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Christian Balz

Publications and source records attributed to Christian Balz.

At least 19 recordsLinked to original sources
arXiv2026

Emergent Dispersive Multipolar Excitations in NaErSe$_{2}$

In most condensed-matter systems, local and collective excitations remain decoupled due to their distinct energy scales. Here, we identify coupled local-collective excitations in the triangular antiferromagnet NaErSe$_2$ by combining neutron spectroscopy with total angular momentum modeling. The low-lying crystalline electric field (CEF) doublets include a dipolar $\Gamma_4$ ground state forming stripe-$x$ order and a $\Gamma_{5,6}$ excited state with dipole-octupole character. High-resolution spectra reveal emergent symmetry-selected dispersions, where magnon branches from the ground state are replicated on higher $\Gamma_4$ levels but couple with the $\Gamma_{5,6}$ levels to form a distinct multipolar band. An applied magnetic field reconstructs the CEF wavefunctions and polarizes the system into a multipolar ferromagnet, further reshaping the spectra. This study demonstrates the emergent coupling of local and collective excitations driven by strong spin-orbit coupling and establishes NaErSe$_2$ as a platform for field-tunable multipolar excitations in frustrated magnets.

cond-mat.str-el↗
arXiv2025

Magnetic excitations in biaxial-strain detwinned $\alpha$-RuCl$_{3}$

The honeycomb magnet $\alpha$-RuCl$_{3}$ has been a leading candidate for realizing the Kitaev quantum spin liquid (QSL), but its intrinsic spin dynamics have remained obscured by crystal twinning. Here we apply biaxial anisotropic strain to detwin $\alpha$-RuCl$_{3}$ single crystals and directly visualize the intrinsic magnetic excitations using inelastic neutron scattering. We discover that the low-energy spin waves emerge from the $M$ points -- transverse to the magnetic Bragg peaks -- providing direct evidence of anisotropic magnetic interactions in $\alpha$-RuCl$_{3}$. The intrinsic spin-wave spectrum imposes stringent constraints on the extended Kitaev Hamiltonian, yielding a refined, quantitatively consistent set of exchange couplings for the zigzag ground state and its low-energy dynamics. Above the magnon band, we uncover broad excitation continua: while a twofold-symmetric feature near 6 meV at $\Gamma$ is consistent with bimagnon scattering, the dominant spectral weight forms a sixfold-symmetric continuum extending up to $\sim 16$ meV that cannot be explained by conventional magnons. This strongly supports the presence of fractionalized excitations-a hallmark of Kitaev QSL physics. Our findings establish biaxial strain as a powerful symmetry-breaking probe to access the intrinsic spin dynamics of Kitaev materials and provide critical benchmarks for refining theoretical models of quantum magnetism in $\alpha$-RuCl$_{3}$.

cond-mat.str-el↗
arXiv2025

Magnetic excitations and exchange parameters of a nickel chain compound PbMn$_2$Ni$_6$Te$_3$O$_{18}$: Neutron scattering and density functional theory studies

We have investigated the quasi-one dimensional Ni-chain compound PbMn$_2$Ni$_6$Te$_2$O$_{18}$ using theoretical DFT calculations, inelastic neutron scattering and optical spectroscopy in order to understand the nature of magnetic exchange interactions. Our inelastic neutron scattering study at 5 K on a powder sample reveals two bands of magnetic excitations, the first near 8 meV and the second near 18 meV originating from the antiferromagnetic zone center near $Q$ = 1~\AA. On the other hand at 100 K (which is above T$_N$ = 86 K) a broad diffuse scattering signal is observed indicating the presence of short range magnetic correlations. We have analyzed the magnetic excitations based on the Linear Spin Wave Theory (LSWT) and compared the experimentally estimated exchange parameters with the DFT calculations. Our analysis reveals that the value of the exchange parameter at the larger distance (d=3.654 $\AA$) $J_3$=4.21(8) meV between Ni-Ni (from inter-chain) is the strongest amongst the allowed six exchange parameters, which suggests that this system is not really a quasi-one-dimensional and confirmed by the absence of a Haldane gap. We have also presented the electronic structure calculations. The spin-polarized partial density of states (DOS) projected onto the Mn-d and Ni-d orbitals reveals that the Ni-d$_{x^2-y^2}$ contribution is dominant below the Fermi level in the spin-up and spin-down channel, while a minimal contribution from spin-up Mn states in the occupied region, suggesting a nearly high-spin state. The estimated N\'eel temperature, based on experimental exchange parameters is found to be in close agreement with the experimental value.

