Frustrated Antiferromagnets Research Articles

Antiferromagnetic Frustration Behavior with Face-Sharing CuAs4 Tetrahedrons in Conducting ACu6As3 (A = Li and Na).

New mixed-valence copper pnictides ACu6As3 (A = Li and Na) adopt a quasi-2D structure type, featuring alkalis and [Cu6As3]- slabs along the c-axis alternatively. The face-sharing connection between CuAs4 polyhedra leads to a higher valence state for the inside Cu ions than that of Cu ions with the other connectivity way. This is confirmed by X-ray photoemission spectroscopy results. The Cu2+ with near spin 1/2 located on bilayer triangular lattice is found to exhibit a peculiar hump in magnetic susceptibility along the c-axis and, most strikingly, nearly a constant at low temperatures from 1.8 K down to 0.4 K. Besides, high hole mobilities, 68.58 and 645.16 cm2 V-1 S-1, are observed in LiCu6As3 and NaCu6As3, respectively. These compounds provide a novel material system for researching the relationship among structure, valence state, and spin correlation in frustrated lattice.

Strain‐driven Switching Between Antiferromagnetic States in Frustrated Antiferromagnet UO2 Probed by Exchange Bias Effect

AbstractFrustrated antiferromagnets offer a captivating platform to study the intricate relationship of magnetic interactions, geometric constraints, and emergent phenomena. By controlling spin orientations, these materials can be tailored for applications in spintronics and quantum information processing. The research focuses on the interplay of magnetic and exchange anisotropy effects in artificial heterostructures based on a canonical frustrated antiferromagnet, UO2. The potential to manipulate the spin directions in this material and switch between distinct antiferromagnetic (AFM) states is investigated using substrate‐induced strain. The phenomenon is probed using exchange bias effects in stoichiometric UO2/Fe3O4 bilayers. By employing many‐body first‐principles calculations magnetic configurations in the UO2 layers are identified. Even a minor tetragonal distortion triggers a transition between AFM states of different symmetries, driven by a robust alteration of single‐ion anisotropy due to the distortion. Consequently, this change influences the arrangement of magnetic moments at the UO2/Fe3O4 interface, affecting the magnitude of exchange bias. The findings showcase how epitaxial strain can effectively manipulate the AFM states in frustrated antiferromagnets by controlling single‐site anisotropy.

Magnons in the fan phase of anisotropic frustrated antiferromagnets

Elementary excitations spectrum of the fan phase of anisotropic frustrated antiferromagnets is discussed analytically. In the linear spin-wave approximation, the spectrum is determined by the Hamiltonian, including normal, anomalous, and umklapp terms. The latter mix states with momenta which differ by two modulation vectors of the fan structure. This mixing leads to essential rearrangement of the low-energy part of the spectrum, which is shown to consist of a gapless phason branch with linear dispersion and a gapped “optical” branch, which corresponds to the fan structure amplitude oscillations. In the high-energy part of the spectrum, the effect of the umklapps is negligible, and the excitations are similar to the magnons of the fully polarized phase.

Thermal features of Heisenberg antiferromagnets on edge- versus corner-sharing triangular-based lattices: a message from spin waves

We propose a new scheme of modifying spin waves so as to describe the thermodynamic properties of various noncollinear antiferromagnets with particular interest in a comparison between edge- versus corner-sharing triangular-based lattices. The well-known modified spin-wave theory for collinear antiferromagnets diagonalizes a bosonic Hamiltonian subject to the constraint that the total staggered magnetization be zero. Applying this scheme to frustrated noncollinear antiferromagnets ends in a poor thermodynamics, missing the optimal ground state and breaking the local U(1) rotational symmetry. We find such a plausible double-constraint condition for spin spirals as to spontaneously go back to the traditional single-constraint condition at the onset of a collinear Néel-ordered classical ground state. We first diagonalize only the bilinear terms in Holstein-Primakoff boson operators on the order of spin magnitude S and then bring these linear spin waves into interaction in a perturbative rather than variational manner. We demonstrate specific-heat calculations in terms of thus-modified interacting spin waves on various triangular-based lattices. In zero dimension, modified-spin-wave findings in comparison with finite-temperature Lanczos calculations turn out so successful as to reproduce the monomodal and bimodal specific-heat temperature profiles of the triangular-based edge-sharing Platonic and corner-sharing Archimedean polyhedral-lattice antiferromagnets, respectively. In two dimensions, high-temperature series expansions and tensor-network-based renormalization-group calculations are still controversial especially at low temperatures, and under such circumstances, modified spin waves interestingly predict that the specific heat of the kagome-lattice antiferromagnet in the corner-sharing geometry remains having both mid-temperature broad maximum and low-temperature narrow peak in the thermodynamic limit, while the specific heat of the triangular-lattice antiferromagnet in the edge-sharing geometry retains a low-temperature sharp peak followed by a mid-temperature weak anormaly in the thermodynamic limit. By further calculating one-magnon spectral functions in terms of our newly developed double-constraint modified spin-wave theory, we reveal that not only the elaborate modification scheme but also quantum corrections, especially those caused by the O(S 0) primary self-energies, are key ingredients in the successful description of triangular-based-lattice noncollinear antiferromagnets over the whole temperature range of absolute zero to infinity.

