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FeF3, with its half-filled Fe3+ 3d orbital, hence zero orbital angular momentum and S = 5/2, is often put forward as a prototypical highly frustrated classical Heisenberg pyrochlore antiferromagnet. By employing ab initio density functional theory, we obtain an effective spin Hamiltonian for this material. This Hamiltonian contains nearest-neighbor antiferromagnetic Heisenberg, biquadratic, and Dzyaloshinskii-Moriya interactions as dominant terms and we use Monte Carlo simulations to investigate the nonzero temperature properties of this minimal model. We find that upon decreasing temperature, the system passes through a Coulomb phase, composed of short-range correlated coplanar states, before transforming into an "all-in/all-out" (AIAO) state via a very weakly first-order transition at a critical temperature Tc ≈ 22 K, in good agreement with the experimental value for a reasonable set of Coulomb interaction U and Hund's coupling JH describing the material. Despite the transition being first order, the AIAO order parameter evolves below Tc with a power-law behavior characterized by a pseudo "critical exponent" β ≈ 0.18 in accord with experiment. We comment on the origin of this unusual β value. [ABSTRACT FROM AUTHOR]

First-principles calculations are performed to investigate f magnetism in A 2 Ti 2 O 7 (A=Eu, Gd, Tb, Dy, Ho, Er, Yb) magnetic pyrochlore oxides. The Hubbard U parameter and the relativistic spin orbit correction are applied for a more accurate description of the electronic structure of the systems. It is argued that the main obstacle for the first-principles study of these systems is the multi-minima solutions of their electronic configuration. Among the studied pyrochlores, Gd 2 Ti 2 O 7 shows the least multi-minima problem. The crystal electric field theory is applied for phenomenological comparison of the calculated spin and orbital moments with the experimental data. [ABSTRACT FROM AUTHOR]