Orthorhombic fulleride (CH${}_3$NH${}_2$)K${}_3$C${}_{60}$ close to Mott-Hubbard instability: Ab initio study

We study the electronic structure and magnetic interactions in methylamine-intercalated orthorhombic alkali-doped fullerene $\left({\mathrm{CH}}_3{\mathrm{NH}}_2\right){\mathrm{K}}_3{\mathrm{C}}_{60}$ within the density functional theory. As in the simpler ammonia intercalated compound $\left({\mathrm{NH}}_3\right){\mathrm{K}}_3{\mathrm{C}}_{60}$, the orthorhombic crystal-field anisotropy $\Delta$ lifts the $t_1\mathrm{u}$ triple degeneracy at the $\Gamma$ point and drives the system deep into the Mott-insulating phase. However, the computed $\Delta$ and conduction electron bandwidth $W$ cannot alone account for the abnormally low experimental Néel temperature, $T_{\mathrm{N}}=11$ K, of the methylamine compound, compared to the much higher value $T_{\mathrm{N}}=40$ K of the ammonia one. Significant interactions between ${\mathrm{CH}}_3{\mathrm{NH}}_2$ and ${\mathrm{C}}_{60}^{3-}$ are responsible for the stabilization of particular fullerene-cage distortions and the ensuing low-spin $S=1/2$ state. These interactions also seem to affect the magnetic properties, as interfullerene exchange interactions depend on the relative orientation of deformations of neighboring ${\mathrm{C}}_{60}^{3-}$ molecules. For the ferro-orientational order of ${\mathrm{CH}}_3{\mathrm{NH}}_2$-K${}^{+}$ groups we find an apparent reduced dimensionality in magnetic exchange interactions, which may explain the suppressed Néel temperature. The disorder in exchange interactions caused by orientational disorder of ${\mathrm{CH}}_3{\mathrm{NH}}_2$-K${}^{+}$ groups could further contribute to this suppression.

Figure 1

(a) Band structure and DOS for the room temperature ${\mathrm{MAK}}_3{\mathrm{C}}_{60}$ crystal structure. Red solid line is the interpolated band structure using the maximally localized Wannier orbitals; see text for details. Black solid line is the total DOS; the red dot-dashed line, green dash-dot-dotted line, and blue dashed line represent the PDOS on the first, second, and the third Wannier orbital, respectively. (b) The splitting of $t_1\mathrm{u}$ bands at the $\Gamma$ point, defining the orthorhombic crystal-field anisotropy.

Figure 2

MSDT phase diagram for fullerides adapted from Ref.20 including ${\mathrm{MAK}}_3{\mathrm{C}}_{60}$ position. Inset: Pressure dependence of the bandwidth computed for the room-temperature ${\mathrm{MAK}}_3{\mathrm{C}}_{60}$ structure. The horizontal line marks the critical bandwidth 0.74 eV where ${(U/W)}_c=1.35$ and where metal-insulator transition is expected.

Figure 3

Radial molecular distortions of ${\mathrm{C}}_{60}^{3-}$ ions in (a) orthorhombic ${\mathrm{C}}_{60}^{3-}$ expanded structure, (b) ${\mathrm{K}}_3{\mathrm{C}}_{60}$ orthorhombic environment. The size of blue circles and red squares is proportional to the amount of positive and negative deviations from the mean ${\mathrm{C}}_{60}$ radius at a given carbon site, respectively.

Figure 4

${\mathrm{C}}_{60}$ radial deformations of ${\mathrm{MAK}}_3{\mathrm{C}}_{60}$ for (a) room-temperature structure with relaxed ${\mathrm{C}}_{60}$ atom positions only and (b) completely relaxed room-temperature structure. Blue spheres correspond to inward distortions of the ${\mathrm{C}}_{60}$ cage, and red boxes represent outward cage distortions. The sizes of the markers scale linearly with the amount of distortion.

Figure 5

A maximally localized Wannier orbital obtained for the ${\mathrm{MAK}}_3{\mathrm{C}}_{60}$ structure. A isowave function surface at levels $\pm$65$\%$ of maximal value is depicted in red and blue for the positive and negative phase, respectively.[39]