Heisenberg Antiferromagnet Research Articles

Collapsing Behavior of the Ferrimagnetic Ground State of the S = 1/2 Heisenberg Antiferromagnet on the Lieb Lattice due to Frustration

Collapsing Behavior of the Ferrimagnetic Ground State of the <i>S</i> = 1/2 Heisenberg Antiferromagnet on the Lieb Lattice due to Frustration

Gapped quantum spin liquid in a triangular-lattice Ising-type antiferromagnet PrMgAl11O19

In the search of quantum spin liquid (QSL), spin-1/2 triangular-lattice Heisenberg antiferromagnets have always been viewed as fertile soils. Despite the true magnetically ordered ground state, anisotropy has been considered to play a significant role in stabilizing a QSL state. However, the nature and ground state of the most anisotropic case, the triangular-lattice Ising antiferromagnet (TLIAF), remain elusive and controversial. Here, we report specific-heat and thermal-conductivity measurements on a newly discovered Ising-type QSL candidate PrMgAl11O19. At zero field, the magnetic specific heat shows a quadratic temperature dependence. On the contrary, no direct positive magnetic contribution to thermal conductivity is detected, ruling out the presence of mobile gapless fermionic excitations. Further analysis of phonon thermal conductivity reveals that the phonons are strongly scattered by thermally activated magnetic excitations out of a gap, which exhibits a linear dependence with magnetic field. These results demonstrate that the spin-1/2 TLIAF PrMgAl11O19 has a gapped Z2 QSL ground state. Published by the American Physical Society 2024

Discovering Classical Spin Liquids by Topological Search of High Symmetry Nets.

Spin liquids are a paradigmatic example of a nontrivial state of matter. The search for new spin liquids is a key interdisciplinary challenge. Geometrical frustration-where the geometry of the net that the spins occupy precludes the generation of a simple ordered state-is a particularly fruitful way to generate these intrinsically disordered states. Prior focus has been on a handful of high symmetry nets. There are, however, many three-dimensional nets, each of which has the potential to form unique states. In this paper, we investigate the high symmetry nets-those which are both vertex- and edge-transitive-for the simplest possible interaction sets: nearest-neighbor couplings of antiferromagnetic Heisenberg and Ising spins. While the well-known crs (pyrochlore) net is the only nearest-neighbor Heisenberg antiferromagnet which does not order, we identify two new frustrated nets (lcx and thp) possessing finite temperature Heisenberg spin-liquid states with strongly suppressed magnetic ordering and noncollinear ground states. With Ising spins, we identify three new classical spin liquids that do not order down to T/J = 0.01. We highlight materials that contain these high symmetry nets, and which could, if substituted with appropriate magnetic ions, potentially host these unusual states. Our systematic survey will guide searches for novel magnetic phases.

Magnon Confinement on the Two-Dimensional Penrose Lattice: Perpendicular-Space Analysis of the Dynamic Structure Factor

Employing the spin-wave formalism within and beyond the harmonic-oscillator approx-imation, we study the dynamic structure factors of spin-12 nearest-neighbor quantum Heisenberg antiferromagnets on two-dimensional quasiperiodic lattices with particular emphasis on a mag-netic analog to the well-known confined states of a hopping Hamiltonian for independent electrons on a two-dimensional Penrose lattice. We present comprehensive calculations on the C5v Penrose tiling in comparison with the C8v Ammann–Beenker tiling, revealing their decagonal and octagonal antiferromagnetic microstructures. Their dynamic spin structure factors both exhibit linear soft modes emergent at magnetic Bragg wavevectors and have nearly or fairly flat scattering bands, signifying magnetic excitations localized in some way, at several different energies in a self-similar manner. In particular, the lowest-lying highly flat mode is distinctive of the Penrose lattice, which is mediated by its unique antiferromagnons confined within tricoordinated sites only, unlike their itinerant electron counterparts involving pentacoordinated, as well as tricoordinated, sites. Bringing harmonic antiferromagnons into higher-order quantum interaction splits, the lowest-lying nearly flat scattering band in two, each mediated by further confined antiferromagnons, which is fully demonstrated and throughly visualized in the perpendicular as well as real spaces. We disclose superconfined antiferromagnons on the two-dimensional Penrose lattice.

