Structural and antiferromagnetic properties of Sm-doped chrysene

The experimental discovery of superconductivity was reported in Sm-doped chrysene with Tc∼5 K, which provides vital material for exploring unique superconducting mechanism of rare-earth metal doped polycyclic aromatic hydrocarbons. Here the crystal, electronic structures and magnetic characteristics of Sm-doped chrysene have been investigated by the first-principles calculation using the generalized gradient approximation (GGA) plus U method, also including van der Waals correction. We find that Sm-doped chrysene with C2/c space group is the most stable where doped Sm atoms stay on the relative middle of chrysene molecules. This material is stabilized at antiferromagnetic ground-state with the metallic feature. The calculated spin magnetic moment of Sm atom indicates that there are two electrons transferring from Sm to chrysene molecule. Within the framework of GGA+U, the C-2p electronic states mainly contribute to the Fermi surface. Electronic correlation effects are significant to understand the superco...


I. INTRODUCTION
3][4] In these class of organic superconductors, alkali metal atoms are intercalated into the interstitial space of aromatic molecules, consequently, electrons of alkali metal can be transferred to the aromatic molecules and leading to the superconductivity.Interestingly, the magnetism is not negligible in these PAH superconductors, and indeed magnetic measurements showed strong magnetic characteristics in these materials. 2,3Recently a new class of PAH superconductor were reported experimentally with T c ∼ 5 Kelvin for Sm-doped phenanthrene 5 and ∼ 6 Kelvin for Sm-doped chrysene. 6Comparing with K-doped PAHs, it is the introduction of magnetic atoms that results in the superconductivity in Sm-doped PAHs.Thus, exploring possible magnetic interactions in Sm-doped PAHs is vital for understanding the competing magnetic-superconductive mechanism.Furthermore, the crystal structures of PAH superconductors and the positions of doped metal atoms, which are foremost to explore electronic properties and superconducting mechanism, are difficult to be determined experimentally a Electronic mail: gh.zhong@siat.ac.cn 2158-3226/2017/7(5)/055707/6

II. COMPUTATIONAL METHODS
The crystal, electronic structures and magnetic characteristics of Sm 1 C 18 H 12 were systematically investigated by the first-principles calculation using the generalized gradient approximation (GGA) 7 plus on-site Coulomb energy U (namely GGA+U 8,9 ) implemented in the VASP package, 10 also with van der Waals (vdW) 11 corrections included.The cutoff energy for plane wave basis was set as 320 eV.All the optimizations were performed using the conjugate-gradient algorithm.The Monkhorst-Pack k-point grids were generated according to the specified k-point separation 0.04 Å 1 for relaxation and 0.02 Å 1 for self-consistency calculation.The convergence thresholds were set as 10 4 eV in energy and 10 2 eV/Å in force.
Our previous studies have confirmed the GGA plus vdW correction in vdW-DF2 version 11 can accurately predict the crystal lattice parameters of PAHs. 12Here, the first two rows of Table I list the experimental and optimized crystal lattice parameters of pristine chrysene (C 18 H 12 ).The lattice parameters of C 18 H 12 calculated by vdW-DF2 functional is in good agreement with the experimental values, 13 which can verify the reliability of vdW-DF2 functional.In view of the proposed experimental crystal structure, 6 we have investigated several crystal structures for one Sm atom doped chrysene with the most possible symmetries of C2/c, P2 1 and P1 space groups.To explore the magnetism of this Sm 1 C 18 H 12 system, we set three initial spin configurations of non-magnetic (NM), ferromagnetic (FM), and antiferromagnetic (AFM) for all the structures, respectively.The AFM configuration defined as spin antiparallel of Sm atoms between two Sm atomic layers.For local Sm-4f electrons, we adapted the GGA+U method to analyze the strong electronic correlation effects in the system, where U is chosen as 5.5 eV. 14Of course, the influence of U parameter to electronic properties was also discussed since a different value of U was adopted in Sm-doped phenanthrene. 15In addition, our calculation also included the spin-orbit coupling (SOC) to examine the contributions of spin moment and orbital moment to total magnetic moment.

