We determine the effective total spin J of local moments formed from acceptor states bound to Mn ions in GaAs by evaluating their magnetic Chern numbers. When individual Mn atoms are close to the sample surface, the total spin changes from J=1 to J=2, due to quenching of the acceptor orbital moment. For Mn pairs in bulk, the total J depends on pair orientation in the GaAs lattice and on the separation between the Mn atoms. We point out that Berry curvature variation as a function of local moment orientation can profoundly influence the quantum-spin dynamics of these magnetic entities.

We employ a kinetic-exchange tight-binding model to calculate the magnetic interaction and anisotropy energies of a pair of substitutional Mn atoms in GaAs as a function of their separation distance and direction. We find that the most energetically stable configuration is usually one in which the spins are ferromagnetically aligned along the vector connecting the Mn atoms. The ferromagnetic configuration is characterized by a splitting of the topmost unoccupied acceptor levels, which is visible in scanning tunneling microscope studies when the pair is close to the surface and is strongly dependent on pair orientation. The largest acceptor splittings occur when the Mn pair is oriented along the < 110 > symmetry direction and the smallest when they are oriented along < 100 >. We show explicitly that the acceptor splitting is not simply related to the effective exchange interaction between the Mn local moments. The exchange interaction constant is instead more directly related to the width of the distribution of all impurity levels-occupied and unoccupied. When the Mn pair is at the < 110 > GaAs surface, both acceptor splitting and effective exchange interaction are very small except for the smallest possible Mn separation.

Motivated by recent scanning tunnel microscopy (STM) experiments, we present a theoretical study of the electronic and magnetic properties of the Mn-induced acceptor level obtained by substituting a single Ga atom in the (110) surface layer of GaAs or in one of the atoms layers below the surface. We employ a kinetic-exchange tight-binding model in which the relaxation of the (110) surface is taken into account. The acceptor wave function is strongly anisotropic in space and its detailed features depend on the depth of the sublayer in which the Mn atom is located. The local-density-of-states (LDOS) on the (110) surface associated with the acceptor level is more sensitive to the direction of the Mn magnetic moment when the Mn atom is located further below the surface. We show that the total magnetic anisotropy energy of the system is due almost entirely to the dependence of the acceptor level energy on Mn spin orientation, and that this quantity is strongly dependent on the depth of the Mn atom.

By combining field-theoretical methods and ab initio calculations, we construct an effective Hamiltonian with a single giant-spin degree of freedom, which is capable of describing the low-energy spin dynamics of ferromagnetic metal nano-clusters consisting of up to a few tens of atoms. In our procedure, the magnetic moment direction of the Kohn–Sham spin density functional wave function is constrained by means of a penalty functional, which allows us to explore the entire parameter space of directions, and to extract the magnetic anisotropy energy and Berry curvature functionals. The average of the Berry curvature over all magnetization directions is a Chern number—a topological invariant that can only take on values equal to multiples of one-half, which represents the dimension of the Hilbert space of the effective spin system. The spin Hamiltonian is obtained by quantizing the classical anisotropy energy functional, after performing a change of variables to a constant Berry curvature space. The purpose of this paper is to examine the impact of the topological effect from the Berry curvature on the low-energy total-spin-system dynamics. To this end, we study small transition-metal clusters: Co_n (n=2,…,5), Rh₂, Ni₂, Pd₂, Mn_xN_y, and Co₃Fe₂.