Multiferroic quantum material Ba2Cu1−xMnxGe2O7 (0 ≤ x ≤ 1) as a potential candidate for frustrated Heisenberg antiferromagnet

Multiferroic Ba2CuGe2O7 was anticipated as a potential member of the exciting group of materials hosting a skyrmion or vortex lattice because of its profound Dzyaloshinskii–Moriya interaction (DMI) and the absence of single ion anisotropy (SIA). This phase, however, could not be evidenced and instead, it exhibits a complex incommensurate antiferromagnetic (AFM) cycloidal structure. Its sister compound Ba2MnGe2O7, in contrast, is characterized by a relatively strong in-plane exchange interaction that competes with a non-vanishing SIA and the weak DMI, resulting in a quasi-two-dimensional commensurate AFM structure. Considering this versatility in the magnetic interactions, a mixed solid solution of Cu and Mn in Ba2Cu1−xMnxGe2O7 can hold an interesting playground for its interactive DMI and SIA depending on the mixed spin states of the transition metal ions towards the skyrmion physics. Here, we present a detailed study of the micro- and macroscopic spin structure of the Ba2Cu1−xMnxGe2O7 solid solution series using high-resolution neutron powder diffraction techniques. We have developed a remarkably rich magnetic phase diagram as a function of the applied magnetic field and x, which consists of two end-line phases separated by a potentially quantum-critical phase at x = 0.57. An AFM conical structure at zero magnetic field is demonstrated to persist up to x = 0.50. Our results provide crucial information on the spin structure and magnetic properties, which are necessary for the general understanding and theoretical developments on multiferroicity in the frame of skyrmion type or frustrated AFM lattice where DMI and SIA play an important role.

Emergent Spin-Gapped Magnetization Plateaus in a Spin-1/2 Perfect Kagome Antiferromagnet.

The two-dimensional spin-1/2 kagome Heisenberg antiferromagnet is believed to host quantum spin liquid (QSL) states with no magnetic order, but its ground state remains largely elusive. An important outstanding question concerns the presence or absence of the 1/9 magnetization plateau, where exotic quantum states, including topological ones, are expected to emerge. Here we report the magnetization of a recently discovered kagome QSL candidate YCu_{3}(OH)_{6.5}Br_{2.5} up to 57T. Above 50T, a clear magnetization plateau at 1/3 of the saturation moment of Cu^{2+} ions is observed, supporting that this material provides an ideal platform for the kagome Heisenberg antiferromagnet. Remarkably, we found another magnetization plateau around 20T, which is attributed to the 1/9 plateau. The temperature dependence of this plateau reveals the presence of the spin gap. The observation of 1/9 and 1/3 plateaus highlights the emergence of novel states in quantum spin systems.

Precise spin-wave model for one-, two-, and three-dimensional Heisenberg antiferromagnets inclusive of dipolar interactions

Precise spin-wave model for one-, two-, and three-dimensional Heisenberg antiferromagnets inclusive of dipolar interactions

Construction of Ideal One-Dimensional Spin Chains by Topochemical Dehydration/Rehydration Route.

