arXiv subjects

K. C. Rule

Publications and source records attributed to K. C. Rule.

At least 19 recordsLinked to original sources

arXiv2026

Van Hove singularities at the $L$-face of the lutetium nitride phonon dispersion

We report the structural and vibrational properties of the prototypical 4$f$-filled nonmagnetic member LuN of the lanthanide nitrides, \textit{Ln}N, with elastic and inelastic neutron scattering data at $4$~K. We find a peak in the generalized density of states which, through input from a DFT+$U$ computation, we ascribe to a van Hove singularity on the fourfold-degenerate $L$-face of the Brillouin zone. This work advances the understanding of phonon dynamics in \textit{Ln}N beyond the $\Gamma$-point.

cond-mat.mtrl-sci↗

arXiv2026

Competing Ordering Modes in the Distorted Quantum Kagome Material Clinoatacamite Cu$_2$Cl(OH)$_3$

We have studied the magnetic properties of clinoatacamite Cu$_2$Cl(OH)$_3$, the parent compound of the quantum spin liquid candidate herbertsmithite and a longstanding puzzle among frustrated quantum magnets. As we reveal using density-functional theory, clinoatacamite belongs to the class of distorted kagome antiferromagnets with the kagome plane being embedded into a low-symmetry crystal structure. By means of thermodynamic measurements, muon spin rotation/relaxation as well as neutron diffraction on single crystals, we find in zero magnetic field complex behavior below $T_\mathrm{I}$ = 18.1 K which unfolds in three temperature regions I-III. We propose this complexity in multicritical clinoatacamite to arise from the competition of antiferromagnetic ordering modes from the underconstrained manifold of modes, which can lead to a metamagnetic texture in zero field.

cond-mat.str-el↗

arXiv2025

The Magnetic Ground State of Atacamite Cu$_2$Cl(OH)$_3$: The Crucial Role of Frustrated Zigzag Chains Revealed by Inelastic Neutron Scattering

We report inelastic neutron scattering (INS) measurements on the magnetically frustrated $S=\frac12$ sawtooth-chain compound atacamite Cu$_2$Cl(OH)$_3$ featuring inequivalent Cu(1) and Cu(2) sites. Transverse to the sawtooth chains, INS reveals two dispersive spin-wave modes and a gap of at least 0.75 meV. This behavior is rationalized within a zigzag-chain model of Cu(2) spins in an effective magnetic field of Cu(1) spins. The model is compatible with first-principles calculations and accounts for INS dispersions within linear spin-wave theory calculations. Our results reveal a unique case of an effective separation of energy scales between two differently oriented one-dimensional chains, with the zigzag-chain model being essential to fully characterize atacamite's low-energy magnetism.

cond-mat.str-el↗

arXiv2024

Atacamite Cu$_2$Cl(OH)$_3$ in High Magnetic Fields: Quantum Criticality and Dimensional Reduction of a Sawtooth-Chain Compound

We report an extensive high-field study of atacamite Cu$_2$Cl(OH)$_3$, a material realization of quantum sawtooth chains with weak interchain couplings, in continuous and pulsed magnetic fields up to 58 T. In particular, we have mapped the entropy landscape for fields as high as 35 T and have identified a field-induced quantum critical point at 21.9(1) T for $\mathbf{H} \parallel c$ axis. The quantum critical point separates field regions with and without magnetic order, evidenced by our thermodynamic study and $^1$H nuclear magnetic resonance spectroscopy, but lies far below full saturation of the magnetization. Corroborated by numerical results using density-matrix renormalization group (DMRG) calculations, we find this behavior associated with a dimensional reduction of the spin system: the sawtooth chain effectively decouples into an antiferromagnetic spin-$1/2$ chain (backbone of the sawtooth chain) in the presence of an exchange field produced by the remaining field-polarized spins.

cond-mat.str-el↗

arXiv2024

Understanding spin currents from magnon dispersion and polarization: Spin-Seebeck effect and neutron scattering study on Tb3Fe5O12

