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DOE OSTI2024

First access to ELM-free negative triangularity at low aspect ratio

A plasma scenario with negative triangularity (NT) shaping is achieved on MAST-U for the first time. While edge localized modes (ELMs) are eventually suppressed as the triangularity is decreased below δ ≲ –0.06, an extended period of H-mode operation with Type-III ELMs is sustained at less negative δ even through access to the second stability region for ideal ballooning modes is closed. This documents a qualitative difference from the ELM-free access conditions documented in NT scenarios on conventional aspect ratio machines. The electron temperature at the pedestal top drops across the transition to ELM-free operation, but a steady rise in core temperature as δ is decreased allows for similar normalized β in the ELM-free NT and H-mode positive triangularity shapes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Phase Diagram of the Easy-Axis Triangular-Lattice 𝐽 1 −𝐽 2 Model

Our work studies the largely unexplored phase diagram of the S = 1/2 easy-axis triangular-lattice J 1 -J 2 model, motivated by recent interest in rare-earth and transition-metal compounds that exhibit strong quantum fluctuations and broad spin excitation continua—hallmarks of spin-liquid behavior. Combining density-matrix renormalization group simulations with analytical insights, we present a comprehensive study of the model that describes these materials. Our results provide compelling evidence for a robust spin-liquid phase stabilized between the exotic supersolid Y phase and the collinear stripe phase, remarkably persistent even in the presence of symmetry-breaking anisotropy. Additionally, we analyze the supersolid Y phase, offering a quantitative characterization of its order parameters and clarifying the surprising absence of a ferromagnetic moment; both features relevant to recent experiments on Ising-like triangular-lattice magnets. Altogether, our work provides the necessary framework and important theoretical guidance to the ongoing searches of the spin liquid and other exotic states in the rare-earth and transition-metal triangular-lattice compounds, as well as for advancing the understanding of anisotropic-exchange magnets.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Two Distinct Cu(II)-V(IV) Superexchange Interactions with Similar Bond Angles in a Triangular ?CuV2? Fragment

The strength and sign of superexchange interactions are often predicted on the basis of the bond angles between magnetic ions, but complications may arise in situations with a nontrivial arrangement of the magnetic orbitals. We report on a novel molecular tetramer compound [Cu(H2O)dmbpy]2[V2O2F8] (dmbpy = 4,4 '-dimethyl-2,2 ' bipyridyl) that is composed of triangular "CuV2" fragments and displays a spin gap behavior. By combining first-principles calculations and electronic models, we reveal that superexchange Cu-V interactions carry drastically diHerent coupling strengths along two Cu-F-V pathways with comparable bond angles in the triangular "CuV2" fragment. Counterintuitively, their strong disparity is found to originate from the restricted symmetry of the half-filled Cu dx2-y2 orbital stabilized by the crystal field, leading to one dominating antiferromagnetic Cu-V coupling in each fragment. We revisit the magnetic properties of the reported spin-gapped chain compound [enH2]Cu(H2O)2[V2O2F8] (enH2 = ethylene diammonium) containing similar triangular "CuV2" fragments, and the magnetic behavior of the molecular tetramer and the chain compounds is rationalized as that of weakly coupled spin dimers and spin trimers, respectively. This work demonstrates that fundamentally diHerent magnetic couplings can be observed between magnetic ions with similar bond angles in a single spin motif, thus providing a strategy to introduce various exchange interactions combined with low dimensionality in heterometallic Cu(II)-V(IV) compounds.

