Magnetic ordering in C 60 polymers with partially broken intermolecular bonds V. V. Belavin, 1 L. G. Bulusheva, 1 A. V. Okotrub, 1 and T. L. Makarova 2 1 Nikolaev Institute of Inorganic Chemistry SB RAS, Prospekt Ak. Lavrenteva 3, 630090, Novosibirsk, Russia 2 Department of Physics, Umea University, S-90187 Umea, Sweden (Received 14 April 2004; published 7 October 2004) The possibility of formation of radical centers in a hexagonal C 60 polymeric layer, without damage to the fullerene cages, is shown. The geometry optimization of C 60 trimers and tetramers using the semiempirical AM1 method has revealed that linking of molecules through a single bond is preferred for multiplet states of system. The density of unpaired electrons is mainly localized in the vicinity of the single bonds producing narrow energy bands near the Fermi level of hexagonal C 60 polymers. The magnetic state of the polymer depends on the number and location of single bonds in a polymeric layer. DOI: 10.1103/PhysRevB.70.155402 PACS number(s): 72.80.Rj, 75.50.Xx, 31.15.Ct I. INTRODUCTION Ferromagnetic behavior of the rhombohedral C 60 polymer 1 was one of the unexpected discoveries in the field of research of fullerenes under high pressure. The samples, synthesized at temperatures and pressures close to the con- ditions of C 60 collapse, showed a history dependent magnetic behavior (hysteresis) up to 500 K. The magnetic carbon samples were prepared at three pressures: 2.5, 2 6, 1,3 and 9 GPa 4 at temperatures approximately 100 K lower than that which causes C 60 cage damage. It had been assumed that magnetic ordering in the rhombohedral polymer is caused by the defects developed in the polymeric network under ex- treme synthetic conditions. Transmission electron micros- copy shows that the radical centers are formed in the poly- meric state before collapse, without damage to the fullerene cages. 4 This is confirmed by the Raman and x-ray measurements. 2 For the explanation of the origin of magnetism, various models have been offered. Thus it was shown 5 that occur- rence of atomic vacancies in C 60 molecules comprising the hexagonal polymerized layer results in the appearance of lo- calized electronic spins. Carbon radicals could be introduced by negative Gaussian curvature 6 arising from fullerene coa- lescence. The Stone–Wales transformations of C 60 molecules were found to result in opened cage structures acquiring a magnetic moment of several Bohr magnetons. 7 Finally, in Ref. 8, it was shown that the state responsible for the pres- ence of magnetic interactions in the C 60 dimer is the triplet state obtained when one of the two interfragment C–C bonds is broken under the influence of applied pressure. Moreover, total energy calculations have shown that the triplet state of the species remains magnetically active after load removal. 8 Based on the experimental data 1–4 and in opposition to the previous models 5–7 we propose an alternative mechanism of formation of radical centers in C 60 polymers where the ap- pearance of magnetic moments is due to a partial breaking of intermolecular bonds. We propose that this kind of structural modification is the most plausible under the synthesis condi- tions used, and our arguments are the following. The angles in four-membered rings bridging the molecules in the poly- mer are equal to 90°, 9 i.e., far from the tetrahedral value characteristic of sp 3 -hybridized carbon. The resulting struc- tural strain should considerably reduce the dissociation en- ergy of the intermolecular bond compared with that of the intramolecular one, thus we believe that the defects appear- ing in the polymerized C 60 layers under the extreme synthe- sis conditions are neither vacancies nor coalescence, but rather broken interfullerene bonds. The purpose of the present work is the quantum-chemical modeling of the structures of polymerized C 60 , which give the origin of spin moments and the conditions for their or- dering. We have constructed several models representing molecular clusters of polymerized C 60 , in which some of the molecules are linked through a single bond (one intermo- lecular C–C bond). Thus we have modeled an effect of high temperature of synthesis. The geometry of model structures was optimized in singlet and multiplet states to find the con- ditions that stabilize single bond formation. II. DETAILS OF CALCULATIONS We took one trimer and two tetramer structures (Fig. 1) comprising covalently bonded C 60 molecules, where we broke one or two of the interfullerene bonds in the four membered rings arising from 2+2 cycloaddition. In the initial structures, the distance between atoms A' and B',C' and D', previously participating in the formation of intermo- lecular bonds, was taken as 2.4 Å: this spacing prevents co- valent bonding. The breakage of one of the two intermolecu- lar bonds in structure I gives rise to two unpaired electrons. Antiparallel and parallel alignment of the electron spins re- sults in the singlet and triplet states of the system, respec- tively. For the structures II and III, the spin state arises from the spin of the four localized electrons. These four spins can be coupled either as singlet, triplet, or quintet states. The geometry of the molecular clusters so constructed was opti- mized with the unrestricted Hartree-Fock self-consistent field method using semiempirical AM1 parametrization 10 within the GAMESS package. 11 The geometry was relaxed without any symmetry constraints to the gradient value of 10 -4 Ha/Bohr. The optimized geometry of clusters was then used for the construction of hexagonal layers of polymerized C 60 and the calculation of band electronic structure of polymeric layers PHYSICAL REVIEW B 70, 155402 (2004) 1098-0121/2004/70(15)/155402(5)/$22.50 ©2004 The American Physical Society 70 155402-1