Antiferromagnetic ordering of magnetic moments due to cavity trapped electrons in sodium electrosodalite: A zero-fieldμSRstudy

Abstract

The long-range magnetic ordering of ${\mathrm{Na}}_{4}^{3+}$ clusters with spin $S=1/2$ on a body-centered-cubic lattice in sodium electrosodalite has been studied in zero applied magnetic field by positive muons as local magnetic probes. An experimental determination of the temperature dependence of the magnetic order parameter of an s-electron antiferromagnet is presented. The order parameter is measured via the local magnetic field at the muon site ${(B}_{\mathrm{loc}}).$ The temperature dependence ${B}_{\mathrm{loc}}(T)$ exhibits critical behavior near the N\'eel temperature ${T}_{\mathrm{N}}=(50.3\ifmmode\pm\else\textpm\fi{}0.2)\mathrm{K}.$ The critical exponent $\ensuremath{\beta}=(0.36\ifmmode\pm\else\textpm\fi{}0.1)$ is close to the predicted value for a three-dimensional Heisenberg system. The precession signal is ascribed to muons in a diamagnetic state. A fraction of muons not contributing to the precession signal below ${T}_{\mathrm{N}}$ is ascribed partly to muons in domains which are not magnetically ordered and partly to muons forming a bound state with an unpaired electron.