splitting of the Landau levels $N\ge 1$ on the ratio of Zeeman energy to cyclotron energy. In the low-field antiferromagnetic phase, the splitting is well explained by the (Zeeman) spin splitting, from which we have found that the effective $g$ factor of the Dirac fermion depends significantly on the Fermi energy. In the high-field antiferromagnetic phase, on the other hand, the SdH oscillation was found to change in a complex manner as a function of the tilt angle of the field, implying the lifting of the valley degeneracy as well as the spin degeneracy.

We report that the layered semiconductors ${\mathrm{CeTe}}_{2-x}{\mathrm{Sb}}_x$ with low charge carrier density $\le 2\times {10}^{18}{\mathrm{cm}}^{-3}$ exhibit giant negative magnetoresistance exceeding two digits at 2 K. The drastic decrease in electrical resistivity is induced by the transition from the antiferromagnetic to the forced-ferromagnetic state with a wide range of electrical resistivities [approximately 20 to $(3\times {10}^7)\mathrm{\Omega }\mathrm{cm}$] in zero magnetic field. In contrast, the negative magnetoresistance almost disappears in the low-resistivity sample with much higher carrier density ($\sim 2.4\times {10}^{20}{\mathrm{cm}}^{-3}$). These results indicate that the observed giant magnetoresistance is driven by a substantial change in the mobility of the magnetic polarons. In ${\mathrm{CeTe}}_{2-x}{\mathrm{Sb}}_x$, the charge carrier density is variable by several digits by the substitution of Te with Sb. Consequently, the giant negative magnetoresistance is preserved within a wide range of electrical resistivity as long as the magnetic polaron density is low enough that the magnetic polarons rarely overlap each other. The magnetic polaron diameter is discussed using the samples' carrier density.