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(a) Magnetic couplings in a 2D triangular layer in Cs2CuCl4: strong bonds J (heavy lines b), smaller frustrating zig-zag bonds J ′ (thin lines). Da are the DzyaloshinskiiMoriya (DM) couplings along the zig-zag bonds; the signs ⊗, ⊙ refer to interactions originating at the central spin SR , see Eq. (3). (b) Odd (black) and even (grey) layers are stacked successively along a (inter-layer spacing a/2) with an offset ζ=0.34 along c. J ′′ (dashed arrow) is the nearest-neighbor inter-layer exchange. (c) (b * , c * ) reciprocal plane showing the near-hexagonal Brillouin zones (thin lines) of the triangular lattice in (a). Black points are zone centers (τ ) and grey points at τ ± Q mark dispersion gap minima in the saturated phase (B > BC ) and where Bragg peaks appear below BC .
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We propose a method for measuring spin Hamiltonians and apply it to the spin- 1/2 Heisenberg antiferromagnet Cs2CuCl4, which shows a 2D fractionalized resonating valence bond state at low fields. By applying strong fields we fully align the spin moment of Cs2CuCl4, transforming it into an effective ferromagnet. In this phase the excitations are con...
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Citations
... Therefore LSWT is expected to be an excellent approximation and should allow for an Table III, reproducing the excitation spectrum. accurate estimation of the "true" (nonrenormalized) exchange constants [57]. ...
... In the TFIM pseudospin language, we are situated in the limit of large transverse fields, meaning that the ground state can be understood as an induced ferromagnet, fully polarized by the transverse field h = produced by the crystal field splitting. Given these circumstances, linear spin-wave theory constitutes an excellent approximation and can be used to extract the "real" (nonrenormalized) exchange parameters of Pr 3 BWO 9 with high fidelity [57]. However, while LSWT fits to our neutron spectra establish that significant correlations in the purported kagome planes are present, they are clearly dwarfed by the dominant out-of-plane interactions, forming frustrated spin-tubes through two competing FM-AFM bonds. ...
We present a thorough experimental investigation on of the rare-earth based frustrated quantum antiferromagnet Pr 3 BWO 9 , a purported spin-liquid candidate on the breathing kagome lattice. This material possesses a disordered ground state with an unusual excitation spectrum involving a coexistence of sharp spin waves and broad continuum excitations. Nevertheless, we show through a combination of thermodynamic, magnetometric, and spectroscopic probes with detailed theoretical modeling that it should be understood in a completely different framework. The crystal field splits the lowest quasidoublet states into two singlets moderately coupled through frustrated superexchange, resulting in a simple effective Hamiltonian of an Ising model in a transverse magnetic field. While our neutron spectroscopy data do point to significant correlations within the kagome planes, the dominant interactions are out-of-plane, forming frustrated triangular spin-tubes through two competing ferro-antiferromagnetic bonds. The resulting ground state is a simple quantum paramagnet, where the presence of strongly hyperfine-coupled nuclear moments and weak structural disorder causes significant modifications to both thermodynamic and dynamic properties.
Published by the American Physical Society 2024
... Our nonlinear spin-wave calculations are all based on the same Heisenberg interaction, J = 0.344(6) meV, determined as described at the beginning of this article by comparing the neutron scattering data to linear spin-wave theory above the saturation field. To obtain a similarly reliable value for the g factor g c , we consider the energy of the upper spin-wave mode at the Γ point, ℏω Γ , for fields applied with μ 0 H∥c at 10.5 T and 11 T. Assuming that these fields are not significantly below the saturation field, we fit the linear spin-wave expression ℏω Γ = μ B g c H [see Fig. 3a] and readily obtain g c = 1.509(6) 31 . The out-of-plane saturation field is then found to be H s,c = 3J/ (g c μ B ) ≈ 11.8 T, which justifies our initial assumption and agrees with the magnetization data presented in ref. 19 . ...
