Stephen E. Nagler
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Stephen E. Nagler has a total of 220 co-authors. Here are the top co-authors by number of shared publications:
- David Alan Tennant
University of Tennessee
12 shared publications - Arnab Banerjee
School of Studies in Environmental Science, Pt. Ravishankar Shukla University, Raipur, India
8 shared publications - Matthew B. Stone
Oak Ridge National Laboratory
8 shared publications - Jiaqiang Yan
Oak Ridge National Laboratory
7 shared publications - Garrett E. Granroth
Oak Ridge National Laboratory
5 shared publications Paula Lampen-Kelley
Department of Materials Science and Engineering, University of Tennessee, Knoxville, USA
5 shared publications
Latest Publications
- 25 September 2025
- Published by American Physical Society (APS) in Physical Review B
- Vol. 112 (9)
Magnetic properties of metastable honeycomb- 25 September 2025
- Published by American Physical Society (APS) in Physical Review B
- Vol. 112 (9)
Magnetic properties of metastable honeycomb- 26 March 2024
- Published by American Physical Society (APS) in Physical Review B
- Vol. 109 (10) , 104432
Experimental evidence for nonspherical magnetic form factor inThe Mott insulator 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 , particularly for a true quantitative treatment of inelastic neutron scattering data. Here we present the experimentally derived magnetic form factor of in the low spin state using polarized neutron diffraction within the paramagnetic regime on high-quality single crystals of . We observe strong evidence of an anisotropic form factor, expected of the spin-orbit coupled ground state. We model the static magnetization density in increasing complexity from simple isotropic cases, to a multipolar expansion, and, finally, ab initio calculations of the generalized ground state. Comparison of both single ion models and inclusion of anions support the presence of hybridization of with the surrounding ligands.- 26 March 2024
- Published by American Physical Society (APS) in Physical Review B
- Vol. 109 (10) , 104432
Experimental evidence for nonspherical magnetic form factor inThe Mott insulator 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 , particularly for a true quantitative treatment of inelastic neutron scattering data. Here we present the experimentally derived magnetic form factor of in the low spin state using polarized neutron diffraction within the paramagnetic regime on high-quality single crystals of . We observe strong evidence of an anisotropic form factor, expected of the spin-orbit coupled ground state. We model the static magnetization density in increasing complexity from simple isotropic cases, to a multipolar expansion, and, finally, ab initio calculations of the generalized ground state. Comparison of both single ion models and inclusion of anions support the presence of hybridization of with the surrounding ligands.- 4 January 2024
- Published by American Physical Society (APS) in Physical Review B
- Vol. 109 (2) , L020402
Spinon continuum in the Heisenberg quantum chain compoundMagnetic excitations in the spin chain candidate have been investigated by inelastic neutron scattering on a single crystal sample. A spinon continuum with a bandwidth of meV is observed along the chain formed by alternating magnetic and nonmagnetic ions, which reveals the importance of the orbital degree of freedom in determining the chain axis as identified by prior electronic structure calculations. Incipient magnetic Bragg peaks due to weak ferromagnetic interchain couplings emerge when approaching the magnetic transition at K, while the excitations remain gapless within the instrumental resolution. Comparisons to the Bethe ansatz, density matrix renormalization group calculations, and effective field theories confirm as a host of weakly coupled chains dominated by antiferromagnetic intrachain interactions of (1) meV.- 4 January 2024
- Published by American Physical Society (APS) in Physical Review B
- Vol. 109 (2) , L020402
Spinon continuum in the Heisenberg quantum chain compoundMagnetic excitations in the spin chain candidate have been investigated by inelastic neutron scattering on a single crystal sample. A spinon continuum with a bandwidth of meV is observed along the chain formed by alternating magnetic and nonmagnetic ions, which reveals the importance of the orbital degree of freedom in determining the chain axis as identified by prior electronic structure calculations. Incipient magnetic Bragg peaks due to weak ferromagnetic interchain couplings emerge when approaching the magnetic transition at K, while the excitations remain gapless within the instrumental resolution. Comparisons to the Bethe ansatz, density matrix renormalization group calculations, and effective field theories confirm as a host of weakly coupled chains dominated by antiferromagnetic intrachain interactions of (1) meV.- Open Access
