arXiv subjects

T. Lorenz

Publications and source records attributed to T. Lorenz.

At least 19 recordsLinked to original sources

arXiv2024

Spin-orbital-lattice entanglement in the ideal j=1/2 compound K$_2$IrCl$_6$

Mott insulators with spin-orbit entangled j=1/2 moments host intriguing magnetic properties. The j=1/2 wave function requires cubic symmetry, while a noncubic crystal field mixes j=1/2 and 3/2 character. Spectroscopic studies of $5d^5$ iridates typically claim noncubic symmetry, e.g., based on a splitting of the excited j=3/2 quartet. A sizable splitting is particularly puzzling in antifluorite-type K$_2$IrCl$_6$, a frustrated fcc quantum magnet with global cubic symmetry. It raises the fundamental question about the stability of j=1/2 moments against magneto-elastic coupling. Combining resonant inelastic x-ray scattering with optical spectroscopy, we demonstrate that the multi-peak line shape in K$_2$IrCl$_6$ reflects a vibronic character of the j=3/2 states rather than a noncubic crystal field. The quasimolecular crystal structure with well separated IrCl$_6$ octahedra explains the existence of well-defined sidebands that are usually smeared out in solids. Our results highlight the spin-orbital-lattice entangled character of cubic K$_2$IrCl$_6$ with ideal j=1/2 moments.

cond-mat.str-el↗

arXiv2023

Electronic excitations in $5d^4$ J=0 Os$^{4+}$ halides studied by RIXS and optical spectroscopy

We demonstrate that the cubic antifluorite-type halides K$_2$OsCl$_6$, K$_2$OsBr$_6$, and Rb$_2$OsBr$_6$ are excellent realizations of non-magnetic J=0 compounds. The magnetic susceptibility shows the corresponding Van-Vleck type behavior and no sign of defects. We investigate the electronic excitations with two complementary techniques, resonant inelastic x-ray scattering (RIXS) and optical spectroscopy. This powerful combination allows us to thoroughly study, e.g., on-site intra-$t_{2g}$ excitations and $t_{2g}$-to-$e_g$ excitations as well as inter-site excitations across the Mott gap and an exciton below the gap. In this way, we determine the electronic parameters with high accuracy, altogether yielding a comprehensive picture. In K$_2$OsCl$_6$, we find the spin-orbit coupling constant $ζ$=0.34 eV, Hund's coupling $J_H$=0.43 eV, the onset of excitations across the Mott gap at $Δ$=2.2 eV, the cubic crystal-field splitting 10Dq=3.3 eV, and the charge-transfer energy $Δ_{CT}$=4.6 eV. With $J_H/ζ$=1.3, K$_2$OsCl$_6$ is in the intermediate-coupling regime. In a $t_{2g}$-only Kanamori picture, the above values correspond to $ζ^{eff}$=0.41 eV and $J_H^{eff}$=0.28 eV, which is very close to results reported for related $5d^4$ iridates. In the tetragonal phase at 5 K, the non-cubic crystal field causes a peak splitting of the J=1 state as small as 4 meV. Compared to K$_2$OsCl$_6$, the bromides K$_2$OsBr$_6$ and Rb$_2$OsBr$_6$ show about 12-14 % smaller values of 10Dq and $Δ_{CT}$, while the spin-orbit-entangled intra-$t_{2g}$ excitations below 2 eV and hence $ζ$ and $J_H$ are reduced by less than 4 %. Furthermore, the Mott gap in K$_2$OsBr$_6$ is reduced to about 1.8 eV.

cond-mat.str-el↗

arXiv2022

RIXS interferometry and the role of disorder in the quantum magnet Ba$_3$Ti$_{3-x}$Ir$_{x}$O$_9$