III. RESULTS AND DISCUSSION
Chrysene molecule consists of four fused benzene rings arranged in a zigzag manner. 1 Pristine chrysene crystallizes with the space group of C2/c, and the unit cell forms the herringbone pattern with four chrysene molecules in it.Sm is a rare-earth metal with an electron configuration 4f 6 6s 2 .Previous studies suggested that alkali metal-doped phenacene family also showed P2 1 and P1 symmetries, 16 so we focused on the magnetic configurations of Sm 1 C 18 H 12 with C2/c, P2 1 and P1 space groups.
Considering all the possible space groups and magnetic configurations of Sm 1 C 18 H 12 , we have calculated total energies relative to the ground-state of each initial configuration.The results suggest TABLE I. Optimized crystal lattice parameters of pristine chrysene and Sm-doped chrysene.(a) and (b) correspond to the most stable and metastable crystal structures shown in Fig. 1.The dopants moving into the interlayer region will lower the systemic stability, which had been also confirmed in K-doped picene. 17The optimized crystal lattice parameters of these two structures are listed in Table I.From lattice constants, the shape of the most stable structure in theoretical prediction is far from that in experimental measurement, even if it is included in the Hubbard U correction.However, the error of volume of unit cell is only 7.7% which is in a tolerable range.From the point of view of theoretical simulation, the Sm doping reduces the volume of chrysene crystal, which is according with the situation of K-doped PAHs.
For the most stable Sm 1 C 18 H 12 , based on GGA+U (U = 5.5 eV) including the SOC effect, our calculated spin moment is about 5.9 µ B for Sm atom, and the orbital moment of Sm is about -1.6 µ B with the opposite direction to the spin moment.As a result, the total magnetic moment of Sm is 4.3 µ B .The magnetic moment of C and H atoms is very small and ignorable.It is different from that in K-doped PAHs, of which magnetic moment mainly comes from C atoms. 18,19Fig. 1(c) depicts the calculated spin density of the most stable crystal structure showed in Fig. 1(a), and the blue and pink clouds correspond to the different spin directions.The expansion of spin cloud implies the magnitude of corresponding magnetic moments.One can clearly see the antiferromagnetic configurations of Sm atoms.The obvious distinction of spin cloud between C atoms and Sm atoms also indicates that AFM state is mainly induced by the antiferromagnetic states of Sm atoms, instead of C atoms which applies to the situation of K-doped PAHs.Analyzing the magnetism of Sm, we found that the calculated orbital moment (1.6 µ B ) in doped crystal is less than that of isolated atom (∼ 3.4 µ B ).The reason is mainly from the crystal field effect interacted by aromatic molecules.In addition, we found that the spin moment of Sm in doped chrysene is 5.9 µ B , which indicates that Sm ion is at high-spin state with six 4f electrons occupying the spin-up channels.Combining the calculated local magnetic moment of Sm atom with its electron configuration mentioned above, we determine that two electrons are transferred from each Sm atom to chrysene molecules, and Sm ion behaves as the Sm 2+ valence state.The transfer of two electrons in Sm 1 C 18 H 12 is different from those tripotassium-doped picene and phenanthrene. 1,2ig. 2 shows spin polarized density of states (DOS) of the most stable Sm 1 C 18 H 12 with AFM ground-state.The electrons of Sm atoms are transferred to chrysene molecules, leading the system to form a metallic state, which can be obtained by both GGA and GGA+U (U = 5.5 eV) calculations.From the GGA result, there is a sharp peak localized at the Fermi level, and the electronic states at the Fermi level mainly contributed by Sm-4f.However, compared GGA+U with GGA treatment, the electronic correlation effects cause the shift of the sharp DOS peak away from the Fermi level and the obvious spin splitting around Fermi level in Sm 1 C 18 H 12 .As a result, the electronic states at the Fermi level obviously decrease.However, Sm 1 C 18 H 12 still exhibits the metallic feature when U = 5.5 eV, which is different from Sm-doped phenanthrene where behaves as semiconductor with a small gap of 0.12 eV as U = 6 eV. 15To check our results, we have also calculated the total DOS of Sm 1 C 18 H 12 at different U values, such as 6, 7, 8 and 9 eV.The results are shown in Fig. 3.We find that Sm  The projected electronic DOS (PDOS) of a typical C atom and Sm atom obtained by GGA+U (U = 5.5 eV) approach are shown in Fig. 4 for the most stable Sm-doped chrysene.We find that 2p y and 2p z of C atoms equally contribute to the electronic states near the Fermi level while the contribution of C-2p x can be ignored (See Fig. 4(a)).Under GGA+U method, Sm-4f electronic states present apparent spin splitting and are localized below the Fermi level so that the minority-spin states are unoccupied as shown in Fig. 4(b).From the quantity of electronic states at the Fermi level, C-2p and Sm-4f has respectively the value of 1.5 states/eV and 0.1 states/eV around the Fermi level in Sm 1 C 18 H 12 .So C-2p electrons mainly contribute to the electronic states around the Fermi level in Sm 1 C 18 H 12 , which is similar to that in K-doped PAH superconductors.However, the electronic correlation effects can not be ignored in Sm-doped chrysene.Additionally, The spin-up and spindown band structures along the specified paths in the Brillouin zone are shown in Fig. 5.As DOS results discussed above, Sm 1 C 18 H 12 obviously exhibits the metallic feature both spin-up and spindown channels.Interestedly, three bands cross the Fermi level in Sm 1 C 18 H 12 instead of two bands in K-doped picene and phenanthrene. 17,20Our result indicates that Sm-doped chrysene has not only the similarity but also the particularity comparing with K-doped PAH superconductors.A further exhaustive study is imperative to understand the competing magnetic-superconductive mechanism of these rare-earth metal doped PAHs.

