SEARCH · Search NASA

Results for “spin entropy”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 181 records · Page 10

All sources NASA NTRS DOE OSTI

DOE OSTI2022

Theory of thermal properties of magnetic materials with unknown entropy

Theoretical approaches to study thermal properties of magnetic materials typically require accurate models of magnetic interactions in order to define the entropy. Here we introduce a complementary approach for examining thermal properties in magnetic systems where an accepted model for such interactions does not exist. In place of a specific model for magnetic interactions, the approach integrates measurements of temperature dependent magnetization of the studied material into a first principles computational scheme. The approach calculates system pressure from thermally disordered microstates that properly incorporate vibrational and spin subsystems at each temperature as well as the coupling between these subsystems. We apply the approach to calculate phonon modes and to investigate the anomalously low thermal expansion of the classical Invar alloy, Fe 0.65 Ni 0.35 . Here, the calculated phonon dispersions for Invar are in excellent agreement with measured data. The Invar thermal expansion is shown to remain small between 50 K and room temperature, consistent with the experimentally observed low thermal expansion value in this same temperature range. This anomalously small thermal expansion is directly connected to a small positive contribution from lattice thermal disorder that is nearly canceled by a large negative magnetic disorder contribution. By contrast, calculations for bcc Fe show a much larger thermal expansion, consistent with experiment, which is dominated by a large contribution from lattice thermal disorder that is reduced only slightly by a small negative contribution from that of magnetism. These findings give insights into the unusual nature of magnetism and spin-lattice coupling in Invar and Fe. In addition, they give promising preliminary support to the presented new methodology as a complementary way to investigate thermal properties of magnetic materials. The success achieved on Invar and Fe motivates future testing of the approach on other magnetic materials.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Theory of the phase transition in random unitary circuits with measurements

Here, we present a theory of the entanglement transition tuned by measurement strength in qudit chains evolved by random unitary circuits and subject to either weak or random projective measurements. The transition can be understood as a nonanalytic change in the amount of information extracted by the measurements about the initial state of the system, quantified by the Fisher information. To compute the von Neumann entanglement entropy $\textit{S}$ and the Fisher information $\mathcal{F}$, we apply a replica method based on a sequence of quantities $\tilde{S}^{(n)}$ and $\mathcal{F}^{(n)}$ that depend on the $\textit{n}$th moments of density matrices and reduce to $\textit{S}$ and $\mathcal{F}$ in the limit $\textit{n}$ → 1. These quantities with $\textit{n}$ ≥ 2 are mapped to free energies of a classical spin model with $\textit{n}$! internal states in two dimensions with specific boundary conditions. In particular, $\tilde{S}^{(n)}$ is the excess free energy of a domain wall terminating on the top boundary, and $\mathcal{F}^{(n)}$ is related to the magnetization on the bottom boundary. Phase transitions occur as the spin models undergo ordering transitions in the bulk. Taking the limit of large local Hilbert space dimension $\textit{q}$ followed by the replica limit $\textit{n}$ → 1, we obtain the critical measurement probability $p_c$ = 1/2 and identify the transition as a bond percolation in the 2D square lattice in this limit. Finally, we show there is no phase transition if the measurements are allowed in an arbitrary nonlocal basis, thereby highlighting the relation between the phase transition and information scrambling. We establish an explicit connection between the entanglement phase transition and the purification dynamics of a mixed state evolution and discuss implications of our results to experimental observations of the transition and simulability of quantum dynamics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Theoretical antiferromagnetism of ordered face-centered cubic Cr-Ni alloys

