Striped antiferromagnetic order and electronic properties of stoichiometric LiFeAs from first-principles calculations
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Striped antiferromagnetic order and electronic properties ofstoichiometric LiFeAs from first-principles calculations
Yong-Feng Li and Bang-Gui Liu a Institute of Physics, Chinese Academy of Sciences, Beijing 100190, ChinaBeijing National Laboratory for Condensed Matter Physics, Beijing 100190, Chinathe date of receipt and acceptance should be inserted later
Abstract.
We use state-of-the-arts first-principles method to investigate the structural, electronic, andmagnetic properties of stoichiometric LiFeAs. We optimize fully all the structures, including lattice con-stants and internal position parameters, for different magnetic orders. We find the magnetic ground stateby comparing the total energies among all the possible magnetic orders. Our calculated lattice constantsand As internal position are in good agreement with experiment. The experimental fact that no magneticphase transition has been observed at finite temperature can be attributed to the tiny inter-layer spincoupling. Our results show that stoichiometric LiFeAs has almost the same striped antiferromagnetic spinorder as other FeAs-based parent compounds and tetragonal FeSe do, which may imply that all Fe-basedsuperconductors have the same mechanism of superconductivity.
PACS.
Since the discovery of superconductivity in F-doped LaFeAsO[1], many Fe-based superconductors have been achievedby doping appropriate atoms in or applying pressure on R OFeAs ( R : rare earth) [2,3,4], A Fe As ( A : alkaline earth)[5,6,7,8], SrFeAsF [9,10,11,12], LiFeAs [13,14,15,8], andeven FeSe [16,17,18,19]. The highest transition tempera-ture T c has already reached to 55-56 K [4]. Various studieshave been performed to understand their magnetic orders,electronic structures, superconductivity, etc [20,21,22,23,24,25,26,27]. Among the five series of Fe-based supercon-ductors, the LiFeAs series seems to be the simplest FeAs-based superconductors. Many experiments have been doneto promote T c [29,13,30,15,14,28,31,32,33]. It should beeasier to detect the mechanism of the superconductivityin this series. Although there have been some computa-tional studies on LiFeAs[8,34,27], many aspects, even themagnetic properties of stoichiometric LiFeAs, are not elu-cidated. It is highly desirable to solve such basic issues ofLiFeAs for further investigations and future applicationsof the FeAs-based materials.Here, we investigate the structural, electronic, and mag-netic properties of stoichiometric LiFeAs by using state-of-the-arts first-principles calculations. We compare all thepossible magnetic orders, and find the magnetic groundstate in terms of total energy results and force optimiza-tion. Our results show the magnetic ground state features a e-mail: [email protected] a striped antiferromagnetic (SAF) order in the Fe layerand a weak antiferromagnetic (AFM) order in the z direc-tion perpendicular to the Fe layer. Our calculated internalpositions of Li and As are in good agreement with experi-ment. Through analyzing electronic and the magnetic re-sults, we propose a simple spin model to understand theexperimental magnetic properties. Thus, we show that sto-ichiometric LiFeAs has almost the same SAF spin order asother FeAs-based parent compounds and tetragonal FeSedo. More detailed results will be presented in the follow-ing.In next section we shall describe our computationaldetails. In the third section we shall optimize fully all thestructures with different magnetic orders and thus deter-mine the magnetic ground state. In the fourth section weshall present the electronic structures of the ground statephase. Finally, we shall make some discussions and giveour conclusion in the fifth section. We investigate all possible magnetic orders for stoichio-metric LiFeAs by using full-potential linearized augmentedplane wave method within the density functional theory[35], as implemented in package WIEN2k[36,37]. The gen-eralized gradient approximation is used for the exchangeand correlation potentials[38]. We treat Li-2s, Fe-3d4s,and As-4s4p as valence states, Fe-3p and As-3d as semi-core states, and the lower states as the core states. For the
Yong-Feng Li et al.: Striped antiferromagnetic order and electronic properties of stoichiometric LiFeAs
