CaMn$_2$Sb$_2$: Spin Waves Near a Tricritical Point of the Antiferromagnetic Honeycomb Lattice*

The classical Heisenberg model for a honeycomb lattice of spins predicts at least three tricritical points, where three different long range ordered magnetic phases co-exist, depending on the relative strength of the nearest and next-nearest exchange interactions J$_{1,2}$. We performed inelastic neutron scattering at T = 5 K << T$_N$ = 85 K on oriented single crystals of the antiferromagnetic insulator CaMn$_2$Sb$_2$, where the Mn spins $\mu$ = 2.8 $\mu$$_B$/Mn form a corrugated honeycomb lattice. Spin wave excitations were observed up to E $\approx$ 24 meV and these data were fit to the spin wave dispersion expected from the classical Heisenberg model to determine the individual exchange interactions SJ$_{1}$ = 8.22 $\pm$ 0.23 meV, SJ$_{2}$ = 1.29 $\pm$ 0.09 meV, SJ$_{c}$ = -0.56 $\pm$ 0.04 meV, where J$_c$ is the exchange interaction between honeycomb planes. The quantum fluctuations resulting from proximity to the tricritical point at J$_2$/J$_1$ = 1/6 are responsible for the relatively low ordering temperature of CaMn$_2$Sb$_2, $T$_N$ = 85 K, much reduced from the mean field ordering temperature T$_{MFT}$ = 2zJ$_1$S(S+1)/3k$_B$ = 560 K.