Tunnel-diode Resonator Spectroscopy of Quantum Levels in Cr$_{12}$Ln$_{4}$ (Ln=Y,Eu,Gd,Tb,Dy,Ho,Yb) Magnetic Molecules

The differential magnetic susceptibility for a series of Cr$_{12}$Ln$_{4}$ (Ln=Y,Eu,Gd,Tb,Dy,Ho,Yb) magnetic molecules was measured in static (up to 16 T) and pulsed (up to 45 T) magnetic fields using a rf tunnel-diode resonator (TDR). At low temperatures, the behavior of these finite spin systems is governed by discrete energy spectra of the individual molecules. In magnetic field, low-energy quantum levels Zeeman-split, crossing at field values where magnetization exhibits a step corresponding to switching between different spin states. In high fields, we detect multiple level crossings which allow for a detailed mapping of the energy diagram. We then perform quantum Monte Carlo (QMC) using a Heisenberg Hamiltonian with three adjustable exchange constants whose values are chosen so as to optimize agreement with the experimental energy spectrum. The variations in results for the studied molecules are correlated to the magnetic properties of the lanthanide ions.