Fig. 1. (color online). Schematic crystal structure of stoichio-metric LiFeAs (P4/nmm). The biggest ball is Fe atom, themedium As, and the smallest Li. core states, the full relativistic effect is calculated with ra-dial Dirac equations. For valence and semi-core states, therelativistic effect is calculated under the scalar approx-imation, with spin-orbit interaction being neglected[39].We take R mt × K max =7.5 and make the angular expan-sion up to l = 10 in the muffin-tin spheres. We use 1000k points in the first Brillouin zone for different magneticstructures. The self-consistent calculations are controlledby the charge density in real space. The integration of theabsolute charge-density difference between two successiveself-consistent loops, as the convergence standard, is lessthan 0.0001 | e | per unit cell, where e is the electron charge.For all the magnetic structures, we optimize the volume,geometry, and internal position parameters in terms oftotal energy and the force by the standard 1.5 mRy/a.u. Stoichiometric LiFeAs crystallizes into a tetragonal struc-ture with space group P4/nmm at room temperature. Asis shown In Fig. 1, its unit cell consists of one Fe-As layerseparated by two Li layers. The experimental lattice con-stants are a = 3 . c = 6 . z direction, the successive Fe lay-ers can couple ferromagnetically or antiferromagnetically.Thus, we have four different AFM orders, namely, CAF-FM, CAF-AFM, SAF-FM and SAF-AFM. Structural op-timization is done for these six magnetic orders. Our vol-ume optimization results are presented in Fig. 2. The equi-librium volume is determined by the minimum of the totalenergy against volume. The optimized results summarized
40 42 44 46 4820406080100120
Volume ( Å ) SAF-FM SAF-AFM CAF-FM CAF-AFM FM NM E ne r g y ( m e V ) Fig. 2. (color online). The optimization curves of relative to-tal energy (meV) as functions of the volume (˚A ), per for-mula unit, for the six possible magnetic orders of stoichiometricLiFeAs. Table I. The Fe layer in SAF order, either FM or AFM in z direction, is lower than that in other magnetic orders.We conclude that the magnetic ground state of LiFeAsis the magnetic configuration SAF-AFM that the spinsin the Fe layers are in the SAF order and the inter-layermagnetic coupling is a weak AFM interaction. This is thesame as the magnetic ground states of other FeAs-basedparent compounds and tetragonal FeSe[8,12,18,22,23].The equilibrium volume (88.49˚A ) of the ground stateis a little smaller than the experiment value (91.46 ˚A ).The magnetic moment per Fe atom is 1.58 µ B . The mo-ment for the CAF order is smaller. For comparison, wedo similar calculations using LSDA. The LSDA magneticmoment per Fe atom, 0.62 µ B and 0.63 µ B for the SAF-FMand SAF-AFM orders, are much smaller than the GGA re-sults (1.50 µ B and 1.58 µ B ), respectively. The Fe-As layer,especially the Fe-As distance and the Fe-As-Fe angle, isimportant for the ground state of LiFeAs. This can beeasily seen in Table 1 that as the magnetic moment M of Fe atom increases, the values of the distance d Fe − As between Fe and As atoms increases and the Fe-As-Fe an-gles ( α and β ) decreased. The trend of M with different d Fe − As is consistent with previous result calculated withexperimental lattice constants [27]. The Fe-As layer as awhole is quite robust and Li atoms are dispersed indepen-dently between the Fe-As layers, which explains why wecan get exact positions of As atoms (0.2334 compared tothe experiment value 0.2365 ), but a little deviated resultsfor Li atoms (0.3322 to 0.3459). It looks like that the Liatoms play less important roles in the materials. In the following, we study the electronic properties of sto-ichiometric LiFeAs in SAF order. The magnetic structurein the Fe layer is shown in Fig. 3(a). The arrow implies ong-Feng Li et al.: Striped antiferromagnetic order and electronic properties of stoichiometric LiFeAs 3
Table 1.
The relative total energy per unit cell ( E , with that of the lowest SAF-AFM set to zero), the magnetic momentof Fe atom ( M ), the equilibrium volume per unit cell ( V ), the internal position parameters of Li and As ( z Li and z As ), thedistance between Fe and As atoms d Fe − As , two angles formed by Fe1-As-Fe2 ( α ) and Fe1-As-Fe3 ( β ) of LiFeAs in the six possiblemagnetic orders.Name E (meV) M ( µ B ) V (˚A ) z Li z As d Fe − As (˚A) α β FM 140. 0.43 88.47 0.3304 0.2238 2.345 68.8 106.1NM 151. – 87.85 0.3313 0.2237 2.339 68.9 106.1CAF-AFM 151. 1.02 87.83 0.3330 0.2284 2.356 68.4 105.4CAF-FM 148. 1.18 88.45 0.3330 0.2286 2.362 68.3 105.0SAF-FM 2. 1.50 88.31 0.3353 0.2324 2.376 67.8 104.0SAF-AFM 0 1.58 88.49 0.3322 0.2334 2.382 67.6 103.8
JJJ NNN JJJ ✲ y ❵❵❵❵❵❵❵❵❵❵❵❵❵❵❵ ✘✘✘✘✘✘✘✘✘✘✘✘✘✘✘✘✘✘✘✘✘✘✘✘❵❵❵❵❵❵❵❵❵❵❵❵❵❵❵ ✘✘✘✘✘✘✘✘✘✘✘✘ ❵❵❵❵❵❵❵❵❵❵❵❵❵❵❵ .............................. .................................................. ❵❵❵❵❵❵❵❵ ............... ............... ✘✘✘✘✘✘❵❵❵❵❵❵❵❵✘✘✘✘✘✘ .......... r rrrr rrr X YZ Γ U S TR (b)(a)
