Quantum critical fluctuations in a transverse-field Ising magnet.

CoNb2O6is a model system for a spin-1/2 one-dimensional (1D) transverse-field Ising magnet (TFIM) with a rather low three-dimensional (3D) Néel ordering temperature atTN=2.95K. We studied CoNb2O6using ultrasound measurements down to 0.3 K in transverse magnetic fields applied along thebdirection. Upon entering the 3D ordered state, we observe pronounced anomalies in the transverse acoustic modec66. In particular, from 1.3 to 1.5 K and around 4.7 T, this mode reveals an almost diverging softening, which is considerably reduced at lower and higher magnetic fields. We interpret this as an influence of quantum critical fluctuations emerging from the quantum critical point (QCP) of the 1D Ising spin chains at about 4.75 T, which lies below the QCP of the 3D ordering at about 5.4 T. This is clear experimental evidence of the predicted generic phase diagram for a TFIM with superimposed 3D ordering.

Field-Tunable Berezinskii-Kosterlitz-Thouless Correlations in a Heisenberg Magnet.

We report the manifestation of field-induced Berezinskii-Kosterlitz-Thouless (BKT) correlations in the weakly coupled spin-1/2 Heisenberg layers of the molecular-based bulk material [Cu(pz)_{2}(2-HOpy)_{2}](PF_{6})_{2}. At zero field, a transition to long-range order occurs at 1.38 K, caused by a weak intrinsic easy-plane anisotropy and an interlayer exchange of J^{'}/k_{B}≈1 mK. Because of the moderate intralayer exchange coupling of J/k_{B}=6.8 K, the application of laboratory magnetic fields induces a substantial XY anisotropy of the spin correlations. Crucially, this provides a significant BKT regime, as the tiny interlayer exchange J^{'} only induces 3D correlations upon close approach to the BKT transition with its exponential growth in the spin-correlation length. We employ nuclear magnetic resonance measurements to probe the spin correlations that determine the critical temperatures of the BKT transition as well as that of the onset of long-range order. Further, we perform stochastic series expansion quantum Monte Carlo simulations based on the experimentally determined model parameters. Finite-size scaling of the in-plane spin stiffness yields excellent agreement of critical temperatures between theory and experiment, providing clear evidence that the nonmonotonic magnetic phase diagram of [Cu(pz)_{2}(2-HOpy)_{2}](PF_{6})_{2} is determined by the field-tuned XY anisotropy and the concomitant BKT physics.

Signatures of a magnetic-field-induced Lifshitz transition in the ultra-quantum limit of the topological semimetal ZrTe5.

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.

Dimensional reduction and incommensurate dynamic correlations in the [Formula: see text] triangular-lattice antiferromagnet Ca3ReO5Cl2.

The observation of spinon excitations in the [Formula: see text] triangular antiferromagnet Ca3ReO5Cl2 reveals a quasi-one-dimensional (1D) nature of magnetic correlations, in spite of the nominally 2D magnetic structure. This phenomenon is known as frustration-induced dimensional reduction. Here, we present high-field electron spin resonance spectroscopy and magnetization studies of Ca3ReO5Cl2, allowing us not only to refine spin-Hamiltonian parameters, but also to investigate peculiarities of its low-energy spin dynamics. We argue that the presence of the uniform Dzyaloshinskii-Moriya interaction (DMI) shifts the spinon continuum in momentum space and, as a result, opens a zero-field gap at the Γ point. We observed this gap directly. The shift is found to be consistent with the structural modulation in the ordered state, suggesting this material as a perfect model triangular-lattice system, where a pure DMI-spiral ground state can be realized.

Fermi surface of the chiral topological semimetal PtGa.

