- Email: [email protected]
Cr Superlattices
ACTA PHYSICO-CHIMICA SINICA Volume 23, Issue 6, June 2007 Online English edition of the Chinese language journal Cite this article as: Acta Phys. -Chim. Sin., 2007, 23(6): 846-850.
ARTICLE
Electronic Structure and Magnetic Properties of Fe/Cr Superlattices Haiquan Hu*,
Hengshuai Li,
Shouxin Cui,
Wenjun Wang
School of Physics Science & Information Engineering, Liaocheng University, Liaocheng 252059, Shandong Province, P. R. China
Abstract:
The electronic structure and magnetic properties of Fem/Crn (m=3, 4; n=1, 3, 4) superlattice were studied using the
density functional full-potential linearized augmented plane-wave (FLAPW) method. The results showed that the ferromagnetic coupling existed for the adjacent Fe layers in the Fe3/Cr1 and Fe3/Cr3 superlattices and the antiferromagnetic coupling existed for Fe4/Cr4 superlattice in the ground state. The magnetic moments of Cr atoms changed direction from layer to layer, and an antiferromagnetic coupling between Fe and Cr at the interfacial layer could be observed. Key Words:
Electronic structure; Magnetic properties; Density functional theory
Fe layers separated by Cr spacer layers have played a major role in many important discoveries related to the properties of magnetic coupling and electron transport[1]. Depending on the thickness of the intervening Cr layers, the adjacent Fe layers order either ferromagnetically (FM), antiferromagnetically (AFM) or even non-collinearly, which results in an alternation in the scattering condition for electron transport and thus results in the magnetoresistance across the Fe/Cr superlattices[2,3]. The change in magnetic ordering is expected to alter the optical and magneto-optical properties. So there has been considerable interest in studying their various physical properties and in attempting to probe the underlying physical mechanism responsible for the magnetic couplings in the superlattices. To understand the physical origin of the magnetic coupling between two successive Fe layers separated by Cr layers, a lot of studies (including first-principle total energy local density calculations) have been carried out on the Fe/Cr(001) superlattices. Levy et al.[4] used the augmented spherical wave (ASW) method to study the electronic structure and interlayer magnetic coupling of the Fem/Crn(001) (m=3, 4; n=3, 4, 5) systems. Their results showed that the AFM coupling for the Fe layers can be stabilized except in the (m, n)=(3, 3) case, for
which the ferromagnetic configuration is favored. Hideo[5] and Stoeffler et al.[6] obtained the similar moments or moment distributions of the Fe/Cr superlattices using real-space approaches (the self-consistent tight-binding (TB) method and the TB method combined with the recursion method). Herman et al.[7] carried out first-principles self-consistent spin-polarized linearized muffin-tin orbital/atomic sphere approximation (LMTO/ASA) and linearized augmented spherical wave methods/atomic sphere approximation (LASW/ASA) electronic structure calculations based on local spin-density functional theory, and found an alternating sign change in the totalenergy difference between the AFM and FM configurations depending on the thickness (or number) of Cr layers. They noted that their result was inconsistent with experiment. For reconciling the calculated results with experiment, they presumed that the interfacial roughness and the impurities effects might play a significant role. Xu et al.[8] studied the electronic structures and the magnetism of the Fem/Crn(001) (m=1, 3; and n=1, 3, 5, 7) superlattices using the self-consistent linear muffin-tin orbit (LMTO) method with the combined correction term[8], and found that for the Fem/Crn(001) systems containing three (or perhaps more) Fe layers, the FM ordering dominated over the AFM states, whereas for the Fem/Crn(001) systems
Received: November 29, 2006; Revised: January 27, 2007. * Corresponding author. Email: [email protected]. The project was supported by the HI-TECH Research and Development Program of China (2004AA32G090), and the Natural Science Foundation of Shandong Province, China (Y2006A02). Copyright © 2007, Chinese Chemical Society and College of Chemistry and Molecular Engineering, Peking University. Published by Elsevier BV. All rights reserved. Chinese edition available online at www.whxb.pku.edu.cn
Haiquan Hu et al. / Acta Physico-Chimica Sinica, 2007, 23(6): 846-850
containing a single Fe layer the AFM interactions might slightly exceed the FM interactions. These studies are all not accurate enough and the analyses are not explained in detail. In this study, the electronic structures and interlayer magnetic coupling of bcc Fem/Crn(001) (m=3, 4; n=1, 3, 4) superlattices were investigated using the density functional fullpotential linearized augmented plane-wave (FLAPW) method to compare the magnetic properties of Fe/Cr superlattices with different Cr thicknesses[9]. The method of FLAPW was more accurate than other methods. The stable interlayer magnetic coupling (having AFM or FM character) between the two Fe layers separated by Cr layers could be easily determined by comparing their total energies.