Impact of Erbium Doping in the Structural and Magnetic Properties of the Anisotropic and Frustrated SrYb2O4 Antiferromagnet

We present a systematic study of the structural and magnetic properties of a series of powder samples of SrYb2−xErxO4 with different Yb/Er concentrations. Magnetometry and neutron diffraction have been used to study the magnetic ground states of the compound series, while inelastic neutron scattering was used to investigate the crystal field excitations for a chosen concentration. These results show that the crystal structure remains the same for all compositions, while the lattice parameters increase linearly with the Er content. All compounds showed some type of magnetic transition below 1 K, however, both the magnetic structure and nature of the phase transition vary throughout the series. The samples present a non-collinear magnetic structure with the moments lying on the ab plane for low Er content. For high Er content, the magnetic structure is collinear with the moments aligned along the c-axis. A critical concentration is found where there is a bifurcation between zero-field and field-cooled magnetic susceptibility. This irreversible process could be due to the random mixture of single-ion magnetic anisotropies.

Absence of magnetic order and emergence of unconventional fluctuations in the Jeff=12 triangular-lattice antiferromagnet YbBO3

We present the ground state properties of a new quantum antiferromagnet, ${\mathrm{YbBO}}_{3}$, in which the isotropic ${\mathrm{Yb}}^{3+}$ triangular layers are separated by a nonmagnetic layer of partially occupied B and O(2) sites. The magnetization and heat capacity data establish a spin-orbit entangled effective spin ${J}_{\mathrm{eff}}=\frac{1}{2}$ state of ${\mathrm{Yb}}^{3+}$ ions at low temperatures, interacting antiferromagnetically with an intralayer coupling $J/{k}_{\mathrm{B}}\ensuremath{\simeq}0.53$ K. The absence of oscillations and a $1/3$ tail in the zero-field muon asymmetries rules out the onset of magnetic long-range order as well as spin freezing down to 20 mK. An anomalous broad maximum in the temperature-dependent heat capacity with an unusually reduced value and a broad anomaly in the zero-field muon depolarization rate centered at ${T}^{*}\ensuremath{\simeq}0.7J/{k}_{\mathrm{B}}$ provide compelling evidence for a wide fluctuating regime $(0.2\ensuremath{\lesssim}T/J\ensuremath{\le}1.5)$ with slow relaxation. We infer that the fluctuating regime is a universal feature of highly frustrated triangular-lattice antiferromagnets while the absence of magnetic long-range order is due to perfect two-dimensionality of the spin lattice protected by nonmagnetic site disorder.

Local spin dynamics in the geometrically frustrated Mo pyrochlore antiferromagnet Lu2Mo2O5−yN2

The magnetic ground state of oxynitride pyrochlore ${\mathrm{Lu}}_{2}{\mathrm{Mo}}_{2}{\mathrm{O}}_{5\ensuremath{-}y}{\mathrm{N}}_{2}$, a candidate compound for the quantum spin liquid ($S=1/2$, ${\mathrm{Mo}}^{5+}$), was studied by muon spin rotation/relaxation experiment. In contrast to ${\mathrm{Lu}}_{2}{\mathrm{Mo}}_{2}{\mathrm{O}}_{7}$ ($S=1$, ${\mathrm{Mo}}^{4+}$) which exhibits the spin-glass behavior with a freezing temperature ${T}_{g}\ensuremath{\simeq}16\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, no such spin freezing or long-range magnetic order was observed down to 0.3 K. Moreover, two separate magnetic domains were detected below $\ensuremath{\sim}13\phantom{\rule{4pt}{0ex}}\mathrm{K}$, which were characterized by differences in spin dynamics. The first is the ``sporadic'' spin fluctuation seen in frustrated antiferromagnets, where the amplitude of the hyperfine fields suggests that the excitation comprises a local cluster of unpaired spins. The other is rapid paramagnetic fluctuation, which is only weakly suppressed at low temperatures. In place of the paramagnetic fluctuation, the volume fraction for the sporadic fluctuation steadily increases with decreasing temperature, indicating the formation of an excitation gap with a broad distribution of the gap energy involving a null gap.