PtGa is a topological semimetal with giant spin-split Fermi arcs. Here, we report on angular-dependent de Haas-van Alphen (dHvA) measurements combined with band-structure calculations to elucidate the details of the bulk Fermi surface of PtGa. The strong spin-orbit coupling leads to eight bands crossing the Fermi energy that form a multitude of Fermi surfaces with closed extremal orbits and results in very rich dHvA spectra. The large number of experimentally observed dHvA frequencies make the assignment to the equally large number of calculated dHvA orbits challenging. Nevertheless, we find consistency between experiment and calculations verifying the topological character with maximal Chern number of the spin-split Fermi surface.

Origin of the quasi-quantized Hall effect in ZrTe5.

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.

Electric Quadrupolar Contributions in the Magnetic Phases of UNi_{4}B.

We present acoustic signatures of the electric quadrupolar degrees of freedom in the honeycomb-layer compound UNi_{4}B. The transverse ultrasonic mode C_{66} shows softening below 30 K both in the paramagnetic phase and antiferromagnetic phases down to ∼0.33 K. Furthermore, we traced magnetic field-temperature phase diagrams up to 30 T and observed a highly anisotropic elastic response within the honeycomb layer. These observations strongly suggest that Γ_{6}(E_{2g}) electric quadrupolar degrees of freedom in localized 5f^{2} (J=4) states are playing an important role in the magnetic toroidal dipole order and magnetic-field-induced phases of UNi_{4}B, and evidence some of the U ions remain in the paramagnetic state even if the system undergoes magnetic toroidal ordering.

Robust Fermi-Surface Morphology of CeRhIn_{5} across the Putative Field-Induced Quantum Critical Point.

We report a comprehensive de Haas-van Alphen (dHvA) study of the heavy-fermion material CeRhIn_{5} in magnetic fields up to 70 T. Several dHvA frequencies gradually emerge at high fields as a result of magnetic breakdown. Among them is the thermodynamically important ß_{1} branch, which has not been observed so far. Comparison of our angle-dependent dHvA spectra with those of the non-4f compound LaRhIn_{5} and with band-structure calculations evidences that the Ce 4f electrons in CeRhIn_{5} remain localized over the whole field range. This rules out any significant Fermi-surface reconstruction, either at the suggested nematic phase transition at B^{*}≈30 T or at the putative quantum critical point at B_{c}≃50 T. Our results rather demonstrate the robustness of the Fermi surface and the localized nature of the 4f electrons inside and outside of the antiferromagnetic phase.

Mode Conversion and Period Doubling in a Liquid Rubidium Alfvén-Wave Experiment with Coinciding Sound and Alfvén Speeds.

We report Alfvén-wave experiments with liquid rubidium at the Dresden High Magnetic Field Laboratory. Reaching up to 63 T, the pulsed magnetic field exceeds the critical value of 54 T at which the Alfvén speed coincides with the sound speed. At this threshold, we observe a period doubling of an applied 8 kHz cw excitation, which is consistent with the theoretical expectation of a parametric resonance between magnetosonic waves and Alfvén waves. Similar mode conversions are discussed as a possible mechanism for heating the solar corona.

Unconventional Hall response in the quantum limit of HfTe5.

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.

Nature of Magnetic Excitations in the High-Field Phase of α-RuCl_{3}.

We present comprehensive electron spin resonance (ESR) studies of in-plane oriented single crystals of α-RuCl_{3}, a quasi-two-dimensional material with honeycomb structure, focusing on its high-field spin dynamics. The measurements were performed in magnetic fields up to 16 T, applied along the [110] and [100] directions. Several ESR modes were detected. Combining our findings with recent inelastic neutron- and Raman-scattering data, we identified most of the observed excitations. Most importantly, we show that the low-temperature ESR response beyond the boundary of the magnetically ordered region is dominated by single- and two-particle processes with magnons as elementary excitations. The peculiarities of the excitation spectrum in the vicinity of the critical field are discussed.

Splitting of the magnetic monopole pair-creation energy in spin ice.