Experimental Evidence for Non-spherical Magnetic Form Factor in Ru$^{3+}$
The Mott insulator $α$-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 $α$-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.Open AccessExperimental Evidence for Non-spherical Magnetic Form Factor in Ru$^{3+}$
The Mott insulator $α$-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 $α$-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. - Top Cited Papers
- 17 November 2022
- Published by Springer Nature in Nature Materials
- Vol. 22 (1) , 36-41
Planar thermal Hall effect of topological bosons in the Kitaev magnet α-RuCl3
The honeycomb magnet α-RuCl3 has attracted considerable interest because it is proximate to the Kitaev Hamiltonian whose excitations are Majoranas and vortices. The thermal Hall conductivity κxy of Majorana fermions is predicted to be half-quantized. Half-quantization of κxy/T (T, temperature) was recently reported, but this observation has proven difficult to reproduce. Here, we report detailed measurements of κxy on α-RuCl3 with the magnetic field B ∥ a (zigzag axis). In our experiment, κxy/T is observed to be strongly temperature dependent between 0.5 and 10 K. We show that its temperature profile matches the distinct form expected for topological bosonic modes in a Chern-insulator-like model. Our analysis yields magnon band energies in agreement with spectroscopic experiments. At high B, the spin excitations evolve into magnon-like modes with a Chern number of ~1. The bosonic character is incompatible with half-quantization of κxy/T.
- 17 November 2022
- Published by Springer Nature in Nature Materials
- Vol. 22 (1) , 36-41
Top Cited PapersPlanar thermal Hall effect of topological bosons in the Kitaev magnet α-RuCl3
The honeycomb magnet α-RuCl3 has attracted considerable interest because it is proximate to the Kitaev Hamiltonian whose excitations are Majoranas and vortices. The thermal Hall conductivity κxy of Majorana fermions is predicted to be half-quantized. Half-quantization of κxy/T (T, temperature) was recently reported, but this observation has proven difficult to reproduce. Here, we report detailed measurements of κxy on α-RuCl3 with the magnetic field B ∥ a (zigzag axis). In our experiment, κxy/T is observed to be strongly temperature dependent between 0.5 and 10 K. We show that its temperature profile matches the distinct form expected for topological bosonic modes in a Chern-insulator-like model. Our analysis yields magnon band energies in agreement with spectroscopic experiments. At high B, the spin excitations evolve into magnon-like modes with a Chern number of ~1. The bosonic character is incompatible with half-quantization of κxy/T.
- Open Access
- 2 October 2022
- Published by Springer Nature in Nature Communications
- Vol. 13 (1) , 1-7
Quantum wake dynamics in Heisenberg antiferromagnetic chains
Traditional spectroscopy, by its very nature, characterizes physical system properties in the momentum and frequency domains. However, the most interesting and potentially practically useful quantum many-body effects emerge from local, short-time correlations. Here, using inelastic neutron scattering and methods of integrability, we experimentally observe and theoretically describe a local, coherent, long-lived, quasiperiodically oscillating magnetic state emerging out of the distillation of propagating excitations following a local quantum quench in a Heisenberg antiferromagnetic chain. This “quantum wake” displays similarities to Floquet states, discrete time crystals and nonlinear Luttinger liquids. We also show how this technique reveals the non-commutativity of spin operators, and is thus a model-agnostic measure of a magnetic system’s “quantumness.”
- 2 October 2022
- Published by Springer Nature in Nature Communications
- Vol. 13 (1) , 1-7
Open AccessQuantum wake dynamics in Heisenberg antiferromagnetic chains
Traditional spectroscopy, by its very nature, characterizes physical system properties in the momentum and frequency domains. However, the most interesting and potentially practically useful quantum many-body effects emerge from local, short-time correlations. Here, using inelastic neutron scattering and methods of integrability, we experimentally observe and theoretically describe a local, coherent, long-lived, quasiperiodically oscillating magnetic state emerging out of the distillation of propagating excitations following a local quantum quench in a Heisenberg antiferromagnetic chain. This “quantum wake” displays similarities to Floquet states, discrete time crystals and nonlinear Luttinger liquids. We also show how this technique reveals the non-commutativity of spin operators, and is thus a model-agnostic measure of a magnetic system’s “quantumness.”
