A first-principles study of magnetism of lithium fluorosulphate LiFeSO4FTumurbaatar Tsevelmaa, Dorj Odkhuu, Oryong Kwon, and Soon Cheol Hong

Citation: Journal of Applied Physics 113, 17B302 (2013); doi: 10.1063/1.4794723 View online: http://dx.doi.org/10.1063/1.4794723 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/113/17?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Biaxial strain effect on the electronic and magnetic phase transitions in double perovskite La2FeMnO6: A first-principles study J. Appl. Phys. 114, 063713 (2013); 10.1063/1.4818321 Structural and magnetic phase transition of mixed olivines Li x Fe1y Ni y PO4 by lithium deintercalation J. Appl. Phys. 111, 07D722 (2012); 10.1063/1.3678468 Magnetic behavior of Fe(Se,Te) systems: First-principles calculations J. Appl. Phys. 110, 043917 (2011); 10.1063/1.3624759 X-ray magnetic circular dichroism in iron chalcogenides Fe 1 x S : First-principles calculations J. Appl. Phys. 106, 123907 (2009); 10.1063/1.3269719 Magnetic anisotropy in doped and undoped Li Fe P O 4 single crystals J. Appl. Phys. 101, 09N512 (2007); 10.1063/1.2712326

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A first-principles study of magnetism of lithium fluorosulphate LiFeSO4F

Tumurbaatar Tsevelmaa,a) Dorj Odkhuu,a) Oryong Kwon, and Soon Cheol Hongb)

Department of Physics and Energy Harvest Storage Research Center, University of Ulsan, Ulsan 680-749,South Korea

(Presented 17 January 2013; received 5 November 2012; accepted 3 December 2012; published

online 18 March 2013)

Magnetism of tavorite and triplite LixFeSO4F (x¼ 0, 1/2, and 1) has been studied using the

first-principles density-functional theory. It was found that an antiferromagnetic ordering is more

stable compared to a ferromagnetic state and the energy difference between two magnetic states is

reduced when the lithium is intercalated, being consistent with a recent experimental observation

of lowering Neel temperature from 100 K of FeSO4F to 25 K of LiFeSO4F. Furthermore, the

magnetic moment of 3.8 lB/Fe for FeSO4F was found to be oriented along the [010], whereas that

(4.3 lB/Fe) of LiFeSO4F along the [001]. And the magnetic moment and magneto-crystalline

anisotropy were found to be insensitive upon different atomic structures, which imply that the

lithium intercalation affects the spin orientation of Fe rather than the interplay between lattice and

magnetism suggested by an experiment. VC 2013 American Institute of Physics.

[http://dx.doi.org/10.1063/1.4794723]

I. INTRODUCTION

The rechargeable Li-ion battery is one of the most

attractive and useful technology among the modern energy-

storage systems due to its high energy density preserving

low weight and small volume. Much attention has been

focused on seeking abundant and environmentally friendly

cathode materials for Li-ion batteries to be applied to porta-

ble electronic devices, electric vehicles, and stationary

energy-storage systems. At present, a fluorosulfate com-

pound of LiFeSO4F is a promising candidate1,2 for a cathode

material because of its slightly higher operating potentials

(3.6–3.9 V) and higher efficiency than LiFePO4 without an

extra treatment such as carbon coating or nanosizing, retain-

ing low cost comparable to LiFePO4.3,4

Very recently, magnetic structures of the lithiated and

delithiated compounds of LiFeSO4F have been characterized

by a powder neutron diffraction experiment by Melot et al.5

Like phosphate compounds LiMPO4 (M is a 3d transition

metal), both FeSO4F and LiFeSO4F have an antiferromag-

netic (AFM) ground state, even though the fluorosulfate

compounds have different crystal structures of triplite and

tavorite. More interestingly, different easy magnetization

axes were found: AFM spins of Fe atom along the [010] for

the triplite FeSO4F (My¼ 4.32 lB), whereas it is being tilted

magnetization from the y-axis with spin vector components

of Mx¼ 1.73, My¼�2.73, and Mz¼ 1.36 in LiFeSO4F. And

Neel temperatures of FeSO4F and LiFeSO4F were measured

to be 100 K and 25 K, respectively, which are close to those

(125 and 50 K) of FePO4 and LiFePO4.6

Few theoretical studies on magnetism of Li-batteries

have been done. Investigation on their magnetism based on

electronic structure might be very helpful in understanding

charging/discharging process of a Li-battery. In this study, we

investigate the change of magnetic properties of LixFeSO4F

(x¼ 0, 1/2, and 1) by Li charging/discharging, specially empha-

sizing on magnetic orientation, using first-principles calculations.

