The quantum Hall effect (QHE) is traditionally considered to be a purely two-dimensional (2D) phenomenon. Recently, however, a three-dimensional (3D) version of the QHE was reported in the Dirac semimetal ZrTe5. It was proposed to arise from a magnetic-field-driven Fermi surface instability, transforming the original 3D electron system into a stack of 2D sheets. Here, we report thermodynamic, spectroscopic, thermoelectric and charge transport measurements on such ZrTe5 samples. The measured properties: magnetization, ultrasound propagation, scanning tunneling spectroscopy, and Raman spectroscopy, show no signatures of a Fermi surface instability, consistent with in-field single crystal X-ray diffraction. Instead, a direct comparison of the experimental data with linear response calculations based on an effective 3D Dirac Hamiltonian suggests that the quasi-quantization of the observed Hall response emerges from the interplay of the intrinsic properties of the ZrTe5 electronic structure and its Dirac-type semi-metallic character.

Interacting electrons confined to their lowest Landau level in a high magnetic field can form a variety of correlated states, some of which manifest themselves in a Hall effect. Although such states have been predicted to occur in three-dimensional semimetals, a corresponding Hall response has not yet been experimentally observed. Here, we report the observation of an unconventional Hall response in the quantum limit of the bulk semimetal HfTe5, adjacent to the three-dimensional quantum Hall effect of a single electron band at low magnetic fields. The additional plateau-like feature in the Hall conductivity of the lowest Landau level is accompanied by a Shubnikov-de Haas minimum in the longitudinal electrical resistivity and its magnitude relates as 3/5 to the height of the last plateau of the three-dimensional quantum Hall effect. Our findings are consistent with strong electron-electron interactions, stabilizing an unconventional variant of the Hall effect in a three-dimensional material in the quantum limit.

We present the results of a combined ^{7}Li-NMR and diffraction study on LiGa_{0.95}In_{0.05}Cr_{4}O_{8}, a member of the LiGa_{1-x}In_{x}Cr_{4}O_{8} "breathing" pyrochlore family. Via specific heat and NMR measurements, we find that the complex sequence of first-order transitions observed for LiGaCr_{4}O_{8} is replaced by a single second-order transition at T_{f}=11  K. Neutron and x-ray diffraction rule out both structural symmetry lowering and magnetic long-range order as the origin of this transition. Instead, reverse Monte Carlo fitting of the magnetic diffuse scattering indicates that the low-temperature phase may be described as a collinear spin nematic state, characterized by a quadrupolar order parameter. This state also shows signs of short-range order between collinear spin arrangements on tetrahedra, revealed by mapping the reverse Monte Carlo spin configurations onto a three-state color model.

The half-Heusler rare-earth intermetallic GdPtBi has recently gained attention due to peculiar magnetotransport phenomena that have been associated with the possible existence of Weyl fermions, thought to arise from the crossings of spin-split conduction and valence bands. On the other hand, similar magnetotransport phenomena observed in other rare-earth intermetallics have often been attributed to the interaction of itinerant carriers with localized magnetic moments stemming from the 4 f shell of the rare-earth element. In order to address the origin of the magnetotransport phenomena in GdPtBi, we performed a comprehensive study of the magnetization, electrical, and thermal magnetoresistivity on two single-crystalline GdPtBi samples. In addition, we performed an analysis of the Fermi surface via Shubnikov-de Haas oscillations in one of the samples and compared the results to ab initio band structure calculations. Our findings indicate that the electrical and thermal magnetotransport in GdPtBi cannot be solely explained by Weyl physics and is strongly influenced by the interaction of both itinerant charge carriers and phonons with localized magnetic Gd ions and possibly also paramagnetic impurities.

