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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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DOE OSTI2024

Synthesis and characterization of the rare-earth chloride complexes with N,N,N',N' -tetramethylmalonamide

Exploration of the solid-state chemistry of the f-elements and their coordination chemistry can assist in understanding the speciation of these elements in solution, which, in turn, can aid in the interpretation of their chemical behavior in complex liquid-liquid separations. Within these separation processes, malonamides are common organic extractants that are used for complexing both lanthanides and actinides, thus it is relevant to understand the malonamide ligand complexation under various conditions. In this work, we investigate solid-state complexes of the rare-earth chlorides with N,N,N',N' -tetramethylmalonamide (TMMA) across the entire lanthanide series. Here, we isolated two structural families of compounds Ln(TMMA) 2 Cl 3 Ln = La–Dy and [Ln(TMMA) 2 (H 2 O) 4 ]Cl 3 • x H 2 O x = 0,4 Ln = Ho–Lu, showing differences in chloride coordination from the inner-sphere complex for early lanthanides to outer-sphere for the late lanthanides. Both structural series were additionally analyzed by both IR and Raman spectroscopy confirming similarities in malonamide ligand coordination modes, while showing differences in vibrational features associated with chloride and aqua ligand coordination.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Li 3– x Zr x (Ho/Lu) 1– x Cl 6 Solid Electrolytes Enable Ultrahigh-Loading Solid-State Batteries with a Prelithiated Si Anode

We report two new families of lithium metal chloride solid electrolytes Li 3–x Zr x (M) 1–x Cl 6 (0 ≤ x ≤ 0.8; M = Ho or Lu) with ionic conductivities of up to 1.8 mS cm –1 and a low activation energy of 0.34 eV. Structural elucidation via high-resolution neutron diffraction determines the Li ion distribution in trigonal Li 3 HoCl 6 , orthorhombic-I Li 3 LuCl 6 , and orthorhombic-II Li 2.4 Zr 0.6 (Ho/Lu) 0.4 Cl 6 . The last compound exhibits well-connected Li-ion pathways and abundant Li-ion carriers/vacancies to promote diffusion. All-solid-state batteries with Li 2.6 Zr 0.4 (Ho/Lu) 0.6 Cl 6 solid electrolytes and NCM85 cathodes exhibit stable cycling up to 4.6 V vs Li + /Li, which is even preserved up to 4.8 V. Stable cathode interphases are formed for both electrolytes upon cycling to 4.3, 4.6, and 4.8 V cutoff potentials, as identified by a ToF-SIMS analysis. Solid-state cells with a prelithiated Li 0.7 Si anode exhibit a significantly increased initial coulombic efficiency of 94.5% compared to Si and a high areal capacity of up to 16.3 mAh·cm –2 .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Synergic regulation of mechanically interlocked molecules via lanthanide-contraction-based metal modulation and constituent ratios

A set of mechanically interlocked molecules (MIMs) can be synthesized efficiently using a one-pot procedure by selecting different trivalent lanthanide metal cations (M 3+ , M = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, or Lu) and adjusting the proportion of the reaction components. In this system, a flexible tetracationic macrocycle, often referred to as the “Texas-sized molecular box”, interacts with terephthalate dianions and trivalent lanthanide metal cations to form various structures. The transition from metal-organic rotaxane frameworks (MORFs) to metal-containing rotaxane supramolecular organic frameworks (RSOFs) is largely dictated by the lanthanide contraction effect, which leads to a decrease in the coordination number of the lanthanide ions. In addition, the nature of the MIMs within the MORFs can be fine-tuned by varying the ratio of the cation to the other components, allowing for additional control over the interlocked system. Furthermore, these findings demonstrate that the choice of metal cation and adjustments in the building block ratios component represent promising strategies for controlling the structures of MIM-based frameworks.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

A comprehensive approach for elucidating the interplay between 4f n +1 and 4f n 5d 1 configurations in Ln 2+ complexes