1
Method and model
The spin-polarized calculations presented in this study were performed within the generalized gradient approximation (GGA) to density functional theory, using the FLAPW method (WIEN2k)[9]. In this study, the generalized gradient approximation (GGA) (with Perdew-Wang 91 formula[10]) was used to consider the exchange and correlation effects. This approach has been successfully applied to determine the electronic and magnetic properties of many transition metal systems[11,12]. From the calculation, the partial density of states as well as the magnetic moment of each atom in the magnetic unit cell, the electronic band structure throughout the Brillouin zone, and the total energy of a magnetic cell could be found. A common bcc-based structure consisting of m Fe layers and n Cr layers stacked along the (001) direction was constructed to simulate a Fem/Crn(001) superlattices (Fig.1). A weighted average of the lattice constants of the constituents is assumed (i.e., Vegard′s law[13] holds) as in Ref.[8], because both Fe and Cr have the same bcc structure and approximately the same lattice constant (0.287 and 0.288 nm for Fe and Cr, respectively[14]). The thickness of vacuum slab along the z axis is half of the lattice constant. The atomic sphere radii of both Fe and Cr atoms are selected as 2.34 a.u. for all systems. For
both paramagnetic and magnetic (including both AFM and FM) calculations to have the same number of sampling k points in the irreducible wedge of the Brillouin zone, the double primitive cell was considered as a unit cell. Each unit cell contains two formula units. Each layer in the unit cell contains only one atom. In this study, the calculations were started with the iron moments within a layer parallel, and they were aligned ferromagnetically or antiferromagnetically with respect to neighboring iron layers. Initially, the chromium moments were set to zero. After a few iterations, all atomic moments were allowed to relax and determined by selfconsistent iteration. In general, the calculated moments and the absolute value of the total energy increase gradually with increasing number of sampling k points. In this study, a converged ground state was obtained using 3000 k points during self-consistent calculations. These k points correspond to 330, 364, 588 k points in the irreducible Brillouin zone for Fe3/Cr1, Fe3/Cr3, and Fe4/Cr4 systems, respectively. RKmax (RmtKmax, where Kmax is the plane wave cutoff and Rmt is the smallest among all atomic sphere radii), which controls the size of the basis sets in these calculations, is set to be 7.0 to calculate the GGA results. The energy convergence is selected as 0.0001 Ry.
