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Physica B 405 (2010) 277–280

Contents lists available at ScienceDirect

Physica B

0921-45

doi:10.1

� Corr

E-m

journal homepage: www.elsevier.com/locate/physb

Half-metallic ferromagnetic property of FeTiS2 based on first principles

Yanrui Guo a,�, Huiyu Yan a, Guoying Gao b, Qinggong Song a

a College of Science, Civil Aviation University of China, Tianjin 300300, Chinab Department of Physics, Huazhong University of Science and Technology, Wuhan 430074, China

a r t i c l e i n f o

Article history:

Received 21 May 2009

Received in revised form

17 August 2009

Accepted 17 August 2009

PACS:

71.20.Tx

71.20.�b

72.25.�b

Keywords:

Intercalation compounds

Density function theory

Half-metallic ferromagnetic

FeTiS2

26/$ - see front matter & 2009 Elsevier B.V. A

016/j.physb.2009.08.073

esponding author. Tel./fax: +86 2224092514.

ail address: yanrui_g@163.com (Y. Guo).

a b s t r a c t

Based on density function theory and by using the full-potential linearized augmented plane-wave

method within a generalized gradient approximation, the electronic properties of FexTiS2 (x ¼ 1/4, 1/3, 1)

have been calculated. The results show that FeTiS2 exhibits nearly half-metallic ferromagnetic character

with about 100% carrier spin polarization around the EF at the equilibrium lattice constant. When we

change a and c with equal ratio, the half-metallic ferromagnetic property of FeTiS2 is maintained up in the

range of 99–101% and 109–112% of its equilibrium lattice parameters. The half-metallic ferromagnetic

property can also be found in Fe1/4TiS2 and Fe1/3TiS2 when their lattice parameters expand to 110–111%

and 108–111% of equilibrium lattice constants, respectively. The spin up and spin down bands of the Fe-3d

components show large splitting in FeTiS2. The magnetic moment of FeTiS2 per formula unit is 2.0mB,

most of which comes from the Fe atom.

& 2009 Elsevier B.V. All rights reserved.

1. Introduction

The intercalation of 3d transition metals into crystals of TiS2,which have layered structures with van der Waals gaps and areexpressed as MxTiS2, has been studied extensively because thecrystals’ structural and electronic properties are of low dimen-sional character [1–3]. Intercalation compounds FexTiS2 (0oxr1)have attracted much attention because of their dramatic magneticproperties [4–6], and many papers exist on the theoreticalcalculation of their electronic properties [7,8]. To our knowledge,no full-potential calculations exist for FexTiS2. In this paper,we performed first-principles calculation of the propertiesof FexTiS2 (x ¼ 1/4, 1/3, 1) by using the full-potential lineari-zed augmented planewave (FP-LAPW) method, which is one of themost accurate methods for calculation of the electronic structureof solids. Additionally, half-metallic (HM) ferromagnetic materialshave attracted more attention because of the 100% carrier spinpolarization at the EF [9–11]. Based on first-principles calcula-tions, several classes of materials have been predictedto possess characteristics of HM ferromagnetic materials, forexample diluted magnetic semiconductors [12], several Heusleralloys [13], some magnetic oxides and colossal magnetoresistantmaterials [14,15], transition-metal pnictides and chalcogenides

ll rights reserved.

[16], sp-electron ferromagnets in zinc-blende (ZB) structure [17],and several metal carbonides with a rocksalt structure [18].However, there are no reports on the properties of the inter-calation compounds MxTiS2. In this paper, we find thatnovel characters, specifically HM ferromagnetic properties existin FeTiS2.

2. Theoretical details

Based on previous research on the structure of FexTiS2, theFexTiS2 crystals investigated in the present work have space groupP-3m1 for x ¼ 1/4, 1 and R-3 for x ¼ 1/3 [3,4,8,19]. The structuresof FexTiS2 (x ¼ 1/4, 1/3, 1) are shown in Fig. 1. We obtained thelattice constants, shown in Table 1, by fitting the total energy as afunction of volume to the Murnaghan equation of state [20]. Wefound that the calculated lattice parameters agree well with theexperiment results. The predicted lattice parameter a of FeTiS2 isslightly smaller than the experiment results. This may come fromthe limitation of calculation method. Based on density functiontheory, the electronic properties of FexTiS2 (x ¼ 1/4, 1/3, 1) havebeen calculated by using the FP-LAPW method. Our calculationswere performed by using the WIEN2k package [21]. To take intoaccount exchange and correlation effects, the generalized gradientapproximation (GGA) of Perdew, Burke, and Ernzerhof’s formulahas been applied. The spin–orbit coupling has negligible effect onthe ferromagnetism of the systems. The radii Rmt of the muffin tin

