Magnetization of 3He layers in ferromagnetic regime: Cluster size effects

Abstract

Abstract Magnetization of pure 3He monolayers on graphite and solid 3He on 4He-preplated graphite in the ferromagnetic regime is investigated theoretically within a two-dimensional spin-1/2 Heisenberg model in an external magnetic field. We develop an analytical approach based on a second-order two-time Green function formalism which describes the thermodynamic functions for finite as well as for infinite spin systems in the whole temperature range at arbitrary fields h. In particular, the present theory provides a proper description of the magnetization in the intermediate temperature region h T J at h well below the exchange J, that is in the region where the measurements for solid 3He monolayers are usually made. It is known from the experiment that only a part of 3He atoms is involved into ferromagnetic exchange. The ferromagnetic spins form clusters whose size is a function of coverage. The coverage dependences of the exchange constant, saturation magnetization, and average cluster size are found and analyzed. Nonmonotonic variation of the exchange constant with coverage is discussed. The effect of the cluster size on the temperature dependence of the magnetization is studied. To clarify how the cluster shape and boundary conditions affect magnetic properties of nanoclusters we calculate numerically the magnetization of small magnetic systems using the exact diagonalization method.