High-temperature superconductivity in the 3d transition-metal compounds (TMCs), such as copper oxides and iron pnictides, and relativistic Mott insulating state in the 5d TMCs, such as iridium oxides, are among the most extensively studied phenomena in condensed matter physics and materials science. We now begin to explore the novel physics in mixed 3d-5d TMCs not present in the pure 3d or pure 5d ones. Its origin lies in the unusual exchange pathways opened by mixed spin-orbit coupling strengths. Such materials could naturally take the form of the double-perovskite-like structure AB1-xB'xO3 or the ABO3/A'B'O3 heterostructure epitaxy films where, for example, B=3d and B’=5d ions. In this talk, we shall use quasi-one-dimensional (1D) Sr3CuIrO6 and quasi-2D Sr2Ir1-x(Mn, Ru)xO4 to illustrate novel mechanisms of magnetic anisotropy and frustration in mixed 3d-5d systems [1-3]. Sr3CuIrO6 is known as a spin one-half chain ferromagnet exhibiting three unexpected phenomena: (i) large spin excitation gap, (ii) small saturation magnetic moment, and (iii) antiferromagnetic Curie-Weiss behavior of the high-temperature magnetic susceptibility despite ferromagnetic exchange interaction. We explain these puzzles using a first-principles derived effective Hamiltonian with alternating g-factors, namely g = 2 and –3 on the Cu and Ir ions, respectively. Furthermore, we found an exotic magnetic-field driven critical point at which one half of the spins are frozen into a complete order and the other half are fully disordered at zero temperature. The responses of this new state to external stimuli are also unique. In the case of Sr2Ir1-x (Mn, Ru)xO4, a doping-induced spin-flop transition from easy-plane to hard-plane is unveiled and explained. A novel compass-model spin frustration is anticipated to occur in the 3D double perovskite Sr2Ir(Mn, Ru)O6.

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