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First-principles study on the electronic structures of iron phthalocyanine monolayer
Surface Science 526 (2003) 367–374 www.elsevier.com/locate/susc
First-principles study on the electronic structures of iron phthalocyanine monolayer Beata Białek a
a,b
, In Gee Kim a, Jae Il Lee
a,*
Department of Physics, Inha University, 253 Yong-Hyun Dong, Nam-Gu, 402-751 Incheon, South Korea b Institute of Physics, Pedagogical University, 42-200 Czeßstochowa, Poland Received 7 August 2002; accepted for publication 30 December 2002
Abstract The electronic band structure and magnetic properties of iron phthalocyanine (FePc) monolayer were investigated by using the first-principles all-electron full-potential linearized augmented plane wave energy band method. It is found that the ferromagnetic FePc monolayer is energetically more stable than the paramagnetic one. The exchange interaction, which splits the majority and minority bands, influences strongly on the electronic structure near the Fermi level (EF ). Magnetic moment of the central Fe atom is calculated to 1.95 lB . The range of the positive polarization of Fe site is larger in the out-of-plane than in the in-plane direction. The FePc ligand remains paramagnetic. The presence of states at EF indicates the metallic character of FePc monolayer both for the paramagnetic and ferromagnetic states. However, the large density of states at EF of the majority spins in the ferromagnetic state is expected to cause a phase transition to insulating antiferromagnetic state from the metallic ferromagnetic one. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Iron; Density functional calculations; Surface electronic phenomena (work function, surface potential, surface states, etc.)
1. Introduction Phthalocyanine (Pc) is a kind of organic compounds with very interesting chemical and physical properties. A high chemical and thermal stability as well as conducting properties of Pc determines the use of its various compounds in many fields of industry [1,2]. Special attention is paid to transition-metal substituted Pcs (MPcs), which are widely applied for specific optoelectronic devices, gas sen-
*
Corresponding author. Tel.: +82-32-860-7654; fax: +82-32872-7562. E-mail address: [email protected] (J.I. Lee).
sors and solar cells. Among them is iron phthalocyanine (FePc) applied for sensing and effective catalytic properties [1,3–5]. It is well known that any practical application of MPcs is closely related to their electronic structures which have been the subject of both experimental and theoretical investigations for many years. For the case of FePc thin films the experimental study were carried out by means of ultraviolet photoelectron spectroscopy [6–8], and more recently, by photoemission yield spectroscopy [9,10], and by the inverse photoemission spectroscopy [11]. Theoretical studies usually concerned an isolated FePc molecule, and therefore only a discrete electronic structure of FePc was obtained [12,13].
0039-6028/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0039-6028(03)00002-5
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B. Białek et al. / Surface Science 526 (2003) 367–374
The band structure of the periodic systems containing Pc molecules was very seldom investigated theoretically. Only for the case of NiPc, B€ ohm reported the results of the crystal-orbital approach based on a semiempirical Hartree–Fock self-consistent-field model [14]. Kutzler and Ellis applied a discrete variational X a calculation to determine the charge density, molecular potential, eigenvalues and eigenvectors of isolated NiPc molecule, and used these parameters to compute the band structure of a molecular stack [15]. Very recently, Białek et al. applied the all-electron full-potential linearized augmented plane-wave (FLAPW) energy band method in order to determine the electronic structure of NiPc monolayer and bulk [16]. In this paper we present the results of the firstprinciples electronic structure calculations on FePc monolayer by using the FLAPW energy band method. We compare the electronic properties of ferromagnetic FePc monolayer with the paramagnetic one and discuss their band structures. We also discuss the influence of magnetic properties of Fe atom on the monolayer electronic structure.
2. Computational aspects FePc is a large molecule consisted of 57 atoms as presented in Fig. 1. In solid state the molecules aggregate forming crystals of three different polymorphic forms, among them so-called b-phase is known to be the most stable one. The crystal data of the structure of intermediate-spin ground state FePc (S ¼ 1) [17] was used to model a monolayer––a representative for FePc thin film. Similar model has already been used in the case of NiPc [16]. The model monolayer consists of square unit cells containing single FePc molecule. The molecule position is such that its symmetry axes led along the mirror axis of an isoindole unit of FePc cover with the unit cell diagonals. The chosen lattice constant was 25.91 a.u., being the distance between the center of the nearest molecules laying in the (0 0 1) plane of the b-phase of FePc crystal [17]. Pc thin films are highly ordered systems, and in a monolayer the interactions between molecules are very weak, so the model of high symmetry is
Fig. 1. A schematic view of FePc molecule.