Lanthanides (Ln) are typically found in the +3 oxidation state. However, in recent decades, their chemistry has been expanded to include the less stable +2 oxidation state across the entire series except promethium (Pm), facilitated by the coordination of ligands such as trimethylsilylcyclopentadienyl, C 5 H 4 SiMe 3 (Cp'). The [LnCp' 3 ] complexes have been the workhorse for the synthesis and theoretical study of the fundamental aspects of divalent lanthanide chemistry, where experimental and computational evidence have suggested the existence of different ground state (GS) configurations, 4f n+1 or 4f n 5d 1 , depending on the specific metal. Standard reduction potentials and 4f n+1 to 4f n 5d 1 promotion energies have been two factors usually considered to rationalize the occurrence of these variable GS configurations, however the driving force behind this phenomenon is still not clear. In this work we present a comprehensive theoretical approach to shed light on this matter using the [LnCp 3 ] - model systems. We begin by calculating 4f n+1 to 4f n 5d 1 promotion energies and successfully correlate them with existing experimental data. Furthermore, we analyze how changes in the GS charge distribution between the Ln ions, LnCp 3 and the reduced [LnCp 3 ] - complexes (Ln = La, Ce, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb, Lu) correlate with experimental trends in redox potentials and the calculated promotion energies. For this purpose, a comprehensive theoretical work that includes relativistic ligand field density functional theory (LFDFT) and relativistic ab initio wavefunction methods was performed. This study will help the rational design of suitable environments to tune the different GS configurations as well as modulating the spectroscopic properties of new Ln 2+ complexes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Crystal structures and comparisons of potassium rare-earth molybdates KRE(MoO 4 ) 2 (RE = Tb, Dy, Ho, Er, Yb, and Lu)

Six potassium rare-earth molybdates KRE(MoO 4 ) 2 (RE = Tb, Dy, Ho, Er, Yb, and Lu) were synthesized by flux-assisted growth in K 2 Mo 3 O 10 . The crystal structures were determined using single-crystal X-ray diffraction data. The synthesized molybdates crystallize with the orthorhombic Pbcn space group (No. 60). Trendlines for unit-cell parameters were calculated using data from the current study. The unit-cell parameters a and c increase linearly whereas b decreases with larger RE cations, based on crystal radii. The unit-cell volumes increase linearly and the densities decrease linearly with larger RE cations. The average distances between the RE cations and the nearest O atoms increase with larger cations whereas the average distances of Mo—O and K—O do not show specific trends.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Crystal Structures, Optical Behavior, and Magnetic Properties in Hydrated Lanthanide Iron Sulfates

Single crystals of LnFe(SO 4 ) 3 (H 2 O) 2 (Ln = La, Ce, Pr, Nd, Sm, Eu, Gd, Dy, Ho, Er, Tm; compounds 1–11) and LnFe(SO 4 ) 3 (H 2 O) (Ln = Tm, Yb, Lu; compounds 12–14) were synthesized under hydrothermal conditions. Single-crystal X-ray diffraction (SCXRD) analysis revealed that the dihydrated compounds (1–11) crystallize in centrosymmetric (CS) structures, with the lanthanide ions adopting eight-coordinate geometries. In contrast, the monohydrated compounds (12–14) exhibit noncentrosymmetric (NCS) structures, where the lanthanide ions are seven-coordinated. Vibrating sample magnetometry (VSM) confirmed that compounds 2, 4, and 7–11 are paramagnetic below 400 K, with compound 8 displaying the highest magnetic susceptibility. Compounds 1, 5, 6, 13, and 14 show a sharp increase in magnetic susceptibility at Néel temperatures ( T N ) of approximately 72, 76, 70, 58, and 56 K, respectively, indicating antiferromagnetic ordering. High-temperature magnetic susceptibility measurements further support the presence of antiferromagnetic transitions in these compounds. Second harmonic generation (SHG) measurements showed that the noncentrosymmetric Yb (compound 13) and Lu (compound 14) compounds exhibit SHG intensities of 0.3× and 1.6× that of potassium dihydrogen phosphate (KDP), respectively.

anions↗
DOE OSTI2022

Crystal Growth and Phase Formation of High-Entropy Rare-Earth Aluminum Perovskites

