Anisotropy of the molecular magnet V$_{15}$ spin Hamiltonian detected by high-field electron spin resonance

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.