good enough for description of the thin film properties. The geometry of a single FePc molecule of D4h symmetry was also taken from the crystallographic data [17]. The chosen model has P4/ mmm symmetry and there are nine inequivalent atoms (including hydrogens) in the unit cell, to which we shall refer hereafter according to the numbering shown in Fig. 1. Since the rigidity of FePc molecules, we do not perform a geometrical optimization for determining the internal atomic positions. The band structure calculations were performed by means of the all-electron FLAPW method [18]. Lattice harmonics with l 6 8 were considered to describe the charge density, potential and wavefunctions inside each muffin-tin sphere within the radii of 2.3 a.u. for Fe, 1.2 a.u. for C and N, and 0.6 a.u. for H. For the exchange-correlation potential, the generalized gradient approximation (GGA) were employed [19]. About 3500 LAPW basis functions per each ~ k -point, which correspond to an energy cut-off of 13 Ry or 60 LAPWs per atom, were used as a variational set. Integration inside the Brillouin zone was replaced by summation over 21 ~ k -points inside the 1=8 wedge of the irreducible Brillouin zone. All core electrons were treated fully relativistically, while valence states
B. Białek et al. / Surface Science 526 (2003) 367–374
were treated scalar relativistically, without spin– orbit coupling [20]. Self-consistency was assumed when the difference between input and output charge (spin) densities was less than 1 104 electrons/a.u.3
3. Results and discussion In Fig. 2 the total and atom-projected density of states (DOS) calculated for FePc monolayer in the paramagnetic state are presented, where Fermi level (EF ) is set to zero. For easy comparison, the DOS values of the states of the nitrogen atoms and the Fe s and p states are magnified by 40 times, as well as those of C1 atoms are magnified by 80 times. Atom-projected DOS obtained in the paramagnetic calculation reflects well the bondings between the atoms of FePc molecule inner ring. The d states of Fe atom play essential role in shaping the electronic occupied band structure of FePc monolayer in the energy range from )2.4 eV to EF . The states seen at EF are due to not only the d, but also the p states of Fe atom. The states participate in forming the coordinating bonds with pyrole nitrogen atoms (N1) through their p states. Next, both pyrole (N1) and bridged (N2) nitrogens p states overlap with the p states of pyrole carbon (C1) atoms, enhancing the total number of states at EF . For the next occupied band, which is separated from the band at EF by 1.4 eV, most significant are the states of the N1 and N2 atoms and somewhat from the C1 atoms. The strong influence of FePc ligand atoms on the band structure of the monolayer is in accordance with the molecular calculation, which indicates that the energy level next to the highest occupied molecular orbital is associated with FePc ring p electrons [13]. In the energy below )2.4 eV the contribution of the states of Fe atom to the energy bands is marginal, and the band structure is determined mostly by the p states of C, and in a smaller degree, N atoms. In the unoccupied band structure of the paramagnetic FePc monolayer we distinguish the bands separated from each other by a quite large gap. The first unoccupied band is composed from
369
the Fe d and N1, N2, and C p states. The band is separated from the states at EF by 1.3 eV. The components of the second unoccupied band at 2.8 eV, separated from the first one by 0.96 eV, are the same with the first one, but the number of contributing Fe states is higher and the band is broader, because of the larger delocalization of the empty states of N and C atoms. The presence of large number of states at EF indicates magnetic instability. Indeed, by the total energy calculations we found that the energy of the ferromagnetic FePc monolayer is 0.91 eV lower than that of the paramagnetic one. Also, there is considerable difference between the value of work function obtained for the para- and ferromagnetic states, which are 5.09 and 4.76 eV, respectively. The latter value is much closer to the experimental one (4.55 eV) obtained in photoemission yield spectroscopy experiment for an ex-situ evaporated FePc thin film [10]. In Fig. 3 the total and atom-projected DOS obtained for FePc monolayer in the spin-polarized calculation are presented. It is seen that the magnetic properties of Fe atom influence mainly on the electronic band structure of the monolayer near EF . Below )1.8 and above 3.8 eV there is hardly any difference between the bands created by majority and minority electrons, and the DOS picture resembles that obtained in the spin-unpolarized calculation. In contrary, the band structure near EF is affected in a large degree by the magnetic properties of Fe atom. In the energy range from )1.8 to 3.6 eV the band splittings between the majority and minority spins are well seen. The band structure near EF is shaped mostly by the states of the central Fe atom, which also influences the states of the atoms of FePc inner ring. An analysis of the occupied and unoccupied Fe d states confirms the ðd "Þ4 ðd #Þ2 iron intermediate-spin configuration ðS ¼ 1Þ. This agrees with the results of the calculation in the one-electron Hartree–Fock– Slater model done for iron tetraazaporphyrin (FeTAP) [12], which is considered as a parent compound of FePc. The Fe-projected DOS indicates that the incompletely occupied Fe dx2 –y 2 state is the main component of the states observed at EF . Instead of the large number of states seen in the paramagnetic
B. Białek et al. / Surface Science 526 (2003) 367–374
DOS (states/eV·atom)
DOS (states/eV·f.u.)
