Bond-dependent interactions and ill-ordered state in the honeycomb cobaltate BaCo$_2$(AsO$_4$)$_2$

Abstract

The ground state and Hamiltonian of the honeycomb lattice material BaCo$_{2}$(AsO$_{4}$)$_{2}$ hosting magnetic Co$^{2+}$, have been debated for decades. The recent proposal for anisotropic bond-dependent interactions in such honeycomb cobaltates has raised the prospect of revisiting its Hamiltonian in the context of Kitaev physics. To test this hypothesis, we have combined magnetization, ac-susceptibility and neutron scattering measurements on a BaCo$_{2}$(AsO$_{4}$)$_{2}$ single-crystal, together with advanced modeling. Our experimental results highlight a collinear magnetic ground state with intrinsic disorder associated to an average incommensurate propagation vector. Monte Carlo simulations and linear spin wave calculations were performed to obtain a spin model compatible with this unusual ground state, the dispersion of magnetic excitations and a magnetization plateau under magnetic field. We thus show that bond-dependent anisotropic interactions, including Kitaev-like interactions, are necessary to account for the puzzling properties of this long-explored material, and are hence a general ingredient in the cobaltates.

Figures (3)

• Figure 1: (a) Honeycomb plane in BCAO, with the proposed $uudd$ ordered sequence as the basing block of the magnetic structure. The considered Heisenberg exchange interactions are displayed in black. The red, green and blue lines refer to the $x$, $y$, and $z$ bonds respectively, for the anisotropic interactions defined in the local $xyz$ orthogonal frame. (b) Imaginary part of the ac susceptibility $\chi"$ plotted as a function of temperature for various frequencies with $H_{\rm ac}=3.3$ Oe. The inset displays the relaxation times $\tau$ associated to the low and high temperature $\chi"$ peaks (in blue and orange respectively) as a function of inverse temperature. The lines represent fits to Arrhenius laws. (c) Magnetization curves as a function of decreasing magnetic field, measured at T = 1.2 K, 500 mK and 145 mK. Inset : Hysteresis observed at 145 mK while for increasing and decreasing field. Measurements in (b) and (c) were performed with the field applied along ${\bf b}$.
• Figure 2: (a) Magnetic excitation dispersion in the (H 0 4.67$\pm$0.1) direction from neutron inelastic scattering measurements performed on CAMEA at T = 1.5 K. (b) Comparison with S(Q,$\omega$) calculated from Monte Carlo simulations, using the model given in table \ref{['tab:param']}. (c-d) Constant-Q energy scans measured on IN20 at different temperatures, revealing higher energy magnetic excitations. (e) Energy scan measured at the Brillouin zone boundary on IN12 showing several magnetic modes fitted by Lorentz functions. The orange dots in panels (a-b) result from such fits.
• Figure 3: Monte-Carlo simulations using the model given in Table \ref{['tab:param']}: (a) spin structure where the colors represent different orientations of the spins, which are antiparallel within each three 120$^{\circ}$-domains. The inset illustrates the defective $uudd$ pattern for one domain and the flipping of a chain defect. (b-c) Magnetic phase diagrams calculated as a function of $J_{2}$ and $J_{3}$ (b) and $K$ versus $\Gamma'$ at fixed $\Gamma/J_{1}$ = -0.27 (c) using the Luttinger-Tisza method. The colors encode the ground state propagation vector component $k_x$. The interactions corresponding to the best model (see Table \ref{['tab:param']}) are indicated by the black stars. (d) Calculated magnetization curve as a function of magnetic field applied along b with a sketch of the spin arrangements of the different phases.