The spin-Hamiltonian parameters (the g factors g_{i} and the hyperfine structure constants A_{i}, i = x, y, z) and local structure of the Cu^{2+} center in PbTiO_{3} are theoretically studied by using the perturbation formulae of these parameters for a 3d^{9} ion in an orthorhombically elongated octahedra. The orthorhombic center is attributed to Cu^{2+} occupying the host Ti^{4+} site associated with a nearest-neighbouring oxygen vacancy V_{O} along the c-axis, and the impurity Cu^{2+} off-center displacement ΔZ_{L} ( ≈0.18 Å) is smaller than that of the host Ti^{4+} site (ΔZ_{H} ≈ 0.3 Å). Meanwhile, the planar Cu^{2+}-O^{2-} bonds are found to experience the relative variation ΔR ( ≈ 0.098 Å) along the a- and b-axes, respectively, due to the Jahn-Teller effect and the size mismatching substitution of Ti^{4+} by Cu^{2+}. The theoretical spin-Hamiltonian parameters based on the above defect structure agree well with the observed values.
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