Electronic structures and magnetic orders of Fe-vacancies ordered ternary iron selenides TlFe$_{1.5}$Se$_2$ and AFe$_{1.5}$Se$_2$ (A=K, Rb, or Cs)

1.2 MB·English

by  Xun-Wang Yan

Electronic structures and magnetic orders of Fe-vacancies ordered ternary iron
selenides TlFe1.5Se2 and AFe1.5Se2 (A=K, Rb, or Cs)
Xun-Wang Yan1,2, Miao Gao1, Zhong-Yi Lu1,∗ and Tao Xiang2,3†
1Department of Physics, Renmin University of China, Beijing 100872, China
2Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China and
3Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
(Dated: January 21, 2011)
By the first-principles electronic structure calculations, we find that the ground state of the Fe-
1 vacancies ordered TlFe1.5Se2 is a quasi-two-dimensional collinear antiferromagnetic semiconductor
1 with an energy gap of 94 meV, in agreement with experimental measurements. This antiferromag-
0
netic order is driven by the Se-bridged antiferromagnetic superexchange interactions between Fe
2
moments. Similarly, we find that crystals AFe1.5Se2 (A=K, Rb, or Cs) are also antiferromagnetic

n semiconductors but with a zero-gap semiconducting state or semimetallic state nearly degenerated
a with theground states. Thusrich physical properties and phase diagrams are expected.
J

0 PACSnumbers: 74.70.Xa,74.20.Pq,74.20.Mn
2

] The discovery of high transition temperature super-
i
c conductivity in LaFeAsO by partial substitution of O
s with F atoms [1] stimulates great interest on iron pnic-
-
l tides. Other kinds of iron-based compounds were also
r
t reported to show superconductivity after doping or un-
m
der high pressures[2–4]. A ubiquitous feature is that the
. parent compounds of these superconductors are antifer-
t
a romagnetic (AFM) semimetals[5] with either a collinear
m
[6, 7] or bi-collinear[8–10] AFM order below a structural FIG. 1: (Color online) TlFexSe2 with the ZrCuSiAs-type
- transition temperature. structure: (a) a tetragonal unit cell containing two formula
d
units without any vacancy; (b) schematic top view of the
n Very recently the superconductivity was discovered at
Fe-Fe square layer with one quarter Fe-vacancies ordered
o about30KinthepotassiumintercalatedFeSe-layercom-
in rhombus (x = 1.5), in which there are two inequivalent
c
[ pound K0.8Fe2Se2 [11]. Soon after, the superconduc- Fe atoms, namely 2-Fe-neighbored and 3-Fe-neighbored Fe
tivity was also found in the Cs-intercalated compound atoms. (c) schematic top viewof theFe-Fesquarelayer with
2 Cs0.8(FeSe0.98)2 [12] and (Tl,K)-intercalated compound one quarter Fe-vacancies ordered in square (x = 1.5). The
v
5 (Tl,K)FexSe2[13]. These compounds have the ThCr2Si2 filled circles denote the Fe atoms while the empty circles de-
type structure (Fig. 1(a)), isostructural with 122-type note the Fe-vacancies. The square and rectangle enclosed by
1
thesolid lines denote theunit cells.
0 ironpnictidesBaFe2As2[2]. Buttheyshouldberegarded
6 as a new kind of iron-based superconductors since they
2. are chalcogenides rather than pnictides. We have done and an energy gap of 94 meV, and similarly AFe1.5Se2
1 the first-principles electronic structure calculations for
isalsoanAFMsemiconductorbutwith azero-gapsemi-
0 these materials [14]. We find that their parent com-
conducting state or AFM semimetallic state close to the
:1 pounds TlFe2Se2 and AFe2Se2 (A=K or Cs) are also groundstate. This is the first time theoretically to show
v AFM semimetals and the ground states are in a bi-
there exists an AFM insulating state in Fe-based super-
i collinear AFM order.
