Spin dynamics of the spin-1 triangular lattice Heisenberg antiferromagnet K$_2$Ni(SeO$_3$)$_2$

Abstract

Strong quantum fluctuations and unconventional spin dynamics are well established in the spin-1/2 triangular lattice Heisenberg antiferromagnet. However, their survival in the spin-1 case remains an open question. We investigate the spin dynamics of K$_2$Ni(SeO$_3$)$_2$, a nearly ideal spin-1 triangular lattice Heisenberg antiferromagnet, using inelastic neutron scattering. Below the ordering temperature $T_{\rm N}$, we observe coherent one-magnon excitations coexisting with a broad high-energy continuum. Two complementary approaches, a spectrally consistent $1/S$-corrected spin wave theory and a beyond-mean-field Schwinger boson theory, reproduce different facets of the continuum. Neither alone is complete, demonstrating substantial quantum fluctuations survive for $S\!=\!1$ and are reflected primarily in the spectral distribution of the continuum. Above $T_{\rm N}$, the continuum bandwidth is conserved while spectral weight is redistributed as magnons lose spatial coherence. Our results establish K$_2$Ni(SeO$_3$)$_2$ as a model triangular antiferromagnet, identifying bandwidth conservation and the distribution of spectral weight within the continuum as organizing principles to understand the spin dynamics of ordered quantum magnets beyond spin-1/2. Our results highlight the need for controlled calculations of the interacting multi-magnon sector of 2D antiferromagnets.

Figures (13)

• Figure 1: (a) Proposed theoretical treatment of 1-magnon and 2-magnon excitations in TLHAFs as a function of spin-$S$. (b) Crystal structure of $\mathrm{K_2Ni(SeO_3)_2}$, showing the layered triangular network of NiO$_6$ octahedrons with Ni$^{2+}$ ions connected by SeO$_3$ tetrahedrons. (c) The left panel shows momentum ($\bf Q$) and energy ($E$) transfer dependence of the inelastic neutron scattering intensity $I({\bf Q},E)$ measured at $T=2$ K along high-symmetry directions in the triangular-lattice Brillouin zone ${\bf Q} = (H,K,0)$ with out-of-plane integration $\Delta L= [-2, 2]$ r.l.u and $\Delta{\bf Q}_\perp =0.05$ Å$^{-1}$. The right panel is the corresponding neutron scattering intensity calculated using spectrally-consistent $1/S^\ast$-SWT for optimized exchange parameters, convolved with an $E$-dependent Gaussian profile to match the dominant energy-resolution effects of the time-of-flight spectrometer. The faint vertical strike around the K point is a spurious signal from the off-shell calculation. (d) Comparison between the single-magnon dispersion at ${\bf Q}$ and its branches at ${\bf Q} \pm {\bf Q}_{\rm m}$ umklapp-shifted by the propagation vector ${\bf Q}_{\rm m}$ of the underlying 120$^\circ$ magnetic order, together with the calculated two-magnon density of states. (e) Goodness-of-fit landscape obtained from a global least-squares fit of the $1/S^\ast$-SWT calculations to the data, for a two parameter model with nearest-neighbor antiferromagnetic exchange $J$ and easy-plane exchange anisotropy $\Delta$; the star marks the optimal parameter set used throughout this work. (f) Constant-$E$ slices of the scattering intensity in the $(H,K,0)$ plane for several energy windows from $1/S^\ast$-SWT (right panels) and experimental data (left panels) same $L$-integration as (c). The intensity of the last panel in (f) is scaled by a factor two.
• Figure 2: (a) Comparison between the $I({\bf Q},E)$ from Fig. \ref{['fig:1']} and the corresponding $I_{\rm SBT}({\bf Q},E)$ from beyond-mean-field Schwinger boson theory (BMF-SBT) calculation. Vertical white dashed lines mark the momentum positions of the cuts presented in panels (c)–(e). (b) Momentum-dependent intensity profiles obtained by integrating the scattering intensity over the indicated energy windows. Experimental data (symbols) are compared with calculations from $1/S^\ast$-SWT (magneta lines) and BMF-SBT (blue lines). (c)–(e) Constant-momentum cuts as indicated in each panel. Open symbols represent the experimental data, and solid lines show the corresponding $1/S^\ast$-SWT and BMF-SBT calculations. The gray shaded regions are dominated by elastic and background contributions from the experiments. The red arrows mark the energy range where anomalous spectral weight is observed.
• Figure 3: (a-b) Inelastic neutron scattering data for $E_i = 8$ meV at $T\!=\!2\ \mathrm{K}<\!T_{\rm N}$ and $T\!=\!11.5\ \mathrm{K}\!>\!T_{\rm N}$, respectively. (c-d) Corresponding QLLD calculation at the temperature scaled by the exchange interaction $J$. (e-f) The constant-energy cut with integration along the energy $E\!=\![1.0, 4.8]$ meV. Red dots are integrated neutron scattering data, and blue lines are integrated LLD simulations.
• Figure S1: Powder X-ray diffraction data with best-fit structural Rietveld refinements for K$_2$Ni(SeO$_3$)$_2$ at (a) $T=12$ K and (b) $T=299$ K. Nuclear peak positions are indicated by green vertical tick marks, best fit refinements are indicated by the solid red line, data is indicated by the colored circles, and the difference between the data and the best fit is indicated by the dashed blue line at the bottom of the panel. (c) Waterfall plot of all the data collected between $T=12$ K and $T=299$ K, showing no apparent structural phase transition.
• Figure S2: (a) Overview of specific heat $C(T)/T$ data for K$_2$Ni(SeO$_3$)$_2$ taken up to 300 K at 0 and 14 T applied along different directions of the crystal. The solid line is the 0 T fit to the lattice contributions (b) Overview of isothermal magnetization $M(H)$ data with the external field being applied both in the plane of the crystal (red dashed line), and out of the plane (solid blue line).