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Electronic structure and magnetic properties of lithium manganese spinels
Journal of Magnetism and Magnetic Materials 258–259 (2003) 287–289
Electronic structure and magnetic properties of lithium manganese spinels G.E. Grechneva,*, R. Ahujab, B. Johanssonb, O. Erikssonb a
B.Verkin Institute for Low Temperature Physics and Engineering, Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkov 61103, Ukraine b Condensed Matter Theory Group, University of Uppsala, S-75121 Uppsala, Sweden
Abstract Electronic and magnetic structures of the spinel-type lithium–manganese oxides Lix Mn2 O4 ; x ¼ 0; 0:5; 1; are studied ab initio by employing a full-potential LMTO method. The effect of the orthorhombic distortion on electronic structure and magnetism of LiMn2 O4 was investigated, and our calculations do not show a substantial charge ordering at the structural transition from the cubic spinel to the orthorhombic structure. r 2002 Elsevier Science B.V. All rights reserved. Keywords: LiMn2 O4 ; Manganese oxides; Magnetic ordering; Charge ordering
Considerable interest exists in lithium manganese oxides Lix Mn2 O4 ; 0pxp2, due to their application as rechargeable battery electrodes [1]. These oxides derive their properties from the large stability region they have with respect to the Li content, x; which can be varied between 0 and 1 without substantial changes in the spinel structure at room temperatures. The low-temperature (LT) structural transitions are believed to be caused by the cooperative Jahn–Teller distortions, related to Mn3þ ions [1–6]. In particular, the LiMn2 O4 compound, with the average manganese valence +3.5, is regarded as having an equal number of randomly distributed Mnþ4 and Mn3þ ions above room temperature. The high spin Mn3þ ions favor dynamic Jahn– Teller distortions, which are presumably responsible for the structural transition at temperatures TV C285 K, accompanied by a corresponding charge ordering. This transition is believed to be analogous to the Verwey transition in magnetite [2], though only partial segregation of Mnþ4 and Mn3þ ions was found at TV > T > 70 K [5,7]. Spin-glass-like behavior was reported [8] in LiMn2 O4 at LT, whereas a complex
*Corresponding author. Fax: +380-572-322370. E-mail address: [email protected] (G.E. Grechnev).
antiferromagnetic (AFM) state with 1152 magnetic Mn ions was proposed in Ref. [5]. Few theoretical studies have been carried out to reveal basic band structure features for some Lix Mn2 O4 systems [9,10]. The ab initio electronic structure calculations for mixed-valent manganese oxides represent a challenge to the density functional theory (DFT) due to the dynamical Jahn–Teller distortions at Mn3þ ions. Also, it is extremely difficult to find a ground state of frustrated AFM structure among a large number of degenerate non-collinear spin configurations in Lix Mn2 O4 spinels. The objective of the present work is to elucidate the electronic structure of Lix Mn2 O4 spinels, specifically for both systems in the vicinity of the expected Verwey transition, by taking into account spin polarization in a feasible form. The related bulk and magnetic properties of these oxides are evaluated and analyzed in order to reveal possible manifestations of spin, structural, and charge ordering. The cubic spinel LiMn2 O4 has a space group Fd3% m (or O7h ). The delithiated phase Mn2 O4 retains the Fd3% m structure with Li atoms removed from the spinel framework. Below the transition at TV C285 K, the complex orthorhombic phase of LiMn2 O4 (space group Fddd) was established [3]. This structure is actually very close to a large tetragonal cell, which was also proposed