370 50 40 30 20 10 0 -10
50 40 30 20 10 0 -10
Total
FePc
-8
-6
-4
-2 Energy (eV)
0
2
6
Total 40×s 40×p d
Fe
-8
4
-6
-4
-2
0
2
4
6
DOS (states/eV·atom)
DOS (states/eV·atom)
DOS (states/eV·atom)
Energy (eV) 50 40 30 20 10 0 -10
50 40 30 20 10 0 -10
50 40 30 20 10 0 -10
Total s p
40×N1
-8
-6
-4
-2 Energy (eV)
0
2
-6
-4
-2 Energy (eV)
0
2
4
6
Total s p
80×C1
-8
6
Total s p
40×N2
-8
4
-6
-4
-2 Energy (eV)
0
2
4
6
Fig. 2. Total and atom-projected DOS of the paramagnetic FePc monolayer. Labels are in accordance with Fig. 1.
FePc monolayer, we observe that the energy band splitting reduces the number of states at EF to 30% of the paramagnetic one. The splitting of the Fe d states results with appearance of a large peak
which is centered at )1.4 eV––the region, where there was a wide band gap in paramagnetic FePc. Along with the Fe d states splitting we observe a splitting of the p states of C atoms. This causes that
DOS (states/eV·atom·spin)
DOS (states/eV·atom·spin)
DOS (states/eV·f.u.·spin)
B. Białek et al. / Surface Science 526 (2003) 367–374 25 20 15 10 5 0 -5 -10 -15 -20 -25 -10
25 20 15 10 5 0 -5 -10 -15 -20 -25 -10
25 20 15 10 5 0 -5 -10 -15 -20 -25 -10
371
Total
FePc
-8
-6
-4
-2 Energy (eV)
0
2
-6
-4
-2 Energy (eV)
0
2
4
6
Total s p
40×N1
-8
6
Total 80×s 80×p d
Fe
-8
4
-6
-4
-2
0
2
4
6
DOS (states/eV·atom·spin)
DOS (states/eV·atom·spin)
Energy (eV) 25 20 15 10 5 0 -5 -10 -15 -20 -25 -10
25 20 15 10 5 0 -5 -10 -15 -20 -25 -10
Total s p
40×N2
-8
-6
-4
-2 Energy (eV)
0
2
6
Total s p
80×C1
-8
4
-6
-4
-2
0
2
4
Energy (eV)
Fig. 3. Total and atom-projected spin-polarized DOS. Minority spins are factored by the negative values.
6
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two bands are present in the energy region, in which there was an energy gap in the paramagnetic FePc monolayer. The splitting of C states follows the interaction between the spin-up electrons of Fe and N1, and N2 atoms. For all these atoms the bands occupied by spin-up electrons are seen around )1.2 eV. In result, we do not observe a wide energy gap near EF , in the ferromagnetic FePc monolayer. In Fig. 4 the total spin density contour plots of the FePc monolayer unit cell is presented. The plots are drawn in (a) FePc molecule plane and (b) in the plane perpendicular to the molecule through the Fe-N1 bond, cutting in half the C1–C1 and C2–C2 bonds. The solid and dashed lines represent majority and minority spins, respectively. The lowest contour starts from 5 104 electron/ a.u.3 and subsequent lines differ by a factor of 2. It is seen that the majority electrons are accumulated at the ferrous atom, while minority ones fill the remaining space within the FePc inner ring, between the Fe sphere and pyrole nitrogens. Strong
positive polarization of the Fe atom is due to the localized dxz;yz ð"Þ states, while the negative polarization of the remained space inside the molecule inner ring is given by the N1 px;y and Fe dxy # states. There is very weak positive polarization around bridged nitrogens (N2) in the x- and ydirection. The calculated magnetic moments of N atoms, both N1 and N2, are negligible. Unlike the ligand atoms, the Fe magnetic moment is large, equal to 1.95 lB , which is, due to different surrounding of Fe atom, 0.30 lB smaller than magnetic moment of bulk bcc Fe (2.2 lB ) [21]. The obtained value is also smaller than the result of Mulliken population analysis done for FeTAP, which yielded 2.53 unpaired d electrons of Fe atom [12]. The obtained spin density distribution with an outburst of positive charge out of the FePc plane in the z-direction, into the vacuum region, is similar to the observed spin density distribution around the Fe (0 0 1) surface [21]. In contrast to the z-direction, in the FePc plane we observe that
(a)
(b)
C2-C2
C1-C1
N1
Fe
N1
C1-C1
C2-C2
Fig. 4. Spin density contour plot in the unit cell of the FePc model monolayer (a) in the FePc plane, (b) in the plane vertical to FePc. The lowest contour starts from 5:0 104 electrons/a.u.3 and subsequent lines differ by a factor of 2.