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Fig. 1. The structures of FexTiS2 (x ¼ 1/4, 1/3, 1): (a) Fe1/4TiS2, (b) Fe1/3TiS2, and (c), FeTiS2.

Table 1Predicted Lattice constant a and c, total magnetic moment per formula unit (mtot), Fe magnetic moment (mFe), Ti magnetic moment (mTi), S magnetic moment (mS), and

magnetic moment in the interstitial region (min).

Compound Theory Experiment [4]

a (A) c (A) a (A) c (A) mtot (mB) mFe (mB) mTi (mB) mS (mB) min (mB)

Fe1/4TiS2 6.843 5.799 6.836 5.708 2.45 2.86 �0.59 0.22 �0.04

Fe1/3TiS2 5.947 5.783 5.929 5.716 2.40 2.88 �0.65 0.23 �0.06

FeTiS2 3.319 5.891 3.428 5.809 2.00 2.24 �0.28 0.05 �0.01

S (s

tate

s/eV

)

-1.50.01.5 Ti-d

-1.20.01.2 S-p-404 total

Y. Guo et al. / Physica B 405 (2010) 277–280278

spheres are approximately proportional to the correspondingionic radii and are as large as possible under the condition that thespheres do not overlap. The energy cutoff for plane waveexpansion of the functions in the interstitial region isKMax ¼ 7.0/Rmt. We have selected energy of –6.0 Ry to separatethe core from the valence states. Self-consistency is obtained byusing 300 k points in the irreducible Brillouin zone (IBZ). Theiteration process was continued until calculated total energy isconverged to within 0.1 mRy/unit cell.

-0.030.000.03

Energy (eV)

Fe-p-30

42-2-4-6-8 0

3 Fe-dDO

Fig. 2. The spin-resolved total and partial densities of states for FeTiS2. The dotted

line is the Fermi level.

3. Results and discussion

We first present the calculation results of the spin-resolvedtotal densities of states (DOS) for the ferromagnetic state ofFeTiS2. It shows the spin-resolved total and partial DOS of FeTiS2

in Fig. 2. It can be seen that the DOS of the majority spin (spin up)of FeTiS2 are nearly zero at the Fermi level, while the minorityspin (spin down) electrons show metallic characters. Specifically,FeTiS2 has nearly HM ferromagnetic characters with almost 100%electron spin polarization at the EF. The partial DOS correspondingto Fe-3d and Fe-3p, Ti-3d and S-3p components are also displayedin Fig. 2, as they have a decisive effect on the electronic propertiesof FeTiS2. As shown in the figure, the spin up and spin down bandsof the Fe-3d components show large splitting. The spin downFe-3d states hybridize mainly with the Ti-3d states while the spinup Fe-3d states hybridize with the S-3p states. There is no largesplitting in the bands of the Ti-3d and S-3p states.

We also have performed calculations of the spin-resolvedtotal DOS for FexTiS2 (x ¼ 1/4, 1/3). From the calculations, theresults of which are shown in Fig. 3, the shapes of the DOS ofFexTiS2 (x ¼ 1/4, 1/3) are similar to those of FeTiS2, except that the

spin up DOS at the Fermi level is not zero. This means thatthe electron spin polarization at the Fermi level of FexTiS2

(x ¼ 1/4, 1/3) is not as high as that of FeTiS2. This also meansthat the FexTiS2 (x ¼ 1/4, 1/3) do not show the HM ferromagneticcharacters at their equilibrium lattice constant. Because thecorresponding properties of Fe1/4TiS2 are similar to theproperties of Fe1/3TiS2, we only exhibit the partial DOS ofFe1/3TiS2 in Fig. 4. From Fig. 4, we find that the spin up DOS ofFe1/3TiS2 at the Fermi level are mainly due to the Fe-3d, Ti-3d, andS-3p states, which are hybridized strongly with one another. Thestates of Ti-3d and S-3p have little splitting.