2
Results and discussion
One can analyze the ground state of Fem/Crn systems by comparing the energy difference ΔE (ΔE=EFM−EAFM) of FM and AFM configurations. A negative ΔE indicates that the FM configuration is energetically favored with respect to the AFM configuration, and a positive ΔE indicates that the AFM is energetically favored with respect to the FM configuration. Table 1 shows the calculated total-energy differences between the FM and AFM configurations. Note that for Fe4/Cr4 superlattice, the calculated total-energy difference (ΔE) obtained in this study shows a positive value, 20.055×10−21 J, for Fe3/Cr3 superlattice, the difference is −1.308×10−21 J. So the results indicate that the FM state is the preferable phase in the ground state for the Fe3/Cr3 model, and the AFM configuration is the ground state for Fe4/Cr4 system. This result agrees qualitatively with the finding of both theoretical calculations of Levy[4] and Xu[8] et al. and experimental observations[1]. The quantitative differences between the references and results obtained in this study are assumed to result from the use of Table 1 Total-energy differences ΔE (E, ΔE in 10−21 J) for Fem/Crn(001) superlattices using 3000 k points (m, n)
Fig.1 Schematic description of the model structure for Fem/Crn superlattice used in the calculations (m=3, n=1)
EFM
EAFM
ΔE
ΔE[4]
(3, 1) −474.348
−461.268
−13.08
(3, 3) −429.442
−428.134
−1.308
−5.4497
(4, 4) −610.374
−630.429
20.055
13.0794
ΔE[8] −6.9757
The energy of paramagnetic configuration (EPM) is taken as energy zero. ΔE=EFM−EAFM
Haiquan Hu et al. / Acta Physico-Chimica Sinica, 2007, 23(6): 846-850
Table 2 Calculated magnetic moments (in 10−24 A×m2) for the Fem/Crn(001) superlattices Fei
Feb
FM
18.54
23.55
2.6883
AFM
18.73
22.80
0
FM
18.17
22.16
0.1854
0.1854
AFM
19.00
22.80
1.1124
0
FM
18.73
22.16
1.4832
0.8343
AFM
20.21
22.62
1.7613
0.7416
(m, n)
Ordering
(3, 1) (3, 3) (4, 4)
Cri
Crb
Superscripts i and b stand for interface and bulk like atoms, respectively.
different methods. For the Fe3/Cr1(001) system, the total-energy differences are −13.08×10−21 J, the calculated total energy of the FM state is lower than that of the AFM state, so the FM ordering dominates over the AFM state for the Fe3/Cr1(001) system. The populations of the magnetic moments (in 10−24 A×m2) within each atomic sphere for the Fem/Crn(001) superlattices are listed in Table 2. The overall absolute values of the magnetic moments of the Fe layers are not significantly modified by the presence of the Cr layers. For all the calculated systems, the moment on the center (or bulklike) Fe layer is strongly enhanced compared with that (20.394×10−24 A×m2) of pure bulk bcc Fe. On the other hand, the moments on the interfacial Fe layers are generally reduced with respect to those of the pure bcc Fe. The calculated magnetic moment distribution for the Fem/Crn(001) superlattice obtained in this study agrees with those of Refs.[4,8]. A strong hybridization between the Fe d and Cr d states is considered to be responsible for the moment reduction and will be discussed later in view of the density of states. However, the magnetic moments on the Cr sites are generally much smaller than those of the pure bcc Cr spin density wave (SDW) value (5.562×10−24 A×m2)[15]. In Figs. 2−4, the magnetic moments of the atoms in the magnetic unit cell are plotted. Features that are common to all the three structures are: (1) the moments of the iron atoms at the interfaces are smaller than that for bulk Fe of 20.394×10−24 A×m2, (2) the central Fe atoms moments are greater than the
Fig.2 Magnetic moments (μ) of the atoms in the magnetic
Fig.3 Magnetic moments (μ) of the atoms in the magnetic unit cell for (m, n)=(3, 3) Atoms 1−2, 6−8, and 12−13 are chromium, 3−5 and 9−11 are iron.
bulk values, (3) the moments on the chromium atoms are suppressed to varying degrees below their values in the spin density wave (SDW) state found in bulk Cr of 5.562× 10−24A×m2, (4) the Cr moments alternate direction from layer to layer, (5) the coupling between the Fe and Cr atoms at the interfaces is always antiferromagnetic in the ground state. As is well known, the Fe and Cr moments in their own pure bulk states (i.e., the bcc structure) strongly prefer to align parallel and antiparallel to the first nearest neighbor (nn), respectively. For the Fe/Cr(001) systems, the Fe and Cr moments prefer to stay in their bulk form, i.e., the Fe region is always in the ferromagnetic state whereas the Cr region is in the antiferromagnetic state except in the interfacial region. The totalenergy results show a result of the competition between the nn Cr-Cr and Fe-Fe interactions. For Fe3/Cr1 and Fe3/Cr3 systems the FM dominates over AFM. On the other hand, in the case of Fe4/Cr4, the AFM interactions may surpass the FM interactions. The Cr moments can be understand from the following point. In the Fem/Crn(001) superlattices, the magnetization on the adjacent Fe sites can be viewed as a strong perturbation field for the Cr moments, as a result, the variation of the moments on the Cr sites is thought to depend strongly on the Fe moments ordering (or alignment) and on the coupling between
Fig.4 Magnetic moments (μ) of the atoms in the magnetic
unit cell for (m, n)=(3, 1)
unit cell for (m, n)=(4, 4)
Atoms 1, 5, 9 are chromium, 2–4 and 6–8 are iron.