Fig. 3. (a) The magnetic structure of the Fe layer of theLiFeAs ground state, (b) The first brillouin zone of the LiFeAsground-state phase with the high-symmetry points labelled. that the Fe spins align ferromagnetically in the x directionand antiferromagnetically in y direction. Also we showthe first Brillouin zone with key representative points andlines emphasized in Fig. 3(b). The total spin-dependentdensity of states (DOS) and the partial DOSs projectedin the muffin-tin spheres of Fe1, Fe2, Li, and As atomsand in the interstitial region are shown in Fig. 4. Thereis no energy gap near the Fermi level and then it showsa metal feature. For the SAF order, the spins of Fe1 andFe2 are antiparallel, it can be easily recognized in DOS.The DOS can be divided into two energy ranges: from -6.0eV to -3.0 eV and from -3.0 eV to 0 eV (Fermi level). Theformer consists of Fe-3d and As-4p states forming the Fe-As bond. In the latter range, the Fe-3d states play a keyrole. It is easily noted that the Li states have very smallweight in the energy window. The spin exchange splittingshould be mediated by the d-d direct exchange betweenthe nearest Fe atoms and the p-d hybridization betweenFe and As.In Fig. 5 we present the spin-dependent band struc-ture of LiFeAs with Fe1-3d character in SAF order. Theplots look like lines, but consist of hollow circles. The cir-cle diameter is proportional to the weight of Fe1-3d statesat that k point. Compared with DOS, we can find that3d states of Fe play a key role for the magnetic struc-ture. It is clear that the bands become narrow along the z direction. It means that the electron structure showsquite strong two-dimensional character. Also, it can befound that there are hole-like (along Γ -Z) and electron-like (along Z-U) band sections. (cid:1)(cid:0) (cid:2)(cid:3) (cid:4)(cid:5) (cid:6) (cid:7)(cid:8)(cid:9)(cid:10)(cid:11)(cid:12)(cid:13)(cid:14) (cid:15)(cid:16)(cid:17)(cid:18)(cid:19)(cid:20)(cid:21)(cid:22)(cid:23)(cid:24)(cid:25)(cid:26)(cid:27)(cid:28)(cid:29)(cid:30)(cid:31) !" Fig. 4. (color online). Total DOS (states/eV per formula unit)and partial DOS projected in the atomic spheres of Fe1, Fe2,Li, and As and in the interstitial region of the LiFeAs ground-state phase. The upper part is for majority spin and the otherfor minority spin.
The crystal structures with NM, FM, and CAF or-ders have the same tetragonal symmetry, while that withSAF is orthorhombic. Different symmetries lead to twodifferent kinds of crystal field splitting for the Fe-3d state.For the tetragonal symmetry, Fe-d state is split into d z ,d xy , d x − y , and d xz,yz , and for orthorhombic symmetryit is split into five singlets. From Fig. 5 we can see thatthe bands distributions are symmetric along Γ -X and Γ -Y at -3 eV below the Fermi level, but asymmetric nearthe Fermi level. These are different from the previous NMband structures[8,27,34], in which the band distributionsare symmetric along Γ -X and Γ -Y for almost all energyrange below the Fermi level. The total energy results, as summarized in Fig. 2 and Ta-ble I, show that the magnetic interaction in the z directionis weak, and The SAF structure is lower by 140-151 meVper formula unit than the other magnetic configurations.This is consistent with a simple spin model for the Fe Yong-Feng Li et al.: Striped antiferromagnetic order and electronic properties of stoichiometric LiFeAs Γ T Y Γ Z U Γ X R S X U E F E n e r gy ( e V ) Γ T Y Γ Z U Γ X R S X U E F E n e r gy ( e V ) Fig. 5.
The spin-dependent energy bands of the LiFeAsground-state phase. The left part is for majority-spin and theright for minority-spin. The band consists of dots. The biggerthe dot is, the more Fe1-3d character the band at that pointhas. spins, H = P h ij i J ij S i · S j , where S i is the spin operatorat site i and J ij coupling constants between sites i and j .The summation is limited to the nearest site pairs. J ij is J in the y direction, − J in the x direction, and δJ in the z direction. For such spin model, a non-zero δ is necessaryto a finite phase transition temperature[40]. The actual δ must be tiny because no magnetic phase transition is ob-served in stoichiometric LiFeAs at any finite temperature.In summary, we have investigated the structural, elec-tronic, and magnetic properties of stoichiometric LiFeAsby using the density-functional-theory method. We deter-mine the magnetic ground-state by comparing the totalenergies among all the possible magnetic orders. Our DFTresults show the magnetic ground state has the SAF orderin the Fe layer and a weak AFM order in the z direction.Our calculated internal positions of Li and As are in goodagreement with experiment. Through analyzing electronicand the magnetic results, we propose a simple spin modelto understand the experimental magnetic properties. Theexperimental fact that no magnetic phase transition is ob-served at finite temperature can be attributed to the tinyinter-layer spin coupling. Thus, we show that stoichiomet-ric LiFeAs has almost the same SAF spin order as otherFeAs-based parent compounds and tetragonal FeSe do[8,12,18,22,23], which may imply that all Fe-based supercon-ductors have the same mechanism of superconductivity. Acknowledgement. This work is supported by Nature ScienceFoundation of China (Grant Nos. 10874232 and 10774180), bythe Chinese Academy of Sciences (Grant No. KJCX2.YW.W09-5), and by Chinese Department of Science and Technology(Grant No. 2005CB623602).
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