0304-8853/03/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 2 ) 0 1 1 0 6 - X
states eV-1 f.u.-1
(a)
15 10 5 t2g
0
t2g eg
eg
0
-5
5
0
-1
(b)
0
10 states eV-1 f.u.-1
for the LT phase of LiMn2 O4 [5]. Ab initio electronic structure calculations were performed for Lix Mn2 O4 oxides (x=0, 0.5, 1) with a full-potential LMTO method within both the local spin density and the generalized gradient approximations of DFT [11]. The calculations were performed for the spinel structure as well as the orthorhombic structure of LiMn2 O4 for paramagnetic (PM), ferromagnetic (FM), and AFM configurations. For the Lix Mn2 O4 spinel in the AFM configuration two of the manganese atoms in the unit cell were chosen as having spins ‘‘up’’, and the other two as ‘‘down’’ spins along the [0 0 1] direction. In the LT orthorhombic phase of LiMn2 O4 ; the assigned AFM configuration corresponds to alternating planes with ‘‘up’’ and ‘‘down’’ Mn moments. The band structure of Lix Mn2 O4 is governed by a strong hybridization between Mn d- and O p-states, whereas Li atoms are substantially ionized. The densities of electronic states (DOS), NðEÞ; calculated for the AFM phases of LiMn2 O4 in the spinel and the orthorhombic structures, are shown in Fig. 1. In Lix Mn2 O4 spinels the Fermi level, EF ; lies within the non-bonding t2g band, originating predominantly from the d-states of Mn. Below EF a strong hybridization of oxygen p-states and s,p,d-states of manganese gives rise to the filled Mn–O bonding bands. The Mn majority spin t2g d-orbitals are filled for all spin-polarized Lix Mn2 O4 alloys. For the delithiated MnO2 spinel an energy gap is found between the majority and minority t2g bands, and the lithiation process is accompanied by the filling of the weakly bonding minority t2g band. The eg bands are found to be empty in all systems studied. The NðEF Þ in both spinel and orthorhombic LiMn2 O4 systems comes essentially from the d-electrons of Mn, and the contributions of other states are small. The conductivity in LiMn2 O4 was interpreted in terms of hopping of small polarons, related to distortions at Mnþ3 ions [1,7]. On the other hand, the thermoelectric power data were related [7] to an assumed peak in NðEÞ at EF ; which also results from the present calculations (see Fig. 1). The sharp peak of weakly bonding d-states at EF in the spinel AFM phase of LiMn2 O4 implies the presence of a pronounced van Hove singularity in the electronic spectrum. This singularity may cause a possible instability, and it can be seen in Fig. 1, that the orthorhombic (presumably Jahn–Teller driven) distortions produce a lowering of NðEÞ at EF : In line with this we found that the total energy of the orthorhombic phase is lower than that of the LiMn2 O4 spinel. As can be seen in Fig. 1, the distorted coordination octahedra in the orthorhombic phase give rise to wider gaps between t2g and eg bands, and the wider occupied bonding band. Although slight difference in the calculated charge density distribution is found around Mn ions due to the orthorhombic lattice distortions, it is much smaller than the pronounced
states eV-1 f.u.-1
G.E. Grechnev et al. / Journal of Magnetism and Magnetic Materials 258–259 (2003) 287–289
(c) states eV-1 f.u.-1
288
(d)
5
t2g
0
t2g
eg
eg
0
-5
5
0
-1
0 Energy (eV)
Fig. 1. Densities of states for the AFM LiMn2 O4 in the spinel ((a) total DOS; (b) finer structure of DOS at EF ) and the orthorhombic structure ((c) total DOS; (d) finer structure of DOS at EF ). Corresponding Fermi levels are marked with the vertical dashed lines.