One-dimensional (1D) Heisenberg antiferromagnets are of great interest due to their intriguing quantum phenomena. However, the experimental realization of such systems with large spin S remains challenging because even weak interchain interactions induce long-range ordering. In this study, we present an ideal 1D S = 5/2 spin chain antiferromagnet achieved through a multistep topochemical route involving dehydration and rehydration. By desorbing three water molecules from (2,2'-bpy)FeF3(H2O)·2H2O (2,2'-bpy = 2,2'-bipyridyl) at 150 °C and then intercalating two water molecules at room temperature (giving (2,2'-bpy)FeF3·2H2O 1), the initially isolated FeF3ON2 octahedra combine to form corner-sharing FeF4N2 octahedral chains, which are effectively separated by organic and added water molecules. Mössbauer spectroscopy reveals significant dynamical fluctuations down to 2.7 K, despite the presence of strong intrachain interactions. Moreover, results from electron spin resonance (ESR) and heat capacity measurements indicate the absence of long-range order down to 0.5 K. This controlled topochemical dehydration/rehydration approach is further extended to (2,2'-bpy)CrF3·2H2O with S = 3/2 1D chains, thus opening the possibility of obtaining other low-dimensional spin lattices.

Field-controlled multicritical behavior and emergent universality in fully frustrated quantum magnets

Phase transitions in condensed matter are a source of exotic emergent properties. We study the fully frustrated bilayer Heisenberg antiferromagnet to demonstrate that an applied magnetic field creates a previously unknown emergent criticality. The quantum phase diagram contains four states with distinctly different symmetries, all but one pair separated by first-order transitions. We show by quantum Monte Carlo simulations that the thermal phase diagram is dominated by a wall of discontinuities extending between the dimer-triplet phases and the singlet-containing phases. This wall is terminated at finite temperatures by a critical line, which becomes multicritical where the Berezinskii-Kosterlitz-Thouless (BKT) transition of the dimer-triplet antiferromagnet and the thermal Ising transition of the singlet-triplet crystal phase also terminate. The combination of merging symmetries leads to a 4-state Potts universality not contained in the microscopic Hamiltonian, which we interpret within the Ashkin-Teller model. Our results represent a systematic step in understanding emergent phenomena in quantum magnetic materials, including the “Shastry-Sutherland compound” SrCu2(BO3)2.

Giant Parametric Amplification of the Inverse Cotton–Mouton Effect in Antiferromagnetic Crystals

The interaction of light with spins in a Heisenberg antiferromagnet with a negligibly low magnetic anisotropy as in RbMnF3 has been theoretically analyzed. In particular, an optical pump–probe experiment, where coherent terahertz magnons are excited by short pump laser pulses in the antiferromagnet and are then detected by a probe pulse delayed with respect to the pump pulse, has been simulated. It has been shown that the giant increase in the intensity of excitation of terahertz magnons under the influence of the inverse Cotton–Mouton effect occurs near parametric resonance, i.e., in the parametric instability region.

The dilute 3D and three site dimer Heisenberg antiferromagnet: review of some magnetic properties.

Many properties of the spin–½ kagome Heisenberg antiferromagnet remains controversial and receiving continuous attention from theorists and experimentalists due to their fascinating magnetic properties and high heterogeneity coax by the geometrical frustration. In this research we seek and compare the results obtained in our recent article [1] with that of Napel[2] where we elucidate some of the identified magnetic behaviour using the spin–½ Heisenbeg model with the application of Exact Diagonalization and classical Monte-Carlo simulation on three site dimer and 3D simple cubic lattice simulation. The results obtained shows excellent agreement in both papers reviewed with [1] establishing firmly the FM to AFM transition, having a clear transition point referred to mixed phased [2].

Pressure control of magnetic order and excitations in the pyrochlore antiferromagnet MgCr2O4