Terbium gallium garnet (TGG), Tb3Ga5O12, is well known for its applications in laser optics, but also exhibits complex low-temperature magnetism that is not yet fully understood. Its lowtemperature magnetic order is determined by means of time-of-flight neutron powder diffraction. It is found to be a multiaxial antiferromagnet with magnetic Tb 3+ ions forming six sublattices of magnetic moments aligned parallel and anti-parallel to the 100 crystallographic directions of the cubic unit cell. The structure displays strong easy-axis anisotropy with respect to a two-fold axis of symmetry in the local orthorhombic environment of the Tb 3+ sites. The crystal-field splitting within the single-ion ground-state manifold is investigated by inelastic neutron scattering on powder samples. A strong temperature dependence of the quasidoublet ground-state is observed and revised parameters of the crystal-field Hamiltonian are given. The results of bulk magnetic susceptibility and magnetisation measurements are in good agreement with values based on the crystal-field model down to 20 K, where the onset of magnetic correlations is observed.

The quasi-quantized Hall effect (QQHE) is the three-dimensional (3D) counterpart of the integer quantum Hall effect (QHE), exhibited only by two-dimensional (2D) electron systems. It has recently been observed in layered materials, consisting of stacks of weakly coupled 2D platelets that are yet characterized by a 3D anisotropic Fermi surface. However, it is predicted that the quasi-quantized 3D version of the 2D QHE should occur in a much broader class of bulk materials, regardless of the underlying crystal structure. Here, we compare the observation of quasi-quantized plateau-like features in the Hall conductivity of the n-type bulk semiconductor InAs with the predictions for the 3D QQHE in presence of parabolic electron bands. InAs takes form of a cubic crystal without any low-dimensional substructure. The onset of the plateau-like feature in the Hall conductivity scales with $$\sqrt{2/3}k_{\text {F}}^{z}/\pi$$ 2 / 3 k F z / π in units of the conductance quantum and is accompanied by a Shubnikov–de Haas minimum in the longitudinal resistivity, consistent wit the results of calculations. This confirms the suggestion that the 3D QQHE may be a generic effect directly observable in materials with small Fermi surfaces, placed in sufficiently strong magnetic fields.

The quantum limit (QL) of an electron liquid, realised at strong magnetic fields, has long been proposed to host a wealth of strongly correlated states of matter. Electronic states in the QL are, for example, quasi-one dimensional (1D), which implies perfectly nested Fermi surfaces prone to instabilities. Whereas the QL typically requires unreachably strong magnetic fields, the topological semimetal ZrTe5 has been shown to reach the QL at fields of only a few Tesla. Here, we characterize the QL of ZrTe5 at fields up to 64 T by a combination of electrical-transport and ultrasound measurements. We find that the Zeeman effect in ZrTe5 enables an efficient tuning of the 1D Landau band structure with magnetic field. This results in a Lifshitz transition to a 1D Weyl regime in which perfect charge neutrality can be achieved. Since no instability-driven phase transitions destabilise the 1D electron liquid for the investigated field strengths and temperatures, our analysis establishes ZrTe5 as a thoroughly understood platform for potentially inducing more exotic interaction-driven phases at lower temperatures.

Magnetic systems exhibiting spin-canted states have garnered much attention recently for their promising rich exotic properties driven by the real-space spin textures and competing magnetic orders. In this study, we present the structural and magnetic properties of hexagonal 60 nm MnPtGa epitaxial thin films grown by magnetron sputtering on Al2O3(0001) single-crystalline substrates. The MnPtGa film crystallizes in the centrosymmetric P63/ mmc (No. 194) space group, showing perpendicular magnetic anisotropy along the c-axis, with a Curie temperature TC = 263 K. In addition, the MnPtGa film undergoes a spin reorientation transition at Tsr = 160 K. We investigated the MnPtGa magnetic ground states using single-crystal neutron diffraction. A structurally forbidden (001) magnetic Bragg reflection emerges below Tsr, indicating the existence of a spin-canted state, where the magnetic moments align ferromagnetically perpendicular to the basal plane, and a non-zero in-plane component exhibits an antiferromagnetic ordering along the c-axis. At 2 K, the refined magnetic moments of Mn are μz = 4.2(4)  μB and μx = 1.5(3)  μB, projected onto the c-axis and basal plane, respectively. Hence, we determined a 20° Mn spin canting angle off from the c-axis.