B. Białek et al. / Surface Science 526 (2003) 367–374
the positive polarization is very short, actually limited to the Fe site. Negative polarization seen outside the Fe site extends slightly towards the N1 and further to the C1 atoms. Such a strong localization of positive spin density on the central Fe atom in FePc monolayer may be of primary importance when it comes to the properties of FePc thin films. The FePc monolayer with such a rich electronic structure near EF may exhibit metallic properties, which is inconsistent with the electrical measurements: it is a p-type semiconductor, like most MPcs [2]. The calculated metallicity of FePc monolayer is also very different from the results obtained for the similar model NiPc monolayer of which the electronic band structure is characterized as the one of semiconductors (or insulators) with the large energy gap (0.7 eV) between the last occupied and the first unoccupied band [16]. The calculated DOS at EF of the minority spins in the ferromagnetic state is 13.8 states/eV cell, which is still large enough to induce an instability. We expect that there is another magnetic phase, e.g., antiferromagnetic state, in the FePc monolayer. The phase transition between the metallic ferromagnetism and the insulating antiferromagnetism is well known characters of the system [22]. Hence, it is considered that the metallicity of ferromagnetic FePc monolayer in our calculation is an indication of more stable insulating antiferromagnetic phase than ferromagnetic FePc monolayer.
4. Conclusion Ground state electronic structure and magnetic properties of FePc monolayer of P4/mmm symmetry have been calculated using the all-electron FLAPW band method. Both the spin-unpolarized and spin-polarized calculations were carried out for the investigated system. In paramagnetic FePc monolayer the large number of states at EF was found and wide band gaps separated the band from the others in the near EF region. By the total energy calculations we have found that the spinpolarized FePc monolayer is more stable than the paramagnetic one, and has metallic properties. It
373
was found that the magnetic moment of the Fe in the center of FePc molecule is 1.95 lB . The ferrous properties of the central metal atom do not affect much paramagnetic properties of the FePc ligand. In-plane spin distribution is such that only the Fe site is strongly positively polarized, while the Pc ring is very weakly negatively polarized. The Fe site experiences strong positive polarization in the out-of-plane direction, which may play crucial role in the FePc thin film applications as gas sensors or catalyst. We consider that still large DOS at EF in ferromagnetic state is expected to cause insulating antiferromagnetism of the system, via a metal– insulator transition.
Acknowledgements This work was supported by the Korea Science and Engineering Foundation (KOSEF) through the electron Spin Science Center (eSSC) at Pohang University of Science and Technology.
References [1] C.C. Leznoff, A.B.P. Lever, Phthalocyanines. Properties and Applications, VCH Publishers, New York, 1989. [2] J. Simon, J.J. Andre, Molecular Semiconductors, Springer Verlag, Berlin, 1985. [3] Q. Zhou, R.D. Gould, Thin Solid Films 317 (1998) 436. [4] N.A. Bell, J.S. Brooks, S.D. Forder, J.K. Robinson, S.C. Thorpe, Polyhedron 21 (2002) 115. [5] N. Safari, F. Bahadoran, J. Mol. Catal. A 171 (2001) 115. [6] F.I. Vilesov, A.A. Zagrubskii, D.Z. Garbuzov, Sov. Phys. Solid State 5 (1964) 1460. [7] W. Pong, J.A. Smith, J. Appl. Phys. 44 (1973) 174. [8] E.E. Koch, W.D. Grobman, J. Chem. Phys. 67 (1977) 837. [9] J. Szuber, B. Szczepaniak, M. Piwowarczyk, S. Kochowski, A. Opilski, Czech. J. Phys. 43 (1993) 1041. [10] J. Szuber, B. Szczepaniak, S. Kochowski, A. Opilski, Vacuum 46 (1995) 547. [11] H. Yoshida, K. Tsutsumi, N. Sato, J. Electron Spectrosc. Relat. Phenom. 121 (2001) 83. [12] Z. Berkovitch-Yellin, D.E. Ellis, J. Am. Chem. Soc. 103 (1981) 6066. [13] M.-S. Liao, S. Scheiner, J. Chem. Phys. 114 (2001) 9780. [14] M.C. B€ ohm, Phys. Rev. B 28 (1983) 6914. [15] F.W. Kutzler, D.E. Ellis, J. Chem. Phys. 84 (1986) 1033. [16] B. Białek, I.G. Kim, J.I. Lee, Synth. Met. 129 (2002) 151. [17] J.F. Kirner, W. Dow, W.R. Scheidt, Inorg. Chem. 15 (1976) 1685.