Spin Excitation Spectra of Anisotropic Spin-1/2 Triangular Lattice Heisenberg Antiferromagnets.

Investigation of dynamical excitations is difficult but crucial to the understanding of many exotic quantum phenomena discovered in quantum materials. This is particularly true for highly frustrated quantum antiferromagnets whose dynamical properties deviate strongly from theoretical predictions made based on the spin-wave or other approximations. Here, we present a large-scale numerical calculation on the dynamical correlation functions of spin-1/2 triangular Heisenberg model using a state-of-the-art tensor network renormalization group method. The calculated results allow us to gain for the first time a comprehensive picture on the nature of spin excitation spectra in this highly frustrated quantum system. It provides a quantitative account for all the key features of the dynamical spectra disclosed by inelastic neutron scattering measurements for Ba_{3}CoSb_{2}O_{9}, revealing the importance of the interplay between low- and high-energy excitations and its renormalization effect to the low-energy magnon bands and high-energy continuums. We identify the longitudinal Higgs modes in the intermediate-energy scale and predict the energy and momentum dependence of spectral functions along the three principal axes that can be verified by polarized neutron scattering experiments. Furthermore, we find that the spin excitation spectra weakly depend on the anisotropic ratio of the antiferromagnetic interaction.

Classical vertex model dualities in a family of two-dimensional frustrated quantum antiferromagnets

We study a general class of easy-axis spin models on a lattice of corner sharing even-sided polygons with all-to-all interactions within a plaquette. The low energy description corresponds to a quantum dimer model on a dual lattice of even coordination number with a multi dimer constraint. At an appropriately constructed frustration-free Rokhsar-Kivelson (RK) point, the ground state wavefunction can be exactly mapped onto a classical vertex model on the dual lattice. When the dual lattice is bipartite, the vertex models are bonded and are self dual under Wegner's duality, with the self dual point corresponding to the RK point of the original multi-dimer model. We argue that the self dual point is a critical point based on known exact solutions to some of the vertex models. When the dual lattice is non-bipartite, the vertex model is arrowed, and we use numerical methods to argue that there is no phase transition as a function of the vertex weights. Motivated by these wavefunction dualities, we construct two other distinct families of frustration-free Hamiltonians whose ground states can be mapped onto these vertex models. Many of these RK Hamiltonians provably host $\mathbb{Z}_2$ topologically ordered phases.

Cluster quantum Monte Carlo study of two-dimensional weakly coupled frustrated trimer antiferromagnets

We report results from spin trimer-based cluster quantum Monte Carlo simulations for the thermodynamic properties of two-dimensional frustrated quantum antiferromagnets that are composed of weakly-coupled three-spin (trimer) clusters. In particular, we consider the spin-1/2 kagome lattice with a strong breathing distortion, and the triangle-square lattice model proposed previously for the cuprate La${}_4$Cu${}_3$MoO${}_{12}$. For both cases, we demonstrate that an appropriately chosen trimer-based computational basis allows us to significantly reduce the quantum Monte Carlo sign problem down to the low-temperature regime. Besides exploring the thermodynamic behavior for the triangle-square lattice model we also assess a mean field theory-based prediction for the onset of chiral order. For the breathing distorted kagome lattice model, we observe a robust two-peak structure in the specific heat, both in the quantum spin liquid and the lattice-nematic regimes.

Mean-field description of skyrmion lattice in hexagonal frustrated antiferromagnets

Simple mean-field approach for frustrated antiferromagnets on hexagonal lattices, aimed to describe the high-temperature part of the temperature-magnetic field phase diagram, is proposed. It is shown, that an interplay between modulation vector symmetry, Zeeman energy and magneto-dipolar interaction leads to stabilization of the triple-$Q$ skyrmion lattice in a certain region of the phase diagram. Corresponding analytical expressions for phase boundaries are derived. It is argued that the developed theory can be applied for the description of the high-temperature part of the phase diagram observed experimentally for Gd$_2$PdSi$_3$ compound.

Superconducting YAu3Si and Antiferromagnetic GdAu3Si with an Interpenetrating Framework Structure Built from 16-Atom Polyhedra.

