  The molecular compound K$_6$[V$^{IV}_{15}$As$^{III}_6$O$_{42}$(H$_2$O)]
$\cdot$ 8H$_2$O, in short V$_{15}$, has shown important quantum effects such as
coherent spin oscillations. The details of the spin quantum dynamics depend on
the exact form of the spin Hamiltonian. In this study, we present a precise
analysis of the intramolecular interactions in V$_{15}$. To that purpose, we
performed high-field electron spin resonance measurements at 120 GHz and
extracted the resonance fields as a function of crystal orientation and
temperature. The data are compared against simulations using exact
diagonalization to obtain the parameters of the molecular spin Hamiltonian.

Mesoscale and Nanoscale Physics;Materials Science;Quantum Physics