Atoms 1−4, 9−12, and 17 are chromium, 5−8 and 13−16 are iron.
Haiquan Hu et al. / Acta Physico-Chimica Sinica, 2007, 23(6): 846-850
Fig.5 Total density of states (paramagnetic state) for the
Fig.7 Partial density of states (spin-polarized) of the FM
Fem/Crn(001) superlattices with different (m, n)
configuration for the Fe3/Cr3(001) superlattice
(m, n): (a) (3, 1), (b) (3, 3), (c) (4, 4)
(a), (b), Fei d and Cri d are the same as in Fig.6.
Fe and Cr layers. In this study, the density of states (DOS) in their paramagnetic states in Fig.5 was investigated to understand the magnetic behavior of the Fe and Cr atoms in the Fem/Crn(001) superlattices. It is expected that the fundamental features of the total DOS for the Fe/Cr(001) systems will resemble those of their constitutes (i.e., typical of bcc Fe or Cr-like DOS). There are three main features located at approximately −3.5, −2.0, and 0.0 eV, respectively. The spin-dependent DOS of the ground states for Fem/Crn(001) with (m, n)=(3, 1), (3, 3), and (4, 4) are shown in Figs. 6–8. As a characteristic feature, a pervasively strong hybridization between Fe d and Cr d states in the whole energy region from the bottom of the band up to high above Ef is seen. As stated above, the reduction of the interface like Fei and Cri moment is considered to be related to the strong d - d hybridization between the Fe d and Cr d states. It can be observed that the moment of the interface like Fei has a larger value in the AFM configuration of Fe4/Cr4 superlattice than those in FM configuration of Fe3/Cr1 and Fe3/Cr3 super-
Fig.6 Partial density of states (spin-polarized) of the FM configuration for the Fe3/Cr1(001) superlattice (a) and (b) denote spin up and spin down, respectively. Solid and dotted lines denote Fei d and Cri d states, respectively. The superscript i stands for interface like atoms.
Fig.8 Partial density of states (spin-polarized) of the AFM configuration for the Fe4/Cr4(001) superlattice (a), (b), Fei d and Cri d are the same as in Fig.6.
lattices.
3
Conclusions
The results of the first principles FLAPW studies of electronic structure and magnetic properties of both the FM and AFM configurations for Fem/Crn superlattices (m=3, 4; n=1, 3, 4) were presented. The calculated total energy of the FM state was lower than that of the AFM state for Fe3/Cr1 and Fe3/Cr3 superlattices, whereas the energy of the AFM state was lower than that of the FM for Fe4/Cr4 superlattice. For all the calculated systems the moment on the center (or bulklike) Fe layer was strongly enhanced compared with that of pure bulk bcc Fe, but the moments on the interfacial Fe layers were generally reduced. A strong hybridization between the Fe d and Cr d states was considered to be responsible for the moment reduction. The magnetic moments of Cr atoms changed direction from layer to layer. The absolute values of magnetic moments on the Cr sites were generally much smaller than those of the pure bcc Cr spin density wave (SDW) value. An antiferromagnetic coupling existed between Fe and Cr at the interfacial layer.
