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arXiv:2407.20501 · Physical Review Research

Magnon spectra of cuprates beyond spin wave theory

Jiahui Bao, Matthias Gohlke, Jeffrey G. Rau, Nic Shannon

Published Mar 4, 2025• 5 citations
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Abstract

The usual starting point for understanding magnons in cuprate antiferromagnets such as La 2 CuO 4 is a spin model incorporating cyclic exchange, which descends from a one-band Hubbard model, and has parameters taken from fits based on non-interacting spin wave theory. Here we explore whether this provides a reliable description of experiment, using matrix product states (MPS) to calculate magnon spectra beyond spin wave theory. We find that analysis based on low orders of spin wave theory leads to systematic overestimates of exchange parameters, with corresponding errors in estimates of Hubbard t / U . Once these are corrected, the “standard” model provides a good account of magnon dispersion and lineshape in La 2 CuO 4 , but fails to fully capture the continuum observed at high energies. The extension of this analysis to CaCuO 2 and Sr 2 IrO 4 is also discussed.

DOI
10.1103/physrevresearch.7.l012053

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The usual starting point for understanding magnons in cuprate antiferromagnets such as La 2 CuO 4 is a spin model incorporating cyclic exchange, which descends from a one-band Hubbard model, and has parameters taken from fits based on non-interacting spin wave theory. Here we explore whether this provides a reliable description of experiment, using matrix product states (MPS) to calculate magnon spectra beyond spin wave theory. We find that analysis based on low orders of spin wave theory leads to systematic overestimates of exchange parameters, with corresponding errors in estimates of Hubbard t / U . Once these are corrected, the “standard” model provides a good account of magnon dispersion and lineshape in La 2 CuO 4 , but fails to fully capture the continuum observed at high energies. The extension of this analysis to CaCuO 2 and Sr 2 IrO 4 is also discussed.
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Altermagnets, a newly classified type of collinear magnet, exhibit zero magnetization, akin to antiferromagnets, but have spin-split electronic bands, akin to ferromagnets. Their low-energy excitations are predicted to be magnons, but with linear energy-momentum dispersion, typical of antiferromagnets, and additional chiral splitting analogous to those of electronic bands. However, such predictions are made using linear spin wave theory, which considers infinitely long-lived noninteracting magnons. This study employs nonperturbative quantum many-body calculations, via tensor network algorithms, to find how a chiral magnon will acquire finite lifetime and how the bands will shift due to magnon-magnon interaction. Such corrections to noninteracting magnon bands could be detected by Raman scattering experiments, for which the recipe is provided. Although the same interaction effects are often described in magnetism by nonlinearity of the Landau-Lifshitz-Gilbert equation, direct comparison using altermagnetic magnons as the testbed, shows how such classical methods cannot fully reproduce the results of quantum many-body calculations.
Self-energy corrections due to to fermion-magnon interaction are studied in the antiferromagnetic state of the $t\ensuremath{-}{t}^{\ensuremath{'}}\ensuremath{-}{t}^{\ensuremath{''}}$ Hubbard model within the noncrossing approximation in the full UUU range from weak to strong coupling. The role of classical (mean-field) features of fermion and magnon dispersion, associated with finite $U,{t}^{\ensuremath{'}},{t}^{\ensuremath{''}}$, are examined on quantum corrections to quasiparticle energy, weight, one-particle density of states, etc. A finite-UUU induced classical dispersion term, absent in the $t\ensuremath{-}J$ model, is found to play an important role in suppressing the quasiparticle weight for states near k=(0,0)\mathbf{k}=(0,0)k=(0,0), as seen in cuprates. For intermediate UUU, the renormalized antiferromagnetic (AF) band gap is found to be nearly half of the classical value, and the weak-coupling limit is quite nontrivial due to strongly suppressed magnon amplitude. For finite ${t}^{\ensuremath{'}}$, the renormalized AF band gap is shown to vanish at a critical interaction strength Uc{U}_{c}Uc​, yielding a spin fluctuation driven first-order AF insulator--paramagnetic metal transition. Quasiparticle dispersion evaluated with the same set of Hubbard model cuprate parameters, as obtained from a recent magnon spectrum fit, provides excellent agreement with angle-resolved photoemission spectroscopy data for Sr2CuO2Cl2{\mathrm{Sr}}_{2}\mathrm{Cu}{\mathrm{O}}_{2}{\mathrm{Cl}}_{2}Sr2​CuO2​Cl2​.
