Spin Dynamics and Spin-flop transition in Magnetoelectric Effect LiMnPO$_{4}$

Neutron scattering techniques were used to study~the magnetic phase transition and spin dynamics in single crystal~LiMnPO$_{4}$ both with and without magnetic field.~~Elastic scattering confirmed that~LiMnPO$_{4}$ has a collinear antiferromagnetic ground state with~moments along $a$-axis in zero-field. The temperature dependent~order parameter, calculated from the integrated intensity of the (010)~magnetic reflection, was fit to a power law equation, yielding a~transition temperature $T_{N}$ = 33.8 K. By applying magnetic field along the a-axis, the moments rotate from a-axis to the c-axis at a critical field of 3.5 Tesla at 5 K.~ The field dependent (100) and (001) intensities indicate a complicated intermediate state between the ground state and the spin-flop state. The critical field increased from 3.5 Tesla at 5 K to 4.5 Tesla near the transition $T_{N}$. Spin-wave dispersion curves along the three principal axes were measured in the antiferromagnetic state at 4.5 K in zero magnetic field and were analyzed using a 3D Heisenberg~model.