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At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Three-state nematicity in the triangular lattice antiferromagnet Fe 1/3 NbS 2

Nematic order is the breaking of rotational symmetry in the presence of translational invariance. While originally defined in the context of liquid crystals, the concept of nematic order has arisen in crystalline matter with discrete rotational symmetry, most prominently in the tetragonal Fe-based superconductors where the parent state is four-fold symmetric. In this case the nematic director takes on only two directions, and the order parameter in such 'Ising-nematic' systems is a simple scalar. In this study, using a spatially resolved optical polarimetry technique, we show that a qualitatively distinct nematic state arises in the triangular lattice antiferromagnet Fe 1/3 NbS 2 . The crucial difference is that the nematic order on the triangular lattice is a Z 3 or three-state Potts-nematic order parameter. As a consequence, the anisotropy axes of response functions such as the resistivity tensor can be continuously reoriented by external perturbations. This discovery lays the groundwork for devices that exploit analogies with nematic liquid crystals.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Spin Dynamics of Triple-𝐐 Magnetic Orderings in a Triangular Lattice: Implications for Multi-𝐐 Orderings in General Two-Dimensional Lattices

Multi-𝐐 magnetic structures on two-dimensional (2D) lattices provide a key route to realizing topological physics in 2D magnetism. A major experimental challenge is to unambiguously confirm their formation by excluding the possibility of topologically trivial multidomain single- or double-𝐐 magnetic orders, which cannot be distinguished using conventional diffraction techniques. Here, we propose that long-wavelength spin dynamics offers a universal diagnostic for triangular lattices: Triple-𝐐 orders that preserve rotational symmetry and single- or double-𝐐 orders that break it exhibit qualitatively distinct anisotropies in their Goldstone-mode velocities, stemming from fundamental differences in their underlying spin configurations. We validate this concept using the metallic triangular-lattice antiferromagnet Co 0.325 ⁢TaS 2 , which hosts both a stripe-type single-𝐐 state and a triple-𝐐 tetrahedral ordering at different temperatures. Using inelastic neutron-scattering and spin dynamics simulations, we first refine the spin Hamiltonian by fitting the paramagnetic excitation spectra, allowing us to develop an unbiased model independent of magnetic ordering. We then show that the observed velocity profiles of the Goldstone modes agree with the high-temperature model’s predictions: markedly anisotropic for the single-𝐐 phase and near isotropic for the triple-𝐐 phase. Importantly, this contrast persists across various exchange parameters, highlighting its model-independent nature and suggesting potential applicability to other 2D lattice systems. Beyond the long-wavelength regime, we present a substantial discrepancy between the measured and simulated magnon spectra exclusively in the triple-𝐐 phase. We attribute this discrepancy to magnon energy renormalization arising from order-of-magnitude-enhanced magnon-magnon interactions in the triple-𝐐 phase, due to its noncollinear configuration. This work provides universal insight into the dynamical properties of topological multi-𝐐 magnetic orderings in 2D lattice structures, offering a broadly applicable diagnostic to distinguishing them from topologically trivial single- or double-𝐐 counterparts. The unequivocal confirmation of the triple-𝐐 structure in Co 0.325 ⁢TaS 2 further establishes it as a prominent material platform for exploring topological spin textures in the genuine 2D limit.

Park, Pyeongjae [Oak Ridge National Laboratory (OR↗
NASA NTRS1989

Novel local symmetries and chiral-symmetry-broken phases in S = 1/2 triangular-lattice Heisenberg model

Using a nonmean-field approach the triangular-lattice S = 1/2 Heisenberg antiferromagnet with nearest- and next-nearest-neighbor couplings is shown undergo an Ising-type phase transition into a chiral-symmetry-broken phase (Kalmeyer-Laughlin-like state) at small T. Removal of next-nearest-neighbor coupling introduces a local Z2 symmetry, thereby suppressing any finite-T chiral order.