- Open Access
- 21 June 2022
- Published by American Physical Society (APS) in Physical Review Research
- Vol. 4 (2) , L022061
Extraction of interaction parameters for from neutron data using machine learningSingle-crystal inelastic neutron-scattering (INS) 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 (ML)-assisted framework featuring multiple neural network architectures to address this via high-dimensional modeling and numerical methods. A comprehensive data set of diffraction and INS measured on the Kitaev material 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 ML-assisted iterative algorithm was developed to map the uncertainty manifold to match experimental data, a nonlinear autoencoder was used to undertake information compression, and radial basis networks were 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.- 21 June 2022
- Published by American Physical Society (APS) in Physical Review Research
- Vol. 4 (2) , L022061
Open AccessExtraction of interaction parameters for from neutron data using machine learningSingle-crystal inelastic neutron-scattering (INS) 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 (ML)-assisted framework featuring multiple neural network architectures to address this via high-dimensional modeling and numerical methods. A comprehensive data set of diffraction and INS measured on the Kitaev material 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 ML-assisted iterative algorithm was developed to map the uncertainty manifold to match experimental data, a nonlinear autoencoder was used to undertake information compression, and radial basis networks were 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. - Top Cited PapersOpen Access
- 29 April 2022
- Published by American Physical Society (APS) in Physical Review X
- Vol. 12 (2) , 021025
Evidence of a Phonon Hall Effect in the Kitaev Spin Liquid CandidateThe material has been the subject of intense scrutiny as a potential Kitaev quantum spin liquid, predicted to display Majorana fermions as low-energy excitations. In practice, undergoes a transition to a state with antiferromagnetic order below a temperature , but this order can be suppressed by applying an external in-plane magnetic field of . Whether a quantum spin liquid phase exists just above that field is still an open question, but the reported observation of a quantized thermal Hall conductivity at by Kasahara and co-workers [ Nature (London) 559, 227 (2018)] has been interpreted as evidence of itinerant Majorana fermions in the Kitaev quantum spin liquid state. In this study, we reexamine the origin of the thermal Hall conductivity in . Our measurements of on several different crystals yield a temperature dependence very similar to that of the phonon-dominated longitudinal thermal conductivity , for which the natural explanation is that is also mostly carried by phonons. Upon cooling, peaks at , then drops until , whereupon it suddenly increases again. The abrupt increase below is attributed to a sudden reduction in the scattering of phonons by low-energy spin fluctuations as these become partially gapped when the system orders. The fact that also increases suddenly below is strong evidence that the thermal Hall effect in is also carried predominantly by phonons. This implies that any quantized signal from Majorana edge modes would have to come on top of a sizable—and sample-dependent—phonon background.- 29 April 2022
- Published by American Physical Society (APS) in Physical Review X
- Vol. 12 (2) , 021025
Top Cited PapersOpen AccessEvidence of a Phonon Hall Effect in the Kitaev Spin Liquid CandidateThe material has been the subject of intense scrutiny as a potential Kitaev quantum spin liquid, predicted to display Majorana fermions as low-energy excitations. In practice, undergoes a transition to a state with antiferromagnetic order below a temperature , but this order can be suppressed by applying an external in-plane magnetic field of . Whether a quantum spin liquid phase exists just above that field is still an open question, but the reported observation of a quantized thermal Hall conductivity at by Kasahara and co-workers [ Nature (London) 559, 227 (2018)] has been interpreted as evidence of itinerant Majorana fermions in the Kitaev quantum spin liquid state. In this study, we reexamine the origin of the thermal Hall conductivity in . Our measurements of on several different crystals yield a temperature dependence very similar to that of the phonon-dominated longitudinal thermal conductivity , for which the natural explanation is that is also mostly carried by phonons. Upon cooling, peaks at , then drops until , whereupon it suddenly increases again. The abrupt increase below is attributed to a sudden reduction in the scattering of phonons by low-energy spin fluctuations as these become partially gapped when the system orders. The fact that also increases suddenly below is strong evidence that the thermal Hall effect in is also carried predominantly by phonons. This implies that any quantized signal from Majorana edge modes would have to come on top of a sizable—and sample-dependent—phonon background. - Open Access