Magnon spin currents in the ferrimagnetic garnet Tb3Fe5O12 with 4f electrons were examined through the spin-Seebeck effect and neutron scattering measurements. The compound shows a magnetic compensation, where the spin-Seebeck signal reverses above and below Tcomp = 249.5(4) K. Unpolarized neutron scattering unveils two major magnon branches with finite energy gaps, which are well-explained in the framework of spin-wave theory. Their temperature dependencies and the direction of the precession motion of magnetic moments, i.e. magnon polarization, defined using polarized neutrons, explain the reversal at Tcomp and decay of the spin-Seebeck signals at low temperatures. We illustrate an example that momentum- and energy-resolved microscopic information is a prerequisite to understanding the magnon spin current.

cond-mat.str-el↗

arXiv2022

The magnetic dynamics of NiPS$_3$

Neutron spectroscopy measurements have been performed on single crystals of the antiferromagnetic van der Waals compound NiPS$_3$. Linear spin wave theory using a Heisenberg Hamiltonian with single-ion anisotropies has been applied to determine the magnetic exchange parameters and the nature of the anisotropy. The analysis reveals that NiPS$_3$ is less two-dimensional than its sister compounds, with a relatively large ferromagnetic exchange of $J^{\prime} = -0.3$ meV between the layered \emph{ab} planes. In-plane magnetic exchange interactions up to the third nearest-neighbour were required to fit the data. The nearest-neighbour exchange was ferromagnetic with $J_1 = -2.6$ meV, the second neighbour was antiferromagnetic and small with $J_2 = 0.2$ meV, and the dominant antiferromagnetic third neighbour exchange was $J_3 = 13.5$ meV. The anisotropy was shown to be largely XY-like with a small uniaxial component, leading to the appearance of two low-energy spin wave modes in the spin wave spectrum at the Brillouin zone centre. The analysis could reproduce the spin wave energies, however there are discrepancies with the calculated neutron intensities hinting at more exotic phenomena.

cond-mat.str-el↗

arXiv2022

Combining Density-Functional Theory with Low-Temperature, Polarized Terahertz Spectroscopy of Single Crystals Explicates the Fundamental Modes of L-Alanine

Density-functional theory may be used to predict both the frequency and the dipole moment of the fundamental oscillations of molecular crystals. Suitably polarized photons at those frequencies excite such oscillations. Thus, in principle, terahertz spectroscopy may confirm the calculated fundamental modes of amino acids. However, reports to date have multiple shortcomings: (a) material of uncertain purity and morphology and diluted in a binder material is employed; (b) consequently, vibrations along all crystal axes are excited simultaneously; (c) data is restricted to room temperature, where resonances are broad and the background dominant; (d) comparison with theory has been unsatisfactory (in part because the theory assumes zero temperature). Here, we overcome all four obstacles, in reporting detailed low-temperature polarized THz spectra of single-crystal L-alanine, assigning vibrational modes using density-functional theory, and comparing the calculated dipole moment vector direction to the electric field polarization of the measured spectra. Our direct and detailed comparison of theory with experiment corrects previous mode assignments for L-alanine, and reveals unreported modes, previously obscured by closely-spaced spectral absorptions. The fundamental modes are thereby determined.

cond-mat.mtrl-sci↗

arXiv2022

Low-energy spin excitations of the frustrated ferromagnetic $J_1$-$J_2$ chain material linarite, PbCuSO$_4$(OH)$_2$, in applied magnetic fields $\mathbf{H} \parallel b$ axis

We report a study of the spin dynamics of the frustrated ferromagnetic $J_1$-$J_2$ chain compound linarite, PbCuSO$_4$(OH)$_2$, in applied magnetic fields up to field polarization. By means of an extreme-environment inelastic neutron scattering experiment, we have measured the low-energy spin excitations of linarite in fields up to 8.8 T for $\mathbf{H} \parallel b$ axis. We have recorded the spin excitation spectra along $h$, $k$ and $l$ for the field-induced magnetic phases IV, V and the field polarized state close to saturation. By employing first-principles calculations, we estimate the leading magnetic exchanges out of the $bc$ plane and model the dispersion relations using linear spin-wave theory. In this way, we find evidence for a (very weak) residual magnetic exchange coupling out of the $bc$ plane. Together with the previously established dominant intrachain couplings $J_1$ and $J_2$ and the interchain coupling $J_3$, we derive an effective set of exchange couplings for a microscopic description of linarite. Further, we find that the peculiar character of phase V manifests itself in the measured spin dynamics.

cond-mat.str-el↗

arXiv2021

Magnetization process of atacamite: a case of weakly coupled $S = 1/2$ sawtooth chains