Contrary to prior calculations, the Ni-rich ordered structures of the Cr-Ni alloy system are found to be antiferromagnetic under semilocal density-functional theory. The optimization of local magnetic moments significantly increases the driving force for the formation of CrNi 2 , the only experimentally observed intermetallic phase. This structure's ab initio magnetism appears well described by a Heisenberg Hamiltonian with longitudinal spin fluctuations; itinerant Cr moments are induced only by the strength of exchange interactions. The role of magnetism at temperature is less clear and several scenarios are considered based on a review of experimental literature, specifically a failure of the theory, the existence of an overlooked magnetic phase transition, and the coupling of antiferromagnetism to chemical ordering. In conclusion, implications for related commercial and high-entropy alloys are discussed for each case.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Emergent Dimer-Model Topological Order and Quasiparticle Excitations in Liquid Crystals: Combinatorial Vortex Lattices

Liquid crystals have proven to provide a versatile experimental and theoretical platform for studying topological objects such as vortices, skyrmions, and hopfions. In parallel, in hard condensed matter physics, the concept of topological phases and topological order has been introduced in the context of spin liquids to investigate emergent phenomena like quantum Hall effects and high-temperature superconductivity. Here, we bridge these two seemingly disparate perspectives on topology in physics. Combining experiments and simulations, we show how topological defects in liquid crystals can be used as versatile building blocks to create complex, highly degenerate topological phases, which we refer to as “combinatorial vortex lattices” (CVLs). CVLs exhibit extensive residual entropy and support locally stable quasiparticle excitations in the form of charge-conserving topological monopoles, which can act as mobile information carriers and be linked via Dirac strings. CVLs can be rewritten and reconfigured on demand, endowed with various symmetries, and modified through laser-induced topological surgery—an essential capability for information storage and retrieval. We demonstrate experimentally the realization, stability, and precise optical manipulation of CVLs, thus opening new avenues for understanding and technologically exploiting higher-hierarchy topology in liquid crystals and other ordered media.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Disentangling the physics of the attractive Hubbard model as a fully interacting model of fermions via the accessible and symmetry-resolved entanglement entropies

The complicated ways in which electrons interact in many-body systems such as molecules and materials have long been viewed through the lens of local electron correlation and associated correlation functions. However, quantum information science has demonstrated that more global diagnostics of quantum states like the entanglement entropy can provide a complementary and clarifying lens on electronic behavior. One particularly useful measure that can be used to distinguish between quantum and classical sources of entanglement is the accessible entanglement, the entanglement available as a quantum resource for systems subject to conservation laws, such as fixed particle number, due to superselection rules. In this work, we introduce an algorithm and demonstrate how to compute accessible and symmetry-resolved entanglements for interacting fermion systems. This is accomplished by combining an incremental version of the swap algorithm with a recursive auxiliary field quantum Monte Carlo algorithm recently developed by the authors. We apply these tools to study the pairing and charge density waves exhibited in the paradigmatic attractive Hubbard model via entanglement. We find that the particle and spin symmetry-resolved entanglements and their related full probability distribution functions show very clear—and unique—signatures of the underlying electronic behavior even when those features are less pronounced in conventional correlation functions. Altogether, this work provides a systematic means of characterizing the entanglement within quantum systems that can grant a deeper understanding of the complicated electronic behavior that underlies quantum phase transitions and crossovers in many-body systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Cholesterol modulates membrane elasticity via unified biophysical laws

Cholesterol and lipid unsaturation underlie a balance of opposing forces that features prominently in adaptive cell responses to diet and environmental cues. These competing factors have resulted in contradictory observations of membrane elasticity across different measurement scales, requiring chemical specificity to explain incompatible structural and elastic effects. Here, we demonstrate that – unlike macroscopic observations – lipid membranes exhibit a unified elastic behavior in the mesoscopic regime between molecular and macroscopic dimensions. Using nuclear spin techniques and computational analysis, we find that mesoscopic bending moduli follow a universal dependence on the lipid packing density regardless of cholesterol content, lipid unsaturation, or temperature. Our observations reveal that compositional complexity can be explained by simple biophysical laws that directly map membrane elasticity to molecular packing associated with biological function, curvature transformations, and protein interactions. The obtained scaling laws closely align with theoretical predictions based on conformational chain entropy and elastic stress fields. These findings provide unique insights into the membrane design rules optimized by nature and unlock predictive capabilities for guiding the functional performance of lipid-based materials in synthetic biology and real-world applications.