II. COMPUTATION AND CRYSTALLOGRAPHY

The density-functional theory calculations using the

pseudo-potential projector augmented wave (PAW) method

were performed as implemented in the Vienna ab initio sim-

ulation package (VASP) code.7 Exchange-correlation interac-

tion between electrons is described as the generalized

gradient approximation (GGA) by Perdew, Burke, and

Ernzerh (PBE).8 Previous first-principles studies on the phos-

phate compound of LiFePO4 reported that the use of

Hubbard on-site correction gives more consistent results,

particularly the energy band gap, with experiments than con-

ventional density-functional.9,10 Here, we used the same Ueff

value of 4 eV for the Fe site as in LixFeSO4F. A cut-off

energy of 600 eV was chosen for the plane wave expansion

of wave functions. For each x, the Monkhorst-Pack k-point

meshes of 4� 4� 3 and 8� 8� 6 were used for the

Brillouin zone integration for triplite and tavorite phases,

respectively. Convergences with respect to cut-off energy

and number of k-points meshes were checked to insure reli-

able results. To obtain optimized atomic structures, atomic

positions and lattice parameters were fully relaxed.

Crystal structures of FeSO4F and LiFeSO4F are depicted

in Figs. 1(a) and 1(b), respectively. The delithiated com-

pound FeSO4F has a monoclinic lattice (triplite) with a space

group of C2/c, while the lithiated compound LiFeSO4F is

crystallized in a triclinic structure with P�1 (tavorite). In spite

of the different crystal structures, both structures consist of

FeO4F2 octahedra that are bound together at their corners

through F atoms and SO4 tetrahedra that share their oxygen

atom with octahedral. In LiFeSO4F, a Li atom locates in

a tetrahedral site, which shares F-O edge with FeO4F2

a)Tumurbaatar Tsevelmaa and Dorj Odkhuu contributed equally to this

work.b)Author to whom correspondence should be addressed. Electronic mail:

schong@ulsan.ac.kr.

0021-8979/2013/113(17)/17B302/3/$30.00 VC 2013 American Institute of Physics113, 17B302-1

JOURNAL OF APPLIED PHYSICS 113, 17B302 (2013)

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octahedra and oxygen with FeO4F2 octahedra and SO4 tetra-

hedra. The experimental lattice parameters obtained from a

neutron diffraction measurement at room temperature are

a¼ 5.18 A, b¼ 5.49 A, and c¼ 7.23 A (a¼ 106.48�,b¼ 107.18�, and c¼ 97.91�) for the tavorite LiFeSO4F and

a¼ 7.36 A, b¼ 7.09 A, and c¼ 7.37 A (a¼ c¼ 90� and

b¼ 119.77�) for the triplite FeSO4F.5

Energy differences between the aforementioned two

phases of FeSO4F and LiFeSO4F were predicted to be negli-

gible in a recent first-principles study.11 The small energy

differences motivate us to carry out both structures for each

x of 0, 1/2, and 1 in LixFeSO4F. As an example of x¼ 1

case, the unit cell in our calculation contains four formula

units with 32 atoms (four Li, Fe, S, and F, and 16 O atoms)

in the triplite and two formula units with 16 atoms for the

tavorite phase.

III. RESULTS AND DISCUSSION

Before investigating the magnetism, we first optimized

atomic structures of the tavorite and triplite LixFeSO4F.

Optimized lattice parameters a, b, and c of the tavorite

LiFeSO4F were found from GGA (GGAþU) calculations to

be 5.20 (5.22), 5.56 (5.56), 7.31 (7.39) A, and a, b, and cangles to be 106.64 (106.74)�, 107.41 (107.76)�, and 98.04

(97.72)�. Those of the triplite FeSO4F were 7.42 (7.40), 7.19

(7.17), 7.40 (7.39) A, and 119.26 (119.35)�. The GGA results

are closer to experimental ones5 for LiFeSO4F compared to

the GGAþU results, whereas the GGAþU gives more con-

sistent results with experiment for FeSO4F. Small deviation

in physical properties between different density-functionals

is quite typical for the correlated oxide alloys and Li-ion

battery materials.9,10 Overall, our calculated structural prop-

erties reproduce quite well the experimental5 and previous

theoretical ones.11,12 The volume increases slowly with x

for both phases. Structural stability during Li-ion insertion

and extraction is indispensable to durability under a high

cycle.

