Polarized neutron studies of forbidden magnons in the two-dimensional ferromagnetK2CuF4

Polarized inelastic neutron scattering has been used to study the spin dynamics of the quasi-two-dimensional nonmetallic Heisenberg ferromagnet ${\mathrm{K}}_2$ ${\mathrm{CuF}}_4$ in weak magnetic fields at temperature in the vicinity of $T_c$. We have observed underdamped allowed and ‘‘forbidden’’ excitations in constant-Q scans for two different applied magnetic fields over the temperature range from 0.9$T_C$ to 2.9$T_C$. A frequency difference between the allowed magnon and its forbidden counterpart (with the allowed magnon being slightly higher) was also observed. The difference between the allowed and forbidden magnon integrated intensities was found to be directly proportional to the overall magnetization for the two different fields applied. The observations are in agreement with the slowly fluctuating spin-density theory of itinerant ferromagnetism. Surprisingly, the reduction in magnon frequency with increasing temperature follows a $T^{5/2}$ over a wide temperature range. Such dependence is much like that which occurs at low temperatures.