Baskaran, G.↗
DOE OSTI2022

Doped Mott insulators in the triangular-lattice Hubbard model

Here we investigate the evolution of the Mott insulators in the triangular lattice Hubbard Model, as a function of hole doping δ in both the strong and intermediate coupling limits. Using the advanced density matrix renormalization group (DMRG) method, at light hole doping δ ≲ 10%, we find a significant difference between strong and intermediate couplings. Notably, at intermediate coupling an unusual metallic state emerges, with short ranged spin correlations but long ranged spin-chirality order. Moreover, no clear Fermi surface or wave vector is observed, this chiral metal also exhibits staggered loop current, which breaks the translational symmetry. These features disappear on increasing interaction strength or on further doping. At strong coupling, the 120 degree magnetic order of the insulating magnet persists for light doping, and produces hole pockets with a well-defined Fermi surface. On further doping, δ ≈ 10%~20% SDW order and coherent hole Fermi pockets are found at both strong and intermediate couplings. At even higher doping δ ≳ 20%, the SDW order is suppressed and the spin-singlet Cooper pair correlations are simultaneously enhanced. We also briefly comment on the strong particle-hole asymmetry of the model.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Transition from an incommensurate spin density wave to a commensurate magnetic order in a triangular lattice compound Ho 2 PdAl 6 Ge 4

Rare-earth (RE) intermetallics on a triangular lattice are promising candidates for generating interesting magnetic phases due to the complex interplay between Ruderman-Kittel-Kasuya-Yoshida (RKKY) interaction and geometrical frustration. Here, in this work, we report the exotic magnetic structure of a layered compound Ho 2 PdAl 6 Ge 4 with triangular lanthanide nets. Magnetization and heat capacity measurements in zero magnetic field reveal two magnetic phase transitions at T N1 = 10.8 K and T N2 = 6.0 K. Neutron powder diffraction demonstrates a commensurate antiferromagnetic phase with k 1 = (0, 0, 1.5) below T N2 . With increasing temperature, another incommensurate vector appears and therefore, the magnetic structure of the intermediate state is identified as an unusual incommensurate spin density wave with two propagation vectors k 1 = (0, 0, 1.5) and k 2 = (0.0492, 0.0492, 1.5). The magnetic moments in the intermediate state rotate continuously and form an unusual S-shaped wave arrangement in the ab plane, sharing similarities with typical cycloid and helix magnetic orders. These results identify Ho 2 PdAl 6 Ge 4 as a candidate for exploring field-induced topological magnetic phases such as skyrmions, opening the way for further investigations on the family of RE 2 PdAl 6 Ge 4 materials.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Field-tunable BKT and quantum phase transitions in spin-$\frac{1}{2}$ triangular lattice antiferromagnet

Quantum magnetism is one of the most active fields for exploring exotic phases and phase transitions. The recently synthesized Na 2 BaCo(PO 4 ) 2 (NBCP) is an ideal material incarnation of the spin-$\frac{1}{2}$ easy-axis triangular lattice antiferromagnet (TLAF). Experimental evidence shows that NBCP hosts the spin supersolid state with a giant magnetocaloric effect. Theory further predicts that magnetic fields can drive NBCP through Berezinskii-Kosterlitz-Thouless (BKT) and other richer quantum phase transitions. However, detecting these transitions is challenging, as they onset at ultralow temperatures near 60 mK and require high magnetization sensitivity. Using a newly developed gradient force magnetometer in a dilution refrigerator, we mapped the magnetic susceptibility phase diagram down to 30 mK. Our results provide a more comprehensive and accurate understanding of BKT melting of spin supersolidity and several field-tunable quantum phase transitions, which establish NBCP as a model platform for frustrated magnetism and highlight potential applications of its giant magnetocaloric effects.

BKT transition↗
DOE OSTI2021

Magnetic properties and signatures of moment ordering in the triangular lattice antiferromagnet KCeO 2

The magnetic ground state and the crystalline electric field level scheme of the triangular lattice antiferromagnet KCeO 2 are investigated here. Below $T_N$ = 300 mK, KCeO 2 develops signatures of magnetic order in specific heat measurements and low energy inelastic neutron scattering data. Trivalent Ce 3+ ions in the $D_{3d}$ local environment of this compound exhibit large splittings among the lowest three 4$f^1$ Kramers doublets defining for the free ion the $\textit{J}$ = 5/2 sextet and a ground state doublet with dipole character, consistent with recent theoretical predictions by Eldeeb et al. [Phys. Rev. Materials 4, 124001 (2020)]. An unexplained, additional local mode appears, and potential origins of this anomalous mode are discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Quantum Phase Diagram and Spontaneously Emergent Topological Chiral Superconductivity in Doped Triangular-Lattice Mott Insulators