Motivated by several claims of spin-orbit driven spin-liquid physics in hexagonal Ba$_3$Ti$_{3-x}$Ir$_x$O$_9$ hosting Ir2O9 dimers, we report on resonant inelastic x-ray scattering (RIXS) at the Ir L3 edge for different x. We demonstrate that magnetism in Ba$_3$Ti$_{3-x}$Ir$_x$O$_9$ is governed by an unconventional realization of strong disorder, where cation disorder affects the character of the local moments. RIXS interferometry, studying the RIXS intensity over a broad range of transferred momentum q, is ideally suited to assign different excitations to different Ir sites. We find pronounced Ir-Ti site mixing. Both ions are distributed over two crystallographically inequivalent sites, giving rise to a coexistence of quasimolecular singlet states on Ir2O9 dimers and spin-orbit entangled j=1/2 moments of 5d$^5$ Ir$^{4+}$ ions. RIXS reveals different kinds of strong magnetic couplings for different bonding geometries, highlighting the role of cation disorder for the suppression of long-range magnetic order in this family of compounds.

cond-mat.str-el↗

arXiv2021

Multiple field-induced phases in the frustrated triangular magnet Cs$_3$Fe$_2$Br$_9$

The recently discovered material Cs$_3$Fe$_2$Br$_9$ contains Fe$_2$Br$_9$ bi-octahedra forming triangular layers with hexagonal stacking along the $c$ axis. In contrast to isostructural Cr-based compounds, the zero-field ground state is not a nonmagnetic $S=0$ singlet-dimer state. Instead, the Fe$_2$Br$_9$ bi-octahedra host semiclassical $S=5/2$ Fe$^{3+}$ spins with a pronounced easy-axis anisotropy along $c$ and interestingly, the intra-dimer spins are ordered ferromagnetically. The high degree of magnetic frustration due to (various) competing intra- and inter-dimer couplings leads to a surprisingly rich magnetic phase diagram. Already the zero-field ground state is reached via an intermediate phase, and the high-field magnetization and thermal expansion data for $H\parallel c$ identify ten different ordered phases. Among them are phases with constant magnetization of 1/3, respectively 1/2 of the saturation value, and several transitions are strongly hysteretic with pronounced length changes reflecting strong magnetoelastic coupling.

cond-mat.str-el↗

arXiv2021

Single-crystal investigations on the multiferroic material LiFe(WO$_4$)$_2$

The crystal and magnetic structure of multiferroic LiFe(WO$_4$)$_2$ were investigated by temperature and magnetic-field dependent specific heat, susceptibility and neutron diffraction experiments on single crystals. Considering only the two nearest-neighbour magnetic interactions, the system forms a $J_1$, $J_2$ magnetic chain but more extended interactions are sizeable. Two different magnetic phases exhibiting long-range incommensurate order evolve at $T_{\text{N}1}\approx 22.2 \text{ K}$ and $T_{\text{N}2}\approx 19 \text{ K}$. First, a spin-density wave develops with moments lying in the $ac$ plane. In its multiferroic phase below $T_{\text{N}2}$, LiFe(WO$_4$)$_2$ exhibits a spiral arrangement with an additional spin-component along $b$. Therefore, the inverse Dzyaloshinskii-Moriya mechanism fully explains the multiferroic behavior in this material. A partially unbalanced multiferroic domain distribution was observed even in the absence of an applied electric field. For both phases only a slight temperature dependence of the incommensurability was observed and there is no commensurate phase emerging at low temperature or at finite magnetic fields up to $6\text{ T}$. LiFe(WO$_4$)$_2$ thus exhibits a simple phase diagram with the typical sequence of transitions for a type-II multiferroic material.

cond-mat.str-el↗

arXiv2019

Magnetoelectric coupling in a frustrated spinel studied using high-field scanning probe microscopy

Below its Néel temperature, the frustrated magnet CdCr$_2$O$_4$ exhibits an antiferromagnetic spin-spiral ground state. Such states can give rise to a sizable magnetoelectric coupling. In this report, we measure the electric polarization induced in single-crystalline CdCr$_2$O$_4$ by a large applied magnetic field. Because the detection of a macroscopic polarization is hindered by the structural domains in the tetragonal spin-spiral phase, we have pioneered an alternative method of measuring polarization induced by high magnetic fields, using electrostatic force microscopy. This method enables us to measure polarization from nanometer sized areas of the sample surface, as well as imaging how to charge inhomogeneities change with magnetic field.