For each x in the triplite structure, we calculated total

energies of three different AFM configurations [see Fig.

1(a)], Fe1(")Fe2(")Fe3(#)Fe4(#), Fe1(")Fe2(#)Fe3(")Fe4(#),and Fe1(")Fe2(#)Fe3(#)Fe4("), denoted as AFM-1, AFM-2,

and AFM-3, respectively. For the partially delithiated

(x¼ 1/2) system, plausible different Li-ion configurations

were taken into account, and the energy minimum was found

when the Li atoms are positioned at (0,0,0) and (1/2,1/2,1/2)

by the total energy differences of not larger than 0.1 eV/f.u.,

compared to the other configurations. The most stable state

of FeSO4F is AFM-2: The energy differences from AFM-1,

AFM-3, and FM were calculated to be quite small, 0.005

(0.003) eV/f.u., 0.06 (0.05) eV/f.u., and 0.14 (0.07) eV/f.u.,

using the GGA (GGAþU). However, for x¼ 1/2 and x¼ 1,

AFM-1 is most favorable: For x¼ 1=2, the energy differences

from AFM-2, AFM-3, and FM are 0.015 (0.008), 0.056

(0.037) eV/f.u., and 0.06 (0.05) eV/f.u., using the GGA

(GGAþU), and For x¼ 1, the energy differences from

AFM-2, AFM-3, and FM are 0.008 (0.006), 0.01 (0.008)

eV/f.u., and 0.03 (0.008) eV/f.u., using the GGA (GGAþU).

Total energy differences (DE) from the FM state and

magnetic moments of the ground AFM tavorite and triplite

LixFeSO4F states are summarized in Table I. As seen in

Table I, DE is reduced with x. The reduction is consistent

with lowering of Neel temperatures when Li ions are interca-

lated.5 Magnetic moment difference between the different

crystal structures is negligible, not larger than 0.02 lB and

magnetic moments calculated with GGA (GGAþU) of

FeSO4F and LiFeSO4F are 4.02 (4.31) lB and 3.61 (3.79)

lB, respectively. A Hubbard correction results in enhanced

moments of Fe by about 0.2–0.3 lB. The reduction of the

magnetic moment with Li intercalation is consistent with the

measured moments of 4.32 lB for FeSO4F and 3.79 lB for

LiFeSO4F.5 Note that the GGAþU approach reproduces ex-

perimental values better than the GGA one. Furthermore, the

obtained magnetic moments are close to the unpaired elec-

tron spin counts of the ionic model of Fe2þ (4 lB) for

LiFeSO4F and Fe3þ (5 lB) for FeSO4F in high spin-states.

The magnetic easy axis of FeSO4F was observed in an

experiment to be different from that of LiFeSO4F.5 In order

to investigate the magnetic orientation of LixFeSO4F

changed by the Li intercalation, we calculated total energy

FIG. 1. Crystal structures of triplite and tavorite phases. Experimentally, (a) the triplite phase of FeSO4F forms in a monoclinic structure while (b) LiFeSO4F

(tavorite) crystallizes in a triclinic unit cell. The FeO4F2 octahedra and SO4 tetrahedra are depicted in black and blue polyhedral, respectively, where the Fe

and S atoms are placed at center. The O and F atoms sitting at corner of the polyhedrals are represented by small red and green balls, respectively. Four inde-

pendent Fe atoms coordinated by Fe1(3/4,3/4,1/2), Fe2(1/4,1/4,1/2), Fe3(3/4,1/4,0), and Fe4(1/4,3/4,0) are tagged in (a). The Li atom and its tetrahedra are

shown in yellow in (b).

17B302-2 Tsevelmaa et al. J. Appl. Phys. 113, 17B302 (2013)

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for three different magnetization orientations, [001], [010],

and [100], and estimate magneto-crystalline anisotropy

energy (EMCA). The calculated EMCAs of the tavorite and tri-

plite LixFeSO4F (x¼ 0, 1/2, and 1) between the [100] and

[001], and between the [100] and [010] orientations are pre-

sented in Table I, with GGA and GGAþU. The EMCAs were

found to be quite anisotropic due to the low symmetries of

the monoclinic and triclinic structures. In particular, those of

LiFeSO4F are very large in order of meV/f.u. As seen in

Table I, the different structures and the different treatments

for exchange-correlation give the same magnetization orien-

tation even though the numerical values of EMCA show some

differences. The magnetization easy axis of FeSO4F is along

[010] and the hard axis along [001]. The [010] easy axis is

found to be in consistent with an experiment5 whose results

are also presented in Table I for comparison. As x increases,

the spin direction of Fe turns from the [010] to [001].

