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.

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.

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.

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.

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.

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.

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.

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.

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.

Nuclear Magnetic Resonance Signature of the Spin-Nematic Phase in LiCuVO_{4} at High Magnetic Fields.

We report a ^{51}V nuclear magnetic resonance investigation of the frustrated spin-1/2 chain compound LiCuVO_{4}, performed in pulsed magnetic fields and focused on high-field phases up to 56 T. For the crystal orientations H∥c and H∥b, we find a narrow field region just below the magnetic saturation where the local magnetization remains uniform and homogeneous, while its value is field dependent. This behavior is the first microscopic signature of the spin-nematic state, breaking spin-rotation symmetry without generating any transverse dipolar order, and is consistent with theoretical predictions for the LiCuVO_{4} compound.

Entropy Evolution in the Magnetic Phases of Partially Frustrated CePdAl.

In the heavy-fermion metal CePdAl, long-range antiferromagnetic order coexists with geometric frustration of one-third of the Ce moments. At low temperatures, the Kondo effect tends to screen the frustrated moments. We use magnetic fields B to suppress the Kondo screening and study the magnetic phase diagram and the evolution of the entropy with B employing thermodynamic probes. We estimate the frustration by introducing a definition of the frustration parameter based on the enhanced entropy, a fundamental feature of frustrated systems. In the field range where the Kondo screening is suppressed, the liberated moments tend to maximize the magnetic entropy and strongly enhance the frustration. Based on our experiments, this field range may be a promising candidate to search for a quantum spin liquid.

Frustrated magnets in high magnetic fields-selected examples.

An indispensable parameter to study strongly correlated electron systems is the magnetic field. Application of high magnetic fields allows the investigation, modification and control of different states of matter. Specifically for magnetic materials experimental tools applied in such fields are essential for understanding their fundamental properties. Here, we focus on selected high-field studies of frustrated magnetic materials that have been shown to host a broad range of fascinating new and exotic phases. We will give brief insights into the influence of geometrical frustration on the critical behavior of triangular-lattice antiferromagnets, the accurate determination of exchange constants in the high-field saturated state by use of electron spin resonance measurements, and the coupling of magnetic degrees of freedom to the lattice evidenced by ultrasound experiments. The latter technique as well allowed new, partially metastable phases in strong magnetic fields to be revealed.

Microscopic Study of the Fulde-Ferrell-Larkin-Ovchinnikov State in an All-Organic Superconductor.

Quasi-two-dimensional superconductors with a sufficiently weak interlayer coupling allow magnetic flux to penetrate in the form of Josephson vortices for in-plane applied magnetic fields. A consequence is the dominance of the Zeeman interaction over orbital effects. In the clean limit, the normal state is favored over superconductivity for fields greater than the paramagnetic limiting field, unless an intermediate, inhomogeneous state is stabilized. Presented here are nuclear magnetic resonance (NMR) studies of the inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state for ß''-(ET)2SF5CH2CF2SO3. The uniform superconductivity-FFLO transition is identified at an applied field value of 9.3(0.1) T at low temperature (T=130 mK), and evidence for a possible second transition between inhomogeneous states at ∼11 T is presented. The spin polarization distribution inferred from the NMR absorption spectrum compares favorably to a single-Q modulation of the superconducting order parameter.

Origin of the Zero-Field Splitting in Mononuclear Octahedral Mn(IV) Complexes: A Combined Experimental and Theoretical Investigation.

The aim of this work was to determine and understand the origin of the electronic properties of Mn(IV) complexes, especially the zero-field splitting (ZFS), through a combined experimental and theoretical investigation on five well-characterized mononuclear octahedral Mn(IV) compounds, with various coordination spheres (N6, N3O3, N2O4 in both trans (trans-N2O4) and cis configurations (cis-N2O4) and O4S2). High-frequency and -field EPR (HFEPR) spectroscopy has been applied to determine the ZFS parameters of two of these compounds, MnL(trans-N2O4) and MnL(O4S2). While at X-band EPR, the axial-component of the ZFS tensor, D, was estimated to be +0.47 cm(-1) for MnL(O4S2), and a D-value of +2.289(5) cm(-1) was determined by HFEPR, which is the largest D-magnitude ever measured for a Mn(IV) complex. A moderate D value of -0.997(6) cm(-1) has been found for MnL(trans-N2O4). Quantum chemical calculations based on two theoretical frameworks (the Density Functional Theory based on a coupled perturbed approach (CP-DFT) and the hybrid Ligand-Field DFT (LF-DFT)) have been performed to define appropriate methodologies to calculate the ZFS tensor for Mn(IV) centers, to predict the orientation of the magnetic axes with respect to the molecular ones, and to define and quantify the physical origin of the different contributions to the ZFS. Except in the case of MnL(trans-N2O4), the experimental and calculated D values are in good agreement, and the sign of D is well predicted, LF-DFT being more satisfactory than CP-DFT. The calculations performed on MnL(cis-N2O4) are consistent with the orientation of the principal anisotropic axis determined by single-crystal EPR, validating the calculated ZFS tensor orientation. The different contributions to D were analyzed demonstrating that the d-d transitions mainly govern D in Mn(IV) ion. However, a deep analysis evidences that many factors enter into the game, explaining why no obvious magnetostructural correlations can be drawn in this series of Mn(IV) complexes.