The topological superconducting state is a highly sought-after quantum state hosting topological order and Majorana excitations. Here, in this Letter, we explore the mechanism to realize the topological superconductivity (TSC) in the doped Mott insulators with time-reversal symmetry (TRS). Through large-scale density matrix renormalization group study of an extended triangular-lattice t–J model on the six- and eight-leg cylinders, we identify a d + id-wave chiral TSC with spontaneous TRS breaking, which is characterized by a Chern number C=2 and quasi-long-range superconducting order. We map out the quantum phase diagram with by tuning the next-nearest-neighbor (NNN) electron hopping and spin interaction. In the weaker NNN-coupling regime, we identify a pseudogaplike phase with a charge stripe order coexisting with fluctuating superconductivity, which can be tuned into d -wave superconductivity by increasing the doping level and system width. The TSC emerges in the intermediate-coupling regime, which has a transition to a d-wave superconducting phase with larger NNN couplings. The emergence of the TSC is driven by geometrical frustrations and hole dynamics which suppress spin correlation and charge order, leading to a topological quantum phase transition.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Triangular lattice Hubbard model physics at intermediate temperatures

Moiré systems offer an exciting playground to study the many-body effects of strongly correlated electrons in regimes that are not easily accessible in conventional material settings. Motivated by a recent experiment on WSe 2 /WS 2 moiré bilayers [Y. Tang et al., Nature (London) 579, 353 (2020)], which realized a triangular superlattice with a small hopping (of approximately 10 Kelvin), with tunable density of holes, we explore the Hubbard model on the triangular lattice for intermediate temperatures t ≲ T < U. Employing finite-temperature Lanczos calculations and closely following the fitting protocols used in the experiment, we recover the observed trends in the reported Curie-Weiss temperature Θ with filling, using the reported interaction strength U/t=20. Here, we focus on the large increase of |Θ| on decreasing the density below half filling and the sign change of Θ at higher fillings, which signals the onset of ferromagnetism. The increase in |Θ| is also seen in the t–J model (the low-energy limit of the Hubbard model) in the intermediate temperature range, which we clarify is opposite to the trend in its high temperature limit. Differences between the low, intermediate, and high temperature regimes are discussed. Our numerical calculations also capture the crossover between short-range antiferromagnetic to ferromagnetic order in the intermediate temperature regime, a result broadly consistent with the experimental findings. We find that this behavior is a finite-temperature remnant of the underlying zero-temperature phase transition, which we explore with ground-state density matrix renormalization group calculations. We provide evidence of ferromagnetism characterized by weak (but robust) correlations that explain the small Θ seen in the experiment.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Spirals and skyrmions in antiferromagnetic triangular lattices

In this work, we study realizations of spirals and skyrmions in two-dimensional antiferromagnets with a triangular lattice on an inversion-symmetry-breaking substrate. As a possible material realization, we investigate the adsorption of transition-metal atoms (Cr, Mn, Fe, or Co) on a monolayer of MoS 2 , WS 2 , or WSe 2 and obtain the exchange, anisotropy, and Dzyaloshinskii-Moriya interaction parameters using first-principles calculations. Using energy minimization and parallel-tempering Monte Carlo simulations, we determine the magnetic phase diagrams for a wide range of interaction parameters. We find that skyrmion lattices can appear even with weak Dzyaloshinskii-Moriya interactions, but their stability is hindered by magnetic anisotropy. However, a weak easy plane magnetic anisotropy can be beneficial for stabilizing the skyrmion phase. Our results suggest that Cr/MoS 2 , Fe/MoS 2 , and Fe/WSe 2 interfaces can host spin spirals formed from the 120 degrees antiferromagnetic states. Our results further suggest that for interfaces, such as Fe/MoS 2 , the Dzyaloshinskii-Moriya interaction is strong enough to drive the system into a three-sublattice skyrmion lattice in the presence of experimentally feasible external magnetic field.

36 MATERIALS SCIENCE↗
DOE OSTI2023

A j eff = 1/2 Kitaev material on the triangular lattice: the case of NaRuO 2

Motivated by recent reports of a quantum-disordered ground state in the triangular lattice compound NaRuO 2 , we derive a j eff = 1/2 magnetic model for this system by means of first-principles calculations. The pseudospin Hamiltonian is dominated by bond-dependent off-diagonal Γ interactions, complemented by a ferromagnetic Heisenberg exchange and a notably antiferromagnetic Kitaev term. In addition to bilinear interactions, we find a sizable four-spin ring exchange contribution with a strongly anisotropic character, which has been so far overlooked when modeling Kitaev materials. The analysis of the magnetic model, based on the minimization of the classical energy and exact diagonalization of the quantum Hamiltonian, points toward the existence of a rather robust easy-plane ferromagnetic order, which cannot be easily destabilized by physically relevant perturbations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Complete field-induced spectral response of the spin-1/2 triangular-lattice antiferromagnet CsYbSe 2

