The first-principles investigations on magnetic ground-state in Sm-doped phenanthrene

Based on the density functional theory plus the effective Coulomb repulsion U, we have investigated the crystal structure, electronic properties and magnetic characteristics in Sm-doped phenanthrene, recently characterized as a superconductor with Tc∼5−6 Kelvin. Calculated total energies of different magnetic states indicate that Sm-doped phenanthrene is stable at the ferromagnetic ground-state. Considered the strong electronic correlations effect due to the intercalation of Sm-4f electrons, we found that the Sm-4f contributes to the Fermi surface together with C-2p, which is different from K-doped phenanthrene. Compared with alkali-metal-doped phenanthrene, Sm atom has larger local magnetic moment, which suppresses the superconductivity in conventional superconductors. Our results indicate that the electron-electron correlations play an important role in superconductivity of Sm-doped phenanthrene.


I. INTRODUCTION
Recent researches in the field of superconductivity pay attention to the materials containing light elements, in order to achieve higher critical temperature T c and explore the mechanism of superconductivity.Particularly, carbon-based superconductors have attracted significant interest since the discovery of superconductivity in alkali-metal-doped picene with T c ∼ 18 Kelvin. 1After that, a few other alkali-metal-doped polycyclic aromatic hydrocarbons (PAHs) were found to be superconductors, such as phenanthrene (C 14 H 10 ), 2 coronene, 3 and 1,2:8,9-dibenzopentacene 4 with T c of 5, 15, and 33 Kelvin, respectively.In alkali-metal doped PAHs superconductors, the electronic charges are transferred from the doped atoms to aromatic molecules to build the metallic phase.In 2012, the superconductivity with T c ∼ 6 Kelvin in rare-earth-doped phenanthrene was observed, 5 such as La-doped and Sm-doped phenanthrene, which opens a new path to superconductivity in organic materials.Later, the evidence of superconductivity in Sm-doped chrysene and picene was also found with T c s around 4.5 -5.5 Kelvin with small differences by changing the number of carbon atoms. 6Compared with the alkali-metal-doped PAHs, magnetic measurements imply that Sm atoms have much bigger local magnetic moment than K, which is harmful to conventional superconductors.Similar to alkali-metal-doped fullerenes, [7][8][9] many theoretical models suggested electron-electron correlations play an important role in alkali-metal-doped PAHs, [10][11][12][13] and the superconductivity in the system of rare-earth doped PAHs may come from unconventional superconducting mechanism.For rare-earth a Electronic mail: gh.zhong@siat.ac.cn 2158-3226/2017/7(5)/055704/6 metals, Sm has strong local magnetic moment.Then, are rare-earth doped PAH superconductors in nature the same as alkali-metal doped cases?In this work, therefore, we address this issue in the case of Sm-doped phenanthrene (Sm 1 C 14 H 10 ), focusing on the effects induced by Sm intercalated in phenanthrene compared with K-doped phenanthrene.

II. COMPUTATIONAL METHODS
Results for pure phenanthrene, K-doped phenanthrene and Sm-doped phenanthrene in this work were entirely obtained using the projector augmented-wave method of VASP package 14 based on the Perdew-Burke-Ernzerhof generalized gradient approximation (GGA). 15During the optimization of structures, we compared the influence of Van der Waals (vdW) 16 with the experiments parameters and adopted it in the following calculations.Additionally, in order to describe the electron-electron correlation characteristics of local electrons in Sm atoms, we have performed the GGA+U type calculation, 17,18 where U is the on-site Coulomb energy, U and exchange interactions (J) were treated by a single effective parameter U eff = U − J in VASP package.Referring from the literature, 19 we chose U eff = 5.5 eV for Sm atom.The cutoff energy was set as 650 eV for pristine and K-doped phenanthrene and 350 eV for Sm 1 C 14 H 10 , respectively.For integrations in the first Brillouin zone, the Monkhorst-Pack k-point grids are generated according to the specified k-point separation 0.02 Å 1 .Self-consistency calculation is achieved when the variations of the total energy and force on atom converge to a 0.01 meV and 10 3 eV/Å, respectively.