Complexes↗

DOE OSTI2023

NaRuO2: Kitaev-Heisenberg exchange in triangular-lattice setting

Abstract Kitaev exchange, a new paradigm in quantum magnetism research, occurs for 90° metal-ligand-metal links, $${t}_{2g}^{5}$$ t 2 g 5 transition ions, and sizable spin-orbit coupling. It is being studied in honeycomb compounds but also on triangular lattices. While for the former it is known by now that the Kitaev intersite couplings are ferromagnetic, for the latter the situation is unclear. Here we pin down the exchange mechanisms and determine the effective coupling constants in the $${t}_{2g}^{5}$$ t 2 g 5 triangular-lattice material NaRuO 2 , recently found to host a quantum spin liquid ground state. We show that, compared to honeycomb compounds, the characteristic triangular-lattice cation surroundings dramatically affect exchange paths and effective coupling parameters, changing the Kitaev interactions to antiferromagnetic. Quantum chemical analysis combined with subsequent effective spin model simulations provide perspective onto the nature of the experimentally observed quantum spin liquid—it seemingly implies fairly large antiferromagnetic second-neighbor isotropic exchange, and the atypical proximity to ferromagnetic order is related to ferromagnetic nearest-neighbor Heisenberg coupling.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Quantum disordered ground state in the triangular-lattice magnet NaRuO 2

It has long been hoped that spin liquid states might be observed in materials that realize the triangular lattice Hubbard model. However, weak spin-orbit coupling and other small perturbations often induce conventional spin freezing or magnetic ordering. Sufficiently strong spin-orbit coupling, however, can renormalize the electronic wave function and induce anisotropic exchange interactions that promote magnetic frustration. Here we show that the cooperative interplay of spin-orbit coupling and correlation effects in the triangular lattice magnet NaRuO 2 produces an inherently fluctuating magnetic ground state. Despite the presence of a charge gap, we find that low-temperature spin excitations generate a metal-like term in the specific heat and a continuum of excitations in neutron scattering, reminiscent of spin liquid states previously found in triangular lattice organic magnets. Further cooling produces a crossover into a different, highly disordered, spin state whose dynamic spin autocorrelation function reflects persistent fluctuations. Furthermore, these findings establish NaRuO 2 as a cousin to organic, Heisenberg spin liquid compounds with a low-temperature crossover in quantum disorder.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Effect of triangularity on ion-temperature-gradient-driven turbulence

The linear and nonlinear properties of ion-temperature-gradient-driven turbulence with adiabatic electrons are modeled for axisymmetric configurations for a broad range of triangularities δ, both negative and positive. Peak linear growth rates decrease with negative δ but increase and shift toward a finite radial wavenumber kx with positive δ. The growth-rate spectrum broadens as a function of kx with negative δ and significantly narrows with positive δ. Here, the effect of triangularity on linear instability properties can be explained through its impact on magnetic polarization and curvature. Nonlinear heat flux is weakly dependent on triangularity for |δ|≤0.5, decreasing significantly with extreme δ, regardless of sign. Zonal modes play an important role in nonlinear saturation in the configurations studied, and artificially suppressing zonal modes increased nonlinear heat flux by a factor of about four for negative δ, increasing with positive δ by almost a factor of 20. Proxies for zonal-flow damping and drive suggest that zonal flows are enhanced with increasing positive δ.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Different roles of elongation and triangularity in the H-mode pedestal height enhancement through strong plasma shaping

While the peeling–ballooning mode is known to be stabilized by strong plasma shaping in a high-confinement mode (H-mode), a significant difference is found in the roles of elongation and triangularity. The elongation mainly stabilizes the high-n ballooning branch, while the triangularity of the low-n peeling one with some destabilization of the high-n ballooning one, where n is the toroidal mode number. This difference is conjectured mainly due to the magnetic shear effect which is substantially enhanced in a high triangularity regime, giving a destabilization on the ballooning branch, while a stabilization on the peeling one. As shown here, an important consequence of these different roles of the two shape parameters is that they should work together to stabilize simultaneously both branches of the PBM, implying the necessity of synergy between them for the large pedestal height enhancement.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

A comparative study of internal kink stability in EU DEMO designs with negative and positive triangularity

