Magnon Breakdown in a Two Dimensional Triangular Lattice Heisenberg Antiferromagnet of Multiferroic ${\mathrm{LuMnO}}_3$

The breakdown of magnons, the quasiparticles of magnetic systems, has rarely been seen. By using an inelastic neutron scattering technique, we report the observation of spontaneous magnon decay in multiferroic ${\mathrm{LuMnO}}_3$, a simple two dimensional Heisenberg triangular lattice antiferromagnet, with large spin $S=2$. The origin of this rare phenomenon lies in the nonvanishing cubic interaction between magnons in the spin Hamiltonian arising from the noncollinear 120° spin structure. We observed all three key features of the nonlinear effects as theoretically predicted: a rotonlike minimum, a flat mode, and a linewidth broadening, in our inelastic neutron scattering measurements of single crystal ${\mathrm{LuMnO}}_3$. Our results show that quasiparticles in a system hitherto thought of as “classical” can indeed break down.

Figure 1

The structure of ${\mathrm{LuMnO}}_3$ showing the Mn-O plane (left), triangular lattice (right), the trimer units (light triangles), and exchange interactions considered in the spin Hamiltonian (thick lines).

Figure 2

Inelastic neutron scattering data along high symmetric directions: fitted peak positions from TAS data (filled circle), ToF data (open square and the contour map), and the fitted dispersion (solid curves) calculated by linear spin wave theory. The first Brillouin zone labels for the hexagonal unit cell (bottom text line) and triangular unit cell (line above) are also shown, together with a sketch of the triangular Brillouin zone (top right corner). The top panel shows the fitted FWHM of the 20 meV peaks from the ToF data, indicating broad peaks, possibly due to magnon decay, only near ($\frac{1}{2}\frac{1}{2}0$) and ($\frac{1}{2}00$).

Figure 3

Data (a) and linear spin wave theory calculated neutron structure factors convoluted with a 0.8 meV Gaussian (b),(d). (c) Cuts along the vertical lines in the dispersion curves at the $M$, ($\frac{1}{2}00$), (square and solid line) and $K$, ($\frac{1}{2}\overline{\frac{1}{2}}0$), (circle and dashed line) wave vectors and in between, at $Q=((5/12)\overline{\frac{1}{2}}0)$, (triangle and dashed dotted line).

Figure 4

Cuts near the roton minimum showing the three signatures of magnon decay. (a),(b) The minimum in the dispersion of the lowest energy mode at ($\frac{1}{2}\frac{1}{2}0$), the flat dispersion of the higher energy mode at the same point, indicated by the arrows in (a) and (b), and the anomalously broad width of the $\approx 20\mathrm{meV}$ mode in the cuts in (c). In (a) and (b), points (filled circle) indicate the fitted peak positions from energy cuts through the data. In (c), solid lines at the bottom directly below the peak centers indicate the instrumental resolution width. Thin dashed lines indicate individual fitted Voigt peaks, while the solid line is their sum, and points are measured data. The very broad peak at $\approx 32\mathrm{meV}$ in (c) is attributed to two-magnon scattering. (d) The two-magnon density of states calculated using linear spin wave theory from the single-magnon dispersion (solid lines).