X conductor materials.
r An important feature revealed by the latest transport In our calculations the plane wave basis method was
a measurement is that the superconductivity in Tl and K used [15]. We adopted the generalized gradient approx-
intercalated FeSe materials is proximity to an AFM in- imation (GGA) with Perdew-Burke-Ernzerhof formula
sulating phase [13], similar as in high-Tc cuprates. In [16]fortheexchange-correlationpotentials. Theultrasoft
particular, TlFexSe2 (1.3 < x < 1.7) is found to be an pseudopotentials[17]wereusedtomodeltheelectron-ion
AFM insulator, with an activated transport gap of ∼57 interactions. After the full convergency test, the kinetic
meV for x=1.5 [13]. This has revived the discussion on energycut-offandthe chargedensitycut-offofthe plane
the correlation effect in Fe-based superconductors. wave basis were chosen to be 800 eV and 6400 eV, re-
To clarify this issue, we have performed the first- spectively. The Gaussianbroadeningtechniquewasused
principles electronic structure calculations on TlFe1.5Se2 and a mesh of 18×18×9 k-points were sampled for the
and AFe1.5Se2 (A=K, Rb, or Cs). We find that the Brillouin-zoneintegration. Inthecalculations,thelattice
ground state of crystal TlFe1.5Se2 is indeed an AFM parameterswiththeinternalatomiccoordinateswereop-
semiconductor with a collinear AFM order (Fig. 4(b)) timized by the energy minimization. For TlFe1.5Se2, the
2
FIG.2: (Coloronline)ElectronicstructureofTlFe1.5Se2with
theFe-vacanciesorderedinrhombus(Fig. 1b)inthenonmag-
neticstate: (a)thebandstructure,(b)theBrillouinzone,and
(c) the Fermi surface. The Fermi energy sets to zero.
FIG. 4: (Color online) Schematic top view of four possible
magnetic orders in the Fe-Fe square layer with one quarter
Fe-vacancies ordered in rhombus: (a) checkboard Neel order
inwhichthenearestneighboringFemomentsareanti-parallel
ordered;(b)A-collinearAFMorderinwhichtheFemoments
areantiferromangticorderedalongthelinewithoutvacancies;
(c) P-collinear AFM order in Fe moments are antiferromag-
netic ordered along the lines with vacancies; (d) bi-collinear
FIG.3: (Coloronline)ElectronicstructureofTlFe1.5Se2with AFM order. The squares or rectangles enclosed by the solid
the Fe-vacancies ordered in square (Fig. 1c) in the nonmag-
lines denote themagnetic unit cells.
neticsate: (a)thebandstructure,(b)theBrillouinzone,and
(c) the Fermi surface. The Fermi energy sets to zero.
ble magnetic orders in the Fe-vacancies rhombus- and
square-ordered structures, respectively. Among these
optimized tetragonal lattice parameters are found in ex-
magnetic ordered states, we find that the Fe-vacancies
cellent agreement with the experimental ones [13].
rhombus-orderedstructure with an A-collinear AFM or-
TheearlyexperimentssuggestedthattheFe-vacancies
der shown in Fig. 4(b) has the lowest energy. This
in TlFe1.5Se2 are ordered in a rhombus structure as
rhombus order of vacancies agrees with the neutron
shown in Fig. 1(b)[18]. In order to test theoretically
measurement[18]. Our result further suggests that the
whether this structure is truly the groundstate, we have
rhombus-ordered vacancy structure is stabilized by an
also calculated the electronic structure of another pos-
A-collinear AFM order. In the A-collinear AFM state
sible one-quarterFe-vacancies orderedstructure, namely
(Fig. 4(b)), the Fe moments are antiferromagnetically
the square-ordered vacancy structure as shown in Fig.
ordered along the lines without Fe vacancies and ferro-
1(c). In the nonmagnetic state, we find that the energy
magnetically ordered along the lines perpendicular.
ofthesquare-orderedvacancystructureislowerbyabout
12meV/Fethantherhombus-orderedvacancystructure. Similar as in the iron-pnictides[19, 20], we find that
It is noted that an Fe-vacancy only induces small local there is a small structural distortion in TlFe1.5Se2. The
structural deviation (less than 0.04 ˚A) from the origi- lattice constant slightly expands along the AFM direc-
naltetragonalone except for Tlatoms, whichmeans the tion and contracts along the ferromagnetic direction in
covalent bonding between Fe and Se atoms is rather ro- the A-collinear AFM state. This leads to a small energy
bust. Figs. 2 and 3 show the nonmagnetic band struc- gain of ∼1 meV/Fe. We also find that the Fe magnetic
turesandFermisurfacesofTlFe1.5Se2intheFe-vacancies moments between the neighbor layers FeSe are antifer-
rhombus-andsquare-orderedstructures,respectively. In romagnetically ordered. The energy difference between
bothcases,thereareanumberofelectronandholebands the ferromagneticandAFMinterlayermagneticstatesis
crossingtheFermilevel. TheFermisurfacenestingisnot ∼4.9meV/Fe. Thus the groundstate ofTlFe1.5Se2 is an
as strong as in the iron pnictides [5]. A-collinear AFM state with AFM interlayers of FeSe.