Abstract Internal kink (IK) instability is investigated for European demonstration fusion reactor (EU DEMO) plasmas in both negative triangularity (NT) and positive triangularity (PT) configurations. For NT plasmas, the IK becomes more unstable as an ideal conformal wall moves away from the plasma boundary, with the mode growth rate saturating at the wall radial location of about b / a = 1.5 , where a is the plasma minor radius and b the wall radial location. The plasma resistivity destabilizes the IK mode. The effect of sub-sonic toroidal plasma flow is sufficiently weak and can thus be ignored for these EU DEMO equilibria. These results are consistent with those for PT plasmas, albeit with larger mode growth rate in the NT configuration. Both perturbative and self-consistent magneto-hydrodynamic (MHD)-kinetic hybrid calculations predict (partial) stabilization of the IK modes in both NT and PT configurations, with inclusion of various kinetic contributions. Precessional drift motion of trapped fusion-born alphas in EU DEMO produces weak stabilization to the IK mode. Stronger stabilization occurs with the toroidal precession of trapped thermal particles (ions and electrons) and the bounce-transit motion of thermal ions. The stabilization is similar between the NT and PT configurations, due to the similarity of the mode eigenfunction (occupying a nearly circular region in the plasma core) despite the sign difference in the triangularity. The non-perturbative MHD-kinetic hybrid model predicts much less stabilization of the mode than the perturbative model, primarily due to the self-consistent determination of the mode eigenvalue in the former. Generally, no significant difference in the IK mode stability is found between the NT and PT plasmas in EU DEMO.

Physics↗

DOE OSTI2021

Influence of elongation and triangularity on plasma response to resonant magnetic perturbations

Abstract Systematic toroidal modeling of the plasma response to the n = 1–4 ( n is the toroidal mode number) resonant magnetic perturbation (RMP) field is carried out in order to understand the plasma-shaping effect on controlling the type-I edge-localized modes (ELMs) in tokamak experiments. Considered are large variations of the plasma elongation and triangularity at a fixed edge safety factor q a , for limiter plasmas with both single-null (SN) and double-null (DN) divertor-like boundary shapes. Numerical results assuming conformal 3D RMP coils show that (i) the optimum coil phasing between the upper and lower rows for ELM control becomes increasingly sensitive to the plasma elongation with higher- n toroidal spectra, (ii) the optimum coil phasing is however essentially independent of the plasma triangularity for all n = 1–4 RMP fields, (iii) with the same coil current and the optimum coil phasing, high elongation generally favors ELM control but it may be more challenging for plasmas with intermediate elongation and with lower- n ( n = 1–2) RMPs, and (iv) higher triangularity is generally always better for ELM control with all n = 1–4 fields for both DN and SN divertor-like plasma boundary shapes.

Physics↗

DOE OSTI2026

Frustration-driven magnetic correlations in the spin-$\frac{5}{2}$ triangular lattice antiferromagnet RbFe⁢(HPO 3 ) 2

Here, a detailed study of the structural and magnetic properties of a spin-5/2 triangular lattice antiferromagnet RbFe⁢(HPO 3 ) 2 is presented using x-ray diffraction, magnetization, heat capacity, and 31 P nuclear magnetic resonance (NMR) experiments on a polycrystalline sample. The crystal structure features an equilateral triangular lattice of Fe 3+ ions. The thermodynamic measurements reveal the onset of a magnetic long-range order at 𝑇 N⁢1 ≃7.8K in zero field, followed by another low-temperature field-induced ordering at 𝑇 N⁢2 in higher fields. The transition at 𝑇 N⁢1 is further confirmed from the NMR spin lattice relaxation measurements. The value of the frustration ratio (𝑓≃7) implies moderate spin frustration in the compound. The 31 P NMR spectra exhibit two distinct spectral lines corresponding to two inequivalent phosphorus sites (P1 and P2), consistent with the crystal structure. The P1 site is strongly coupled with an isotropic hyperfine coupling of 𝐴$^{iso}_{hf}$ = 0.55⁢(2)⁢ T/𝜇 B while the P2 site is weakly coupled with 𝐴$^{iso}_{hf}$ = 0.25⁢(3)⁢ T/𝜇 B with the Fe 3+ ions. The magnetic susceptibility and NMR shift data are described well assuming a spin-5/2 isotropic triangular lattice antiferromagnetic model with an average exchange coupling of 𝐽/𝑘 B = 2.8⁢(2)⁢K. Below 𝑇 N⁢1 , the spectra evolve into a nearly rectangular powder pattern, indicating a commensurate antiferromagnetic type order. The 31 P spin-lattice relaxation rate well below 𝑇N⁢1 follows a 𝑇 3 temperature dependence, implying a two-magnon Raman scattering mechanism in the ordered state. Three well-defined phase regimes are clearly ascertained in the 𝐻−𝑇 phase diagram, reflecting a weak magnetic anisotropy in the compound.

