Zero-field magnetic resonance of cobalt ion pairs in ZnO nanocrystals

Abstract

Cobalt-doped ZnO nanoparticles (NPs) with different Co concentrations are investigated by means of $X$- and $Q$-band electron spin resonance (ESR) near liquid-helium temperature in both parallel and perpendicular modes. The high crystal quality of the NPs allows for the hyperfine-structure resolution within the single ${\mathrm{Co}}^{2+}$ ions' ESR powder spectra. Depending on cobalt concentration, common additional weak ESR lines are detected which are here demonstrated to arise from some ${\mathrm{Co}}^{2+}$ high-spin pairs with a distance of about 4--6 \AA{}. ESR simulations show that these 3/2 spin pairs are weakly coupled by an isotropic Heisenberg Hamiltonian with either ferromagnetic or antiferromagnetic $J$ coupling constants, almost identical to those previously detected in bulk and microwire ZnO:Co. The presence of substantial (axial) single-ion anisotropy in ZnO:Co makes the different pairs' resonance positions strongly depending on the $J$ value. For resonance frequency $\ensuremath{\nu}$ in the microwave range, four cobalt pairs can satisfy the condition $|J|\ensuremath{\sim}h\ensuremath{\nu}/3$ to resonate at almost zero magnetic field. Such near-zero-field transitions notably resonate in the parallel ESR mode, which is the signature of the gapped nonlinear Zeeman effect, which is of particular interest for highly stable atomic-clock transitions.