Investigations of reaction mixtures REx(Au0.79Si0.21)100–x (RE = Y and Gd) yielded the compounds REAu3Si which adopt a new structure type, referred to as GdAu3Si structure (tP80, P42/mnm, Z = 16, a = 12.8244(6)/12.7702(2) Å, and c = 9.0883(8)/9.0456(2) Å for GdAu3Si/YAu3Si, respectively). REAu3Si was afforded as millimeter-sized faceted crystal specimens from solution growth employing melts with composition RE18(Au0.79Si0.21)82. In the GdAu3Si structure, the Au and Si atoms are strictly ordered and form a framework built of corner-connected, Si-centered, trigonal prismatic units SiAu6. RE atoms distribute on 3 crystallographically different sites and each attain a 16-atom coordination by 12 Au and 4 Si atoms. These 16-atom polyhedra commonly fill the space of the unit cell. The physical properties of REAu3Si were investigated by heat capacity, electrical resistivity, and magnetometry techniques and are discussed in the light of theoretical predictions. YAu3Si exhibits superconductivity around 1 K, whereas GdAu3Si shows a complex magnetic ordering, likely related to frustrated antiferromagnets exhibiting chiral spin textures. GdAu3Si-type phases with interesting magnetic and transport properties may exist in an extended range of ternary RE–Au–Si systems, similar to the compositionally adjacent cubic 1/1 approximants RE(Au,Si)∼6.

Cycloidal Magnetic Order Promoted by Labile Mixed Anionic Paths in M2(SeO3)F2 (M = Mn2+, Ni2+).

Two M2(SeO3)F2 fluoro-selenites (M = Mn2+, Ni2+) have been synthesized using optimized hydrothermal reactions. Their 3D framework consists of 1D-[MO2F2]4-chains of edge-sharing octahedra with a rare topology of alternating O-O and F-F μ2 bridges. The interchain corner-sharing connections are assisted by the mixed O vs F anionic nature and develop a complex set of M-X-M superexchanges as calculated by LDA+U. Their interplay induces prominent in-chain antiferromagnetic frustration, while the interchain exchanges are responsible for the cycloidal magnetic structure observed below TN ≈ 21.5 K in the Ni2+ case. For comparison the Mn2+ compound develops a nearly collinear spin (canted) ordering below TN ≈ 26 K with ferromagnetic chain units.

Resolution of Low-Energy States in Spin-Exchange Transition-Metal Clusters: Case Study of Singlet States in [Fe(III)4S4] Cubanes.

Polynuclear transition-metal (PNTM) clusters owe their catalytic activity to numerous energetically low-lying spin states and stable oxidation states. The characterization of their electronic structure represents one of the greatest challenges of modern chemistry. We propose a theoretical framework that enables the resolution of targeted electronic states with ease and apply it to two [Fe(III)4S4] cubanes. Through direct access to their many-body wave functions, we identify important correlation mechanisms and their interplay with the geometrical distortions observed in these clusters, which are core properties in understanding their catalytic activity. The simulated magnetic coupling constants predicted by our strategy allow us to make qualitative connections between spin interactions and geometrical distortions, demonstrating its predictive power. Moreover, despite its simplicity, the strategy provides magnetic coupling constants in good agreement with the available experimental ones. The complexes are intrinsically frustrated anti-ferromagnets, and the obtained spin structures together with the geometrical distortions represent two possible ways to release spin frustration (spin-driven Jahn–Teller distortion). Our paradigm provides a simple, yet rigorous, route to uncover the electronic structure of PNTM clusters and may be applied to a wide variety of such clusters.

Phase diagram study of a two-dimensional frustrated antiferromagnet via unsupervised machine learning

We apply unsupervised learning techniques to classify the different phases of the $J_1-J_2$ antiferromagnetic Ising model on the honeycomb lattice. We construct the phase diagram of the system using convolutional autoencoders. These neural networks can detect phase transitions in the system via `anomaly detection', without the need for any label or a priori knowledge of the phases. We present different ways of training these autoencoders and we evaluate them to discriminate between distinct magnetic phases. In this process, we highlight the case of high temperature or even random training data. Finally, we analyze the capability of the autoencoder to detect the ground state degeneracy through the reconstruction error.

Decoupling Lattice and Magnetic Instabilities in Frustrated CuMnO2.

The AMnO2 delafossites (A = Na, Cu) are model frustrated antiferromagnets, with triangular layers of Mn3+ spins. At low temperatures (TN = 65 K), a C2/m → P1̅ transition is found in CuMnO2, which breaks frustration and establishes magnetic order. In contrast to this clean transition, A = Na only shows short-range distortions at TN. Here, we report a systematic crystallographic, spectroscopic, and theoretical investigation of CuMnO2. We show that, even in stoichiometric samples, nonzero anisotropic Cu displacements coexist with magnetic order. Using X-ray/neutron diffraction and Raman scattering, we show that high pressures act to decouple these degrees of freedom. This manifests as an isostuctural phase transition at ∼10 GPa, with a reversible collapse of the c-axis. This is shown to be the high-pressure analogue of the c-axis negative thermal expansion seen at ambient pressure. Density functional theory (DFT) simulations confirm that dynamical instabilities of the Cu+ cations and edge-shared MnO6 layers are intertwined at ambient pressure. However, high pressure selectively activates the former, before an eventual predicted reemergence of magnetism at the highest pressures. Our results show that the lattice dynamics and local structure of CuMnO2 are quantitatively different from nonmagnetic Cu delafossites and raise questions about the role of intrinsic inhomogeneity in frustrated antiferromagnets.