cond-mat.mtrl-sci↗

arXiv2019

Spin-orbit entangled j=1/2 moments in Ba$_2$CeIrO$_6$ -- a frustrated fcc quantum magnet

We establish the double perovskite Ba$_2$CeIrO$_6$ as a nearly ideal model system for j=1/2 moments, with resonant inelastic x-ray scattering indicating a deviation of less than 1% from the ideally cubic j=1/2 state. The local j=1/2 moments form an fcc lattice and are found to order antiferromagnetically at $T_N$=14K, more than an order of magnitude below the Curie-Weiss temperature. Model calculations show that the geometric frustration of the fcc Heisenberg antiferromagnet is further enhanced by a next-nearest neighbor exchange, indicated by ab initio theory. Magnetic order is driven by a bond-directional Kitaev exchange and by local distortions via a strong magneto-elastic effect - both effects are typically not expected for j=1/2 compounds making Ba2CeIrO6 a riveting example for the rich physics of spin-orbit entangled Mott insulators.

cond-mat.str-el↗

arXiv2019

Quantum Critical Dynamics of a Heisenberg-Ising Chain in a Longitudinal Field: Many-Body Strings versus Fractional Excitations

We report a high-resolution terahertz spectroscopic study of quantum spin dynamics in the antiferromagnetic Heisenberg-Ising spin-chain compound BaCo$_2$V$_2$O$_8$ as a function of temperature and longitudinal magnetic field. Confined spinon excitations are observed in an antiferromagnetic phase below $T_N\simeq 5.5$ K. In a field-induced gapless phase above $B_c=3.8$ T, we identify many-body string excitations as well as low-energy fractional psinon/antipsinon excitations by comparing to Bethe-Ansatz calculations. In the vicinity of $B_c$, the high-energy string excitations are found to be dynamically dominant over the fractional excitations.

cond-mat.str-el↗

arXiv2019

Resonant inelastic x-ray incarnation of Young's double-slit experiment

Young's archetypal double-slit experiment forms the basis for modern diffraction techniques: the elastic scattering of waves yields an interference pattern that captures the real-space structure. Here, we report on an inelastic incarnation of Young's experiment and demonstrate that resonant inelastic x-ray scattering (RIXS) measures interference patterns which reveal the symmetry and character of electronic excited states in the same way as elastic scattering does for the ground state. A prototypical example is provided by the quasi-molecular electronic structure of insulating Ba3CeIr2O9 with structural Ir dimers and strong spin-orbit coupling. The double 'slits' in this resonant experiment are the highly localized core levels of the two Ir atoms within a dimer. The clear double-slit-type sinusoidal interference patterns that we observe allow us to characterize the electronic excitations, demonstrating the power of RIXS interferometry to unravel the electronic structure of solids containing, e.g., dimers, trimers, ladders, or other superstructures.

cond-mat.str-el↗

arXiv2018

Quantum Criticality of an Ising-like Spin-1/2 Antiferromagnetic Chain in 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 applied transverse magnetic field up to 60 T. While across the Néel temperature of $T_N\sim5$ 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 $B^{c,3D}_\perp=21.4$ T, indicating the suppression of the antiferromagnetic order. At higher fields, the $T(B)$ curve shows a broad minimum at $B^c_\perp = 40$ T, accompanied by a broad minimum in the sound velocity and a saturation-like magnetization. These features signal a quantum phase transition which is further characterized by the divergent behavior of the Grüneisen parameter $Γ_B \propto (B-B^{c}_\perp)^{-1}$. 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.

cond-mat.str-el↗

arXiv2017

Topological quantum phase transition in the Ising-like antiferromagnetic spin chain BaCo$_2$V$_2$O$_8$

