In this thesis, magnetic and critical properties of 3d pyrochlores such as FeF 3 , Y 2 Mn 2 O 7 and NaCaNi 2 F 7 are investigated. For each of these materials, spin Hamiltonian has obtained through ab initio calculations in the framework of Density Functional Theory. Using this Hamiltonian, the critical and Curie-Weiss temperature, as well as magnetic order, are investigated by Monte Carlo simulations. We obtain spin Hamiltonian of FeF3 under the relative volume change with respect to the experimental volume ( ) from -0.2 to 0.2. We show that the spin system undergoes a weakly first-order transition to AIAO at small volumes that turn to a second-order transition close to the experimental structure. However, increasing to ~ 0.2, system shows a transition to a modular spin structure. In the following, we have investigated Y 2 Mn 2 O 7 magnetic properties. There is a discrepancy between the experimental results for the magnetic ground state of Y 2 Mn 2 O 7 . We resolve this issue by employing density functional theory calculations and Monte Carlo simulations. We derive different spin models by varying the Hubbard parameter in ab initio GGA+ U calculations. By comparing Monte Carlo simulations of these models with the experiments, we find a ferromagnetic ground state for Y 2 Mn 2 O 7 as the most compatible with experiments. We also consider Y 2 Mo 2 O 7 as a prototype of the defect-free pyrochlore system with spin-glass behavior and compare it with Y 2 Mn 2 O 7 . Our GGA+ U calculations reveal d orbital degrees of freedom for Y 2 Mo 2 O 7 and a fixed orbital orientation in Y 2 Mn 2 O 7 . Finally, the ground state magnetic properties of NaCaNi 2 F 7 pyrochlore has been determined. It is found that different Na-Ca distributions can change magnetic symmetry of Ni ions in such a way that there are different exchange parameters for each Na-Ca distributions. Dzyaloshinskii-Moriya coupling constant is indirect which means that the ground state has global degeneracy. We have shown that the elastic neutron scattering has different patterns at low temperatures which indicate the ground state is spin-glass.