Fifty years after Anderson’s resonating valence-bond proposal, the spin-1/2 triangular-lattice Heisenberg antiferromagnet (TLHAF) remains the ultimate platform to explore highly entangled quantum spin states in proximity to magnetic order. Yb-based delafossites are ideal candidate TLHAF materials, which allow experimental access to the full range of applied in-plane magnetic fields. We perform a systematic neutron scattering study of CsYbSe 2 , first proving the Heisenberg character of the interactions and quantifying the second-neighbor coupling. We then measure the complex evolution of the excitation spectrum, finding extensive continuum features near the 120°-ordered state, throughout the 1/3-magnetization plateau and beyond this up to saturation. We perform cylinder matrix-product-state (MPS) calculations to obtain an unbiased numerical benchmark for the TLHAF and spectacular agreement with the experimental spectra. The measured and calculated longitudinal spectral functions reflect the role of multi-magnon bound and scattering states. These results provide valuable insight into unconventional field-induced spin excitations in frustrated quantum materials.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Spectral function of the $J_1$ – $J_2$ Heisenberg model on the triangular lattice

Spectral probes, such as neutron scattering, are crucial for characterizing excitations in quantum many-body systems and the properties of quantum materials. Among the most elusive phases of matter are quantum spin liquids, which have no long-range order even at zero temperature and host exotic fractionalized excitations with nontrivial statistics. These phases can occur in frustrated quantum magnets, such as the paradigmatic Heisenberg model with nearest- and next-nearest-neighbor exchange interactions on the triangular lattice, the so-called $J_1$ – $J_2$ model. In this work, we compute the spectral function using large-scale matrix product state simulations across the three different phases of this model's phase diagram, including a quantum spin-liquid phase at intermediate $J_2$/$J_1$. Despite a plethora of theoretical and experimental studies, the exact nature of this phase is still contested, with the dominant candidates being a gapped $\mathbb{Z}_2$, a gapless U(1) Dirac, and a spinon Fermi surface quantum spin-liquid state. We find a V-shaped spectrum near the center of the Brillouin zone ($Γ$ point), a key signature of a spinon Fermi surface, observed in prior neutron scattering experiments. However, we find a small gap near the $Γ$ point, ruling out such a phase. Furthermore, we find localized gapless excitations at the corner of the Brillouin zone boundary (K point) and the middle of the edge of the Brillouin zone boundary (M point), ruling out the gapped $\mathbb{Z}_2$ spin-liquid phase. Here, our results imply that the intermediate spin-liquid phase is a gapless $U(1)$ Dirac spin liquid, and provide clear signatures to detect this phase in future neutron scattering experiments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Magnetic Diffuse Scattering of YBaCo 4 O 7 and LuBaCo 4 O 7 on Kagome and Triangular Lattices

In this work, the magnetic diffuse scattering of YBaCo 4 O 7 and LuBaCo 4 O 7 with alternating kagome and triangular lattices has been studied through neutron scattering measurements on single-crystal samples. In YBaCo 4 O 7 , the line-shape-magnetic-diffuse scattering is observed around the magnetic transition temperature, which is consistent with the Monte Carlo simulation. In LuBaCo 4 O 7 , the line-shape-magnetic-diffuse scattering has not been detected. At low temperature, the propagation vectors of the observed magnetic reflections are different between YBaCo 4 O 7 and LuBaCo 4 O 7 . The structural distortion in RBaCo 4 O 7 is suggested to play a critical role for the magnetic properties.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Chiral spin liquid and quantum phase transition in the triangular-lattice Hofstadter-Hubbard model

Recent advances in moiré engineering motivate the study of lattice models of strongly correlated electrons subjected to substantial orbital magnetic flux. We analyze the triangular-lattice Hofstadter-Hubbard model at one-quarter flux quantum per plaquette and a density of one electron per site, where a chiral spin liquid phase may exist between weak-coupling integer quantum Hall and strong-coupling 120° antiferromagnetic phases. Here, we use matrix product state methods and analytical arguments to investigate this model compactified to cylinders of finite circumference. We uncover a glide particle-hole symmetry operation which, we argue, is spontaneously broken at the quantum Hall to spin liquid transition on odd-circumference cylinders. We numerically verify the spontaneous symmetry breaking and further demonstrate that this transition is associated with algebraic long-range correlations of various spin-singlet, charge-neutral operators. For even-circumference cylinders, the transition becomes a crossover associated with a large correlation length that grows substantially with circumference. Our findings suggest that in the two-dimensional limit, the transition to a chiral spin liquid phase is continuous and features critical fluctuations of the current.