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-6-15

-10

-5

0

5

10

DO

S (s

tate

s/eV

)

Energy (eV)

Fe1/3TiS2

-10

-5

0

5

10 Fe1/4TiS2

-4 -2 0 2 4

Fig. 3. The spin-resolved total DOS for Fe1/4TiS2 and Fe1/3TiS2. The dotted line is

the Fermi level.

-6

-3

0

3

Energy (eV)

S-p

-606

DO

S (s

tate

s/eV

)

Ti-d-0.1

0.0

0.1 Fe-p-303 Fe-d

-4 -2 0 2 4

Fig. 4. The partial DOS of Fe1/3TiS2. The dotted line is the Fermi level.

0.95

2

3

4

5

6

Mag

netic

mom

ent (

µ B)

a/a0

FeTiS2

Fe1/3TiS2

Fe1/4TiS2

1.151.101.051.00

Fig. 5. The total magnetic moment per formula unit for FexTiS2 as a function of

a/a0. The parameters a and c change with equal ratio.

Y. Guo et al. / Physica B 405 (2010) 277–280 279

As shown in Table 1, the calculated total magnetic moment forFexTiS2 (x ¼ 1/4, 1/3, 1) per formula unit is 2.45, 2.40, and 2.00mB,respectively. An integer value of the magnetic moment is acharacteristic feature of HM ferromagnets, which indicates thatFeTiS2 has nearly HM ferromagnetic characters. The totalmagnetic moment of FexTiS2 contains four contributions, oneeach from the Fe atom, the Ti atom, the S atom, and the interstitialregion. From Table 1, we can find that the main contribution to thetotal magnetic moment comes from the Fe atom. The spin statesof Fe in FexTiS2 are all in high spin states. This result is inagreement with other Refs. [7,8]. The direction of moment of theTi ion is opposite to that of the Fe ion.

It is important to study the robustness of nearly half-metallicmaterials with respect to variation in the interatomic distancesbecause the lattice parameters of a grown film depend on thelattice parameters of the substrate. We change a and c with equalratio to study the change of total magnetic moment per formulaunit for FeTiS2. The Fig. 5 shows total magnetic moment performula unit for FexTiS2 as a function of the lattice constant a/a0.The total magnetic moments remain as an integer when3.2858rar3.352 A and 3.6177rar3.7173 A in FeTiS2. Therefore,the half metallicity of FeTiS2 is maintained up in the range of 99–101% and 109–112% of its lattice parameters. Integral totalmagnetic moments can also be found in Fe1/4TiS2 and Fe1/3TiS2

when their lattice parameters expand to 110–111% and108–111% of equilibrium lattice constants, respectively. So thehalf metallicity exists in the two ranges in Fe1/4TiS2 and Fe1/3TiS2.This means that the HM ferromagnetic FexTiS2 (x ¼ 1/4, 1/3, 1) filmcan be fabricated onto appropriate semiconductor substrates. FromFig. 5 we can find that the calculated stability ranges for the ‘half-metallicity’ of FexTiS2 are very narrow. This may be attributed tothe characters of defect NiAs structure of FexTiS2.

4. Conclusions

In summary, we have calculated the electron structure ofFexTiS2 by using the FP-LAPW method. The results show thatFeTiS2 has nearly half-metallic ferromagnetic characters withalmost 100% carrier spin polarization at the EF. The spin up andspin down bands of the Fe-3d components show large splitting,while the bands of the Ti-3d or S-3p states do not show largesplitting. The total magnetic moment for FeTiS2 per formula unitis 2.0mB, which is mainly due to the Fe atom. The HMferromagnetic property is maintained up in the range of99–101% and 109–112% of lattice parameter. The electron spinpolarization of FexTiS2 (x ¼ 1/4, 1/3) at the Fermi level is lowerthan it is in FeTiS2. The half-metallic ferromagnetic property canalso be found in Fe1/4TiS2 and Fe1/3TiS2 when their latticeparameters expand to 110–111% and 108–111% of equilibriumlattice constants, respectively.

Acknowledgment

The work is supported by the Foundation of Civil AviationUniversity of China under Grant no. 07QD07X.

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