Nonreciprocal Phonon Propagation in a Metallic Chiral Magnet.

The phonon magnetochiral effect (MChE) is the nonreciprocal acoustic and thermal transports of phonons caused by the simultaneous breaking of the mirror and time-reversal symmetries. So far, the phonon MChE has been observed only in a ferrimagnetic insulator Cu_{2}OSeO_{3}, where the nonreciprocal response disappears above the Curie temperature of 58 K. Here, we study the nonreciprocal acoustic properties of a room-temperature ferromagnet Co_{9}Zn_{9}Mn_{2} for unveiling the phonon MChE close to room temperature. Surprisingly, the nonreciprocity in this metallic compound is enhanced at higher temperatures and observed up to 250 K. This clear contrast between insulating Cu_{2}OSeO_{3} and metallic Co_{9}Zn_{9}Mn_{2} suggests that metallic magnets have a mechanism to enhance the nonreciprocity at higher temperatures. From the ultrasound and microwave-spectroscopy experiments, we conclude that the magnitude of the phonon MChE of Co_{9}Zn_{9}Mn_{2} mostly depends on the Gilbert damping, which increases at low temperatures and hinders the magnon-phonon hybridization. Our results suggest that the phonon nonreciprocity could be further enhanced by engineering the magnon band of materials.

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.

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.

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.

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.

Field-Induced Magnonic Liquid in the 3D Spin-Dimerized Antiferromagnet Sr_{3}Cr_{2}O_{8}.

We report on ultrasound and magnetization studies in three-dimensional, spin-dimerized Sr_{3}Cr_{2}O_{8} as a function of temperature and external magnetic field up to 61 T. It is well established [A. A. Aczel et al., Phys. Rev. Lett. 103, 207203 (2009)] that this system exhibits a magnonic-superfluid phase between 30 and 60 T and below 8 K. By mapping ultrasound and magnetization anomalies as a function of magnetic field and temperature we establish that this superfluid phase is embedded in a domelike phase regime of a high-temperature magnonic liquid extending up to 18 K. Compared to thermodynamic results, our study indicates that the magnonic liquid could be characterized by an Ising-like order but has lost the coherence of the transverse components.

Erratum: Field-Induced Magnonic Liquid in the 3D Spin-Dimerized Antiferromagnet Sr_{3}Cr_{2}O_{8} [Phys. Rev. Lett. 116, 147201 (2016)].

This corrects the article DOI: 10.1103/PhysRevLett.116.147201.

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.

Unveiling new quantum phases in the Shastry-Sutherland compound SrCu2(BO3)2 up to the saturation magnetic field.

Under magnetic fields, quantum magnets often undergo exotic phase transitions with various kinds of order. The discovery of a sequence of fractional magnetization plateaus in the Shastry-Sutherland compound SrCu2(BO3)2 has played a central role in the high-field research on quantum materials, but so far this system could only be probed up to half the saturation value of the magnetization. Here, we report the first experimental and theoretical investigation of this compound up to the saturation magnetic field of 140 T and beyond. Using ultrasound and magnetostriction techniques combined with extensive tensor-network calculations (iPEPS), several spin-supersolid phases are revealed between the 1/2 plateau and saturation (1/1 plateau). Quite remarkably, the sound velocity of the 1/2 plateau exhibits a drastic decrease of -50%, related to the tetragonal-to-orthorhombic instability of the checkerboard-type magnon crystal. The unveiled nature of this paradigmatic quantum system is a new milestone for exploring exotic quantum states of matter emerging in extreme conditions.

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.

Magnetostructural transitions in a frustrated magnet at high fields.

Ultrasound and magnetization studies of bond-frustrated ZnCr(2)S(4) spinel are performed in static magnetic fields up to 18 T and in pulsed fields up to 62 T. At temperatures below the antiferromagnetic transition at T(N1)≈14 K, the sound velocity as a function of the magnetic field reveals a sequence of steps followed by plateaus indicating a succession of crystallographic structures with constant stiffness. At the same time, the magnetization evolves continuously with a field up to full magnetic polarization without any plateaus in contrast to geometrically frustrated chromium oxide spinels. The observed high-field magnetostructural states are discussed within a H-T phase diagram taking into account the field and temperature evolution of three coexisting spin structures and subsequent lattice transformations induced by the magnetic field.