However,inthe true groundstate whichis inanAFM Fig. 6(a)showsthegroundstateelectronicbandstruc-
order,wefindthattheenergyoftherhombus-orderedva- ture of TlFe1.5Se2. Unlike other parent compounds of
cancystructureislowerby15.1meV/Fethanthesquare- iron pnictides or chalcogenides, TlFe1.5Se2 is an AFM
ordered one. Figs. 4 and 5 show a number of possi- semiconductor,inagreementwithexperimentalmeasure-
3
FIG. 5: (Color online) Schematic top view of two possible
magneticordersintheFe-Fesquarelayer: (a)c-AFMorderin
which thenextnearest Femomentsareanti-parallel ordered;
(b) h-AFM order in which half pairs of the next nearest Fe
momentsinanti-parallelwhiletheotherhalfpairsinparallel.
The squares enclosed by the solid lines denote the magnetic
unit cells.
FIG. 7: (Color online) Projected density of states at the five
Fe-3dorbitalsaround(a)2-Fe-neighboredFeatomand(b)3-
Fe-neighbored atom in the A-collinear AFM ordered ground
state of TlFe1.5Se2. Here the top of the valence band sets
to zero. And x-axis is along the antiferromagnetic direction
whiley-axisisalongtheferromagnetic directioninFig. 4(b).
ments. The energy band gap is found to be ∼ 94 meV,
which is also consistent with the gap value obtained by
the transport measurement, 57.7 meV [13]. The com-
pound TlFe1.5Se2 in the other magnetic orders is found
mostly to be metallic.
There are two inequivalent Fe atoms according to
the number of neighboring Fe atoms if the Fe-vacancies
are rhombus-ordered,namely 2-Fe-neighbored and 3-Fe-
neighbored Fe atoms respectively (see Fig. 1(b)). By
projecting the density of states onto the five 3d orbitals
of Fe (Fig. 7), we find that the five up-spin orbitals
are almost completely filled on both kinds of Fe atoms.
This suggests that the crystal field splitting induced by
Se atoms is small, similar as in iron-pnictides. The mag-
netic moment formed around each Fe atom is found to
beabout2.8µ . ThislargeFemagneticmomentsappar-
B
ently results from the Hund’s rule coupling[19, 20]. The
down spin orbitals are partially filled by d , d , and
yz xy
dx2−y2 orbitals for the 2-Fe-neighbored Fe atoms or by
d and d orbitals for the 3-Fe-neighbored Fe atoms.
yz xy
Such anisotropy among the five down spin orbitals in
TlFe1.5Se2 results from the Fe-vacancies.
FIG.6: (Coloronline)ElectronicbandstructureofTlFe1.5Se2 Inspection of the real space charge distribution in
orAFe1.5Se2 (A=K,Rb,orCs)withonequarterFe-vacancies TlFe1.5Se2 shows that there is a strong covalence bond
ordered in rhombus (see Fig. 1(b)) and with an A-collinear
between the neighbor Fe and Se atoms. This gives rise
AFM order (see Fig. 4 (b)) in the ground state, which
to an effective AFM superexchange interactions bridged
is an antiferromagnetic semiconductor. (a) TlFe1.5Se2; (b)
by the Se atoms between the next nearest neighbor Fe
KFe1.5Se2; (c) RbFe1.5Se2; (d) CsFe1.5Se2. The Brillouin
zone is shown in Fig. 2(b). Here thetop of thevalence band moments, similar as in iron pnictides [19, 20]. If the
sets to zero. Note that Γ-N(Γ-N′) corresponds to the anti- energy of the nonmagnetic state is set to zero, we find
parallel(parallel)-aligned moment line. that the energies of the ferromagnetic, checkboard Neel
AFM,A-collinearAFM,andbi-collinearAFMstatesare
4
(-0.114,-0.217,-0.326,-0.270)eV/FeforTlFe1.5Se2. The Moreover,wealsofindthatthesquare-orderedvacancy
magnetic moment around each Fe atom is found to be structurewithac-AFMorder(Fig. 5(a))andAFMinter-
about 2.5-2.8µB, varying weakly in the above four mag- layersofFeSearemetastableforcrystalAFe1.5Se2(A=K,
netically ordered states, similar as in the iron-pnictides Rb, or Cs). Energetically, it is just higher than the
[19, 20]. If we attribute the energy differences of these groundstateby10.9,7.9,and5.0meV/FeforKFe1.5Se2,
states entirely to the contribution of magnetic interac- RbFe1.5Se2,andCsFe1.5Se2,respectively. Suchasquare-
tions between the spins S~ and model them by the sim- orderedvacancystructurepatternshouldthushaveacer-
pleHeisenbergmodelwiththe nearest(J1), next-nearest tainprobabilityofformationinthecompoundAFe1.5Se2.