Kumarage, Teshani [Virginia Polytechnic Inst. and ↗

DOE OSTI2023

Magnetic frustration driven by conduction carrier blocking in Nd 2 Co 0.85 Si 2.88

The intermetallic compound Nd 2 Co 0.85 Si 2.88 having a triangular lattice could be synthesized in single phase only with defect crystal structure. Investigation through different experimental techniques indicate the presence of two magnetic transitions in the system. As verified experimentally and theoretically, the high-temperature transition $T_H$ ~ 140 K is associated with the development of ferromagnetic interaction between itinerant Co moments, whereas the low-temperature transition at $T_L$ ~ 6.5 K is due to the coupling among Nd–4$\textit{f}$ and Co–3$\textit{d}$ moments, which is antiferromagnetic in nature. Detailed studies of temperature-dependent dc magnetic susceptibility, field dependence of isothermal magnetization, nonequilibrium dynamical behavior, viz., magnetic relaxation, aging effect, magnetic-memory effect, and temperature dependence of heat capacity, along with density functional theory (DFT) calculations, suggest that the ground state is magnetically frustrated spin glass in nature, having competing magnetic interactions of equivalent energies. DFT results further reveal that the 3$\textit{d}$/5$\textit{d}$-conduction carriers are blocked in the system and act as a barrier for the 4$\textit{f}$–4$\textit{f}$ RKKY interactions, resulting in spin frustration. Presence of vacancy defects in the crystal are also conducive to the spin frustration. This is an unique mechanism of magnetic frustration, not emphasized so far in any of the ternary $R_2TX_3$ ($\textit{R}$ = rare earth, $\textit{T}$ = transition elements, and $\textit{X}$ = Si, Ge, In) type compounds. Due to the competing character of the itinerant 3$\textit{d}$ and localized 4$\textit{f}$ moments, the compound exhibits anomalous field dependence of magnetic coercivity. Further, the system also exhibits a considerable magnetic entropy change of –Δ$S_M$ ~ 13.3 J/kg K with a relative cooling power (RCP) of 220 J/kg and adiabatic temperature change $ΔT_{\text{ad}}$ of 6 K for magnetic field change of 70 kOe.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Lindblad many-body scars

Quantum many-body scars have received much recent attention for being both intriguing nonergodic states in otherwise quantum chaotic systems and promising candidates to encode quantum information efficiently. So far, these studies have mostly been restricted to Hermitian systems. Here, we study many-body scars in many-body quantum chaotic systems coupled to a Markovian bath, which we term Lindblad many-body scars. They are defined as simultaneous eigenvectors of the Hamiltonian and dissipative parts of the vectorized Liouvillian. Importantly, because their eigenvalues are purely real, they are not related to revivals. The number and nature of the scars depend on both the symmetry of the Hamiltonian and the choice of jump operators. For a dissipative four-body Sachdev-Ye-Kitaev (SYK) model with 𝑁 fermions, either Majorana or complex, we construct analytically some of these Lindblad scars while others could only be obtained numerically. As an example of the former, we identify 𝑁/2+1 scars for complex fermions due to the 𝑈⁡(1) symmetry of the model and two scars for Majorana fermions as a consequence of the parity symmetry. Similar results are obtained for a dissipative XXZ spin chain. We also characterize the physical properties of Lindblad scars. First, the operator size is independent of the disorder realization and has a vanishing variance. By contrast, the operator size for nonscarred states, believed to be quantum chaotic, is well described by a distribution centered around a specific size and a finite variance, which could be relevant for a precise definition of the eigenstate thermalization hypothesis in dissipative quantum chaos. Moreover, the entanglement entropy of these scars has distinct features such as a strong dependence on the partition choice and, in certain cases, a large entanglement.