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[18] E. Wimmer, H. Krakauer, M. Weinert, A.J. Freeman, Phys. Rev. B 24 (1981) 864, and references therein; M. Weinert, E. Wimmer, A.J. Freeman, Phys. Rev. B 26 (1982) 4571. [19] J.P. Perdew, Y. Wang, Phys. Rev. B 45 (1992) 13244.
[20] D.D. Koelling, B.N. Harmon, J. Phys. C: Solid State Phys. 10 (1977) 3170. [21] S. Ohnishi, A.J. Freeman, M. Weinert, Phys. Rev. B 28 (1983) 6741. [22] M. Imada, A. Fujimori, Y. Tokura, Rev. Mod. Phys. 74 (1998) 1039.
First-principles study on the electronic structures of iron phthalocyanine monolayer Beata Białek a
a,b
, In Gee Kim a, Jae Il Lee
a,*
Department of Physics, Inha University, 253 Yong-Hyun Dong, Nam-Gu, 402-751 Incheon, South Korea b Institute of Physics, Pedagogical University, 42-200 Czeßstochowa, Poland Received 7 August 2002; accepted for publication 30 December 2002
Abstract The electronic band structure and magnetic properties of iron phthalocyanine (FePc) monolayer were investigated by using the first-principles all-electron full-potential linearized augmented plane wave energy band method. It is found that the ferromagnetic FePc monolayer is energetically more stable than the paramagnetic one. The exchange interaction, which splits the majority and minority bands, influences strongly on the electronic structure near the Fermi level (EF ). Magnetic moment of the central Fe atom is calculated to 1.95 lB . The range of the positive polarization of Fe site is larger in the out-of-plane than in the in-plane direction. The FePc ligand remains paramagnetic. The presence of states at EF indicates the metallic character of FePc monolayer both for the paramagnetic and ferromagnetic states. However, the large density of states at EF of the majority spins in the ferromagnetic state is expected to cause a phase transition to insulating antiferromagnetic state from the metallic ferromagnetic one. Ó 2002 Elsevier Science B.V. All rights reserved. Keywords: Iron; Density functional calculations; Surface electronic phenomena (work function, surface potential, surface states, etc.)
1. Introduction Phthalocyanine (Pc) is a kind of organic compounds with very interesting chemical and physical properties. A high chemical and thermal stability as well as conducting properties of Pc determines the use of its various compounds in many fields of industry [1,2]. Special attention is paid to transition-metal substituted Pcs (MPcs), which are widely applied for specific optoelectronic devices, gas sen-
*
Corresponding author. Tel.: +82-32-860-7654; fax: +82-32872-7562. E-mail address: [email protected] (J.I. Lee).
sors and solar cells. Among them is iron phthalocyanine (FePc) applied for sensing and effective catalytic properties [1,3–5]. It is well known that any practical application of MPcs is closely related to their electronic structures which have been the subject of both experimental and theoretical investigations for many years. For the case of FePc thin films the experimental study were carried out by means of ultraviolet photoelectron spectroscopy [6–8], and more recently, by photoemission yield spectroscopy [9,10], and by the inverse photoemission spectroscopy [11]. Theoretical studies usually concerned an isolated FePc molecule, and therefore only a discrete electronic structure of FePc was obtained [12,13].
0039-6028/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0039-6028(03)00002-5
368
B. Białek et al. / Surface Science 526 (2003) 367–374
The band structure of the periodic systems containing Pc molecules was very seldom investigated theoretically. Only for the case of NiPc, B€ ohm reported the results of the crystal-orbital approach based on a semiempirical Hartree–Fock self-consistent-field model [14]. Kutzler and Ellis applied a discrete variational X a calculation to determine the charge density, molecular potential, eigenvalues and eigenvectors of isolated NiPc molecule, and used these parameters to compute the band structure of a molecular stack [15]. Very recently, Białek et al. applied the all-electron full-potential linearized augmented plane-wave (FLAPW) energy band method in order to determine the electronic structure of NiPc monolayer and bulk [16]. In this paper we present the results of the firstprinciples electronic structure calculations on FePc monolayer by using the FLAPW energy band method. We compare the electronic properties of ferromagnetic FePc monolayer with the paramagnetic one and discuss their band structures. We also discuss the influence of magnetic properties of Fe atom on the monolayer electronic structure.