The basis for our understanding of quantum magnetism has been the study of elegantly simple model systems. However, even for the antiferromagnetic honeycomb lattice with isotropic spin interactions–one of the simplest model systems–a detailed understanding of quantum effects is still lacking. Here, using inelastic neutron scattering measurements of the honeycomb lattice material YbCl3, we elucidate how quantum effects renormalize the single-magnon and multimagnon excitations and how this renormalization can be tuned and ultimately driven to the classical limit by applying a magnetic field. Additionally, our work reveals that the quantum effects tuned by the magnetic field not only renormalize the magnetic excitations but also induce a distinctive sharp feature inside the multimagnon continuum. From a more general perspective, this result demonstrates that structures within magnetic continua can occur over a wide experimental parameter space and can be used as a reliable means of identifying quantum phenomena.
... Such magnetic-field tuned transitions are relevant to mainly two classes of spin systems, antiferromagnets and quantum paramagnets. Extensive experiments on both kinds of systems have established the importance of BEC-based perspective in understanding the physics of a wide variety of magnetic compounds under applied magnetic fields [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40]. Here, we propose scenarios where this conventional outcome breaks down. ...
Frustrated spin-systems have traditionally proven challenging to understand, owing to a scarcity of controlled methods for their analyses. By contrast, under strong magnetic fields, certain aspects of spin systems admit simpler and universal description in terms of hardcore bosons. The bosonic formalism is anchored by the phenomenon of Bose-Einstein condensation (BEC), which has helped explain the behaviors of a wide range of magnetic compounds under applied magnetic fields. Here, we focus on the interplay between frustration and externally applied magnetic field to identify instances where the BEC paradigm is no longer applicable. As a representative example, we consider the antiferromagnetic $J_1 - J_2 - J_3$ model on the square lattice in the presence of a uniform external magnetic field, and demonstrate that the frustration-driven suppression of the N\'{e}el order leads to a Lifshitz transition for the hardcore bosons. In the vicinity of the Lifshitz point, the physics becomes unmoored from the BEC paradigm, and the behavior of the system, both at and below the saturation field, is controlled by a Lifshitz multicritical point. We obtain the resultant universal scaling behaviors, and provide strong evidence for the existence of a frustration and magnetic-field driven correlated bosonic liquid state along the entire phase boundary separating the N\'{e}el phase from other magnetically ordered states.
... Compared to Cs 2 CuCl 4 with J/k B = 4.7 K and J ′ /J ≃ 0.30 [21,22], CROC is characterized by about one order of magnitude larger scale of exchange interactions. Fit of the magnetic susceptibility using an anisotropic triangular-lattice model unveiled J/k B = 40.6 ...
... The situation is very different from the case of Cs 2 CuCl 4 , where the incommensurate ordered structure appears to be a combined effect of the frustration, induced by exchange interaction between the spins along chains [9], and DMI. Assuming J/k B = 4.7 K [21,22] and ∆ = 14 GHz [6], we obtain for the soft mode in the magnetically disordered phase q = 0.485. This value is somewhat different from the b component of the ordering wavevector q = (0, 0.472, 0) [9], which results in a twice larger gap at the Γ point [33]. ...
The observation of spinon excitations in the $S=\frac{1}{2}$ triangular antiferromagnet Ca$_3$ReO$_5$Cl$_2$ reveals a quasi-one-dimensional (1D) nature of magnetic correlations, in spite of the nominally 2D magnetic structure. This phenomenon is known as frustration-induced dimensional reduction. Here, we present high-field electron spin resonance spectroscopy and magnetization studies of Ca$_3$ReO$_5$Cl$_2$, allowing us not only to refine spin-Hamiltonian parameters, but also to investigate peculiarities of its low-energy spin dynamics. We argue that the presence of the uniform Dzyaloshinskii-Moriya interaction (DMI) shifts the spinon continuum in momentum space and, as a result, opens a zero-field gap at the $\Gamma$ point. We observed this gap directly. The shift is found to be consistent with the structural modulation in the ordered state, suggesting this material as a perfect model triangular-lattice system, where a pure DMI-spiral ground state can be realized.
... Compared to Cs 2 CuCl 4 with J/k B = 4.7 K and J 0 =J ' 0:30 21,22 , CROC is characterized by about one order of magnitude larger scale of exchange interactions. Fit of the magnetic susceptibility using an anisotropic triangular-lattice model unveiled J/k B = 40.6 ...
