Crystal-Field Origin of the Giant Magnetocrystalline Anisotropy of PrRu$\text{}_{2}$Si$\text{}_{2}$

PrRu$\text{}_{2}$Si$\text{}_{2}$ shows ferromagnetism below 14 K with the ordered moment of 2.7μ$\text{}_{B}$. It exhibits an enormous magnetic anisotropy at 4.2 K with the anisotropy field of about 400 T. We have attrributed the magnetism of PrRu$\text{}_{2}$Si$\text{}_{2}$ to the Pr$\text{}^{3+}$ ions. Thus we performed calculations of the fine electronic structure of the Pr$\text{}^{3+}$ ion in the tetragonal symmetry, relevant to PrRu$\text{}_{2}$Si$\text{}_{2}$, taking into account crystal-field and inter-site exchange interactions. Our calculations reproduce well the zero-temperature moment, the single-crystalline magnetization curves, and giant anisotropy field as 400 T. The magnetocrystalline-anisotropy energy K$\text{}_{1}$ of 59 J/cm$\text{}^{3}$ is the largest known anisotropy - the anisotropy energy of the Nd$\text{}_{2}$Fe$\text{}_{14}$B supermagnet amounts to 12.5 J/cm$\text{}^{3}$ only. Unfortunately, this giant anisotropy is confined to low temperatures only which prohibits its technical applications in the permanent-magnet industry.