Nagpal, V. [Indian Institute of Science Education ↗

DOE OSTI2025

Collinear antiferromagnetic order in a quasi-two-dimensional triangular lattice compound DyNiAl 4 Ge 2

The two-dimensional magnetic triangular lattice, with rare-earth local moments coupled through long-range interactions and hosting strong spin-orbit coupling, serves as an ideal platform for exploring novel quantum phenomena. Here, we report the physical properties of DyNiAl 4 Ge 2 single crystals through comprehensive structural, magnetic, heat capacity, electrical transport, and neutron powder diffraction measurements. DyNiAl 4 Ge 2 crystallizes in a trigonal lattice with the space group $R\bar{3}m$, where Dy atoms form two-dimensional triangular lattice layers within the 𝑎𝑏 plane and stack along the 𝑐 axis. Magnetic susceptibility measurement reveals a magnetic phase transition at 𝑇 𝑁 = 9.0 K, further confirmed by the 𝜆-shaped peak in the heat capacity curve. The obtained temperature-magnetic field phase diagram is relatively simple compared to other isostructural compounds, suggesting the absence of magnetic frustration. This is further evidenced by neutron powder diffraction, which shows a collinear antiferromagnetic ground state with a propagation vector 𝒌 = (0, 0, 1.5), implying the absence of magnetic frustration in DyNiAl 4 Ge 2 . In this magnetic structure, Dy moments are aligned ferromagnetically within each triangular layer and arranged antiferromagnetically between adjacent layers along the 𝑐 axis. In conclusion, our results establish DyNiAl 4 Ge 2 as a model system for understanding the interplay between RKKY interaction and geometrical frustration in this family of compounds.

Wu, HengHeng [Chinese Academy of Sciences (CAS), S↗

DOE OSTI2020

Static and dynamic spin properties in the quantum triangular lattice antiferromagnet Ag 2 CoO 2

In Ag 2 CoO 2 , Co forms triangular lattice layers, which are separated by the metallic (Ag 2 ) block. The magnetic susceptibility and heat capacity measurements show that this material exhibits an antiferromagnetic transition at T N =17.5 K and the Weiss temperature (T Θ ) and the effective moment are -274 K and 1.62μ B , respectively, indicating that the Co ion carries spin (S) 1/2 and has a strongly frustrated state with T Θ /T N =15.7. A density functional theory calculation confirmed that the valence state of the Co ions is 2+ and the low-spin state with S=1/2 is realized at reduced on-site Coulomb interaction on Co. We performed elastic and inelastic neutron scattering experiments in a powder sample of Ag 2 CoO 2 . Although no noticeable magnetic Bragg peaks were observed below T N , distinct magnetic excitations were observed in the inelastic neutron scattering experiments. The excitations are consistent with those expected for the S=1/2 Heisenberg triangular lattice antiferromagnet. These results suggest that the ordered moment is reduced due to the quantum effect, which explains the absence of the magnetic Bragg peaks. Our results thus suggest that Ag 2 CoO 2 is a good candidate to realize a quantum Heisenberg triangular lattice antiferromagnet.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Pseudospin versus magnetic dipole moment ordering in the isosceles triangular lattice material K 3 Er(VO 4 ) 2