The first part of this thesis presents the theoretical study of an anomaly of unknown origin in the excitation spectrum of the Quantumspin-1/2 Heisenberg Square lattice Anti-Ferromagnet. The anomaly manifests itself in Inelastic Neutron Scattering data for short wavelength/high energy excitations. Instead of the expected sharp semi-classical harmonic modes, a broad continuum emerges suggesting the possibility of fractionalized excitations. A theoretical framework based on the Gutzwiller projection is developed and allows to link the observed continuum to unbound fractional quasiparticle pairs while the sharp harmonic excitations may be described by bound ones. The second part of this thesis presents the detailed theoretical modeling of the spin-wave dispersion relation measured in insulating cuprate materials. Starting from the one-band Hubbard model with extended hopping amplitudes, an effective low-energy theory is derived allowing to describe on the same footing different insulating cuprate magnetic excitation spectra. The effective theory is fitted against experimental data and microscopic model parameters are extracted. The high level of details included in our effective theory allows a consistent characterization of the studied materials as measured by various magnetic or electronic experimental techniques.
The spectral-weight distribution in recent neutron scattering experiments on the parent compound La2{}_{2}2​CuO4{}_{4}4​ (LCO), which are limited in energy range to about 450 meV, is studied in the framework of the Hubbard model on the square lattice with effective nearest-neighbor transfer integral ttt and on-site repulsion UUU. Our study combines a number of numerical and theoretical approaches, including, in addition to standard treatments, density matrix renormalization group calculations for Hubbard cylinders and a suitable spinon approach for the spin excitations. The latter spin-12\frac{1}{2}21​ spinons are the spins of the rotated electrons that singly occupy sites. These rotated electrons are mapped from the electrons by a uniquely defined unitary transformation, in which rotated-electron single and double occupancy are good quantum numbers for finite interaction values. Our results confirm that the U/8tU/8tU/8t magnitude suitable to LCO corresponds to intermediate UUU values smaller than the bandwidth 8t8t8t, which we estimate to be $8t\ensuremath{\approx}2.36$ eV for $U/8t\ensuremath{\approx}0.76$. This confirms the unsuitability of the conventional linear spin-wave theory. Our theoretical studies provide evidence for the occurrence of ground-state ddd-wave spinon pairing in the half-filled Hubbard model on the square lattice. This pairing applies only to the rotated-electron spin degrees of freedom, but it could play a role in a possible electron ddd-wave pairing formation upon hole doping. We find that the higher-energy spin spectral weight extends to about 566 meV and is located at and near the momentum $[\ensuremath{\pi},\ensuremath{\pi}]$. The continuum weight energy-integrated intensity vanishes or is extremely small at momentum $[\ensuremath{\pi},0]$. This behavior of this intensity is consistent with that of the spin waves observed in recent high-energy neutron scattering experiments, which are damped at the momentum $[\ensuremath{\pi},0]$. We suggest that future LCO neutron scattering experiments scan the energies between 450 and 566 meV and momenta around $[\ensuremath{\pi},\ensuremath{\pi}]$.
Spin waves (magnons) in two dimensions are the potential glue in high-temperature superconductors so that their quantitative understanding is mandatory. Yet even for the fundamental case of the undoped Heisenberg model on the square lattice a consistent picture is still lacking. Significant spectral continua are taken as evidence of the existence of fractional excitations (spinons), but descriptions in terms of spinons fail to show the established absence of an energy gap. Here a fully consistent picture of the dynamics in the square-lattice quantum antiferromagnet is provided which agrees with the experimental findings. The key step is to capture (i) the strong attractive interaction between the spin waves and (ii) the vertex corrections of the observables.