(J2), and next-next nearest (J3) neighbor interactions In conclusion, we have performed the first principles
and ignore the anisotropy caused by the Fe vacancies
calculationsfortheelectronicstructureandmagneticor-
[J139]=,w7emfienVd/tSh2atfoJr1T=lF3e91.m5SeeV2./SIn2,oJb2ta=in6in0gmtheeVs/eSv2a,luaensd, odferTolFfeT1.5lFSee12.5wSiet2h. thWeerhfionmdbtuhsa-otrdthereedcrFyestvaalcsatnrucicetsuirne
thecontributionfromitinerantelectronsisignored. Sim-
a collinear antiferromagnetic order is energetically the
ailnardlyJ3w=e fi8nmdetVh/aSt2J1fo=r K3F7em1.5eSVe/2S(2s,eeJ2be=low64fomremVo/rSe)2., mtwoos-tdismtaebnlsei.onTahleagnrtoifuenrrdomstaagteneotficTslFeme1i.c5oSne2duisctaorquwaistih-
To quantify the electronic correlation effect in
an energy gap of 94 meV. Our result is consistent with
TlFe1.5Se2, we have performed a GGA+U calculation. both neutron and transport measurements. We further
We find that the energy band gap increases dramati-
predictthatcrystalAFe1.5Se2(A=K,Rb,orCs)isanan-
cally with the Coulomb interactionU. When U is larger
tiferromagneticsemiconductorlike TlFe1.5Se2, andthere
than 2 eV, the energy band gap is over 190 meV, which
is a zero-gap semiconducting state or antiferromagnetic
is significantly larger than the measurement value of 57
semimetallic state nearly degenerated with the ground
meV[13]. This suggests that the magnetic ordering and
state for RbFe1.5Se2 or CsFe1.5Se2.
the energy band gap are driven mainly by the exchange
effect, rather than the correlation effect. This work is partially supported by National Natural
Here we emphasize that the calculation convergency Science Foundation of China and by National Program
test needs to be elaborated. An enoughhigh energycut- for Basic Research of MOST, China.
off and a set of sufficient many k-points are required to
ensure the correct ground state, namely an AFM semi-
conductor obtained. Otherwise, the calculations always
yield a metallic state rather than semiconducting state.
∗ Electronic address: [email protected]
We have further performed the first-principles elec- † Electronic address: [email protected]
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or Cs). Like TlFe1.5Se2, we find that crystal AFe1.5Se2 J. Am.Chem. Soc. 130, 3296 (2008).
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[5] F. Ma and Z.-Y. Lu,Phys. Rev.B 78, 033111 (2008).
to be 121, 69, and 26 meV for KFe1.5Se2, RbFe1.5Se2, [6] C. dela Cruzet al.,Nature(London) 453, 899 (2008).
and CsFe1.5Se2, respectively. [7] J. Dong et al.,Europhys.Lett. 83, 27006 (2008).
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RbFe1.5Se2, and CsFe1.5Se2 in the A-collinear AFM or- [9] W. Bao et al., Phys.Rev.Lett. 102, 247001 (2009).
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higher thanthe AFM interlayersofFeSe by 8.9,5.2,and
[12] A. Krzton-Maziopa, et al.,arXiv:1012.3637.
2.8 meV/Fe, respectively. In such a case with the fer-
[13] M. Fang, et al.,arXiv:1012.5236.
romagnetic interlayers of FeSe, crystals TlFe1.5Se2 and [14] X.W. Yan, M. Gao, Z.Y. Lu, and T. Xiang,
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rectbandgapsof20and32meVanddirectgapsof46and [15] P. Giannozzi, et al.,http://www.quantum-espresso.org.
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comesazero-gapsemiconductorwhilecrystalCsFe1.5Se2 Lett. 77, 3865 (1996).
[17] D. Vanderbilt,Phys. Rev.B 41, 7892 (1990).
becomes an AFM semimetal with the electron and hole
[18] H. Sabrowsky, et al., J. Magn. Magn. Mater. 54-57,
carrierdensitiesof7.47×1019/cm3 and7.35×1019/cm3,
1497-1498 (1986).
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