Spin- 1 / 2 antiferromagnetic triangular lattice models are paradigms of geometrical frustration, revealing very different ground states and quantum effects depending on the nature of anisotropies in the model. Due to strong spin orbit coupling and crystal field effects, rare-earth ions can form pseudospin- 1 / 2 magnetic moments with anisotropic single-ion and exchange properties. Thus, rare-earth-based triangular lattices enable the exploration of this interplay between frustration and anisotropy. Here we study one such case, the rare-earth double vanadate glaserite material K 3 Er ( VO 4 ) 2 , which is a quasi-two-dimensional (2D) isosceles triangular antiferromagnet. Our specific heat and neutron powder diffraction data from K 3 Er ( VO 4 ) 2 reveal a transition to long range magnetic order at T N = 155 ± 5 mK which accounts for all R ln 2 entropy. Furthermore, we observe what appears to be a coexistence of three-dimensional (3D) and quasi-2D order below T N . The quasi-2D order leads to an anisotropic Warren-like peak profile for ( h k 0 ) reflections, while the 3D order is best-described by layers of antiferromagnetic b -aligned moments alternating with layers of zero moment. Our magnetic susceptibility data reveal that Er 3 + takes on a strong X Y single-ion anisotropy in K 3 Er ( VO 4 ) 2 , leading to vanishing moments when pseudospins are oriented along c . Thus, the magnetic structure, when considered from the pseudospin point of view could comprise of alternating layers of b -axis and c -axis aligned antiferromagnetism.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Stripe antiferromagnetic ground state of the ideal triangular lattice compound KErSe 2

Rare-earth triangular lattice materials have been proposed as a good platform for the investigation of frustrated magnetic ground states. KErSe 2 , with the delafossite structure, contains perfect two-dimensional Er 3 + triangular layers separated by potassium ions, realizing this ideal configuration and inviting study. In this study, we investigate the magnetism of KErSe 2 at millikelvin temperatures by heat capacity and neutron powder diffraction. Heat capacity results reveal a magnetic transition at 0.2 K in zero applied field. This long-range order is suppressed by an applied magnetic field of 0.5 T below 0.08 K. Neutron powder diffraction suggests that the zero-field magnetic structure orders with k = ( 1 2 , 0 , 1 2 ) in a stripe spin structure. Unexpectedly, Er is found to have a reduced moment of 3.06(1) μ B /Er in the ordered state, and diffuse magnetic scattering, which originates at higher temperatures, is found to persist in the ordered state, potentially indicating magnetic fluctuations. Neutron diffraction collected under an applied field shows a metamagnetic transition at ~ 0.5 T to ferromagnetic order with k = ( 0 , 0 , 0 ) and two possible structures, which are likely dependent on the applied field direction. The zero-field stripe spin structure can be explained by the anisotropic interactions or the first-, second-, and third-neighbor couplings in the antiferromagnetic triangular lattice.

2-dimensional systems↗

DOE OSTI2023

Weak trimerization in the frustrated two-dimensional triangular Heisenberg antiferromagnet Lu y Y 1-y MnO 3

To understand the 2D triangular Heisenberg antiferromagnetic system, we investigated the magnetic structures and the dynamics of Lu y Y 1-y MnO 3 in detail. The substitutions are adjusted to the Mn atomic position close to x Mn =$\frac{1}{3}$. The neutron powder diffraction data claims that the magnetic structure of Lu y Y 1-y MnO 3 is described as a mixture of Γ 3 (P6' 3 cm') and Γ 4 (P6' 3 c'm) at the x Mn position for y=0.15, 0.30, and 0.45. The ratio of Γ 3 and Γ 4 depends on temperature and composition and the fraction of Γ 3 increases upon cooling, while no clear trimerization was observed at the xMn position. We estimated exchange parameters from the analysis of the low-energy part of the spin waves. The results showed a weak trimerization effect on cooling because the nearest-neighbor exchange interaction is slightly enhanced. The temperature dependence of the spin-wave dispersion around the Γ point shows that the spin gap closes with increasing temperature because the exchange interactions in the nearest Mn-Mn neighbor become smaller. Gapless diffusive magnetic excitation from a Mn triangular lattice has been observed in a wide range in Q and E space of Lu y Y 1-y MnO 3 . We found that Lu 0.3 Y 0.7 MnO 3 could be an ideal case to investigate the trimerization, frustrated magnetism, and magnetoelastic coupling often observed in two-dimensional triangular lattice Heisenberg antiferromagnet systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2023

