Structural and Magnetic Properties of Gd$_{3}$N@C$_{80}$

Using relativistic and on-site correlation corrected density functional theory, we have investigated the structural and magnetic properties of recently synthesized Gd$_{3}$N@C$_{80}$. The most stable structure of Gd$_{3}$N@C$_{80}$ has the three magnetic Gd ions pointing to the centers of hexagons in C$_{80}$. The magnetic ground state of this structure has the three coplanar spins ($S$ = 7/2) offset by 120$^{o}$ angles. At the same time, the state with the highest multiplicity, where all the spins are parallel aligned, is found only about 4.5 meV higher in energy. Therefore, at room temperature, we expect Gd$_{3}$N@C$_{80}$ to be paramagnetic with spin fluctuating between different multiplicities.