Divic, Stefan [University of Pennsylvania, Philade↗
DOE OSTI2022

Two-dimensional quantum universality in the spin-1/2 triangular-lattice quantum antiferromagnet Na 2 BaCo(PO 4 ) 2

An interplay of geometrical frustration and strong quantum fluctuations in a spin-1/2 triangular-lattice antiferromagnet (TAF) can lead to exotic quantum states. Here, we report the neutron-scattering, magnetization, specific heat, and magnetocaloric studies of the recently discovered spin-1/2 TAF Na 2 BaCo(PO 4 ) 2 , which can be described by a spin-1/2 easy axis XXZ model. The zero-field neutron diffraction experiment reveals an incommensurate antiferromagnetic ground state with a significantly reduced ordered moment of about 0.54(2) μ B /Co. Different magnetic phase diagrams with magnetic fields in the a b plane and along the easy c -axis were extracted based on the magnetic susceptibility, specific heat, and elastic neutron-scattering results. In addition, two-dimensional (2D) spin dispersion in the triangular plane was observed in the high-field polarized state, and microscopic exchange parameters of the spin Hamiltonian have been determined through the linear spin wave theory. Consistently, quantum critical behaviors with the universality class of d = 2 and ν z = 1 were established in the vicinity of the saturation field, where a Bose–Einstein condensation (BEC) of diluted magnons occurs. The newly discovered quantum criticality and fractional magnetization phase in this ideal spin-1/2 TAF present exciting opportunities for exploring exotic quantum phenomena.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Magnetic phase diagram and multiple field-induced states in the intermetallic triangular-lattice antiferromagnet NdAuAl 4 Ge 2 with Ising-like spins

Geometrical frustration and the enhancement of strong quantum fluctuations in two-dimensional triangular antiferromagnets can lead to various intriguing phenomena. Here, in this work, we studied the spin-1/2 triangular lattice antiferromagnet NdAuAl 4 Ge 2 . Thermodynamic and transport properties, such as magnetization and specific heat together with the resistivity measurements were performed. In zero field, two successive phase transitions were observed at T N1 = 1.75 ± 0.02 and T N2 = 0.49 ± 0.02 K, respectively. Under magnetic field, XXZ-type anisotropy was revealed with the moments pointing along the easy c axis. For B∥c, multiple field-induced states were observed, and the magnetic phase diagram was established based on the specific-heat and magnetization data. The temperature-dependent resistivity measurements indicate that NdAuAl 4 Ge 2 is a good metal. It is very likely that both the long-range Ruderman-Kittel-Kasuya-Yosida interactions and the geometrical frustration play important roles in this case.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Quenched disorder in the triangular lattice antiferromagnet YbZn 2⁢ GaO 5

We investigate the crystal electric field (CEF) excitations of Yb 3+ ions in powder samples of the triangular-lattice rare-earth-based antiferromagnet YbZn 2⁢ GaO 5 using inelastic neutron scattering (INS). Three CEF excitations from the ground-state Kramers doublet were observed, each exhibiting significant broadening beyond instrumental resolution. Combining temperature-dependent INS and neutron powder diffraction, we identify a significant static contribution to this broadening and attribute it to heterogeneous coordination of Yb 3+ ions due to Ga 3+ /Zn 2+ site mixing. Rietveld refinement of neutron powder diffraction indicates that 35% of Ga occupies the Zn site and 60% of Zn occupies the Ga site. We show with a point charge model for the CEF Hamiltonian that heterogeneous coordination of Yb3+ ions leads to broadened CEF peaks. First-principles calculations demonstrate that the random Ga 3+ /Zn 2+ distribution can produce the distortions of the YbO 6 octahedra observed from neutron diffraction. Because the documented heterogeneity will extend to exchange interactions, our results suggest that disorder is a significant factor in the unusual magnetism previously reported in YbZn 2 ⁢GaO 5 , including broad low-energy magnetic excitations and the absence of magnetic ordering down to 0.3 K.

Crystal field excitations↗