Since the seminal ideas of Berezinskii, Kosterlitz and Thouless, topological excitations are at the heart of our understanding of a whole novel class of phase transitions. In most of the cases, those transitions are controlled by a single type of topological objects. There are however some situations, still poorly understood, where two dual topological excitations fight to control the phase diagram and the transition. Finding experimental realization of such cases is thus of considerable interest. We show here that this situation occurs in BaCo$_2$V$_2$O$_8$, a spin-1/2 Ising-like quasi-one dimensional antiferromagnet when subjected to a uniform magnetic field transverse to the Ising axis. Using neutron scattering experiments, we measure a drastic modification of the quantum excitations beyond a critical value of the magnetic field. This quantum phase transition is identified, through a comparison with theoretical calculations, to be a transition between two different types of solitonic topological objects, which are captured by different components of the dynamical structure factor.

cond-mat.str-el↗

arXiv2017

Magnetic shape-memory effect in SrRuO$_3$

Like most perovskites, SrRuO$_3$ exhibits structural phase transitions associated with rotations of the RuO$_6$ octahedra. The application of moderate magnetic fields in the ferromagnetically ordered state allows one to fully control these structural distortions, although the ferromagnetic order occurs at six times lower temperature than the structural distortion. Our neutron diffraction and macroscopic measurements unambiguously show that magnetic fields rearrange structural domains, and that for the field along a cubic [110]$_c$ direction a fully detwinned crystal is obtained. Subsequent heating above the Curie temperature causes a magnetic shape-memory effect, where the initial structural domains recover.

cond-mat.mtrl-sci↗

arXiv2016

Strong magnetoelastic coupling at the transition from harmonic to anharmonic order in NaFe(WO$_4$)$_2$ with 3d$^5$ configuration

The crystal structure of the double tungstate NaFe(WO$_4$)$_2$ arises from that of the spin-driven multiferroic MnWO$_4$ by inserting non-magnetic Na layers. NaFe(WO$_4$)$_2$ exhibits a three-dimensional incommensurate spin-spiral structure at low temperature and zero magnetic field, which, however, competes with commensurate order induced by magnetic field. The incommensurate zero-field phase corresponds to the condensation of a single irreducible representation but it does not imply ferroelectric polarization because spirals with opposite chirality coexist. Sizable anharmonic modulations emerge in this incommensurate structure, which are accompanied by large magneto-elastic anomalies, while the onset of the harmonic order is invisible in the thermal expansion coefficient. In magnetic fields applied along the monoclinic axis, we observe a first-order transition to a commensurate structure that again is accompanied by large magneto-elastic effects. The large magnetoelastic coupling, a reduction of the $b$ lattice parameter, is thus associated only with the commensurate order. Upon releasing the field at low temperature, the magnetic order transforms to another commensurate structure that considerably differs from the incommensurate low-temperature phase emerging upon zero-field cooling. The latter phase, which exhibits a reduced ordered moment, seems to be metastable.

cond-mat.str-el↗

arXiv2015

Suppression of Pauling's Residual Entropy in Dilute Spin Ice (Dy$_{1-x}$Y$_x$)$_2$Ti$_2$O$_7$

Around 0.5 K, the entropy of the spin-ice Dy$_2$Ti$_2$O$_7$ has a plateau-like feature close to Pauling's residual entropy derived originally for water ice, but an unambiguous quantification towards lower temperature is prevented by ultra-slow thermal equilibration. Based on specific heat data of (Dy$_{1-x}$Y$_x$)$_2$Ti$_2$O$_7$ we analyze the influence of non-magnetic dilution on the low-temperature entropy. With increasing x, the ultra-slow thermal equilibration rapidly vanishes, the low-temperature entropy systematically decreases and its temperature dependence strongly increases. These data suggest that a non-degenerate ground state is realized in (Dy$_{1-x}$Y$_x$)$_2$Ti$_2$O$_7$ for intermediate dilution. This contradicts the expected zero-temperature residual entropy obtained from a generalization of Pauling's theory for dilute spin ice, but is supported by Monte Carlo simulations.