Pressure-induced phase transition in the J1−J2 square lattice antiferromagnet RbMoOPO4Cl

We report results of magnetization and $^{31}$P NMR measurements under high pressure up to 6.4~GPa on RbMoOPO$_4$Cl, which is a frustrated square-lattice antiferromagnet with competing nearest-neighbor and next-nearest-neighbor interactions. Anomalies in the pressure dependences of the NMR shift and the transferred hyperfine coupling constants indicate a structural phase transition at 2.6~GPa, which is likely to break mirror symmetry and triggers significant change of the exchange interactions. In fact, the NMR spectra in magnetically ordered states reveal a change from the columnar antiferromagnetic (CAF) order below 3.3~GPa to the N\'{e}el antiferromagnetic (NAF) order above 3.9~GPa. The spin lattice relaxation rate $1/T_1$ also indicates a change of dominant magnetic fluctuations from CAF-type to NAF-type with pressure. Although the NMR spectra in the intermediate pressure region between 3.3 and 3.9 GPa show coexistence of the CAF and NAF phases, a certain component of $1/T_1$ shows paramagnetic behavior with persistent spin fluctuations, leaving possibility for a quantum disordered phase. The easy-plane anisotropy of spin fluctuations with unusual nonmonotonic temperature dependence at ambient pressure gets reversed to the Ising anisotropy at high pressures. This unexpected anisotropic behavior for a spin 1/2 system may be ascribed to the strong spin-orbit coupling of Mo-4$d$ electrons.

Thermodynamically stable skyrmion lattice in a tetragonal frustrated antiferromagnet with dipolar interaction

Motivated by recent experimental results on GdRu$_2$Si$_2$ [Khanh, N.D., Nakajima, T., Yu, X. et al., \emph{Nat. Nanotechnol.} \textbf{15}, 444-449 (2020)], where nanometric square skyrmion lattice was observed, we propose simple analytical mean-field description of the high-temperature part of the phase diagram of centrosymmetric tetragonal frustrated antiferromagnets with dipolar interaction in the external magnetic field. In the reciprocal space dipolar forces provide momentum dependent biaxial anisotropy. It is shown that in tetragonal lattice in the large part of the Brillouin zone for mutually perpendicular modulation vectors in the $ab$ plane this anisotropy has mutually perpendicular easy axes and collinear middle axes, what leads to double-Q modulated spin structure stabilization. The latter turns out to be a square skyrmion lattice in the large part of its stability region with the topological charge $\pm 1$ per magnetic unit cell, which is determined by the frustrated exchange coupling, and, thus, nanometer-sized. In the presence of additional single-ion easy-axis anisotropy, easy and middle axes can be swapped, which leads to different phase diagram. It is argued that the latter case is relevant to GdRu$_2$Si$_2$.

Phase competition in frustrated anisotropic antiferromagnet in strong magnetic field

We discuss theoretically a frustrated Heisenberg antiferromagnet in magnetic field close to the saturation one. It is demonstrated that a small biaxial anisotropy and/or the magnetic dipolar interaction produce a delicate balance between phases with a commensurate canted, incommensurate helical (conical), and fan spin orderings. As a result, different sequences of phase transitions are realized depending on values of these small anisotropic interactions. We derive analytical expressions for critical fields and ground-state energies of the phases which are in a quantitative agreement with our and previous Monte-Carlo simulations.

Geometrical Frustration and Planar Triangular Antiferromagnetism in Quasi-Three-Dimensional Artificial Spin Architecture.

We present a realization of highly frustrated planar triangular antiferromagnetism achieved in a quasi-three-dimensional artificial spin system consisting of monodomain Ising-type nanomagnets lithographically arranged onto a deep-etched silicon substrate. We demonstrate how the three-dimensional spin architecture results in the first direct observation of long-range ordered planar triangular antiferromagnetism, in addition to a highly disordered phase with short-range correlations, once competing interactions are perfectly tuned. Our work demonstrates how escaping two-dimensional restrictions can lead to new types of magnetically frustrated metamaterials.