In this work, we demonstrate for the first time the crystal growth of high-entropy rare-earth (RE) aluminum perovskites (REAlO 3 ) using the micro-pulling-down method to inform future exploration of functional crystals. To determine how composition affects phase formation, we formulate equiatomic compositions containing five REs from the following list: Lu, Yb, Tm, Er, Y, Ho, Dy, Tb, Gd, Eu, Sm, Nd, Pr, Ce, La. To test whether combinations of REs with similar ionic radii may favor a single phase, compositions containing REs with consecutive or nonconsecutive ionic radius values were formulated. Powder and single-crystal X-ray diffraction indicate that crystals containing only REs with similar ionic radii that form orthorhombic single-RE REAlO 3 are a single phase. Crystals containing REs with dissimilar ionic radii or mixtures of REs that form orthorhombic, rhombohedral, and tetragonal single-RE REAlO 3 are a mixture of phases. The elemental distribution in single-phase crystals analyzed via electron probe microanalysis confirms no evidence of preferential incorporation of any of the constituent REs. The distribution and composition of secondary phases were analyzed via scanning electron microscopy and energy dispersive spectroscopy; secondary phases were seen as a small region in the center of the crystals with branching features closer to the outer surface.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Comprehensive Synthesis and Structural Trends in Tetramethyl Diglycolamide (TMDGA) Nitrate Complexes with Lanthanides and Americium

Complexes of N,N,N',N'-tetramethyl diglycolamide (TMDGA), a hydrophilic diglycolamide (DGA) proposed as an aqueous phase holdback reagent, have been crystallized for the majority of the lanthanide series (excluding promethium), yttrium, and americium to deepen our structural understanding of trivalent metal ion (M 3+ ) DGA coordination compounds in the presence of nitrate counter-anions. The presented collection of 16 complexes with accompanying single-crystal structures, taking formulas [M(TMDGA) 3 ][M(NO 3 ) 6 ] (M = La, Ce, Pr, Nd, Sm, Am), [M(TMDGA) 3 ][M(NO 3 ) 5 (H 2 O)] 1–x [M(NO 3 ) 4 (H 2 O) 2 ] x (NO 3 ) 1+x (M = Eu, Gd, Tb, Dy, Ho, Er, Tm, Yb), [M(TMDGA) 3 ] 2 [M(NO 3 ) 4 (H 2 O) 2 ] 0.75 [M(NO 3 ) 5 (H 2 O)] 1.25 (NO 3 ) 2.75 ·H 2 O (M = Lu), and [M(TMDGA) 3 ][M(NO 3 ) 5 (H 2 O)](NO 3 )·CH 3 OH (M = Y) were all synthesized via solvent diffusion of reaction mixtures containing the metal nitrate M(NO 3 ) 3 ·nH 2 O and TMDGA. Single-crystal X-ray diffraction analyses of these new structures show that each TMDGA complex comprises of three TMDGA ligands coordinating the metal ion via carbonyl and etheric oxygen atoms forming [M(TMDGA) 3 ] 3+ cations. Spectroscopy measurements under high pressure displayed notable differences in the f → f transition shifting between that of Nd(III) and Am(III). Shifting of transitions by 2.0 nm were observed in Nd up to 8.50 ± 0.09 GPa, while Am saw shifting between 11.0 to 13.5 nm at pressures up to 20.06 ± 1.90 GPa. The local geometry in these complexes is a distorted spherical capped square antiprism (CSAPR-9) except for of the yttrium complex, which exhibits a distorted spherical tricapped trigonal prismatic (TCTPR-9) geometry. Further, the anions that form concomitantly with the TMDGA complexes are composed of hexanitrato species for the early lanthanide ions (lanthanum to samarium); whereas the remaining smaller lanthanides did not possess sufficiently large ionic radii to coordinate six bidentate nitrate anions, instead, one or two nitrate anions are situated in the outer sphere. The systematic progression of changes in the anionic environments of these complexes outlines the changing coordination habits afforded by the lanthanide contraction.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Expanding the Transuranic Metal–Organic Framework Portfolio: The Optical Properties of Americium(III) MOF-76