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arXiv2025

From continuum excitations to sharp magnons via transverse magnetic field in the spin-1/2 Ising-like triangular lattice antiferromagnet Na2BaCo(PO4)2

We report high-resolution inelastic neutron scattering measurements of the excitation spectrum in large single crystals of the spin-1/2 triangular lattice Ising-like antiferromagnet Na2BaCo(PO4)2 in magnetic fields applied transverse to the Ising axis. In the high-field polarized phase above a critical field $B_{C}$ we observe sharp magnons, as expected in the case of no exchange disorder. Through simultaneous fits to the dispersions including data in polarizing field along the Ising axis, we obtain an excellent match to an Ising-like XXZ Hamiltonian and rule out previously proposed Kitaev exchanges. In the intermediate-field phase below $B_{C}$, we observe three dispersive modes, out of which only the lowest energy one is sharp and the others are broad and overlap with continuum scattering. We propose that the broadening effects are due to magnon decays into two-magnon excitations and confirm that such processes are kinematically allowed. The continuum scattering becomes progressively stronger upon lowering field and, at 0.25 T and zero field, it dominates the complete spectrum with no clear evidence for even broadened magnon modes. We discuss the relevance of the continuous manifold of mean-field degenerate ground states of the refined Hamiltonian for capturing the observed spectrum in zero field, and compare the data with the one- and two-magnon spectrum averaged over this manifold. We also propose a model of the interlayer couplings to explain the observed finite interlayer magnetic propagation vector of the zero-field magnetic order; this requires the breaking of the mirror symmetry in the nominal P-3m1 space group and through refinement of x-ray diffraction data on an untwinned single crystal, we indeed confirm a rotation of the CoO6 octahedra around the c-axis, which lowers the symmetry to P-3.

cond-mat.str-el↗
arXiv2025

Long-range magnetic interactions in Nd$_2$PdSi$_3$ and the formation of skyrmion phases in centrosymmetric metals

We present an extensive X-ray and neutron scattering study of the structure and magnetic excitations of Nd$_2$PdSi$_3$, a sister compound of Gd$_2$PdSi$_3$ which was recently found to host a skyrmion lattice phase despite its centrosymmetric crystal structure. Dispersive magnetic excitations were measured throughout the Brillouin zone and modeled to determine the magnetic interactions between Nd ions. Our analysis reveals that the magnetic interactions in this system extend over large distances and are significantly affected by a crystallographic superstructure formed by ordering of the Pd and Si atoms. The results suggest that the mechanism for the skyrmion phase formation in this family of materials, specifically Gd$_2$PdSi$_3$, is through the long-range RKKY interactions rather than short-range triangular-lattice frustration.

cond-mat.str-el↗
arXiv2025

Two-stage evolution of magnetic correlations in spiral spin liquid material, Ca$_{10}$Cr$_{7}$O$_{28}$

We present an X-band and tunable high-frequency/high-field electron spin resonance (HF-ESR) study of single-crystalline Ca$_{10}$Cr$_{7}$O$_{28}$, which constitutes alternating antiferromagnetic and ferromagnetic kagome bilayers. At high temperatures, a phonon-assisted relaxation process is evoked to account for the pronounced increase of the linewidth in an exchange-narrowing regime ($k_{\rm B}T\gg J$). In contrast, at low temperatures ($k_{\rm B}T\lesssim J$), a power-law behavior in line narrowing is observed. Our data reveal two distinct power-law regimes for the linewidth which crossover at $T^*\approx 7.5$~K. Notably, the intriguing evolution of the ESR linewidth in this alternating kagome bilayer system with opposite sign of exchange interactions highlights distinct spin dynamics compared to those in a uniform kagome antiferromagnet.

cond-mat.str-el↗
arXiv2025

Emergent ferromagnetic ladder excitations in heavy fermion superconductor CeSb$_{2}$

Low-dimensional spin fluctuations play a crucial role in unconventional superconductors, with quasi-one-dimensional spin excitations potentially linked with spin-triplet superconductivity. The heavy fermion superconductor CeSb$_2$ exhibits an unusual large inverted S-shaped upper critical field that suggests a possible triplet pairing state within its pressure-induced superconducting dome. Using inelastic neutron scattering, we discover quasi-one-dimensional magnetic excitations in CeSb$_2$ emerging from nearly square Ce layers with minor orthorhombic deformation. We show that the data are well described by a ferromagnetic spin ladder model, where the "rungs" of the ladder straddle Ce bilayers. Moreover, we find that diffuse excitations akin to those in the ordered phase persist well above $T_{\rm N}$, suggesting that quasi-one-dimensional ferromagnetic paramagnons may significantly contribute to the unusual superconductivity that appears under pressure once magnetic order is suppressed.