We present a combined experimental and theoretical study of the mineral atacamite Cu$_2$Cl(OH)$_3$. Density functional theory yields a Hamiltonian describing anisotropic sawtooth chains with weak 3D connections. Experimentally, we fully characterize the antiferromagnetically ordered state. Magnetic order shows a complex evolution with the magnetic field, while, starting at 31.5 T, we observe a plateau-like magnetization at about $M_{\rm sat}/2$. Based on complementary theoretical approaches, we show that the latter is unrelated to the known magnetization plateau of a sawtooth chain. Instead, we provide evidence that the magnetization process in atacamite is a field-driven canting of a 3D network of weakly coupled sawtooth chains that form giant moments.

cond-mat.str-el↗

arXiv2019

The magnetic phase diagram of the frustrated spin chain compound linarite, PbCuSO$_4$(OH)$_2$, as seen by neutron diffraction and $^1$H-NMR

We report on a detailed neutron diffraction and $^1$H-NMR study on the frustrated spin-1/2 chain material linarite, PbCuSO$_4$(OH)$_2$, where competing ferromagnetic nearest neighbor and antiferromagnetic next-nearest neighbor interactions lead to frustration. From the magnetic Bragg peak intensity studied down to 60 mK, the magnetic moment per Cu atom is obtained within the whole magnetic phase diagram for $H \parallel b$ axis. Further, we establish the detailed configurations of the shift of the SDW propagation vector in phase V with field and temperature. Finally, combining our neutron diffraction results with those from a low-temperature/high-field NMR study we find an even more complex phase diagram close to the quasi-saturation field suggesting that bound two-magnon excitations are the lowest energy excitations close to and in the quasi-saturation regime. Qualitatively and semi-quantitatively, we relate such behavior to $XYZ$ exchange anisotropy and contributions from the Dzyaloshinsky-Moriya interaction to affect the magnetic properties of linarite.

cond-mat.str-el↗

arXiv2017

The dynamics of linarite: Observations of magnetic excitations

Here we present inelastic neutron scattering measurements from the frustrated, quantum spin-1/2 chain material linarite, PbCuSO_4(OH)_2. Time of flight data, taken at 0.5K and zero applied magnetic field reveals low-energy dispersive spin wave excitations below 1.5meV both parallel and perpendicular to the Cu-chain direction. From this we confirm that the interchain couplings within linarite are around 10% of the nearest neighbour intrachain interactions. We analyse the data within both linear spin-wave theory and density matrix renormalisation group theories and establish the main magnetic exchange interactions and the simplest realistic Hamiltonian for this material.

cond-mat.str-el↗

arXiv2015

Quantum phase transitions and decoupling of magnetic sublattices in the quasi-two-dimensional Ising magnet Co3V2O8 in a transverse magnetic field

The application of a magnetic field transverse to the easy axis, Ising direction in the quasi-two-dimensional Kagome staircase magnet, Co3V2O8, induces three quantum phase transitions at low temperatures, ultimately producing a novel high field polarized state, with two distinct sublattices. New time-of-flight neutron scattering techniques, accompanied by large angular access, high magnetic field infrastructure allow the mapping of a sequence of ferromagnetic and incommensurate phases and their accompanying spin excitations. At least one of the transitions to incommensurate phases at μ0Hc1~6.25 T and μ0Hc2~7 T is discontinuous, while the final quantum critical point at μ0Hc3~13 T is continuous.

cond-mat.str-el↗

arXiv2015

Complex field-induced states in Linarite PbCuSO$_4$(OH)$_2$ with a variety of high-order exotic SDW$_p$ states

Low-temperature neutron diffraction and NMR studies of field-induced phases in linarite are presented for magnetic fields $H \parallel b$ axis. A two-step spin-flop transition is observed as well as a transition transforming a helical magnetic ground state into an unusual magnetic phase with sine-wave modulated moments $\parallel H$. An effective $\tilde{J}_1$-$\tilde{J}_2$ single-chain model with a magnetization-dependent frustration ratio $α_{\rm eff} = -\tilde{J}_2/\tilde{J}_1$ is proposed. The latter is governed by skew interchain couplings and shifted to the vicinity of the ferromagnetic critical point. It explains qualitatively the observation of a rich variety of exotic (for strongly correlated cuprate spin-1/2 Heisenberg systems) longitudinal collinear spin-density wave SDW$_p$ states ($9 \geq p \geq 2$).

