Single-Q and Double-Q magnetic orders: A Theoretical Analysis of Inelastic Neutron Scattering in a Centrosymmetric Structure

TL;DR

This work analyzes how multi-Q magnetic order manifests in centrosymmetric 2D magnets via inelastic neutron scattering. Using a square-lattice $J_1$-$J_2$-$J_3$ Heisenberg model with anisotropic exchanges, the authors map a phase diagram including Spiral I, Spiral II, Helix, and unequal Double-Q states, and compute both static structure factors and dynamical response. Employing Holstein–Primakoff and Bogoliubov transformations, they predict Goldstone modes at the ordering wavevectors and a roton-like feature in the dynamical structure factor, with distinctive signatures that can distinguish multi-Q states from multi-domain single-Q configurations. Comparison with low-energy INS data on Sr$_3$Fe$_2$O$_7$ shows qualitative agreement, and the authors advocate higher-energy measurements to test the predicted roton features, corroborating related results by Mostovoy and colleagues. These findings provide concrete, testable INS signatures for complex multi-Q magnetism in centrosymmetric materials.

Abstract

Recent discoveries of multi-\textbf{Q} magnetic structures in centrosymmetric compounds have stimulated growing interest in their microscopic origin and observable properties. Here, we calculate the dynamical magnetic structure factor for a double-\textbf{Q} magnetic structure and compare it with that of a single-\textbf{Q} configuration.

Figures (4)

• Figure 1: Ground state of the isotropic $J_1\!-\!J_2\!-\!J_3$ Heisenberg model of a classical spin system. The states an b described as helices with the corresponding propagation vectors $\mathbf{Q}$. Parameters: $J_2 =1$.
• Figure 2: Ground state of the anisotropic Heisenberg model. The diagram reveals several magnetic phases: Spiral I --- a spiral phase with spin rotation in XY plane, Spiral II --- a spiral phase with magnetic rotating plane prependicular to $(1,-1)$, Helix --- a "proper screw" rotation perpendicular to $(1,1)$ and Double-Q configurations.
• Figure 3: Spin structures (a-c). The in-plane components $S^x$ and $S^y$ are depicted as arrows and the out-of-plane component $S^z$ is presented by color: a) Spiral I, b) Helix, c) Double-Q, (d-f) corresponding magnetic structure factors. Parameters for the Double-Q state: $J_1 = -7.2$, $J_2 = 1.05$, $J_3 = 2.1$, $\Delta_2 = -0.36$, and $\delta_1 = 0.072$. Parameters for the Spiral and Helix states: $J_1 = -2J_2\cos\theta - 4J_3\cos\theta$, $J_2 = 1.05$, $J_3 = 2.1$, $\Delta_{1,2,3} = 0$, $\delta_{1,2,3} = 0$.
• Figure 4: Contour maps of calculated intensities of inelastic neutron scattering $\text{I}(\textbf{q},\omega)$: a) Spiral I, b) Helix, c) Double-Q.