Reported here is the synthesis, crystal structure, and solid-state characterization of a new americium containing metal–organic framework (MOF), [Am(C 9 H 3 O 6 )(H 2 O)], MOF-76(Am). This material is constructed from Am 3+ metal centers and 1,3,5-tricarboxylic acid (BTC) ligands, forming a porous three-dimensional framework that is isostructural with several known trivalent lanthanide (Ln) analogs (e.g., Ce, Nd, and Sm–Lu). The Am 3+ ions have seven coordinates and assume a distorted, capped trigonal prismatic geometry with C1 symmetry. The Am 3+ –O bonds were studied via infrared spectroscopy and compared to several MOF-76(Ln) analogs, where Ln = Nd 3+ , Eu 3+ , Tb 3+ , and Ho 3+ . The results show that the strength of the ligand carboxylate stretching and bending modes increase with Nd 3+ < Eu 3+ < Am 3+ < Tb 3+ < Ho 3+ , suggesting the metal–oxygen bonds are predominantly ionic. Optical absorbance spectroscopy measurements reveal strong f–f transitions; some exhibit pronounced crystal field splitting. The photoluminescence spectrum contains weak Am 3+ -based emission that is achieved through direct and indirect metal center excitation. The weak emissive behavior is somewhat surprising given that ligand-to-metal resonance energy transfer is efficient in the isoelectronic Eu 3+ (4f 6 ) and related Tb 3+ (4f 8 ) analogs. The optical properties were explored further within a series of heterometallic MOF-76(Tb 1–x Am x ) (x = 0.8, 0.2, and 0.1) samples, and the results reveal enhanced Am 3+ photoluminescence.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Effect of f -element complexation on the radiolysis of 2-ethylhexylphosphonic acid mono-2-ethylhexyl ester (HEH[EHP])

A systematic study of the impact on the chemical reactivity of the oxidising n-dodecane radical cation (RH˙ + ) with f-element complexed 2-ethylhexylphosphonic acid mono-2-ethylhexyl ester (HEH[EHP]) has been undertaken utilizing time-resolved electron pulse radiolysis/transient absorption spectroscopy and high-level quantum mechanical calculations. Lanthanide ion complexed species, [Ln((HEH[EHP]) 2 ) 3 ], exhibited vastly increased reactivity (over 10× faster) in comparison to the non-complexed ligand in n-dodecane solvent, whose rate coefficient was k = (4.66 ± 0.22) × 10 9 M -1 s -1 . Similar reactivity enhancement was also observed for the corresponding americium ion complex, k = (5.58 ± 0.30) × 10 10 M -1 s -1 . The vastly increased reactivity of these f-element complexes was not due to simple increased diffusion-control of these reactions; rather, enhanced hole transfer mechanisms for the complexes were calculated to become energetically more favourable. Interestingly, the observed reactivity trend with lanthanide ion size was not linear; instead, the rate coefficients showed an initial increase (Lu to Yb) followed by a decrease (Tm to Ho), followed by another increase (Dy to La). This behaviour was excellently predicted by the calculated reaction volumes of these complexes. In conclusion, complementary cobalt-60 gamma irradiations for select lanthanide complexes demonstrated that the measured kinetic differences translated to increased ligand degradation at steady-state timescales, affording ~38% increase in ligand loss of a 1:1 [La((HEH[EHP]) 2 ) 3 ]: HEH[EHP] ratio system.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Pyridinium Salts of Dehydrated Lanthanide Polychlorides

