Quantitative theory of magnetic properties of elemental praseodymium

Elemental Pr metal is unique among rare-earth elements in featuring a localized partially filled 4<i>f</i> shell without ordered magnetism. Experimental evidence attributes this absence of magnetism to a singlet crystal-field (CF) ground state of the Pr 4<i>f</i> ² configuration. Here, we construct an effective magnetic Hamiltonian for dhcp Pr, by combining density-functional theory with dynamical mean-field theory, in the quasiatomic Hubbard-I approximation. Our calculations fully determine the CF potential and predict singlet CF ground states for both inequivalent Pr sites. The intersite exchange interactions, obtained from the magnetic force theorem, are insufficient to close the CF gap to the magnetic doublets. Hence, ab-initio theory is demonstrated to explain the non-magnetic state of elemental Pr. We also find that the singlet ground state remains robust preventing conventional magnetic orders at the (0001) surface of Pr. Nevertheless, the gap between the ground state and the lowest excited singlet is significantly reduced at the surface, opening the possibility for exotic two-dimensional multipolar orders to emerge within this two-singlet manifold.