charge ordering for Mnþ3 and Mnþ4 ions, which is expected for the Verwey transition. The calculated properties of Lix Mn2 O4 compounds are given in Table 1. In all the systems studied, the assumed simplified AFM phases have the lowest total energies, though the total energies of FM phases appeared to be only slightly higher. For the MnO2 spinel there is a good agreement of the calculated Mn moment with the moments, evaluated either from the neutron studies [4] or from the Curie–Weiss (CW) analysis [8] (2.8 mB ). According to a number of neutron studies [3,5,6] the magnetic unit cell of the LiMn2 O4 spinel appeared to be very complex, presumably due to geometrical frustration of the AFM coupling in this structure, combined with mixed-valent distribution of Mn ions. The observed partial charge ordering at LT [3,5] and a large number of quasi-ground states available [8] are apparently consistent with the results of our calculations, that give very close total energies and
G.E. Grechnev et al. / Journal of Magnetism and Magnetic Materials 258–259 (2003) 287–289 Table 1 Calculated properties of Lix Mn2 O4 : Average magnetic moment of Mn, MMn ; is in mB : Total energies DE; in eV/f.u., are defined with respect to the total energy of the corresponding PM spinel. DOS at EF ; NðEF Þ; is in states/(eV f.u.) Structure
Phase
MMn
DE
NðEF Þ
Mn2 O4 spinel
FM AFM
2.78 2.77
1.38 1.44
0 0
LiMn2 O4 spinel
FM AFM
2.50 2.49
1.45 1.48
5.2 6.6
LiMn2 O4 orthorhomb.
FM AFM
2.27 2.28
1.50 1.53
2.9 4.2
magnetic moments for the FM and the AFM structures. A CW-like behavior was observed in the temperature dependence of the magnetic susceptibility w for Lix Mn2 O4 compounds [4,5,8]. In the PM phase, AFMlike coupling appeared to be dominant, providing comparatively large and negative paramagnetic Curie temperatures, jYjX100 K. The frustrated AFM structure is presumably related to the suppression of the transition temperatures and to deviations of w1 ðTÞ from the CW behavior. Therefore, the apparent CW moment per Mn ion can vary considerably from the calculated spin-only value. For the LiMn2 O4 spinel, the CW spin moment, 3.2 mB ; appeared to be larger than the calculated one (2.5 mB ), and smaller than the spinonly value corresponding to the expected average valence of Mnþ3:5 : In summary, the AFM coupling is proven to be favorable for the Lix Mn2 O4 spinels. For the simplified AFM structures of LiMn2 O4 ; the calculations have not produced a substantial charge ordering at the transition from the cubic to the orthorhombic structure. Instead, the transition seems to be driven by a Jahn–Teller-like
289
distortion of the d-band. This study supports a view, that a strong coupling of the conduction electrons to local Jahn–Teller distortions is important for kinetic properties of Lix Mn2 O4 spinels, as well as for magnetic ordering in these compounds. Manganese oxides are usually considered as strongly correlated systems, which can not be treated appropriately by the DFT. However, the present calculations described a number of ground state properties observed in Lix Mn2 O4 oxides. This work was supported by Swedish Natural Science Research Council (VR) and Swedish Foundation for Strategic Research (SSF).
References [1] J.B. Goodenough, Solid State Ionics 69 (1994) 184. [2] J.B. Goodenough, Magnetism and the Chemical Bond, Wiley, New York, 1963. [3] J. Rodriguez-Carvajal, G. Rousse, C. Masquelier, M. Hervieu, Phys. Rev. Lett. 81 (1998) 4660. [4] J.E. Greedan, N.P. Raju, A.S. Wills, S.M. Shaw, Chem. Mater. 10 (1998) 3058. [5] A.S. Wills, N.P. Raju, J.E. Greedan, Chem. Mater. 11 (1999) 1510. [6] Y. Oohara, J. Sugiyama, M. Kontani, J. Phys. Soc. Jpn. 68 (1999) 242. [7] J. Molenda, K. Swierczek, M. Molenda, J. Marzec, Solid State Ionics 135 (2000) 53. [8] Y. Jang, B. Huang, F.C. Chou, D.R. Sadoway, J. Appl. Phys. 87 (2000) 7382. . [9] H. Berg, K. Goransson, B. Nol.ang, J.O. Thomas, J. Mater. Chem. 9 (1999) 2813. [10] S.K. Mishra, G. Ceder, Phys. Rev. B 59 (1999) 6120. [11] J.M. Wills, O. Eriksson, in: H. Dreysse (Ed.), Electronic Structure and Physical Properties of Solids, Springer, Berlin, 2000.