The reaction of lanthanide (Ln) chloride hydrates ([Ln(H 2 O) n (Cl) 3 ]) with pyridine (py) yielded a set of dehydrated pyridinium (py-H) Ln-polychloride salts. These species were crystallographically characterized as [[py-H-py][py-H] 2 [LnCl 6 ]] (Ln-6; Ln = La, Ce, Pr, Nd, Sm, Eu, Gd) or [[py-H] 2 [LnCl 5 (py)]] ((Ln-5; Ln = Tb, Dy, Ho, Er, Tm, Yb, Lu). The Ln-6 metal centers adopt an octahedral (OC-6) geometry, binding six Cl ligands. The -3 charge is off-set by two py-H moieties and a di-pyridinium (py-H-py) ion. For the Ln-5 species, an OC-6 anion is formed by the Ln cation binding a single py and five Cl ligands. The remaining -2 charge is offset by two py-H + cations that H-bond to the anion. Significant H-bonding occurs between the various cation/anion moieties inducing the molecular stability. The change in structure from the Ln-6 to Ln-5 is believed to be due to the Ln-contraction producing a smaller unit cell, which prevents formation of the py-H-py + cation, leading to the loss of the H-bonding-induced stability. Based on this, it was determined that the Ln-5 structures only exist when the lattice energy is small. While dehydrated polychloride salts can be produced by simply mixing in pyridine, the final structures adopted result from a delicate balance of cation size, Coulombic charge, and stabilizing H-bonding.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Astrometric Microlensing by Primordial Black Holes with the Roman Space Telescope

Abstract Primordial black holes (PBHs) could explain some fraction of dark matter and shed light on many areas of early-Universe physics. Despite over half a century of research interest, a PBH population has so far eluded detection. The most competitive constraints on the fraction of dark matter comprised of PBHs ( f DM ) in the (10 −9 –10) M ⊙ mass ranges come from photometric microlensing and bound f DM ≲ 10 −2 –10 −1 . With the advent of the Roman Space Telescope with its submilliarcsecond astrometric capabilities and its planned Galactic Bulge Time Domain Survey (GBTDS), detecting astrometric microlensing signatures will become routine. Compared with photometric microlensing, astrometric microlensing signals are sensitive to different lens masses–distance configurations and contain different information, making it a complimentary lensing probe. At submilliarcsecond astrometric precision, astrometric microlensing signals are typically detectable at larger lens–source separations than photometric signals, suggesting a microlensing detection channel of pure astrometric events. We use a Galactic simulation to predict the number of detectable microlensing events during the GBTDS via this pure astrometric microlensing channel. Assuming an absolute astrometric precision floor for bright stars of 0.1 mas for the GBTDS, we find that the number of detectable events peaks at ≈10 3 f DM for a population of 1 M ⊙ PBHs and tapers to ≈10 f DM and ≈100 f DM at 10 −4 M ⊙ and 10 3 M ⊙ , respectively. Accounting for the distinguishability of PBHs from stellar lenses, we conclude the GBTDS will be sensitive to a PBH population at f DM down to ≈10 −1 –10 −3 for (10 −1 –10 2 ) M ⊙ likely yielding novel PBH constraints.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Adsorption of Rare Earth Elements onto DNA-Functionalized Mesoporous Carbon

The recovery and separation of rare earth elements (REEs) are of national importance owing to the specific usages, high demand, and low supply of these elements. In this research, we have investigated the adsorption of rare earth elements onto DNA-functionalized mesoporous carbons with a BET surface area of 605 m2/g and a median mesopore width of 48 Å. Additionally, three types of single-stranded DNA, one with 100 base units of thymine, another with 20 units of thymine, and the third, a 2000 unit long DNA from salmon milt were grafted on the carboxylated mesoporous carbon surface. All of the DNA-functionalized mesoporous carbons demonstrated higher adsorption of REEs compared to pristine mesoporous carbon and DNA grafted with 100 units of thymine demonstrated slightly higher adsorbed amounts compared to others. Pure neodymium (Nd(III)) adsorption in the aqueous phase demonstrated an adsorbed amount of 110.4 mg/g with respect to the initial concentration of 500 mg/g. A pH variation study with pure Nd(III) demonstrated that the adsorbed amount is higher at elevated pH compared to that at lower pH, thereby suggesting possible recovery at lower pH. Adsorption of a mixture of 16 REEs, including Sc, Lu, Tm, Yb, Er, Ho, Tb, Dy, Y, Eu, Gd, Sm, Ce, Nd, Pr, and La revealed that the adsorbed amount increased with an increase in the atomic weight and metallic radii of elements within the lanthanides. The calculation of the distribution coefficients for all of the equilibrium adsorption amounts suggested that adsorption is more effective in the lower concentration region. The Nd L3-edge X-ray absorption near edge structure (XANES) confirmed a 3+ oxidation state of Nd in the adsorbed phase. The extended X-ray absorption fine structure (EXAFS) confirmed the local atomic structure relaxation of Nd complexes in the adsorbed phase and shortening of the Nd–O bond distance by about 0.03–0.04 Å, which may be associated with their local complexation at the carbon surface.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Effect of nitrogen doping and pressure on the stability of $\mathrm{LuH_3}$