MgCr2O4 is one of the best-known realizations of the pyrochlore-lattice Heisenberg antiferromagnet. The strong antiferromagnetic exchange interactions are perturbed by small further-neighbor exchanges such that this compound may in principle realize a spiral spin liquid (SSL) phase in the zero-temperature limit. However, a spin Jahn-Teller transition below TN≈13 K yields a complicated long-range magnetic order with multiple coexisting propagation vectors. We present neutron scattering and thermomagnetic measurements of MgCr2O4 samples under applied hydrostatic pressure up to P=1.7 GPa demonstrating the existence of multiple close-lying nearly degenerate magnetic ground states. We show that the application of hydrostatic pressure increases the ordering temperature by around 0.8 K per GPa and increases the bandwidth of the magnetic excitations by around 0.5 meV per GPa. We also evidence a strong tendency for the preferential occupation of a subset of magnetic domains under pressure. In particular, we show that the k=(0,0,1) magnetic phase, which is almost negligible at ambient pressure, dramatically increases in spectral weight under pressure. This modifies the spectrum of magnetic excitations, which we interpret unambiguously as spin waves from multiple magnetic domains. Moreover, we report that the application of pressure reveals a feature in the magnetic susceptibility above the magnetostructural transition. We interpret this as the onset of a short-range ordered phase associated with k=(0,0,1), previously not observed in magnetometry measurements. Published by the American Physical Society 2024

Possible chiral spin liquid state in the S = 1/2 kagome Heisenberg model

The nature of the ground state for the S = 1/2 Kagome Heisenberg antiferromagnet (KHAF) has been elusive. We revisit this challenging problem and provide numerical evidence that its ground state is a chiral spin liquid. Combining the density matrix renormalization group method with analytical analyses, we demonstrate that the previously observed chiral spin liquid phase in the KHAF with longer-range couplings is stable in a broader region of the phase diagram. We characterize the nature of the ground state by computing energy derivatives, revealing the ground-state degeneracy arising from the spontaneous breaking of the time-reversal symmetry, and targeting the semion sector. We further investigate the phase diagram in the vicinity of the KHAF and observe a 3×3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\sqrt{3}\ imes \\sqrt{3}$$\\end{document} magnetically ordered phase and two valence-bond crystal phases.

Candidate quantum disordered intermediate phase in the Heisenberg antiferromagnet on the maple-leaf lattice

Candidate quantum disordered intermediate phase in the Heisenberg antiferromagnet on the maple-leaf lattice

Anomalous scaling corrections and quantum phase diagram of the Heisenberg antiferromagnet on the spatially anisotropic honeycomb lattice

Anomalous scaling corrections and quantum phase diagram of the Heisenberg antiferromagnet on the spatially anisotropic honeycomb lattice

Quantum spin nematic phase in a square-lattice iridate.

Spin nematic is a magnetic analogue of classical liquid crystals, a fourth state of matter exhibiting characteristics of both liquid and solid1,2. Particularly intriguing is a valence-bond spin nematic3-5, in which spins are quantum entangled to form a multipolar order without breaking time-reversal symmetry, but its unambiguous experimental realization remains elusive. Here we establish a spin nematic phase in the square-lattice iridate Sr2IrO4, which approximately realizes a pseudospin one-half Heisenberg antiferromagnet in the strong spin-orbit coupling limit6-9. Upon cooling, the transition into the spin nematic phase at TC ≈ 263 K is marked by a divergence in the static spin quadrupole susceptibility extracted from our Raman spectra and concomitant emergence of a collective mode associated with the spontaneous breaking of rotational symmetries. The quadrupolar order persists in the antiferromagnetic phase below TN ≈ 230 K and becomes directly observable through its interference with the antiferromagnetic order in resonant X-ray diffraction, which allows us to uniquely determine its spatial structure. Further, we find using resonant inelastic X-ray scattering a complete breakdown of coherent magnon excitations at short-wavelength scales, suggesting a many-body quantum entanglement in the antiferromagnetic state10,11. Taken together, our results reveal a quantum order underlying the Néel antiferromagnet that is widely believed to be intimately connected to the mechanism of high-temperature superconductivity12,13.