Electronic structure and magnetic properties of lithium manganese spinels G.E. Grechneva,*, R. Ahujab, B. Johanssonb, O. Erikssonb a
B.Verkin Institute for Low Temperature Physics and Engineering, Academy of Sciences of Ukraine, 47 Lenin Ave., Kharkov 61103, Ukraine b Condensed Matter Theory Group, University of Uppsala, S-75121 Uppsala, Sweden
Abstract Electronic and magnetic structures of the spinel-type lithium–manganese oxides Lix Mn2 O4 ; x ¼ 0; 0:5; 1; are studied ab initio by employing a full-potential LMTO method. The effect of the orthorhombic distortion on electronic structure and magnetism of LiMn2 O4 was investigated, and our calculations do not show a substantial charge ordering at the structural transition from the cubic spinel to the orthorhombic structure. r 2002 Elsevier Science B.V. All rights reserved. Keywords: LiMn2 O4 ; Manganese oxides; Magnetic ordering; Charge ordering
Considerable interest exists in lithium manganese oxides Lix Mn2 O4 ; 0pxp2, due to their application as rechargeable battery electrodes [1]. These oxides derive their properties from the large stability region they have with respect to the Li content, x; which can be varied between 0 and 1 without substantial changes in the spinel structure at room temperatures. The low-temperature (LT) structural transitions are believed to be caused by the cooperative Jahn–Teller distortions, related to Mn3þ ions [1–6]. In particular, the LiMn2 O4 compound, with the average manganese valence +3.5, is regarded as having an equal number of randomly distributed Mnþ4 and Mn3þ ions above room temperature. The high spin Mn3þ ions favor dynamic Jahn– Teller distortions, which are presumably responsible for the structural transition at temperatures TV C285 K, accompanied by a corresponding charge ordering. This transition is believed to be analogous to the Verwey transition in magnetite [2], though only partial segregation of Mnþ4 and Mn3þ ions was found at TV > T > 70 K [5,7]. Spin-glass-like behavior was reported [8] in LiMn2 O4 at LT, whereas a complex
*Corresponding author. Fax: +380-572-322370. E-mail address: [email protected] (G.E. Grechnev).
antiferromagnetic (AFM) state with 1152 magnetic Mn ions was proposed in Ref. [5]. Few theoretical studies have been carried out to reveal basic band structure features for some Lix Mn2 O4 systems [9,10]. The ab initio electronic structure calculations for mixed-valent manganese oxides represent a challenge to the density functional theory (DFT) due to the dynamical Jahn–Teller distortions at Mn3þ ions. Also, it is extremely difficult to find a ground state of frustrated AFM structure among a large number of degenerate non-collinear spin configurations in Lix Mn2 O4 spinels. The objective of the present work is to elucidate the electronic structure of Lix Mn2 O4 spinels, specifically for both systems in the vicinity of the expected Verwey transition, by taking into account spin polarization in a feasible form. The related bulk and magnetic properties of these oxides are evaluated and analyzed in order to reveal possible manifestations of spin, structural, and charge ordering. The cubic spinel LiMn2 O4 has a space group Fd3% m (or O7h ). The delithiated phase Mn2 O4 retains the Fd3% m structure with Li atoms removed from the spinel framework. Below the transition at TV C285 K, the complex orthorhombic phase of LiMn2 O4 (space group Fddd) was established [3]. This structure is actually very close to a large tetragonal cell, which was also proposed
