We construct effective magnetic Hamiltonians by using the first-principles electronic-structure calculations. These Hamiltonians are used to determine the ground state of solids and nanostructures, and, at T > O, using the methods of- statistical mechanics, also their magnetic properties as a function of temperature. The present approach is highly flexible and it makes possible to find magnetic structure of complex systems with the accuracy of ab initio methods. As illustrations we show (i) how the magnetic structure at T = 0 and at T ? 0 can be determined for systems with anisotropic exchange and for systems with several sublattices, (ii) why the magnetic moment in fcc-nickel is unstable upon reversal, and (iii) how to calculate the size of magnetic moment in fcc-Ni at the Curie temperature, which is important for explanation of the spin-disorder resistivity in Ni.
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