2. Computational aspects FePc is a large molecule consisted of 57 atoms as presented in Fig. 1. In solid state the molecules aggregate forming crystals of three different polymorphic forms, among them so-called b-phase is known to be the most stable one. The crystal data of the structure of intermediate-spin ground state FePc (S ¼ 1) [17] was used to model a monolayer––a representative for FePc thin film. Similar model has already been used in the case of NiPc [16]. The model monolayer consists of square unit cells containing single FePc molecule. The molecule position is such that its symmetry axes led along the mirror axis of an isoindole unit of FePc cover with the unit cell diagonals. The chosen lattice constant was 25.91 a.u., being the distance between the center of the nearest molecules laying in the (0 0 1) plane of the b-phase of FePc crystal [17]. Pc thin films are highly ordered systems, and in a monolayer the interactions between molecules are very weak, so the model of high symmetry is
Fig. 1. A schematic view of FePc molecule.
good enough for description of the thin film properties. The geometry of a single FePc molecule of D4h symmetry was also taken from the crystallographic data [17]. The chosen model has P4/ mmm symmetry and there are nine inequivalent atoms (including hydrogens) in the unit cell, to which we shall refer hereafter according to the numbering shown in Fig. 1. Since the rigidity of FePc molecules, we do not perform a geometrical optimization for determining the internal atomic positions. The band structure calculations were performed by means of the all-electron FLAPW method [18]. Lattice harmonics with l 6 8 were considered to describe the charge density, potential and wavefunctions inside each muffin-tin sphere within the radii of 2.3 a.u. for Fe, 1.2 a.u. for C and N, and 0.6 a.u. for H. For the exchange-correlation potential, the generalized gradient approximation (GGA) were employed [19]. About 3500 LAPW basis functions per each ~ k -point, which correspond to an energy cut-off of 13 Ry or 60 LAPWs per atom, were used as a variational set. Integration inside the Brillouin zone was replaced by summation over 21 ~ k -points inside the 1=8 wedge of the irreducible Brillouin zone. All core electrons were treated fully relativistically, while valence states
B. Białek et al. / Surface Science 526 (2003) 367–374
were treated scalar relativistically, without spin– orbit coupling [20]. Self-consistency was assumed when the difference between input and output charge (spin) densities was less than 1 104 electrons/a.u.3
3. Results and discussion In Fig. 2 the total and atom-projected density of states (DOS) calculated for FePc monolayer in the paramagnetic state are presented, where Fermi level (EF ) is set to zero. For easy comparison, the DOS values of the states of the nitrogen atoms and the Fe s and p states are magnified by 40 times, as well as those of C1 atoms are magnified by 80 times. Atom-projected DOS obtained in the paramagnetic calculation reflects well the bondings between the atoms of FePc molecule inner ring. The d states of Fe atom play essential role in shaping the electronic occupied band structure of FePc monolayer in the energy range from )2.4 eV to EF . The states seen at EF are due to not only the d, but also the p states of Fe atom. The states participate in forming the coordinating bonds with pyrole nitrogen atoms (N1) through their p states. Next, both pyrole (N1) and bridged (N2) nitrogens p states overlap with the p states of pyrole carbon (C1) atoms, enhancing the total number of states at EF . For the next occupied band, which is separated from the band at EF by 1.4 eV, most significant are the states of the N1 and N2 atoms and somewhat from the C1 atoms. The strong influence of FePc ligand atoms on the band structure of the monolayer is in accordance with the molecular calculation, which indicates that the energy level next to the highest occupied molecular orbital is associated with FePc ring p electrons [13]. In the energy below )2.4 eV the contribution of the states of Fe atom to the energy bands is marginal, and the band structure is determined mostly by the p states of C, and in a smaller degree, N atoms. In the unoccupied band structure of the paramagnetic FePc monolayer we distinguish the bands separated from each other by a quite large gap. The first unoccupied band is composed from