cond-mat.supr-con↗
arXiv2024

Wannier states and spin supersolid physics in the triangular antiferromagnet K$_2$Co(SeO$_3$)$_2$

We combine ultra-high-resolution inelastic neutron scattering and quantum Monte Carlo simulations to study thermodynamics and spin excitations in the spin-supersolid phase of the triangular lattice XXZ antiferromagnet K$_2$Co(SeO$_3$)$_2$ under zero and non-zero magnetic field. BKT transitions signaling the onset of Ising and supersolid order are clearly identified, and the Wannier entropy is experimentally recovered just above the supersolid phase. At low temperatures, with an experimental resolution of about 23 $\mu$eV, no discrete coherent magnon modes are resolved within a broad scattering continuum. Alongside gapless excitations, a pseudo-Goldstone mode with a 0.06 meV gap is observed. A second, higher-energy continuum replaces single-spin-flip excitations of the Ising model. Under applied fields, the continuum evolves into coherent spin waves, with Goldstone and pseudo-Goldstone sectors responding differently. The experiments and simulations show excellent quantitative agreement.

cond-mat.str-el↗
arXiv2023

Experimental Evidence for Non-spherical Magnetic Form Factor in Ru$^{3+}$

The Mott insulator $\alpha$-RuCl$_3$ has generated great interest in the community due to its possible field-induced Kitaev quantum spin liquid state. Despite enormous effort spent trying to obtain the form of the low energy Hamiltonian, there is currently no agreed upon set of parameters which is able to explain all of the data. A key piece of missing information lies in the determination of the magnetic form factor of Ru$^{3+}$, particularly for a true quantitative treatment of inelastic neutron scattering data. Here we present the experimentally derived magnetic form factor of Ru$^{3+}$ in the low spin 4$d^5$ state using polarized neutron diffraction within the paramagnetic regime on high quality single crystals of $\alpha$-RuCl$_3$. We observe strong evidence of an anisotropic form factor, expected of the spin-orbit coupled $j_{\textrm{eff}} = \frac{1}{2}$ ground state. We model the static magnetization density in increasing complexity from simple isotropic cases, to a multipolar expansion, and finally \emph{ab initio} calculations of the generalized $j_{\textrm{eff}} = \frac{1}{2}$ ground state. Comparison of both single ion models and inclusion of Cl$^-$ anions support the presence of hybridization of Ru$^{3+}$ with the surrounding Cl$^{-}$ ligands.

cond-mat.str-el↗
arXiv2023

Weyl metallic state induced by helical magnetic order

In the rapidly expanding field of topological materials there is growing interest in systems whose topological electronic band features can be induced or controlled by magnetism. Magnetic Weyl semimetals, which contain linear band crossings near the Fermi level, are of particular interest owing to their exotic charge and spin transport properties. Up to now, the majority of magnetic Weyl semimetals have been realized in ferro- or ferrimagnetically ordered compounds, but a disadvantage of these materials for practical use is their stray magnetic field which limits the minimum size of devices. Here we show that Weyl nodes can be induced by a helical spin configuration, in which the magnetization is fully compensated. Using a combination of neutron diffraction and resonant elastic x-ray scattering, we find that EuCuAs develops a planar helical structure below $T_\textrm{N}$ = 14.5 K which induces Weyl nodes along the $\Gamma$--A high symmetry line in the Brillouin zone.