Eigenstate thermalization↗

DOE OSTI2023

Measures of complexity and entanglement in many-fermion systems

There is no unique and widely accepted definition of the complexity measure (CM) of a many-fermion wave function in the presence of interactions. The simplest many-fermion wave function is a Slater determinant. In shell-model or configuration interaction (CI) and other related methods, the state is represented as a superposition of a large number of Slater determinants, which in the case of CI calculations reaches about 20 billion terms [Johnson, arXiv:1809.07869]. Although in practice this number has been used as a CM for decades, it is ill defined: it is not unique, and it depends on the particular type and the number of single-particle wave functions used to construct the Slater determinants. Further, the canonical wave functions and/or natural orbitals [Löwdin, Adv. Phys. 5, 1 (1956); Löwdin and Shull, Phys. Rev. 101, 1730 (1956); Bardeen et al., Phys. Rev. 108, 1175 (1957); N. N. Bogoljubov, Il Nuovo Cimento 7, 794 (1958); Valatin, Il Nuovo Cimento 7, 843 (1958); de Gennes, Superconductivity of Metals and Alloys (CRC Press, Boca Raton, FL, 1999); Ring and Schuck, The Nuclear Many-Body Problem, 1st ed. (Springer-Verlag, Berlin, 2004)] and their corresponding occupation probabilities are intrinsic properties of any many-body wave function, irrespective of the representation, and they provide a unique solution to characterize the CM. The non-negative orbital entanglement entropy, which vanishes for a Slater determinant, provides the simplest CM, while a more complete measure of complexity is the entanglement spectrum. We illustrate these aspects in the case of a complex nonequilibrium time-dependent process, induced nuclear fission described within a real-time density functional theory framework extended to superfluid systems, which can describe simultaneously the long-range and the short-range correlations between fermions. The orbital entanglement entropy of the fissioning nucleus illustrates the localization mechanism of the many-body wave function in Fock and/or Hilbert space. The (minimal) number of Slater determinants required to represent such a complex many-body wave function with a well-defined number of particles in the case presented here is about 10 500 . The realistic case of the highly nonequilibrium nuclear fission process illustrated here is equivalent to a system of 23.328×10 9 interacting quantum spin-1/2 particles, a very large system for the study of quantum entanglement.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Entanglement features of random neural network quantum states

Restricted Boltzmann machines (RBMs) are a class of neural networks that have been successfully employed as a variational ansatz for quantum many-body wave functions. Here, we develop an analytic method to study quantum many-body spin states encoded by random RBMs with independent and identically distributed complex Gaussian weights. By mapping the computation of ensemble-averaged quantities to statistical mechanics models, we are able to investigate the parameter space of the RBM ensemble in the thermodynamic limit. We discover qualitatively distinct wave functions by varying RBM parameters, which correspond to distinct phases in the equivalent statistical mechanics model. Notably, there is a regime in which the typical RBM states have near-maximal entanglement entropy in the thermodynamic limit, similar to that of Haar-random states. However, these states generically exhibit nonergodic behavior in the Ising basis, and do not form quantum state designs, making them distinguishable from Haar-random states.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Gauge-free duality in pure square spin ice: Topological currents and monopoles

We consider pure square spin ice, that is, square ice, where only nearest neighbors are coupled. The gauge-free duality between the perpendicular and collinear structure leads to a natural description in terms of topological currents and charges as the relevant degrees of freedom. That, in turn, can be expressed via a continuous field theory where the discrete spins are subsumed into entropic interactions among charges and currents. This approach produces structure factors, correlations, and susceptibilities for spins, monopoles, and currents. It also generalizes the height formalism of the disordered ground state to non-zero temperature. The framework can be applied to the zoology of recent experimental results, especially realizations on quantum annealers, and can be expanded to include longer range interactions.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Structural complexity of snapshots of two-dimensional Fermi-Hubbard systems