cond-mat.str-el↗

arXiv2014

Luttinger-Liquid Behavior in the Alternating Spin-Chain System Copper Nitrate

We determine the phase diagram of copper nitrate Cu(NO$_3$)$_2\cdot$2.5D$_2$O in the context of quantum phase transitions and novel states of matter. We establish this compound as an ideal candidate to study quasi-1D Luttinger liquids, 3D Bose-Einstein-Condensation of triplons, and the crossover between 1D and 3D physics. Magnetocaloric effect, magnetization, and neutron scattering data provide clear evidence for transitions into a Luttinger liquid regime and a 3D long-range ordered phase as function of field and temperature. Theoretical simulations of this model material allow us to fully establish the phase diagram and to discuss it in the context of dimerized spin systems.

cond-mat.str-el↗

arXiv2013

Thermodynamic Properties of the Anisotropic Frustrated Spin-chain Compound Linarite PbCuSO$_4$(OH)$_2$

We present a comprehensive macroscopic thermodynamic study of the quasi-one-dimensional (1D) $s = \tfrac{1}{2}$ frustrated spin-chain system linarite. Susceptibility, magnetization, specific heat, magnetocaloric effect, magnetostriction, and thermal-expansion measurements were performed to characterize the magnetic phase diagram. In particular, for magnetic fields along the b axis five different magnetic regions have been detected, some of them exhibiting short-range-order effects. The experimental magnetic entropy and magnetization are compared to a theoretical modelling of these quantities using DMRG and TMRG approaches. Within the framework of a purely 1D isotropic model Hamiltonian, only a qualitative agreement between theory and the experimental data can be achieved. Instead, it is demonstrated that a significant symmetric anisotropic exchange of about 10% is necessary to account for the basic experimental observations, including the 3D saturation field, and which in turn might stabilize a triatic (three-magnon) multipolar phase.

cond-mat.str-el↗

arXiv2013

Gains from the upgrade of the cold neutron triple-axis spectrometer FLEXX at the BER-II reactor

The upgrade of the cold neutron triple-axis spectrometer FLEXX is described. We discuss the characterisation of the gains from the new primary spectrometer, including a larger guide and double focussing monochromator, and present measurements of the energy and momentum resolution and of the neutron flux of the instrument. We found an order of magnitude gain in intensity (at the cost of coarser momentum resolution), and that the incoherent elastic energy widths are measurably narrower than before the upgrade. The much improved count rate should allow the use of smaller single crystals samples and thus enable the upgraded FLEXX spectrometer to continue making leading edge measurements.

physics.ins-det↗

arXiv2012

Asymmetric Thermal Lineshape Broadening in a Gapped 3-Dimensional Antiferromagnet - Evidence for Strong Correlations at Finite Temperature

It is widely believed that magnetic excitations become increasingly incoherent as temperature is raised due to random collisions which limit their lifetime. This picture is based on spin-wave calculations for gapless magnets in 2 and 3 dimensions and is observed experimentally as a symmetric Lorentzian broadening in energy. Here, we investigate a three-dimensional dimer antiferromagnet and find unexpectedly that the broadening is asymmetric - indicating that far from thermal decoherence, the excitations behave collectively like a strongly correlated gas. This result suggests that a temperature activated coherent state of quasi-particles is not confined to special cases like the highly dimerized spin-1/2 chain but is found generally in dimerized antiferromagnets of all dimensionalities and perhaps gapped magnets in general.

cond-mat.str-el↗

arXiv2012

Magnetic soft modes in the locally distorted triangular antiferromagnet alpha-CaCr2O4

In this paper we explore the phase diagram and excitations of a distorted triangular lattice antiferromagnet. The unique two-dimensional distortion considered here is very different from the 'isosceles'-type distortion that has been extensively investigated. We show that it is able to stabilize a 120° spin structure for a large range of exchange interaction values, while new structures are found for extreme distortions. A physical realization of this model is α-CaCr2O4 which has 120° structure but lies very close to the phase boundary. This is verified by inelastic neutron scattering which reveals unusual roton-like minima at reciprocal space points different from those corresponding to the magnetic order.

cond-mat.str-el↗