Single molecule magnets (SMMs) are molecules possessing large magnetic moments due to coupling between the electron spins of transition metal ions. When SMMs are deposited onto a metal surface they tend to undergo uncontrolled structural deformations, which weakens the interactions between transition metal ions and reduces the magnetic moment. This is one reason why SMMs are yet to be used in real applications. We have been exploring the effect of structural deformations on the magnetic properties of SMMs using stochastic models. In the first part of this presentation, a Heisenberg-type model with randomly fluctuating exchange couplings between transition metal ions will be discussed. Analysis of this model predicts that SMMs containing 20 - 50 transition metal ions arranged in a small number of ring-type configurations possess -weak topological invariant- magnetic moments. This means that the magnetic moments only depend upon how the transition metals in the molecule are arranged, and are very insensitive to deformations in the shape of the molecule (Proc. Roy. Soc. A. 469, 2013, 20130373). The second part of this presentation will introduce the stochastic Boltzmann equation approach to studying magnetic relaxation in SMMs. This equation gives the time-evolution of the probability density of the density matrix for the spin state of the molecule, and assumes that the vibrational modes undergo a stochastic frequency modulation due to coupling with the environment. A trajectory simulation method for solving the stochastic Boltzmann equation under a new -relaxation time approximation- will be outlined, and a calculation for the important case of the Mn12O12(O2CCH3)16 molecule will be presented. It will be shown that the stochastic Boltzmann equation is an efficient method for studying the competition between thermal relaxation and spin tunneling in the magnetic relaxation of SMMs under a variety of parameter regimes.
This is joint work with Kelley T. Reaves (Lynntech, formerly Texas A&M University and Advanced Institute for Materials Research, Tohoku University, Japan), Filippo F. Federici (Helsinki University), Ikutaro Hamada (National Institute for Materials Research, Japan), Helmut G. Katzgraber (Texas A&M University and Santa Fe Institute), and Winfried Teizer (Texas A&M University and Advanced Institute for Materials Research, Tohoku University, Japan).