Static and dynamical properties of the spin-$\frac{5}{2}$ nearly ideal triangular lattice antiferromagnet $\mathrm{Ba_3}$ $\mathrm{MnSb_2}$ $\mathrm{O_9}$

Here, we study the ground state and spin excitations in Ba 3 MnSb 2 O 9 , an easy-plane S = 5/2 triangular lattice antiferromagnet. By combining single-crystal neutron scattering, electric spin resonance (ESR), and spin wave calculations, we determine the frustrated quasi-two-dimensional spin Hamiltonian parameters describing the material. While the material has a slight monoclinic structural distortion, which could allow for isosceles-triangular exchanges and biaxial anisotropy by symmetry, we observe no deviation from the behavior expected for spin waves in the in-plane $120$° state. Even the easy-plane anisotropy is so small that it can only be detected by ESR in our study. In conjunction with the quasi-two-dimensionality, our study establishes that Ba 3 MnSb 2 O 9 is a nearly ideal triangular lattice antiferromagnet with the quasiclassical spin S = 5/2, which suggests that it has the potential for an experimental study of Z- or Z 2 -vortex excitations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Structural and magnetic characterization of CeTa 7 ⁢O 19 and YbTa 7 ⁢ O 19 with a two-dimensional pseudospin-$\frac{1}{2}$ triangular lattice

Triangular lattice antiferromagnets are prototypes for frustrated magnetism and may potentially realize novel quantum magnetic states such as a quantum spin-liquid ground state. A recent work suggests NdTa 7 ⁢O 19 with rare-earth triangular lattice is a quantum spin-liquid candidate and highlights the large family of rare-earth heptatantalates as a framework for quantum magnetism investigation. Here, in this paper, we report the structural and magnetic characterization of CeTa 7 ⁢ O 19 and YbTa 7 ⁢ O 19 . Both compounds are isostructural to NdTa 7 ⁢O 19 with no detectable structural disorder. For CeTa 7 ⁢O 19 , the crystal field energy levels and parameters are determined by inelastic neutron scattering measurements. Based on the crystal field result, the magnetic susceptibility data could be well fitted and explained, which reveals that CeTa 7 ⁢O 19 is a highly anisotropic Ising triangular-lattice antiferromagnet (𝑔 𝑧 ⁡/𝑔 𝑥⁢𝑦 ∼ 3) with very weak exchange interaction (J ∼ 0.22 K). For YbTa 7⁢ O 19 , millimeter-sized single crystals could be grown. The anisotropic magnetization and electron spin resonance data show that YbTa 7⁢ O 19 has a contrasting in-plane magnetic anisotropy with 𝑔 𝑧 ⁡/𝑔 𝑥⁢𝑦 ∼ 0.67 similar as that of YbMgGaO 4 . The above results indicate that CeTa7⁢ O 19 and YbTa 7 ⁢O 19 with pseudospin-1/2 ground states might either be quantum spin-liquid candidate materials or find applications in adiabatic demagnetization refrigeration due to the weak exchange interaction.

Pan, Feihao↗

DOE OSTI2024

Reaction plane correlated triangular flow in Au + Au collisions at $\sqrt{s_{NN}}$ = 3 GeV

Here, we measure triangular flow relative to the reaction plane at 3 GeV center-of-mass energy in Au + Au collisions at the BNL Relativistic Heavy Ion Collider. A significant v 3 signal for protons is observed, which increases for higher rapidity, higher transverse momentum, and more peripheral collisions. The triangular flow is essentially rapidity-odd with a slope at midrapidity, dv 3 /dy| (y=0) , opposite in sign compared to the slope for directed flow. No significant v 3 signal is observed for charged pions and kaons. Comparisons with models suggest that a mean field potential is required to describe these results, and that the triangular shape of the participant nucleons is the result of stopping and nuclear geometry.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