The observation of spinon excitations in the S=12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S=\frac{1}{2}$$\end{document} triangular antiferromagnet Ca3ReO5Cl2 reveals a quasi-one-dimensional (1D) nature of magnetic correlations, in spite of the nominally 2D magnetic structure. This phenomenon is known as frustration-induced dimensional reduction. Here, we present high-field electron spin resonance spectroscopy and magnetization studies of Ca3ReO5Cl2, allowing us not only to refine spin-Hamiltonian parameters, but also to investigate peculiarities of its low-energy spin dynamics. We argue that the presence of the uniform Dzyaloshinskii-Moriya interaction (DMI) shifts the spinon continuum in momentum space and, as a result, opens a zero-field gap at the Γ point. We observed this gap directly. The shift is found to be consistent with the structural modulation in the ordered state, suggesting this material as a perfect model triangular-lattice system, where a pure DMI-spiral ground state can be realized.
... Going beyond the isotropic exchange, the Dzyaloshinsky-Moriya interaction [38,39] arises in systems with broken inversion symmetry due to spin-orbit coupling, and leads to nonreciprocal magnon propagation in ferromagnets, i.e., a different frequency of magnons with wave vectors k and −k [40][41][42]. This asymmetry in the spectrum is widely used for the experimental determination of the Dzyaloshinsky-Moriya interaction [43,44]. ...
... This is a consequence of the antiferromagnetic alignment of the spins irrespective of the inertial dynamics. Only the positive gyromagnetic ratio is shown in Fig. 8. Due to the finite value of η, the effective gyromagnetic ratio of precession spin waves in Eq. (40) is decreased at zero wave vector stronger than in ferromagnets, since b AFM b FM (k = 0). However, at increasing wave vector the gyromagnetic ratio increases, in contrast to the ferromagnetic case. ...
Inertial effects in spin dynamics are theoretically predicted to emerge at ultrashort time scales, but their experimental signatures are often ambiguous. Here we calculate the spin-wave spectrum in ferromagnets and two-sublattice antiferromagnets in the presence of inertial effects. It is shown how precession and nutation spin waves hybridize with each other, leading to the renormalization of the frequencies, the group velocities, the effective gyromagnetic ratios, and the effective damping parameters. Possible ways of distinguishing between the signatures of inertial dynamics and similar effects explainable within conventional models are discussed.
... Crucially, this produces well-defined magnon modes within the plateau phase, whose gapped dispersion can be calculated via nonlinear spin wave theory [5,40]. This observation allows us to extract the Hamiltonian parameters without the need for reaching the fully polarized magnetic state (the saturation field is prohibitively large for most trialgular QSL candidate materials [5,42]). The problem thus becomes tractable by studying the magnons in the plateau phase. ...
... The study here shows that KYbSe 2 is an excellent example of a spin-1/2 2 / 1 Heisenberg magnet on a triangular lattice. The use of nonlinear spin-wave theory at an intermediate-rather than fully saturated-field provides an alternative method to that in Ref. [42] which requires a fully polarized system. This is then applicable not only to other delafossite materials but also other candidate spin liquids where the saturation field cannot be reached. ...
Quantum spin liquids (QSL) are theoretical states of matter with long-range entanglement and exotic quasiparticles. However, they elude quantitative theory, rendering their underlying phases mysterious, and hampering experimental efforts to determine candidate materials' interactions. Here we study resonating valence bond QSL candidate material KYbSe$_2$ in its 1/3 plateau phase, where quantitative theory is tractable. We measure the magnon modes within this phase using inelastic neutron scattering and fit them using nonlinear spin wave theory, and we also fit the heat capacity using high temperature series expansion. Both fits yield the same magnetic Hamiltonian to within uncertainty, confirming previous estimates and showing the Heisenberg $J_2/J_1$ to be an accurate model for KYbSe$_2$, and confirming its status as a proximate QSL.
... Going beyond the isotropic exchange, the Dzyaloshinsky-Moriya interaction [38,39] arises in systems with broken inversion symmetry due to spin-orbit coupling, and leads to non-reciprocal magnon propagation in ferromagnets, i.e., a different frequency of magnons with wave vectors k and −k [40][41][42]. This asymmetry in the spectrum is widely used for the experimental determination of the Dzyaloshinsky-Moriya interaction [43,44]. ...