0304-8853/03/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 0 4 - 8 8 5 3 ( 0 2 ) 0 1 1 0 6 - X
states eV-1 f.u.-1
(a)
15 10 5 t2g
0
t2g eg
eg
0
-5
5
0
-1
(b)
0
10 states eV-1 f.u.-1
for the LT phase of LiMn2 O4 [5]. Ab initio electronic structure calculations were performed for Lix Mn2 O4 oxides (x=0, 0.5, 1) with a full-potential LMTO method within both the local spin density and the generalized gradient approximations of DFT [11]. The calculations were performed for the spinel structure as well as the orthorhombic structure of LiMn2 O4 for paramagnetic (PM), ferromagnetic (FM), and AFM configurations. For the Lix Mn2 O4 spinel in the AFM configuration two of the manganese atoms in the unit cell were chosen as having spins ‘‘up’’, and the other two as ‘‘down’’ spins along the [0 0 1] direction. In the LT orthorhombic phase of LiMn2 O4 ; the assigned AFM configuration corresponds to alternating planes with ‘‘up’’ and ‘‘down’’ Mn moments. The band structure of Lix Mn2 O4 is governed by a strong hybridization between Mn d- and O p-states, whereas Li atoms are substantially ionized. The densities of electronic states (DOS), NðEÞ; calculated for the AFM phases of LiMn2 O4 in the spinel and the orthorhombic structures, are shown in Fig. 1. In Lix Mn2 O4 spinels the Fermi level, EF ; lies within the non-bonding t2g band, originating predominantly from the d-states of Mn. Below EF a strong hybridization of oxygen p-states and s,p,d-states of manganese gives rise to the filled Mn–O bonding bands. The Mn majority spin t2g d-orbitals are filled for all spin-polarized Lix Mn2 O4 alloys. For the delithiated MnO2 spinel an energy gap is found between the majority and minority t2g bands, and the lithiation process is accompanied by the filling of the weakly bonding minority t2g band. The eg bands are found to be empty in all systems studied. The NðEF Þ in both spinel and orthorhombic LiMn2 O4 systems comes essentially from the d-electrons of Mn, and the contributions of other states are small. The conductivity in LiMn2 O4 was interpreted in terms of hopping of small polarons, related to distortions at Mnþ3 ions [1,7]. On the other hand, the thermoelectric power data were related [7] to an assumed peak in NðEÞ at EF ; which also results from the present calculations (see Fig. 1). The sharp peak of weakly bonding d-states at EF in the spinel AFM phase of LiMn2 O4 implies the presence of a pronounced van Hove singularity in the electronic spectrum. This singularity may cause a possible instability, and it can be seen in Fig. 1, that the orthorhombic (presumably Jahn–Teller driven) distortions produce a lowering of NðEÞ at EF : In line with this we found that the total energy of the orthorhombic phase is lower than that of the LiMn2 O4 spinel. As can be seen in Fig. 1, the distorted coordination octahedra in the orthorhombic phase give rise to wider gaps between t2g and eg bands, and the wider occupied bonding band. Although slight difference in the calculated charge density distribution is found around Mn ions due to the orthorhombic lattice distortions, it is much smaller than the pronounced
states eV-1 f.u.-1
G.E. Grechnev et al. / Journal of Magnetism and Magnetic Materials 258–259 (2003) 287–289
(c) states eV-1 f.u.-1
288
(d)
5
t2g
0
t2g
eg
eg
0
-5
5
0
-1
0 Energy (eV)
Fig. 1. Densities of states for the AFM LiMn2 O4 in the spinel ((a) total DOS; (b) finer structure of DOS at EF ) and the orthorhombic structure ((c) total DOS; (d) finer structure of DOS at EF ). Corresponding Fermi levels are marked with the vertical dashed lines.
