Scouting the Magnetic Frontier

Past literature has shown, using Monte-Carlo simulations and the Thomas-Reich-Khun sum rules, that there are fundamental upper-bounds to the physically allowed electric nonlinear susceptibilities and other figures of merit pertaining to applications of nonlinear electric response. Those techniques are generalized in this research from one-dimensional electric systems to three-dimensional magnetic systems. The space of first magnetic hyperpolarizabilities is analyzed to determine if a fundamental upper-bound exists. The crux of the problem is to resolve a dipole free sum over states expression for the magnetic hyperpolarizability, which is critical for the validity of the Monte-Carlo approach. The dipole free sum over states expression is verified using exactly solved three-dimensional quantum potentials. Techniques for extrapolating a physical upper bound for the landscape of first magnetic hyperpolarizabilities are discussed.