The development of quantum gas microscopy for two-dimensional optical lattices has provided an unparalleled tool to study the Fermi-Hubbard model (FHM) with ultracold atoms. Spin-resolved projective measurements, or snapshots, have played a significant role in quantifying correlation functions, theory verification, and thus the uncovering of underlying physical phenomena such as antiferromagnetism at commensurate filling on bipartite lattices and other charge and spin correlations, as well as dynamical properties at various densities. Here we employ a recent concept, the multiscale structural complexity, and show that when computed for the snapshots (of single spin species, local moments, or total density) it can provide a theory-free property, immediately accessible to experiments. Specifically, after benchmarking results for Ising and $XY$ models, we study the structural complexity of snapshots of the repulsive FHM in the two-dimensional square lattice as a function of doping and temperature. We generate projective measurements using determinant quantum Monte Carlo and compare their complexities against those from the experiment. We demonstrate that these complexities are linked to relevant physical observables such as the entropy and double occupancy. Their behaviors capture the development of correlations and relevant length scales in the system. Furthermore, we provide an open-source code in python which can be implemented into data analysis routines in experimental settings for the square lattice.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Trajectory Ensemble Methods Provide Single-Molecule Statistics for Quantum Dynamical Systems

The emergence of experiments capable of probing quantum dynamics at the single-molecule level requires the development of new theoretical tools capable of simulating and analyzing these dynamics beyond an ensemble-averaged description. In this article, we present an efficient method for sampling and simulating the dynamics of the individual quantum systems that make up an ensemble and apply it to study the nonequilibrium dynamics of the ubiquitous spin-boson model. We generate an ensemble of single-system trajectories, and we analyze this trajectory ensemble using tools from classical statistical mechanics. Our results demonstrate that the dynamics of quantum coherence is highly heterogeneous at the single-system level due to variations in the initial bath configuration, which significantly affects the transient exchange of coherence between the system and its bath. Here, we observe that single systems tend to retain coherence over time scales longer than that of the ensemble. We also compute a novel thermodynamic entanglement entropy that quantifies a thermodynamic driving force favoring system–bath entanglement.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Symmetry Breaking and Ascending in the Magnetic Kagome Metal FeGe

Spontaneous symmetry breaking—the phenomenon in which an infinitesimal perturbation can cause the system to break the underlying symmetry—is a cornerstone concept in the understanding of interacting solid-state systems. In a typical series of temperature-driven phase transitions, higher-temperature phases are more symmetric due to the stabilizing effect of entropy that becomes dominant as the temperature is increased. However, the opposite is rare but possible when there are multiple degrees of freedom in the system. Here, we present such an example of a symmetry-ascending phenomenon upon cooling in a magnetic kagome metal FeGe by utilizing neutron Larmor diffraction and Raman spectroscopy. FeGe has a kagome lattice structure with simple A-type antiferromagnetic order below Néel temperature T N ≈ 400 K and a charge density wave (CDW) transition at T CDW ≈ 110 K , followed by a spin-canting transition at around 60 K. In the paramagnetic state at 460 K, we confirm that the crystal structure is indeed a hexagonal kagome lattice. On cooling to around T N , the crystal structure changes from hexagonal to monoclinic with in-plane lattice distortions on the order of 10 − 4 and the associated splitting of the double-degenerate phonon mode of the pristine kagome lattice. Upon further cooling to T CDW , the kagome lattice shows a small negative thermal expansion, and the crystal structure gradually becomes more symmetric upon further cooling. A tendency of increasing the crystalline symmetry upon cooling is unusual; it originates from an extremely weak structural instability that coexists and competes with the CDW and magnetic orders. These observations are against the expectations for a simple model with a single order parameter and hence can only be explained by a Landau free energy expansion that takes into account multiple lattice, charge, and spin degrees of freedom. Thus, the determination of the crystalline lattice symmetry as well as the unusual spin-lattice coupling is a first step towards understanding the rich electronic and magnetic properties of the system, and it sheds new light on intertwined orders where the lattice degree of freedom is no longer dominant. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Evolution of noncollinear magnetism in magnetocaloric MnPtGa