charge ordering for Mnþ3 and Mnþ4 ions, which is expected for the Verwey transition. The calculated properties of Lix Mn2 O4 compounds are given in Table 1. In all the systems studied, the assumed simplified AFM phases have the lowest total energies, though the total energies of FM phases appeared to be only slightly higher. For the MnO2 spinel there is a good agreement of the calculated Mn moment with the moments, evaluated either from the neutron studies [4] or from the Curie–Weiss (CW) analysis [8] (2.8 mB ). According to a number of neutron studies [3,5,6] the magnetic unit cell of the LiMn2 O4 spinel appeared to be very complex, presumably due to geometrical frustration of the AFM coupling in this structure, combined with mixed-valent distribution of Mn ions. The observed partial charge ordering at LT [3,5] and a large number of quasi-ground states available [8] are apparently consistent with the results of our calculations, that give very close total energies and
G.E. Grechnev et al. / Journal of Magnetism and Magnetic Materials 258–259 (2003) 287–289 Table 1 Calculated properties of Lix Mn2 O4 : Average magnetic moment of Mn, MMn ; is in mB : Total energies DE; in eV/f.u., are defined with respect to the total energy of the corresponding PM spinel. DOS at EF ; NðEF Þ; is in states/(eV f.u.) Structure
Phase
MMn
DE
NðEF Þ
Mn2 O4 spinel
FM AFM
2.78 2.77
1.38 1.44
0 0
LiMn2 O4 spinel
FM AFM
2.50 2.49
1.45 1.48
5.2 6.6
LiMn2 O4 orthorhomb.
FM AFM
2.27 2.28
1.50 1.53
2.9 4.2
magnetic moments for the FM and the AFM structures. A CW-like behavior was observed in the temperature dependence of the magnetic susceptibility w for Lix Mn2 O4 compounds [4,5,8]. In the PM phase, AFMlike coupling appeared to be dominant, providing comparatively large and negative paramagnetic Curie temperatures, jYjX100 K. The frustrated AFM structure is presumably related to the suppression of the transition temperatures and to deviations of w1 ðTÞ from the CW behavior. Therefore, the apparent CW moment per Mn ion can vary considerably from the calculated spin-only value. For the LiMn2 O4 spinel, the CW spin moment, 3.2 mB ; appeared to be larger than the calculated one (2.5 mB ), and smaller than the spinonly value corresponding to the expected average valence of Mnþ3:5 : In summary, the AFM coupling is proven to be favorable for the Lix Mn2 O4 spinels. For the simplified AFM structures of LiMn2 O4 ; the calculations have not produced a substantial charge ordering at the transition from the cubic to the orthorhombic structure. Instead, the transition seems to be driven by a Jahn–Teller-like
289
distortion of the d-band. This study supports a view, that a strong coupling of the conduction electrons to local Jahn–Teller distortions is important for kinetic properties of Lix Mn2 O4 spinels, as well as for magnetic ordering in these compounds. Manganese oxides are usually considered as strongly correlated systems, which can not be treated appropriately by the DFT. However, the present calculations described a number of ground state properties observed in Lix Mn2 O4 oxides. This work was supported by Swedish Natural Science Research Council (VR) and Swedish Foundation for Strategic Research (SSF).
References [1] J.B. Goodenough, Solid State Ionics 69 (1994) 184. [2] J.B. Goodenough, Magnetism and the Chemical Bond, Wiley, New York, 1963. [3] J. Rodriguez-Carvajal, G. Rousse, C. Masquelier, M. Hervieu, Phys. Rev. Lett. 81 (1998) 4660. [4] J.E. Greedan, N.P. Raju, A.S. Wills, S.M. Shaw, Chem. Mater. 10 (1998) 3058. [5] A.S. Wills, N.P. Raju, J.E. Greedan, Chem. Mater. 11 (1999) 1510. [6] Y. Oohara, J. Sugiyama, M. Kontani, J. Phys. Soc. Jpn. 68 (1999) 242. [7] J. Molenda, K. Swierczek, M. Molenda, J. Marzec, Solid State Ionics 135 (2000) 53. [8] Y. Jang, B. Huang, F.C. Chou, D.R. Sadoway, J. Appl. Phys. 87 (2000) 7382. . [9] H. Berg, K. Goransson, B. Nol.ang, J.O. Thomas, J. Mater. Chem. 9 (1999) 2813. [10] S.K. Mishra, G. Ceder, Phys. Rev. B 59 (1999) 6120. [11] J.M. Wills, O. Eriksson, in: H. Dreysse (Ed.), Electronic Structure and Physical Properties of Solids, Springer, Berlin, 2000.