Inertial effects in spin dynamics are theoretically predicted to emerge at ultrashort time scales, but their experimental signatures are often ambiguous. Here, we calculate the spin-wave spectrum in ferromagnets and two-sublattice antiferromagnets in the presence of inertial effects. It is shown how precession and nutation spin waves hybridize with each other, leading to the renormalization of the frequencies, the group velocities, the effective gyromagnetic ratios and the effective damping parameters. Possible ways of distinguishing between the signatures of inertial dynamics and similar effects explainable within conventional models are discussed.
... This model may be relevant in several compounds where the effective spins lie on chains coupled triangularly. Some of them are inorganic, such as Cs 2 CuCl 4 and Cs 2 CuBr 4 [56][57][58][59], and some are organic like κ-(ET) 2 Cu 2 (CN) 3 and Me 3 EtSb[Pd(dmit) 2 ] 2 [60][61][62][63][64]. On the other hand, there are some theoretical studies, but none of them fully agree on the corresponding quantum phase diagram [13,28,[64][65][66][67][68]. On one side, for J /J > 1, some VMC studies predict a two-dimensional QSL phase for 1. 18 J /J 1.67 and a one-dimensional one for the decoupled chains limit (J /J 1.67) [66,69]. ...
The spin-$\frac12$ triangular lattice antiferromagnetic Heisenberg model has
been for a long time the prototypical model of magnetic frustration. However,
only very recently this model has been proposed to be realized in the
Ba$_8$CoNb$_6$O$_{24}$ compound. The ground-state and thermodynamic properties
are evaluated from a high-temperature series expansions interpolation method,
called "entropy method", and compared to experiments. We find a ground-state
energy $e_0 = -0.5445(2)$ in perfect agreement with exact diagonalization
results. We also calculate the specific heat and entropy at all temperatures,
finding a good agreement with the latest experiments, and evaluate which
further interactions could improve the comparison. We explore the spatially
anisotropic triangular lattice and provide evidence that supports the existence
of a gapped spin liquid between the square and triangular lattices.
... Not only does this geometry have multiple materials realizations, but each generation of materials has opened a new dimension in research [56]. Triangular organic compounds drove a discussion of proximity to the Mott transition [5][6][7][8], Cs 2 CuCl 4 and Cs 2 CuBr 4 [58][59][60][61][62] drove studies of the spatially anisotropic (J-J ) triangular-lattice models [57,63], and the cobaltates Ba 3 CoNb 2 O 9 [64,65], Ba 3 CoSb 2 O 9 [66][67][68], and Ba 8 CoNb 6 O 24 [69] spurred the consideration of spin-anisotropic triangular lattices with XXZ symmetry. In recent years, Yb-based triangular-lattice materials have sparked very strong interest in further spin anisotropies, in the form of J ++ and J +z terms [38,48,70], all of which widen considerably the scope for finding QSL states. ...
A primary goal at the interface of theoretical and experimental quantum magnetism is the investigation of exotic spin states, mostly notably quantum spin liquids (QSLs) that realize phenomena including quasiparticle fractionalization, long-ranged entanglement, and topological order. Magnetic rare-earth ions go beyond the straightforward paradigm of geometrical frustration in Heisenberg antiferromagnets by introducing competing energy scales, and in particular their strong spin-orbit coupling creates multiple split crystal electric-field (CEF) levels, leading to anisotropic effective spin models with intrinsic frustration. While rare-earth delafossites have a triangular-lattice geometry and thus have gained recent attention as candidates for hosting spin-1/2 QSL physics, the reliable extraction of effective spin models from the initial many-parameter CEF spectrum is a hard problem. Using the example of CsYbSe2, we demonstrate the unambiguous extraction of the Stevens operators dictating the full CEF spectrum of Yb3+ by translating these into parameters with a direct physical interpretation. Specifically, we combine low-field susceptibility measurements with resonant torsion magnetometry (RTM) experiments in fields up to 60 T to determine a sufficiently large number of physical parameters—effective Zeeman splittings, anisotropic van Vleck coefficients, and magnetotropic coefficients—that the set of Stevens operator coefficients is unique. Our crucial identification of the strong corrections to the Zeeman splitting of Kramers doublets as van Vleck coefficients has direct consequences for the interpretation of all anisotropic magnetic susceptibility measurements. Our results allow us to determine the nature and validity of an effective spin-1/2 model for CsYbSe2, to provide input for theoretical studies of such models on the triangular lattice, and to provide additional materials insight into routes for achieving magnetic frustration and candidate QSL systems in rare-earth compounds.