Ultrasound measurement technique for the single-turn-coil magnets.

Ultrasound is a powerful means to study numerous phenomena of condensed-matter physics as acoustic waves couple strongly to structural, magnetic, orbital, and charge degrees of freedom. In this paper, we present such a technique combined with single-turn coils (STCs) that generate magnetic fields beyond 100 T with the typical pulse duration of 6 µs. As a benchmark of this technique, the ultrasound results for MnCr2S4, Cu6[Si6O18]·6H2O, and liquid oxygen are shown. The resolution for the relative sound-velocity change in the STC is estimated as Δv/v ∼ 10-3, which is sufficient to study various field-induced phase transitions and critical phenomena.

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.

Sub-lattice of Jahn-Teller centers in hexaferrite crystal.

A novel type of sub-lattice of the Jahn-Teller (JT) centers was arranged in Ti-doped barium hexaferrite BaFe12O19. In the un-doped crystal all iron ions, sitting in five different crystallographic positions, are Fe3+ in the high-spin configuration (S = 5/2) and have a non-degenerate ground state. We show that the electron-donor Ti substitution converts the ions to Fe2+ predominantly in tetrahedral coordination, resulting in doubly-degenerate states subject to the [Formula: see text] problem of the JT effect. The arranged JT complexes, Fe2+O4, their adiabatic potential energy, non-linear and quantum dynamics, have been studied by means of ultrasound and terahertz-infrared spectroscopies. The JT complexes are sensitive to external stress and applied magnetic field. For that reason, the properties of the doped crystal can be controlled by the amount and state of the JT complexes.

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.

Magnetic phase diagram of the helimagnetic spinel compound ZnCr2Se4 revisited by small-angle neutron scattering.

We performed small-angle neutron scattering (SANS) measurements on the helimagnetic spinel compound ZnCr2Se4. The ground state of this material is a multi-domain spin-spiral phase, which undergoes domain selection in a magnetic field and reportedly exhibits a transition to a proposed spin-nematic phase at higher fields. We observed a continuous change in the magnetic structure as a function of field and temperature, as well as a weak discontinuous jump in the spiral pitch across the domain-selection transition upon increasing field. From our SANS results we have established the absence of any long-range magnetic order in the high-field (spin-nematic) phase. We also found that all the observed phase transitions are surprisingly isotropic with respect to the field direction.

High-field magnetization and magnetoelasticity of single crystalline HoFe5Al7.

Magnetization and ultrasound measurements have been performed in pulsed magnetic fields up to 60 T on a ferrimagnetic HoFe5Al7 single crystal (Curie temperature TC = 216 K, compensation point Tcomp = 65 K) with a tetragonal crystal structure of the ThMn12-type. The compound exhibits a high magnetic anisotropy of the easy-plane type. A large anisotropy is also observed within the basal plane having an easy-magnetization direction along the [110] axis with the spontaneous magnetic moment Ms = 2 µB/f.u. at T = 2 K. Along the easy axis, two first-order field-induced magnetic transitions are observed. At both transitions sharp anomalies in the acoustic properties are found. The critical fields of the transitions depend on temperature in a different manner. Within molecular-field theory and using the high-field magnetization data the Ho-Fe inter-sublattice exchange parameter has been determined to be nHoFe ≈ 4 T/µB. The magnetoelasticity has also been probed by magnetization measurements under hydrostatic pressure. TC decreases with a rate dTC/dp = -10 K/GPa, whereas Tcomp increases with dTcomp/dp = 3.5 K/GPa.

Ultrasound study of FeCr2S4 in high magnetic fields.

We report on ultrasound studies of FeCr2S4 in static and pulsed magnetic fields exhibiting an orbital-order transition at 9 K. A longitudinal acoustic mode exhibits distinct features in the phase space of temperature and magnetic field due to magnetic and structural transformations. Pulsed-field measurements show significant differences in the sound velocity below and above the orbital-ordering transition as well as the spin-reorientation transition at 60 K. Our results indicate a reduction of the magnetocrystalline anisotropy on entering the orbitally ordered phase.