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We analyze the possibility of the nanoscale phase separation manifesting itself in the formation of ferromagnetic (FM) polarons (FM droplets) in the general situation of doped anisotropic three- and two-dimensional antiferromagnets. In these cases, we calculate the shape of the most energetically favorable droplets. We show that the binding energy and the volume of a FM droplet in the three-dimensional (3D) case depend only upon two universal parameters J = (Jₓ + Jᵧ + Jᵦ) S² and t₄₅₅ = (tₓtᵧtᵦ) ^1/3, where J and t₄₅₅ are effective antiferromagnetic (AFM) exchange and hopping integrals, respectively. In the two-dimensional (2D) case, these parameters have the form J = (Jₓ + Jᵧ) S² and t₄₅₅ = (tₓtᵧ) ^1/2. The most favorable shape of a ferromagnetic droplet corresponds to an ellipse in the 2D case and to an ellipsoid in the 3D case.
Kagan et al. (Fri,) studied this question.