- 27 April 2022
- Published by Springer Nature in Research Square
Planar thermal Hall effect of topological bosons in the Kitaev magnet α-RuCl3
In the field of quantum spin liquids [1-3], the honeycomb magnet α-RuCl3 has attracted considerable interest because it is proximate to the Kitaev Hamiltonian HK [4-12]. In 2006, Kitaev [13] published the exact solution for the ground state of HK, and found that the excitations are Majoranas and vortices. The thermal Hall conductivity κxy of Majorana fermions is predicted to be half-quantized [13]. This effect has been reported in α-RuCl3 [17,18], but this observation has proven difficult to reproduce [19,20] and remains highly controversial. We report detailed measurements of the Onsager-like planar thermal Hall conductivity κxy in α-RuCl3, a spin-liquid candidate of topical interest. With the thermal current JQ and magnetic field B||a (zigzag axis), the observed κxy/T varies strongly with temperature T (1-10 K). Using a novel fitting procedure, we show that this temperature dependence matches the distinct form expected for topological bosonic modes in a Chern insulator-like model. Our analysis yields band energies that are in agreement with earlier experiments and that the excitations evolve into increasingly magnon-like modes at high B with a Chern number ≈ 1. The bosonic character is incompatible with half-quantization of κxy/T.
- 27 April 2022
- Published by Springer Nature in Research Square
Open AccessPlanar thermal Hall effect of topological bosons in the Kitaev magnet α-RuCl3
In the field of quantum spin liquids [1-3], the honeycomb magnet α-RuCl3 has attracted considerable interest because it is proximate to the Kitaev Hamiltonian HK [4-12]. In 2006, Kitaev [13] published the exact solution for the ground state of HK, and found that the excitations are Majoranas and vortices. The thermal Hall conductivity κxy of Majorana fermions is predicted to be half-quantized [13]. This effect has been reported in α-RuCl3 [17,18], but this observation has proven difficult to reproduce [19,20] and remains highly controversial. We report detailed measurements of the Onsager-like planar thermal Hall conductivity κxy in α-RuCl3, a spin-liquid candidate of topical interest. With the thermal current JQ and magnetic field B||a (zigzag axis), the observed κxy/T varies strongly with temperature T (1-10 K). Using a novel fitting procedure, we show that this temperature dependence matches the distinct form expected for topological bosonic modes in a Chern insulator-like model. Our analysis yields band energies that are in agreement with earlier experiments and that the excitations evolve into increasingly magnon-like modes at high B with a Chern number ≈ 1. The bosonic character is incompatible with half-quantization of κxy/T.
- 2 March 2022
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 128 (9) , 097201
Dirac Magnons, Nodal Lines, and Nodal Plane in Elemental Gadolinium
We investigate the magnetic excitations of elemental gadolinium (Gd) using inelastic neutron scattering, showing that Gd is a Dirac magnon material with nodal lines at and nodal planes at half integer . We find an anisotropic intensity winding around the -point Dirac magnon cone, which is interpreted to indicate Berry phase physics. Using linear spin wave theory calculations, we show the nodal lines have nontrivial Berry phases, and topological surface modes. We also discuss the origin of the nodal plane in terms of a screw-axis symmetry, and introduce a topological invariant characterizing its presence and effect on the scattering intensity. Together, these results indicate a highly nontrivial topology, which is generic to hexagonal close packed ferromagnets. We discuss potential implications for other such systems.- 2 March 2022
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 128 (9) , 097201
Dirac Magnons, Nodal Lines, and Nodal Plane in Elemental Gadolinium
We investigate the magnetic excitations of elemental gadolinium (Gd) using inelastic neutron scattering, showing that Gd is a Dirac magnon material with nodal lines at and nodal planes at half integer . We find an anisotropic intensity winding around the -point Dirac magnon cone, which is interpreted to indicate Berry phase physics. Using linear spin wave theory calculations, we show the nodal lines have nontrivial Berry phases, and topological surface modes. We also discuss the origin of the nodal plane in terms of a screw-axis symmetry, and introduce a topological invariant characterizing its presence and effect on the scattering intensity. Together, these results indicate a highly nontrivial topology, which is generic to hexagonal close packed ferromagnets. We discuss potential implications for other such systems.