cond-mat.str-el↗
arXiv2022

Low-dimensional metal-organic magnets as a route towards the S=2 Haldane phase

Metal-organic magnets (MOMs), modular magnetic materials where metal atoms are connected by organic linkers, are promising candidates for next-generation quantum technologies. MOMs readily form low-dimensional structures, and so are ideal systems to realise physical examples of key quantum models, including the Haldane phase, where a topological excitation gap occurs in integer-spin antiferromagnetic (AFM) chains. Thus far the Haldane phase has only been identified for $S=1$, with $S \geq 2$ still unrealised because the larger spin imposes more stringent requirements on the magnetic interactions. Here, we report the structure and magnetic properties of CrCl$_2$(pym) (pym=pyrimidine), a new quasi-1D $S=2$ AFM MOM. We show, using X-ray and neutron diffraction, bulk property measurements, density-functional theory calculations and inelastic neutron spectroscopy (INS) that CrCl$_2$(pym) consists of AFM CrCl$_2$ spin chains ($J_1=-1.13(4)\;$meV) which are weakly ferromagnetically coupled through bridging pym ($J_2=0.10(2)\;$meV), with easy-axis anisotropy ($D=-0.15(3)\;$meV). We find that although small compared to $J_1$, these additional interactions are sufficient to prevent observation of the Haldane phase in this material. Nevertheless, the proximity to the Haldane phase together with the modularity of MOMs suggests that layered Cr(II) MOMs are a promising family to search for the elusive $S=2$ Haldane phase.

cond-mat.str-el↗
arXiv2022

Magnetic ground state of the Kitaev Na$_2$Co$_2$TeO$_6$ spin liquid candidate

As a candidate Kitaev material, Na$_2$Co$_2$TeO$_6$ exhibits intriguing magnetism on a honeycomb lattice that is believed to be $C_3$-symmetric. Here we report a neutron diffraction study of high quality single crystals under $a$-axis magnetic fields. Our data support the less common notion of a magnetic ground state that corresponds to a triple-$\mathbf{q}$ magnetic structure with $C_3$ symmetry, rather than the multi-domain zigzag structure typically assumed in prototype Kitaev spin liquid candidates. In particular, we find that the field is unable to repopulate the supposed zigzag domains, where the only alternative explanation is that the domains are strongly pinned by hitherto unidentified structural reasons. If the triple-$\mathbf{q}$ structure is correct then this requires reevaluation of many candidate Kitaev materials. We also find that fields beyond about 10 Tesla suppress the long range antiferromagnetic order, allowing new magnetic behavior to emerge different from that expected for a spin liquid.

cond-mat.str-el↗
arXiv2022

Finite temperature tensor network algorithm for frustrated two-dimensional quantum materials

Aimed at a more realistic classical description of natural quantum systems, we present a two-dimensional tensor network algorithm to study finite temperature properties of frustrated model quantum systems and real quantum materials. For this purpose, we introduce the infinite projected entangled simplex operator ansatz to study thermodynamic properties. To obtain state-of-the-art benchmarking results, we explore the highly challenging spin-1/2 Heisenberg anti-ferromagnet on the Kagome lattice, a system for which we investigate the melting of the magnetization plateaus at finite magnetic field and temperature. Making close connection to actual experimental data of real quantum materials, we go on to studying the finite temperature properties of Ca$_{10}$Cr$_7$O$_{28}$. We compare the magnetization curve of this material in the presence of an external magnetic field at finite temperature with classically simulated data. As a first theoretical tool that incorporates both thermal fluctuations as well as quantum correlations in the study of this material, our work contributes to settling the existing controversy between the experimental data and previous theoretical works on the magnetization process.

cond-mat.str-el↗
arXiv2022

Magnetic field effects in an octupolar quantum spin liquid candidate

Quantum spin liquid (QSL) is a disordered state of quantum-mechanically entangled spins commonly arising from frustrated magnetic dipolar interactions. However, QSL in some pyrochlore magnets can also come from frustrated magnetic octupolar interactions. Although the key signature for both dipolar and octupolar interaction-driven QSL is the presence of a spin excitation continuum (spinons) arising from the spin quantum number fractionalization, an external magnetic field-induced ferromagnetic order will transform the spinons into conventional spin waves in a dipolar QSL. By contrast, in an octupole QSL, the spin waves carry octupole moments that do not couple, in the leading order, to the external magnetic field or to neutron moments but will contribute to the field dependence of the heat capacity. Here we use neutron scattering to show that the application of a large external magnetic field to Ce2Zr2O7, an octupolar QSL candidate, induces an Anderson-Higgs transition by condensing the spinons into a static ferromagnetic ordered state with octupolar spin waves invisible to neutrons but contributing to the heat capacity. Our theoretical calculations also provide a microscopic, qualitative understanding for the presence of octupole scattering at large wavevectors in Ce2Sn2O7 pyrochlore, and its absence in Ce2Zr2O7. Therefore, our results identify Ce2Zr2O7 as a strong candidate for an octupolar U (1) QSL, establishing that frustrated magnetic octupolar interactions are responsible for QSL properties in Ce-based pyrochlore magnets.

