Raman scattering studies of the temperature- and magnetic field-dependent studies of the single molecule magnet Mn$_{12}$-acetate*

Single molecule magnets (SMMs) have attracted much interest since they were first reported in 1991. SMMs are a class of metal-organic compounds that show superparamagnetic behavior below a certain blocking temperature at the molecular scale. We present a study of the temperature- and magnetic-field-dependence of the single molecule magnet Mn$_{12}$-acetate using Raman scattering. Temperature-dependent measurements show an anomalous phonon behavior near 200K, indicating a lower crystal symmetry than tetragonal and supporting the inclusion of a second-order rhombic term $E(S^2_x - S^2_y)$ in the Hamiltonian, consistent with previous neutron and X-ray studies. Our field-dependent measurements near 3K show that a magnetic field oriented perpendicular to the Mn$_{12}$ magnetization direction does not affect the phonon vibrational energies. However, when the magnetic field is oriented along the easy-axis direction, there is a clear phonon mode splitting at 540 cm$^{-1}$, indicating a strong spin-phonon coupling associated with this phonon mode and the existence of a fourth-order anisotropy term in the Hamiltonian for Mn$_{12}$ acetate. The field-induced nonzero local transverse term may be responsible for a small tilt of the anisotropy axis and the odd resonance tunneling.