The thermodynamics in spin-ice systems are governed by emergent magnetic monopole excitations and, until now, the creation of a pair of these topological defects was associated with one specific pair-creation energy. Here, we show that the electric dipole moments inherent to the magnetic monopoles lift the degeneracy of their creation process and lead to a splitting of the pair-creation energy. We consider this finding to extend the model of magnetic relaxation in spin-ice systems and show that an electric dipole interaction in the theoretically estimated order of magnitude leads to a splitting which can explain the controversially discussed discrepancies between the measured temperature dependence of the magnetic relaxation times and previous theory. By applying our extended model to experimental data of, various spin-ice systems, we show its universal applicability and determine a dependence of the electric dipole interaction on the system parameters, which is in accordance with the theoretical model of electric dipole formation.

Evidence for an Fulde-Ferrell-Larkin-Ovchinnikov State with Segmented Vortices in the BCS-BEC-Crossover Superconductor FeSe.

We present resistivity and thermal-conductivity measurements of superconducting FeSe in intense magnetic fields up to 35 T applied parallel to the ab plane. At low temperatures, the upper critical field µ_{0}H_{c2}^{ab} shows an anomalous upturn, while thermal conductivity exhibits a discontinuous jump at µ_{0}H^{*}≈24 T well below µ_{0}H_{c2}^{ab}, indicating a first-order phase transition in the superconducting state. This demonstrates the emergence of a distinct field-induced superconducting phase. Moreover, the broad resistive transition at high temperatures abruptly becomes sharp upon entering the high-field phase, indicating a dramatic change of the magnetic-flux properties. We attribute the high-field phase to the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state, where the formation of planar nodes gives rise to a segmentation of the flux-line lattice. We point out that strongly orbital-dependent pairing as well as spin-orbit interactions, the multiband nature, and the extremely small Fermi energy are important for the formation of the FFLO state in FeSe.

Fermi surface of LaFe2P2-a detailed density functional study.

Angular-dependent de Haas-van Alphen measurements allow the mapping of Fermi surfaces in great detail with high accuracy. Density functional electronic-structure calculations can be carried out with high precision, but depend crucially on the used structural information and the applied calculational approximations. We report in a detailed study the sensitivity of the calculated electronic band structure of the 122 compound LaFe2P2 on (i) the exact P position in the unit cell, parametrized by a so-called z parameter, and on (ii) the treatment of the La 4f  states. Depending on the chosen exchange and correlation-potential approximation, the calculated z parameter varies slightly and corresponding small but distinctive differences in the calculated band structure and Fermi-surface topology appear. Similarly, topology changes appear when the energy of the mostly unoccupied La 4f  states is corrected regarding their experimentally observed position. The calculated results are compared to experimental de Haas-van Alphen data. Our findings show a high sensitivity of the calculated band structure on the pnictide z position and the need for an accurate experimental determination of this parameter at low temperatures, and a particular need for a sophisticated treatment of the La 4f  states. Thus, this is not only crucial for the special case of LaFe2P2 studied here, but of importance for the precise determination of the band structure of related 122 materials and La containing compounds in general.

Evidence for the Single-Site Quadrupolar Kondo Effect in the Dilute Non-Kramers System Y_{1-x}Pr_{x}Ir_{2}Zn_{20}.

Acoustic signatures of the single-site quadrupolar Kondo effect in Y_{0.966}Pr_{0.034}Ir_{2}Zn_{20} are presented. The elastic constant (C_{11}-C_{12})/2, corresponding to the Γ_{3}(E)-symmetry electric-quadrupolar response, reveals a logarithmic temperature dependence of the quadrupolar susceptibility in the low-magnetic-field region below ∼0.3 K. Furthermore, the Curie-type divergence of the elastic constant down to ∼1 K indicates that the Pr ions in this diluted system have a non-Kramers ground-state doublet. These observations evidence the single-site quadrupolar Kondo effect, as previously suggested based on specific-heat and electrical-resistivity data.

Viscosity measurements in pulsed magnetic fields by using a quartz-crystal microbalance.

