\(\mu ^+\)SR Study on ferromagnetism of Na-K alloy clusters in zeolite low-silica X

Na-K alloy clusters can be formed by loading guest K atoms into the cages of zeolite low-silica X (LSX), which contains both Na \(^+\) ${}^{+}$ and K \(^+\) ${}^{+}$ ions. Ferromagnetism is known to occur in the insulator phase when the host LSX is relatively Na-rich. In this work, the magnetic properties of this material are studied using positive muon spin rotation/relaxation ( \(\mu ^+\) ${\mu }^{+}$ SR) technique. The zero-field \(\mu ^+\) ${\mu }^{+}$ SR spectra show a significant increase in the relaxation rate below the Curie temperature of about 10 K. The longitudinal field \(\mu ^+\) ${\mu }^{+}$ SR spectra at 1.9 K show the decoupling behavior of a static local magnetic field with a broad distribution from a few to several tens of gauss. The magnetic volume fraction is estimated to be higher than 72% from the relaxation amplitude. Thus, the ferromagnetism of this material is intrinsic and not due to impurities. The broad distribution of the local field can be explained by a magnetic model in which not all \(\beta \) $\beta$ -cages of LSX are occupied by the localized moment of the clusters.