cond-mat.str-el↗
arXiv2022

Extraction of the interaction parameters for $\alpha-$RuCl$_3$ from neutron data using machine learning

Single crystal inelastic neutron scattering data contain rich information about the structure and dynamics of a material. Yet the challenge of matching sophisticated theoretical models with large data volumes is compounded by computational complexity and the ill-posed nature of the inverse scattering problem. Here we utilize a novel machine-learning-assisted framework featuring multiple neural network architectures to address this via high-dimensional modeling and numerical methods. A comprehensive data set of diffraction and inelastic neutron scattering measured on the Kitaev material $\alpha-$RuCl$_3$ is processed to extract its Hamiltonian. Semiclassical Landau-Lifshitz dynamics and Monte-Carlo simulations were employed to explore the parameter space of an extended Kitaev-Heisenberg Hamiltonian. A machine-learning-assisted iterative algorithm was developed to map the uncertainty manifold to match experimental data; a non-linear autoencoder used to undertake information compression; and Radial Basis networks utilized as fast surrogates for diffraction and dynamics simulations to predict potential spin Hamiltonians with uncertainty. Exact diagonalization calculations were employed to assess the impact of quantum fluctuations on the selected parameters around the best prediction.

cond-mat.str-el↗
arXiv2021

A model for coupled $4f-3d$ magnetic spectra: a neutron scattering study of the Yb$-$Fe hybridisation in Yb$_3$Fe$_5$O$_{12}$

In this work, we explore experimentally and theoretically the spectrum of magnetic excitations of the Fe$^{3+}$ and Yb$^{3+}$ ions in ytterbium iron garnet (Yb$_3$Fe$_5$O$_{12}$). We present a complete description of the crystal-field splitting of the $4f$ states of Yb$^{3+}$, including the effect of the exchange field generated by the magnetically ordered Fe subsystem. We also consider a further effect of the Fe-Yb exchange interaction, which is to hybridise the Yb crystal field excitations with the Fe spin-wave modes at positions in the Brillouin zone where the two types of excitations cross. We present detailed measurements of these hybridised excitations, and propose a framework which can be used in the quantitative analysis of the coupled spectra in terms of the anisotropic $4f-3d$ exchange interaction.

cond-mat.str-el↗
arXiv2021

Field-induced intermediate ordered phase and anisotropic interlayer interactions in $α$-RuCl$_3$

In $α$-RuCl$_3$, an external magnetic field applied within the honeycomb plane can induce a transition from a magnetically ordered state to a disordered state that is potentially related to the Kitaev quantum spin liquid. In zero field, single crystals with minimal stacking faults display a low-temperature state with in-plane zigzag antiferromagnetic order and a three-layer periodicity in the direction perpendicular to the honeycomb planes. Here, we present angle-dependent magnetization, ac susceptibility, and thermal transport data that demonstrate the presence of an additional intermediate-field ordered state at fields below the transition to the disordered phase. Neutron diffraction results show that the magnetic structure in this phase is characterized by a six-layer periodicity in the direction perpendicular to the honeycomb planes. Theoretically, the intermediate ordered phase can be accounted for by including spin-anisotropic couplings between the layers in a three-dimensional spin model. Together, this demonstrates the importance of interlayer exchange interactions in $α$-RuCl$_3$.

cond-mat.str-el↗
arXiv2019

Finite field regime for a quantum spin liquid in $α$-RuCl$_3$

An external magnetic field can induce a transition in $α$-RuCl$_3$ from an ordered zigzag state to a disordered state that is possibly related to the Kitaev quantum spin liquid. Here we present new field dependent inelastic neutron scattering and magnetocaloric effect measurements implying the existence of an additional transition out of the quantum spin liquid phase at an upper field limit $B_u$. The neutron scattering shows three distinct regimes of magnetic response. In the low field ordered state the response shows magnon peaks; the intermediate field regime shows only continuum scattering, and above $B_u$ the response shows sharp magnon peaks at the lower bound of a strong continuum. Measurable dispersion of magnon modes along the $(0,0,L)$ direction implies non-negligible inter-plane interactions. Combining the magnetocaloric effect measurements with other data a $T-B$ phase diagram is constructed. The results constrain the range where one might expect to observe quantum spin liquid behavior in $α$-RuCl$_3$.

cond-mat.str-el↗