III. RESULTS AND DISCUSSION
Pristine phenanthrene displays a P2 1 symmetry at room temperature.Each unit cell contains two molecules which are arranged in herringbone structure forming a layer parallel to ab plane, and then the molecular layers are stacked along the c axis.The optimized structure are shown in Fig. 1(a).After full relaxation of the lattice parameters and the atomic coordinates, the optimized parameters are in good agreement with the ones in experiments. 20If van der Waals interaction is not considered in the calculation, the optimized lattice parameters will be far from experimental ones.As listed in Table I, the functional of local density approximation results in the contraction of the lattice parameters in three directions, 21 while the functional of GGA leads to the expansion of the lattice parameters. 22ccording to the differences between these two computational conditions, we come to a conclusion that van der Waals plays an important role in predicting the crystal structures for phenanthrene and related compounds, which has been put forward by Naghavi et al. 22 and Yan et al. 23 With potassium intercalated into the phenanthrene, 2 the lattice parameters of nominal K 3 C 14 H 10 measured at room temperature show a contraction of the lattice parameters and a small increase in the angle β.In order to compare Sm-doped with K-doped situations, we calculated K 1 C 14 H 10 and K 3 C 14 H 10 of the K-doped phenanthrene to find out the distinction among cases.The dopants of these aromatic compounds, like picene and phenanthrene, are ordinarily thought to be intruded into the intralayer insertion.In the present work, we have calculated plenty of different initial structures and  generated the most stable structures with minimum energies for K-doped and Sm-doped phenanthrene.
As shown in Fig. 1(b), one K atom per phenanthrene molecule is introduced into system, this K atom is situated on the center of organic molecule viewing on ac plane.Continuing to add K atoms to three for each organic molecule, as shown in Fig. 1(c), two K atoms are pushed toward to the end of organic molecule viewing on ac plane.Analyzing the total energies of different configurations, we found that K atoms moving into the interlayer region of organic molecules will decrease the stability of doped system.As for the Sm-doped phenanthrene, we started from optimized parameters of pure phenanthrene with Sm atoms inserted, referring to the nominal concentration of Sm 1 C 14 H 10 .After relaxing dozens of initial structures, we obtained the most stable configuration with the lowest energy, shown in Fig. 1(d).Differing from K 1 C 14 H 10 , Sm atom does not located in the middle of the molecule.Similar to K 3 C 14 H 10 , the introduction of Sm atoms leads to the larger distortion of organic molecules.In experiments, the unit cell volume slightly expands for Sm 1 C 14 H 10 , compared with pristine phenanthrene.But in our calculation result, the unit cell volume is reduced for the contractions of b and c, which could be explained by the tortuosity of phenanthrene molecule.
Since Sm is a magnetic atom, its introduction will lead to a strong magnetic system.To investigate the magnetism of this Sm-doped phenanthrene, we set four initial spin configurations including nonmagnetic (NM), ferromagnetic (FM), and anti-ferromagnetic (AFM).The AFM configurations contain two types: (1) the spin antiparalleling in unit-cell by two Sm atoms (defined as AFM-1); (2) the spin antiparalleling between different unit-cells with paralleling in the same unit-cell (defined as AFM-2).In AFM-2 type, we examine several different arrangement modes with four supercells at most.After calculating the total energies of the initial spin configurations, all the situations converge into FM ground-state.We could conclude that the Sm-doped phenanthrene is stable at the FM groundstate.Within the framework of GGA functional, the magnetic moment of Sm atom is 5.63 µ B /atom.Based on the GGA+U method, we obtained that the magnetic moment of Sm atom reaches to 6.15 µ B /atom.In K-doped phenanthrene, K atoms do not exhibit magnetism, while the whole organic system has weak AFM magnetism with the magnetic moment of 0.3 µ B /f.u.from the C atomic contribution. 24So comparing with K-doped phenanthrene, Sm-doped phenanthrene has stronger magnetism.
Under the same functional of GGA, we investigated the difference of the electronic structures between Sm-doped phenanthrene and K-doped cases.The electronic band structure along a selected path in the Brillouin zone and total density of states (DOS) for K 1 C 14 H 10 , K 3 C 14 H 10 and Sm 1 C 14 H 10 are shown in Fig. 2. The pristine phenanthrene is a direct band gap semiconductor.The introduction of K atoms makes charge transfer to phenanthrene molecules, which results in the shift of Fermi level toward to higher energy.As a result, the transition occurs from semiconductor to metal.In K 1 C 14 H 10 shown in Fig. 2(a), the Fermi level crosses the bottom edge of conduction bands, while in K 3 C 14 H 10 shown in Fig. 2(b), it crosses the top edge of conduction bands.The electronic states near the Fermi level are mainly contributed by C-2p.Namely, the superconductivity in K-doped phenanthrene originates from the intramolecular transport of C-2p electrons.Different from K-doped phenanthrene, Sm 1 C 14 H 10 exhibits the spin half-metal behavior as shown in Figs.2(c) and 2(d).In the majority-spin channel, a large number of Sm-4f electronic states are localized at the Fermi level to produce metallic feature, while in the minority-spin channel, the lack of electronic states near the Fermi level forms a energy gap of 0.53 eV.Sm-4f electrons mainly contribute to the electronic states near the Fermi level.From this result based on GGA, we believe that the superconductivity has the fundamental distinction between Sm-doped phenanthrene and K-doped cases.However, the superconducting critical temperature in Sm-doped phenanthrene has not huge difference relative to K-doped phenanthrene.Actually, the T c of 6 Kelvin in Sm-doped phenanthrene is only slightly higher than 5.6 Kelvin in K-doped phenanthrene in experiments. 2,5Hence, GGA functional does not accurately describe the electronic characteristics of Sm-4f electrons.
It has been well-known that the sharp peak induced by local Sm-4f electrons means the strong electronic correlation effect which is beyond the GGA functional.In this work, therefore, we adopted the GGA+U type calculation to simulate the nature of local electrons.For Sm 1 C 14 H 10 , we have calculated projected density of states (PDOS) on atomic orbitals by using respectively GGA and GGA+U methods.As mentioned above, within the framework of the standard density functional theory, the PDOS shown in Fig. 3(a) emerges the half-metal character.In the majority-spin channel, a sharp PDOS peak of Sm-4f is localized at the Fermi level.Considering the electronic correlation effects, we found that the Sm 1 C 14 H 10 is still a half-metal.However, as shown in Fig. 3(b), the electronic states of Sm-4f in majority-spin channel are pushed toward to lower energy levels while those in minority-spin channel toward to higher energy levels.Thus, Sm-4f states are far away from the Fermi level, only small contribution to the Fermi surfaces.Different from K-doped phenanthrene, the C-2p contributes to the electronic states at the Fermi level together with Sm-4f.However, comparing with GGA results, the DOS value at the Fermi level obviously decreases in the GGA+U calculation.Corresponding to the electronic contributions to the Fermi surface, the T c for the Sm-doped phenanthrene (6.0 Kelvin) is slightly higher than K-doped phenanthrene (5.6 Kelvin) in experiments.Experiments and our calculation results show that Sm atom has much bigger magnetic moment than that of K atom.Strong local magnetic moments usually breaks up the spin singlet Cooper pairs, therefore suppressing superconductivity in conventional superconductors.This abnormal phenomenon can not be explained by the conventional theory of superconductivity.Electronic correlations play an indispensable role in this system.But here we can not use any effective model to estimate the transition temperature.Interestingly, researchers obtained the comparable value with experimental one by means of conventional BCS electron-phonon coupling in K-doped PAHs. 25,26This indicates that in this kind of system, the electron phonon coupling is also indispensable.

