Ferromagnetism induced by strains in Pd nanoparticles

The origin of the ferromagnetism that appears in the core region of Pd nanoparticles is discussed. According to many previous theoretical calculations, the onset of this ferromagnetism is closely related to the crystal structure and defects. In order to consider the contribution of crystal structure to the appearance of ferromagnetism in the Pd nanoparticles, we performed x-ray diffraction experiments and Warren-Averbach analysis. The results revealed that the standard deviation of strain $\ensuremath{\Delta}\ensuremath{\epsilon}$ showed a positive correlation with the saturation magnetization, with the ferromagnetism appearing when $\ensuremath{\Delta}\ensuremath{\epsilon}$ became larger than about 0.5%. This suggests that the strains induce internal ferromagnetism in the Pd nanoparticle. Compared to the critical magnitude of the strain at which ferromagnetism is predicted by the theoretical calculations, however, the estimated $\ensuremath{\Delta}\ensuremath{\epsilon}$ is too small to explain the origin of ferromagnetism. Therefore, the strains smaller than the theoretical predictions should also give rise to the ferromagnetism or the strains should contribute to the magnetism not only through lattice expansion but also through changes in the crystal symmetry.