IV. CONCLUSIONS
In conclusion, we have investigated the crystal, magnetic characteristics and electronic structures of Sm 1 C 18 H 12 by the first-principles calculation using GGA+U approach, also including vdW correction.With the help of full optimization, we found that Sm-doped chrysene with C2/c space group is the most stable, where doped Sm atoms stay on the relative middle of chrysene molecules.And for different magnetic configurations, it is indicated that Sm-doped chrysene is stabilized at the AFM ground-state with the metallic feature.The spin moment and orbital moment of Sm atom at the ground-state is respectively 5.9 µ B and -1.6 µ B , which shows that two electrons are transferred from Sm to chrysene molecule in Sm 1 C 18 H 12 .Within the framework of GGA+U, the electronic states around the Fermi level are mainly contributed by C-2p, and three bands cross the Fermi level.The results indicate that the electronic correlation effects are not to be ignored to understand the superconductivity in Sm 1 C 18 H 12 as well as other PAHs doped by rare-earth elements.
Fig. 1(a), and Fig. 1(b) shows the relatively metastable crystal structure of Sm 1 C 18 H 12 which is a FM stable state with the same C2/c space group.In the most stable structure, Sm atoms are seated on the bridge of 1/2-benzene ring and 3/4-benzene ring of chrysene molecules as shown in Fig. 1(a).While Sm atoms stays on the interlayer region of chrysene molecules in the metastable Sm 1 C 18 H 12 , as shown in Fig. 1(b).

FIG. 1 .
FIG. 1. Crystal structures and spin density distributions of Sm 1 C 18 H 12 .Pink spheres represent Sm atoms.Top panels display the side view and bottom panels display the top views direction.(a) and (b) respectively corresponds to the most stable and metastable crystal structures of Sm 1 C 18 H 12 .(c) depicts the calculated spin density of the most stable crystal structure showed in (a).The different colours of spin density in (c) represent the different spin directions.
FIG. 3. Calculated total DOS of the most stable Sm 1 C 18 H 12 based on the GGA+U method with different U values.Zero energy denotes the Fermi level.

FIG. 4 .
FIG. 4. Calculated PDOS onto the 2p (p x , p y , and p z ) orbitals of C atom (a) and 4f orbitals of Sm atom (b) of the most stable Sm-doped chrysene.The inset figure in (b) shows the PDOS of Sm-4f atoms around the Fermi level (from -1 eV to 1 eV).Zero energy denotes the Fermi level.

FIG. 5 .
FIG. 5. Band structure of the most stable Sm 1 C 18 H 12 .(a) and (b) represent spin-up and spin-down electronic features respectively.
to the sample preparation and divergence of superconducting mechanism of PAH superconductors.Therefore in this work, based on the first-principles calculation, we theoretically predicted the crystal structures, electronic properties as well as the magnetic configurations of Sm-doped chrysene (Sm 1 C 18 H 12 ) whose precise nature is still unknown.This study is helpful for achieving a better understanding of the microstructure, magnetism and superconductivity for rare-earth-doped PAHs in the case of Sm 1 C 18 H 12 .