Viscosity measurements in combination with pulsed magnetic fields are developed by use of a quartz-crystal microbalance (QCM). When the QCM is immersed in liquid, the resonant frequency, f0, and the quality factor, Q, of the QCM change depending on (ρη)0.5, where ρ is the mass density and η the viscosity. During the magnetic-field pulse, f0 and Q of the QCM are simultaneously measured by a ringdown technique. The typical resolution of (ρη)0.5 is 0.5%. As a benchmark, the viscosity of liquid oxygen is measured up to 55 T.

Phonon Magnetochiral Effect.

The magnetochiral effect (MCE) of phonons, a nonreciprocal acoustic propagation arising due to symmetry principles, is demonstrated in the chiral-lattice ferrimagnet Cu_{2}OSeO_{3}. Our high-resolution ultrasound experiments reveal that the sound velocity differs for parallel and antiparallel propagation with respect to the external magnetic field. The sign of the nonreciprocity depends on the chirality of the crystal in accordance with the selection rule of the MCE. The nonreciprocity is enhanced below the magnetic ordering temperature and at higher ultrasound frequencies, which is quantitatively explained by a proposed magnon-phonon hybridization mechanism.

Microscopic Nature of the First-Order Field-Induced Phase Transition in the Strongly Anisotropic Ferrimagnet HoFe_{5}Al_{7}.

We report on x-ray magnetic circular dichroism experiments in pulsed fields up to 30 T to follow the rotations of individual magnetic moments through the field-induced phase transition in the ferrimagnet HoFe_{5}Al_{7}. Near the ground state, we observe simultaneous stepwise rotations of the Ho and Fe moments and explain them using a two-sublattice model for an anisotropic ferrimagnet with weak intersublattice exchange interactions. Near the compensation point, we find two phase transitions. The additional magnetization jump reflects the fact that the Ho moment is no longer rigid as the applied field acts against the intersublattice exchange field.

Pressure-tuning the quantum spin Hamiltonian of the triangular lattice antiferromagnet Cs2CuCl4.

Quantum triangular-lattice antiferromagnets are important prototype systems to investigate numerous phenomena of the geometrical frustration in condensed matter. Apart from highly unusual magnetic properties, they possess a rich phase diagram (ranging from an unfrustrated square lattice to a quantum spin liquid), yet to be confirmed experimentally. One major obstacle in this area of research is the lack of materials with appropriate (ideally tuned) magnetic parameters. Using Cs2CuCl4 as a model system, we demonstrate an alternative approach, where, instead of the chemical composition, the spin Hamiltonian is altered by hydrostatic pressure. The approach combines high-pressure electron spin resonance and r.f. susceptibility measurements, allowing us not only to quasi-continuously tune the exchange parameters, but also to accurately monitor them. Our experiments indicate a substantial increase of the exchange coupling ratio from 0.3 to 0.42 at a pressure of 1.8 GPa, revealing a number of emergent field-induced phases.

Quantum Criticality of an Ising-like Spin-1/2 Antiferromagnetic Chain in a Transverse Magnetic Field.

We report on magnetization, sound-velocity, and magnetocaloric-effect measurements of the Ising-like spin-1/2 antiferromagnetic chain system BaCo_{2}V_{2}O_{8} as a function of temperature down to 1.3 K and an applied transverse magnetic field up to 60 T. While across the Néel temperature of T_{N}∼5 K anomalies in magnetization and sound velocity confirm the antiferromagnetic ordering transition, at the lowest temperature the field-dependent measurements reveal a sharp softening of sound velocity v(B) and a clear minimum of temperature T(B) at B_{⊥}^{c,3D}=21.4 T, indicating the suppression of the antiferromagnetic order. At higher fields, the T(B) curve shows a broad minimum at B_{⊥}^{c}=40 T, accompanied by a broad minimum in the sound velocity and a saturationlike magnetization. These features signal a quantum phase transition, which is further characterized by the divergent behavior of the Grüneisen parameter Γ_{B}∝(B-B_{⊥}^{c})^{-1}. By contrast, around the critical field, the Grüneisen parameter converges as temperature decreases, pointing to a quantum critical point of the one-dimensional transverse-field Ising model.