IV. CONCLUSIONS
In summary, we study the crystal structures and electronic properties of Sm-doped phenanthrene, and make comparisons with K-doped phenanthrene.Van der Waals functional is considered to reveal the non-local interactions, while GGA+U method is considered to describe the electronic correlation effects during the calculations.The Sm-doped phenanthrene is a FM half-metal, and Sm atom has much larger local magnetic moment of 6.15 µ B /atom.In Sm-doped phenanthrene, Sm-4f makes great contribution to total DOS around the Fermi level together with C-2p, while the Fermi surface is mainly contributed by C-2p in K-doped phenanthrene.The FM correlations induced by Sm-4f local electrons suppress the conventional superconductivity in Sm-doped phenanthrene.The superconductivity in Sm-doped phenanthrene should be driven by electron-phonon interactions together with the electronelectron correlations.Further studies on various concentrations of Sm and superconductivity are expected in the future.

FIG. 2 .
FIG. 2. Calculated electronic band structure and total DOS based on the GGA method.(a) and (b) respectively correspond to K 1 C 14 H 10 and K 3 C 14 H 10 of K-doped phenanthrene.(c) and (d) represent majority-spin and minority-spin channels of electronic features of Sm-doped phenanthrene.Zero energy denotes the Fermi level.

FIG. 3 .
FIG. 3. Calculated PDOS of C atoms and Sm atoms.(a) and (b) correspond to GGA and GGA+U methods, respectively.

TABLE I .
Crystal parameters of pristine phenanthrene and Sm-doped phenanthrene.