MnPtGa crystallizes in the hexagonal Ni 2 In structure type in space group P6 3 /mmc and has been reported to display a ferromagnetic Curie temperature near 220K. Here we find a transition near T c = 236 K to a ferromagnetic state, albeit with a reduced moment from what is expected for collinear ordering. The peak magnetocaloric entropy change was determined to be ΔS M = –1.9 J kg –1 K –1 for an applied magnetic field of H = 5 T at the ferromagnetic ordering temperature. Magnetostructural coupling manifests as a change in the slope of the thermal expansion coefficients of the c lattice parameter near T c , with a negative spontaneous volume magnetostriction; ω = –300 ppm at 190K. In this work, neutron powder diffraction studies of the magnetic ground state reveal an evolution in complexity as temperature decreases: from a ferromagnet, to a canted antiferromagnet, to the eventual formation of a spin-density-wave state at low temperatures.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Comparison of the dielectric and magnetocaloric properties of bulk and film of GdFe 0.5 Cr 0.5 O 3

Here, we report a comparison of the magnetic, magnetocaloric, and dielectric properties of 50% iron substituted GdCrO 3 (GdFe 0.5 Cr 0.5 O 3 ) bulk pellet and 960 nm thick film of GdFe 0.5 Cr 0.5 O 3 (GFCO). The 960 nm film was synthesized on a platinized-silicon substrate by chem. soln. deposition and spin-coating methods. The X-ray diffraction scans of the bulk sample and the film as well as the morphology of the film as examined by the field-emission scanning electron microscope indicate phase-pure and polycrystalline nature of these samples. XPS was used to deermine the valence states of Gd, Fe, and Cr. The temp. dependence of the dielectric const. from 225 to 700 K shows peaks at T C = 525 K for the bulk and ≈450 K for the film due to ferroelectric to paraelectric transitions, since elec. polarization vs elec. field hysteresis loops are observed. at room temp. The dielectric studies in the bulk GFCO for T > T C indicate a relaxor-like behavior. The measurements of the magnetization (M) of the samples as a function of temp. (5-350 K) and magnetic field (H) up to 7 T (=70 kOe) depict hysteresis behavior at low temps. due to the canted antiferromagnetic order of Fe 3+ /Cr 3+ below the Néel temp. of ≈275 K. The M vs H isotherms at various temps. are used to det. and compare the magnetic entropy change (-ΔS) and relative cooling power (RCP) of the two samples, yielding (-ΔS) = 30.7 J/kg K (18.8 J/kg K) and RCP = 566.5 J/kg (375 J/kg) for the bulk (960 nm film) samples of GFCO at 7 K and 7 T, resp. The plot of RCP vs T shows that magnetic cooling for this system is most effective for T < 30 K. Comparatively smaller magnitudes of (-ΔS) and RCP for the film vis-a-vis the bulk sample of GFCO scale with its reduced magnetization. This suggests that further improvements in the quality of the films are needed to improve their magnetization and hence their magnetocaloric properties, possibly making them useful for on-chip cooling in miniaturized devices.

36 MATERIALS SCIENCE↗

DOE OSTI2024

A supersymmetric SYK model with a curious low energy behavior

We consider N = 2,4 supersymmetric SYK models that have a peculiar low energy behavior, with the entropy going like S = S 0 + (constant)T a , where a ≠ 1. The large N equations for these models are a generalization of equations that have been previously studied as an unjustified truncation of the planar diagrams describing the BFSS matrix quantum mechanics or other related matrix models. Here we reanalyze these equations in order to better understand the low energy physics of these models. We find that the scalar fields develop large expectation values which explore the low energy valleys in the potential. The low energy physics is dominated by quadratic fluctuations around these values. These models were previously conjectured to have a spin glass phase. We did not find any evidence for this phase by using the usual diagnostics, such as searching for replica symmetry breaking solutions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

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↗