A report on the near-ambient superconductivity in a nitrogen-doped lutetium hydride has stimulated great interest in this material [Dasenbrock-Gammon et al. , Nature (London) 615, 244 (2023)]. While its superconductivity is still a subject of debate, the structure of the claimed cubic phase remains uncertain. In this work, we study the effect of nitrogen doping and pressure on the energetic and dynamic stability of cubic $\mathrm{LuH_3}$. Our findings indicate that both pressure and nitrogen doping can enhance the stability of the cubic $\mathrm{LuH_3}$ phase. Here, we propose a $\mathrm{Lu_8}$$\mathrm{H_{21}}$$\mathrm{Lu}$ structure that exhibits a stable phonon, reasonable thermodynamic stability at 1 GPa, and an x-ray diffraction pattern similar to the experimental data. However, we do not observe electron-phonon coupling in the zone-center phonon modes of these crystal structures.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Localized electronic and vibrational states in amorphous diamond

Amorphous diamond structures are generated by quenching high-density high-temperature liquid carbon using tight-binding molecular-dynamics simulations. We show that the generated amorphous diamond structures are predominated by strong tetrahedral bonds with the sp 3 bonding fraction as high as 97%, thus exhibit an ultra-high incompressibility and a wide band gap close to those of crystalline diamond. A small amount of sp 2 bonding defects in the amorphous sample contributes to localized electronic states in the band gap while large local strain gives rise to localization of vibrational modes at both high and low frequency regimes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Axion optical induction of antiferromagnetic order

Using circularly polarized light to control quantum matter is a highly intriguing topic in physics, chemistry and biology. Previous studies have demonstrated helicity-dependent optical control of chirality and magnetization, with important implications in asymmetric synthesis in chemistry; homochirality in biomolecules; and ferromagnetic spintronics. We report the surprising observation of helicity-dependent optical control of fully compensated antiferromagnetic order in two-dimensional even-layered MnBi 2 Te 4 , a topological axion insulator with neither chirality nor magnetization. Furthermore, to understand this control, we study an antiferromagnetic circular dichroism, which appears only in reflection but is absent in transmission. We show that the optical control and circular dichroism both arise from the optical axion electrodynamics. Our axion induction provides the possibility to optically control a family of PT-symmetric antiferromagnets (P, inversion; T, time-reversal) such as Cr 2 O 3 , even-layered CrI3 and possibly the pseudo-gap state in cuprates. In MnBi 2 Te 4 , this further opens the door for optical writing of a dissipationless circuit formed by topological edge states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2026

Higher symmetry breaking and nonreciprocity in a driven-dissipative Dicke model

Higher symmetries in interacting many-body systems often give rise to new phases and unexpected dynamical behavior. Here, we theoretically investigate a variant of the Dicke model with higher-order discrete symmetry, resulting from complex-valued coupling coefficients between quantum emitters and a bosonic mode. We propose a driven-dissipative realization of this model focusing on optomechanical response of a driven atom tweezer array comprised of 𝑛 subensembles and placed within an optical cavity, with the phase of the driving field advancing stepwise between subensembles. Examining stationary points and their dynamical stability, we identify a phase diagram for 𝑛≥3 with three distinctive features: a ℤ 𝑛 (ℤ 2⁢𝑛 ) symmetry-breaking superradiant phase for even (odd) 𝑛, a normal unbroken-symmetry phase that is dynamically unstable due to nonreciprocal forces between emitters, and a first-order phase transition separating these phases. This 𝑛-phase Dicke model may be equivalently realized in a variety of optomechanical or optomagnonic settings, where it can serve as a test bed for studying high-order symmetry breaking and nonreciprocal interactions in open systems.

Non-reciprocal propagation↗