Establishing the fundamental magnetic interactions in the chiral Skyrmionic Mott insulator Cu(2)OSeO(3) by terahertz electron spin resonance.

The recent discovery of Skyrmions in Cu(2)OSeO(3) has established a new platform to create and manipulate Skyrmionic spin textures. We use high-field electron spin resonance with a terahertz free-electron laser and pulsed magnetic fields up to 64 T to probe and quantify its microscopic spin-spin interactions. In addition to the previously observed long-wavelength Goldstone mode, this technique probes also the high-energy part of the excitation spectrum which is inaccessible by standard low-frequency electron spin resonance. Fitting the behavior of the observed modes in magnetic field to a theoretical framework establishes experimentally that the fundamental magnetic building blocks of this Skyrmionic magnet are rigid, highly entangled and weakly coupled tetrahedra.

Direct determination of exchange parameters in Cs2CuBr4 and Cs2CuCl4: high-field electron-spin-resonance studies.

Spin-1/2 Heisenberg antiferromagnets Cs2CuCl4 and Cs2CuBr4 with distorted triangular-lattice structures are studied by means of electron spin resonance spectroscopy in magnetic fields up to the saturation field and above. In the magnetically saturated phase, quantum fluctuations are fully suppressed, and the spin dynamics is defined by ordinary magnons. This allows us to accurately describe the magnetic excitation spectra in both materials and, using the harmonic spin-wave theory, to determine their exchange parameters. The viability of the proposed method was proven by applying it to Cs2CuCl4, yielding J/kB=4.7(2) K, J'/kB=1.42(7) K, [J'/J≃0.30] and revealing good agreement with inelastic neutron-scattering results. For the isostructural Cs2CuBr4, we obtain J/kB=14.9(7) K, J'/kB=6.1(3) K, [J'/J≃0.41], providing exact and conclusive information on the exchange couplings in this frustrated spin system.

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.

Unconventional magnetostructural transition in CoCr2O4 at high magnetic fields.

The magnetic-field and temperature dependencies of the ultrasound propagation and magnetization of single-crystalline CoCr(2)O(4) have been studied in static and pulsed magnetic fields up to 14 and 62 T, respectively. Distinct anomalies with significant changes in the sound velocity and attenuation are found in this spinel compound at the onset of long-range incommensurate-spiral-spin order at T(s)=27 K and at the transition from the incommensurate to the commensurate states at T(l)=14 K, evidencing strong spin-lattice coupling. While the magnetization evolves gradually with the field, steplike increments in the ultrasound clearly signal a transition into a new magnetostructural state between 6.2 and 16.5 K and at high magnetic fields. We argue that this is a high-symmetry phase with only the longitudinal component of the magnetization being ordered, while the transverse helical component remains disordered. This phase is metastable in an extended H-T phase space.

Angle-dependent evolution of the Fulde-Ferrell-Larkin-Ovchinnikov state in an organic superconductor.

We report magnetic-field and angular-dependent high-resolution specific-heat measurements of the organic superconductor ß''-(BEDT-TTF)2SF5CH2CF2SO3. When the magnetic field is aligned precisely within the conducting BEDT-TTF layer, at low temperatures a clear upturn of the upper critical field beyond the Pauli limit of 9.73 T is observed, hinting at the emergence of a Fulde-Ferrell-Larkin-Ovchinnikov state. This upturn disappears when the field is oriented out of plane by more than ∼0.5 deg. For smaller out-of-plane angles, the specific-heat anomaly at T(c) sharpens and a second peaky phase transition appears within the superconducting state.