369
the Fe d and N1, N2, and C p states. The band is separated from the states at EF by 1.3 eV. The components of the second unoccupied band at 2.8 eV, separated from the first one by 0.96 eV, are the same with the first one, but the number of contributing Fe states is higher and the band is broader, because of the larger delocalization of the empty states of N and C atoms. The presence of large number of states at EF indicates magnetic instability. Indeed, by the total energy calculations we found that the energy of the ferromagnetic FePc monolayer is 0.91 eV lower than that of the paramagnetic one. Also, there is considerable difference between the value of work function obtained for the para- and ferromagnetic states, which are 5.09 and 4.76 eV, respectively. The latter value is much closer to the experimental one (4.55 eV) obtained in photoemission yield spectroscopy experiment for an ex-situ evaporated FePc thin film [10]. In Fig. 3 the total and atom-projected DOS obtained for FePc monolayer in the spin-polarized calculation are presented. It is seen that the magnetic properties of Fe atom influence mainly on the electronic band structure of the monolayer near EF . Below )1.8 and above 3.8 eV there is hardly any difference between the bands created by majority and minority electrons, and the DOS picture resembles that obtained in the spin-unpolarized calculation. In contrary, the band structure near EF is affected in a large degree by the magnetic properties of Fe atom. In the energy range from )1.8 to 3.6 eV the band splittings between the majority and minority spins are well seen. The band structure near EF is shaped mostly by the states of the central Fe atom, which also influences the states of the atoms of FePc inner ring. An analysis of the occupied and unoccupied Fe d states confirms the ðd "Þ4 ðd #Þ2 iron intermediate-spin configuration ðS ¼ 1Þ. This agrees with the results of the calculation in the one-electron Hartree–Fock– Slater model done for iron tetraazaporphyrin (FeTAP) [12], which is considered as a parent compound of FePc. The Fe-projected DOS indicates that the incompletely occupied Fe dx2 –y 2 state is the main component of the states observed at EF . Instead of the large number of states seen in the paramagnetic
B. Białek et al. / Surface Science 526 (2003) 367–374
DOS (states/eV·atom)
DOS (states/eV·f.u.)
370 50 40 30 20 10 0 -10
50 40 30 20 10 0 -10
Total
FePc
-8
-6
-4
-2 Energy (eV)
0
2
6
Total 40×s 40×p d
Fe
-8
4
-6
-4
-2
0
2
4
6
DOS (states/eV·atom)
DOS (states/eV·atom)
DOS (states/eV·atom)
Energy (eV) 50 40 30 20 10 0 -10
50 40 30 20 10 0 -10
50 40 30 20 10 0 -10
Total s p
40×N1
-8
-6
-4
-2 Energy (eV)
0
2
-6
-4
-2 Energy (eV)
0
2
4
6
Total s p
80×C1
-8
6
Total s p
40×N2
-8
4
-6
-4
-2 Energy (eV)
0
2
4
6
Fig. 2. Total and atom-projected DOS of the paramagnetic FePc monolayer. Labels are in accordance with Fig. 1.
FePc monolayer, we observe that the energy band splitting reduces the number of states at EF to 30% of the paramagnetic one. The splitting of the Fe d states results with appearance of a large peak
which is centered at )1.4 eV––the region, where there was a wide band gap in paramagnetic FePc. Along with the Fe d states splitting we observe a splitting of the p states of C atoms. This causes that
DOS (states/eV·atom·spin)
DOS (states/eV·atom·spin)
DOS (states/eV·f.u.·spin)
B. Białek et al. / Surface Science 526 (2003) 367–374 25 20 15 10 5 0 -5 -10 -15 -20 -25 -10
25 20 15 10 5 0 -5 -10 -15 -20 -25 -10
25 20 15 10 5 0 -5 -10 -15 -20 -25 -10
371
Total
FePc
-8
-6
-4
-2 Energy (eV)
0
2
-6
-4
-2 Energy (eV)
0
2
4
6
Total s p
40×N1
-8
6
Total 80×s 80×p d
Fe
-8
4
-6
-4
-2
0
2
4
6
DOS (states/eV·atom·spin)
DOS (states/eV·atom·spin)
Energy (eV) 25 20 15 10 5 0 -5 -10 -15 -20 -25 -10
25 20 15 10 5 0 -5 -10 -15 -20 -25 -10
Total s p
40×N2
-8
-6
-4
-2 Energy (eV)
0
2
6
Total s p
80×C1
-8
4
-6
-4
-2
0
2
4
Energy (eV)
Fig. 3. Total and atom-projected spin-polarized DOS. Minority spins are factored by the negative values.
