Evidence of 3$d$-4$f$ antiferromagnetic coupling in strain-tuned PrCo$_{0.5}$Ni$_{0.5}$O$_{3-\delta}$ epitaxial films

The strong exchange interaction between 3$d$-4$f$ magnetic sublattice in rare-earth perovskites introduces a variety of complex magnetic states hosting fascinating electronic ground states with exotic properties. Especially when it comes to rare-earth nickelate and cobaltite perovskites, tuning their rich magnetic phase diagram and spin-state transitions make them potential candidates for spintronic applications. Here, we report the observation of antiferromagnetic coupling between Pr 4$f$ and Ni/Co 3$d$ magnetic sublattices and its tunability with strain in PrCo$_{0.5}$Ni$_{0.5}$O$_{3-\delta}$ (PCNO) thin films. SQUID magnetization measurements reveal ferromagnetic (FM) ordering around 25 K, followed by a spin glass transition at low temperatures subject to spin reorientation. Competing magnetic interactions arise owing to the 3$d$-4$f$ antiferromagnetic (AFM) coupling between Pr and Co/Ni sublattice as revealed by the X-ray absorption spectroscopy (XAS) and X-ray magnetic circular dichroism (XMCD) at the Pr $M_{4,5}$ and Co/Ni $L_{2,3}$ absorption edges. Strain dependence on these AFM coupling reveals an increase (decrease) in the AFM exchange interaction for tensile (compressive) strained films, leading to a net decrease (increase) in the magnetization of PCNO films at low temperatures. The relative increase in low-temperature negative magnetoresistance for compressively strained films also reflects the enhanced ferromagnetic ordering in the system. The angle-dependent magnetoresistance measurements reveal a two-fold anisotropic magnetoresistance (AMR) in tensile strained PCNO films. In contrast, temperature-dependent switching of AMR accompanied by a two- to four-fold symmetry crossover is observed for LaAlO$_3$-grown compressive strained films.