Spin gap in quasi-one-dimensional S = 3/2 antiferromagnet CoTi2O5

Quasi-one-dimensional (1D) antiferromagnets are known to display intriguing phenomena especially when there is a spin gap in their spin-excitation spectra. Here we demonstrate that a spin gap exists in the quasi-1D Heisenberg antiferromagnet CoTi2O5 with highly ordered Co2+/Ti4+ occupation, in which the Co2+ ions with S = 3/2 form a 1D spin chain along the a-axis. CoTi2O5 undergoes an antiferromagnetic transition at T N ∼ 24 K and exhibits obvious anisotropic magnetic susceptibility even in the paramagnetic region. Although a gapless magnetic ground state is usually expected in a quasi-1D Heisenberg antiferromagnet with half-integer spins, by analyzing the specific heat, the thermal conductivity, and the spin-lattice relaxation rate (1/T 1) as a function of temperature, we found that a spin gap is opened in the spin-excitation spectrum of CoTi2O5 around T N, manifested by the rapid decrease of magnetic specific heat to zero, the double-peak characteristic in thermal conductivity, and the exponential decay of 1/T 1 below T N. Both the magnetic measurements and the first-principles calculations results indicate that there is spin-orbit coupling in CoTi2O5, which induces the magnetic anisotropy in CoTi2O5, and then opens the spin gap at low temperature.

Complete field-induced spectral response of the spin-1/2 triangular-lattice antiferromagnet CsYbSe2

Fifty years after Anderson’s resonating valence-bond proposal, the spin-1/2 triangular-lattice Heisenberg antiferromagnet (TLHAF) remains the ultimate platform to explore highly entangled quantum spin states in proximity to magnetic order. Yb-based delafossites are ideal candidate TLHAF materials, which allow experimental access to the full range of applied in-plane magnetic fields. We perform a systematic neutron scattering study of CsYbSe2, first proving the Heisenberg character of the interactions and quantifying the second-neighbor coupling. We then measure the complex evolution of the excitation spectrum, finding extensive continuum features near the 120°-ordered state, throughout the 1/3-magnetization plateau and beyond this up to saturation. We perform cylinder matrix-product-state (MPS) calculations to obtain an unbiased numerical benchmark for the TLHAF and spectacular agreement with the experimental spectra. The measured and calculated longitudinal spectral functions reflect the role of multi-magnon bound and scattering states. These results provide valuable insight into unconventional field-induced spin excitations in frustrated quantum materials.

Frustrated magnetism of the spin-1 kagome antiferromagnet β-BaNi3(VO4)2(OH)2

We propose the newly synthesized β-BaNi3(VO4)2(OH)2 (space group: ) as a candidate for the spin-1 kagome Heisenberg antiferromagnet (KHA). The compound features a uniform kagome lattice of Ni2+ (S = 1) ions with a large interlayer distance. High-field measurements at low temperatures reveal a susceptibility local minimum at ∼9 T, resembling a 1/3 magnetization plateau as predicted by the pure S = 1 KHA model. Below ∼6 K, approximately 1% of the spins exhibit spin-glass order, which may be attributed to the nanocrystalline grain size of ∼50 nm. Despite the antiferromagnetic exchange coupling strength of ∼7 K, the majority of spins remain disordered down to ∼0.1 K as indicated by the observed power-law behaviors in magnetic specific heat . Our results demonstrate that the low-energy magnetic excitations in β-BaNi3(VO4)2(OH)2 are gapless, which contradicts the current theoretical expectations of the ideal model.

Abundance of Hard-Hexagon Crystals in the Quantum Pyrochlore Antiferromagnet.

We propose a simple family of valence-bond crystals as potential ground states of the S=1/2 and S=1 Heisenberg antiferromagnet on the pyrochlore lattice. Exponentially numerous in the linear size of the system, these can be visualized as hard-hexagon coverings, with each hexagon representing a resonating valence-bond ring. This ensemble spontaneously breaks rotation, inversion, and translation symmetries. A simple, yet accurate, variational wave function allows a precise determination of the energy, confirmed by the density matrix renormalization group and numerical linked cluster expansion, and extended by an analysis of excited states. The identification of the origin of the stability indicates applicability to a broad class of frustrated lattices, which we demonstrate for the checkerboard and ruby lattices. Our work suggests a perspective on such quantum magnets, in which unfrustrated motifs are effectively uncoupled by the frustration of their interactions.