6
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B. Białek et al. / Surface Science 526 (2003) 367–374
two bands are present in the energy region, in which there was an energy gap in the paramagnetic FePc monolayer. The splitting of C states follows the interaction between the spin-up electrons of Fe and N1, and N2 atoms. For all these atoms the bands occupied by spin-up electrons are seen around )1.2 eV. In result, we do not observe a wide energy gap near EF , in the ferromagnetic FePc monolayer. In Fig. 4 the total spin density contour plots of the FePc monolayer unit cell is presented. The plots are drawn in (a) FePc molecule plane and (b) in the plane perpendicular to the molecule through the Fe-N1 bond, cutting in half the C1–C1 and C2–C2 bonds. The solid and dashed lines represent majority and minority spins, respectively. The lowest contour starts from 5 104 electron/ a.u.3 and subsequent lines differ by a factor of 2. It is seen that the majority electrons are accumulated at the ferrous atom, while minority ones fill the remaining space within the FePc inner ring, between the Fe sphere and pyrole nitrogens. Strong
positive polarization of the Fe atom is due to the localized dxz;yz ð"Þ states, while the negative polarization of the remained space inside the molecule inner ring is given by the N1 px;y and Fe dxy # states. There is very weak positive polarization around bridged nitrogens (N2) in the x- and ydirection. The calculated magnetic moments of N atoms, both N1 and N2, are negligible. Unlike the ligand atoms, the Fe magnetic moment is large, equal to 1.95 lB , which is, due to different surrounding of Fe atom, 0.30 lB smaller than magnetic moment of bulk bcc Fe (2.2 lB ) [21]. The obtained value is also smaller than the result of Mulliken population analysis done for FeTAP, which yielded 2.53 unpaired d electrons of Fe atom [12]. The obtained spin density distribution with an outburst of positive charge out of the FePc plane in the z-direction, into the vacuum region, is similar to the observed spin density distribution around the Fe (0 0 1) surface [21]. In contrast to the z-direction, in the FePc plane we observe that
(a)
(b)
C2-C2
C1-C1
N1
Fe
N1
C1-C1
C2-C2
Fig. 4. Spin density contour plot in the unit cell of the FePc model monolayer (a) in the FePc plane, (b) in the plane vertical to FePc. The lowest contour starts from 5:0 104 electrons/a.u.3 and subsequent lines differ by a factor of 2.
B. Białek et al. / Surface Science 526 (2003) 367–374
the positive polarization is very short, actually limited to the Fe site. Negative polarization seen outside the Fe site extends slightly towards the N1 and further to the C1 atoms. Such a strong localization of positive spin density on the central Fe atom in FePc monolayer may be of primary importance when it comes to the properties of FePc thin films. The FePc monolayer with such a rich electronic structure near EF may exhibit metallic properties, which is inconsistent with the electrical measurements: it is a p-type semiconductor, like most MPcs [2]. The calculated metallicity of FePc monolayer is also very different from the results obtained for the similar model NiPc monolayer of which the electronic band structure is characterized as the one of semiconductors (or insulators) with the large energy gap (0.7 eV) between the last occupied and the first unoccupied band [16]. The calculated DOS at EF of the minority spins in the ferromagnetic state is 13.8 states/eV cell, which is still large enough to induce an instability. We expect that there is another magnetic phase, e.g., antiferromagnetic state, in the FePc monolayer. The phase transition between the metallic ferromagnetism and the insulating antiferromagnetism is well known characters of the system [22]. Hence, it is considered that the metallicity of ferromagnetic FePc monolayer in our calculation is an indication of more stable insulating antiferromagnetic phase than ferromagnetic FePc monolayer.
4. Conclusion Ground state electronic structure and magnetic properties of FePc monolayer of P4/mmm symmetry have been calculated using the all-electron FLAPW band method. Both the spin-unpolarized and spin-polarized calculations were carried out for the investigated system. In paramagnetic FePc monolayer the large number of states at EF was found and wide band gaps separated the band from the others in the near EF region. By the total energy calculations we have found that the spinpolarized FePc monolayer is more stable than the paramagnetic one, and has metallic properties. It
373
was found that the magnetic moment of the Fe in the center of FePc molecule is 1.95 lB . The ferrous properties of the central metal atom do not affect much paramagnetic properties of the FePc ligand. In-plane spin distribution is such that only the Fe site is strongly positively polarized, while the Pc ring is very weakly negatively polarized. The Fe site experiences strong positive polarization in the out-of-plane direction, which may play crucial role in the FePc thin film applications as gas sensors or catalyst. We consider that still large DOS at EF in ferromagnetic state is expected to cause insulating antiferromagnetism of the system, via a metal– insulator transition.
Acknowledgements This work was supported by the Korea Science and Engineering Foundation (KOSEF) through the electron Spin Science Center (eSSC) at Pohang University of Science and Technology.
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