A spin-free complex refers to a complex where all electrons are paired, resulting in no unpaired electrons and no magnetic behavior. Among the given metal ions, Cu\(^{2+}\) has a 3d\(^{9}\) electron configuration in its high-spin state, which can be arranged in a way that results in no unpaired electrons in its complex, making it spin-free.
Thus, the correct answer is Cu\(^{2+}\).