cond-mat.str-el↗

arXiv2015

Spin-orbital excitation continuum and anomalous electron-phonon interaction in the Mott insulator LaTiO$_3$

Raman scattering experiments on stoichiometric, Mott-insulating LaTiO$_3$ over a wide range of excitation energies reveal a broad electronic continuum which is featureless in the paramagnetic state, but develops a gap of $\sim 800$ cm$^{-1}$ upon cooling below the Néel temperature $T_N = 146$ K. In the antiferromagnetic state, the spectral weight below the gap is transferred to well-defined spectral features due to spin and orbital excitations. Low-energy phonons exhibit pronounced Fano anomalies indicative of strong interaction with the electron system for $T > T_N$, but become sharp and symmetric for $T < T_N$. The electronic continuum and the marked renormalization of the phonon lifetime by the onset of magnetic order are highly unusual for Mott insulators and indicate liquid-like correlations between spins and orbitals.

cond-mat.str-el↗

arXiv2014

Low-temperature ordered phases of the spin-$\frac{1}{2}$ XXZ chain system Cs$_2$CoCl$_4$

In this study the magnetic order of the spin-1/2 XXZ chain system Cs$_2$CoCl$_4$ in a temperature range from 50 mK to 0.5 K and in applied magnetic fields up to 3.5 T is investigated by high-resolution measurements of the thermal expansion and the specific heat. Applying magnetic fields along a or c suppresses $T_\textrm{N}$ completely at about 2.1 T. In addition, we find an adjacent intermediate phase before the magnetization saturates close to 2.5 T. For magnetic fields applied along b, a surprisingly rich phase diagram arises. Two additional transitions are observed at critical fields $μ_0 H_{SF1}\simeq 0.25$ T and $μ_0 H_{SF2}\simeq 0.7$ T, which we propose to arise from a two-stage spin-flop transition.

cond-mat.str-el↗

arXiv2014

Magnetoelectric properties of $A_2$[FeCl$_5$(H$_2$O)] with $A = $ K, Rb, Cs

The compounds $A_2$[FeCl$_5$(H$_2$O)] with $A=$ K, Rb, Cs are identified as new linear magnetoelectric materials. We present a detailed investigation of their linear magnetoelectric properties by measurements of pyroelectric currents, dielectric constants and magnetization. The anisotropy of the linear magnetoelectric effect of the K-based and Rb-based compound is consistent with the magnetic point group $m'm'm'$, already reported in literature. A symmetry analysis of the magnetoelectric effect of the Cs-based compound allows to determine the magnetic point group $mmm'$ and to develop a model for its magnetic structure. In addition, magnetic-field versus temperature phase diagrams are derived and compared to the closely related multiferroic (NH$_4$)$_2$[FeCl$_5$(H$_2$O)].

cond-mat.str-el↗

arXiv2014

Anisotropy study of multiferroicity in the pyroxene NaFeGe$_2$O$_6$

We present a study of the anisotropy of the dielectric, magnetic and magnetoelastic properties of the multiferroic clinopyroxene NaFeGe$_2$O$_6$. Pyroelectric currents, dielectric constants and magnetic susceptibilities as well as the thermal expansion and the magnetostriction were examined on large synthetic single crystals of NaFeGe$_2$O$_6$. The spontaneous electric polarization detected below $T_{\rm C}\simeq 11.6$ K in an antiferromagnetically ordered state ($T_{\rm N}\simeq 13$ K) is mainly lying within the $ac$ plane with a small component along $b$, indicating a triclinic symmetry of the multiferroic phase of NaFeGe$_2$O$_6$. The electric polarization can be strongly modified by applying magnetic fields along different directions. We derive detailed magnetic-field versus temperature phase diagrams and identify three multiferroic low-temperature phases, which are separated by a non-ferroelectric, antiferromagnetically ordered state from the paramagnetic high-temperature phase.

cond-mat.str-el↗