Eventually, tavorite (triplite) LiFeSO4F has the magnetiza-

tion easy axis of [001] by the energy differences of 0.52

(0.53) and 0.09 (0.11) meV/f.u. compared to [100] and

[010], respectively, when GGAþU was used. The easy axis

of [001] is inconsistent with an experimental observation of

magnetization, Mx¼ 1.73, My¼�2.73, and Mz¼ 1.36 lB.

The discrepancy should be clarified in further study.

Calculated band gaps of about 2.24 eV for triplite

FeSO4F and 3.78 eV for tavorite LiFeSO4F are reasonably

consistent with the previous theoretical results, about

1.5–1.85 eV for FeSO4F and 3.43–3.60 eV for LiFeSO4F.11,12

The majority-spin Fe bands of FeSO4F are strongly local-

ized, while all the minority-spin bands are above the Fermi

level. This indicates that the five d-orbitals split by crystal

field are filled by five majority-spin electrons of Feþ3 of

FeSO4F. As x increases, the Fermi level shifts to the unoccu-

pied state because of the increase of the number of electrons

in the unit cell. An additional one electron of Feþ2 in

LiFeSO4F occupies in the minority-spin state just below the

Fermi level. As a consequence, the large exchange-splitting

between the minority- and majority-spin states of FeSO4F is

reduced for LiFeSO4F, i.e., decrease in magnetic moment as

shown in Table I. Thus, the band features describe well the

electronic configurations of the high-spin state in the crystal

field theory.

IV. CONCLUSION

In summary, we have studied the magnetism and elec-

tronic structures for different phases of tavorite and triplite

of fluorosulfate LixFeSO4F (x ¼ 0,1/2, and 1) by means of

the first principles density-functional theory. The AFM

ordering is found to be ground state regardless of the atomic

structure and Li concentration. The decrease in magnetic

energy from x¼ 0 to x¼ 1 implies the experimentally observed

AFM ordering temperatures of 100 K of the triplite FeSO4F

and 25 K for the tavorite LiFeSO4F. These AFM configurations

are attributed to the super-exchange interaction between differ-

ent Fe oxidation states (Fe3þ in FeSO4F and Fe2þ in

LiFeSO4F) that results in change of magnetic moment; 3.8 lB

for Fe2þ and 4.3 lB for Fe3þ. Finally, being consistent with

experiment, the easy magnetization axis of Fe in LixFeSO4F is

found to be altered during the charging/discharging.

ACKNOWLEDGMENTS

The research was supported by grants from the Basic

Research (2010-0008842) and Priority Research Centers

Program (2009-0093818) through the NRF funded by the

MEST.

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TABLE I. Magnetic energy DE (in the unit of eV/f.u.) between FM and AFM [DE¼Etot(AFM)�Etot(FM)], magnetic moment (lB/atom) of Fe, and EMCA

(meV/f.u.) between different crystallographic directions [100] and [001], and [100] and [010] for tavorite and triplite phases of LixFeSO4F with x¼ 0, 1/2, and

1. Both GGA and GGAþU results are shown and compared with an available experimental data.

DE Magnetic moment EMCA(E100�E001) EMCA(E100�E010)

LixFeSO4F Method Tavorite Triplite Tavorite Triplite Tavorite Triplite Tavorite Triplite

x¼ 0 GGA �0.11 �0.14 4.02 4.02 �0.07 �0.045 0.02 0.02

GGAþU �0.05 �0.07 4.31 4.31 �0.04 �0.015 0.01 0.02

Exp5 4.32 Mx¼ 0, My¼ 4.32, Mz¼ 0

x¼ 1/2 GGA �0.08 �0.06 3.86 3.86 0.59 0.76 0.21 0.9

GGAþU �0.05 �0.05 4.02 4.04 0.32 0.31 0.14 0.3

x¼ 1 GGA �0.02 �0.03 3.61 3.59 0.94 1.21 0.15 0.31

GGAþU �0.006 �0.008 3.79 3.76 0.52 0.53 0.09 0.11

Exp5 3.79 Mx¼ 1.73, My¼�2.73, Mz¼ 1.36

17B302-3 Tsevelmaa et al. J. Appl. Phys. 113, 17B302 (2013)

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