Haiquan Hu et al. / Acta Physico-Chimica Sinica, 2007, 23(6): 846-850
References 1 Pierce, D. T.; Unguris, J.; Celotta, R. J.; Stiles, M. D. J. Magn. Magn. Mater., 1999, 200: 290 2 Parkin, S. S. P.; More, N.; Roche, K. P. Phys. Rev. Lett., 1990, 4: 2304 3 Zhang, J. F.; Ali, M.; Chen, H. Journal of Southwest China Normal University (Natural Science), 2005, 30: 1061 4 Levy, P. M.; Ounadjela, K.; Zhang, S.; Wang, Y.; Sommers, C. B.; Fert, A. J. Appl. Phys., 1990, 67: 5914 5 Hideo, H. Phys. Rev. B, 1990, 42: 2368 6 Ounadjela, K.; Sommers, C. B.; Fert, A.; Stoeffler, D.; Gautier, F.; Moruzzi, V. L. Europhys. Lett., 1991, 15: 875 7 Herman, F.; Juergen, S.; Mark, V. S. J. Appl. Phys., 1991, 69:
4783 8 Xu, J. H.; Freeman, A. J. Phys. Rev. B, 1993, 47: 165 9 Blaha, P.; Schwarz, K.; Madsen, G. K. H.; Kvasnicka, D.; Luitz, J. WIEN2k, Vienna: Vienna University of Technology, 2002 10 Perdew, J. P.; Wang, Y. Phys. Rev. B, 1992, 45: 13244 11 Gavrilenko, V. I.; Wu, R. J. Magn. Magn. Mater., 2003, 260: 330 12 Wu, R. Q.; Freeman, A. J. J. Magn. Magn. Mater., 1999, 200: 498 13 Cahn, R. W.; Haasen, P. Physical mettallurgy. Amsterdam, NorthHolland, 1983: 178 14 Kittel, C. Introduction to solid state physics. 5th ed. New York: Wiley, 1976: 31 15 Fawcett, E. Rev. Mod. Phys., 1988, 60: 209
ARTICLE
Electronic Structure and Magnetic Properties of Fe/Cr Superlattices Haiquan Hu*,
Hengshuai Li,
Shouxin Cui,
Wenjun Wang
School of Physics Science & Information Engineering, Liaocheng University, Liaocheng 252059, Shandong Province, P. R. China
Abstract:
The electronic structure and magnetic properties of Fem/Crn (m=3, 4; n=1, 3, 4) superlattice were studied using the
density functional full-potential linearized augmented plane-wave (FLAPW) method. The results showed that the ferromagnetic coupling existed for the adjacent Fe layers in the Fe3/Cr1 and Fe3/Cr3 superlattices and the antiferromagnetic coupling existed for Fe4/Cr4 superlattice in the ground state. The magnetic moments of Cr atoms changed direction from layer to layer, and an antiferromagnetic coupling between Fe and Cr at the interfacial layer could be observed. Key Words:
Electronic structure; Magnetic properties; Density functional theory
Fe layers separated by Cr spacer layers have played a major role in many important discoveries related to the properties of magnetic coupling and electron transport[1]. Depending on the thickness of the intervening Cr layers, the adjacent Fe layers order either ferromagnetically (FM), antiferromagnetically (AFM) or even non-collinearly, which results in an alternation in the scattering condition for electron transport and thus results in the magnetoresistance across the Fe/Cr superlattices[2,3]. The change in magnetic ordering is expected to alter the optical and magneto-optical properties. So there has been considerable interest in studying their various physical properties and in attempting to probe the underlying physical mechanism responsible for the magnetic couplings in the superlattices. To understand the physical origin of the magnetic coupling between two successive Fe layers separated by Cr layers, a lot of studies (including first-principle total energy local density calculations) have been carried out on the Fe/Cr(001) superlattices. Levy et al.[4] used the augmented spherical wave (ASW) method to study the electronic structure and interlayer magnetic coupling of the Fem/Crn(001) (m=3, 4; n=3, 4, 5) systems. Their results showed that the AFM coupling for the Fe layers can be stabilized except in the (m, n)=(3, 3) case, for
which the ferromagnetic configuration is favored. Hideo[5] and Stoeffler et al.[6] obtained the similar moments or moment distributions of the Fe/Cr superlattices using real-space approaches (the self-consistent tight-binding (TB) method and the TB method combined with the recursion method). Herman et al.[7] carried out first-principles self-consistent spin-polarized linearized muffin-tin orbital/atomic sphere approximation (LMTO/ASA) and linearized augmented spherical wave methods/atomic sphere approximation (LASW/ASA) electronic structure calculations based on local spin-density functional theory, and found an alternating sign change in the totalenergy difference between the AFM and FM configurations depending on the thickness (or number) of Cr layers. They noted that their result was inconsistent with experiment. For reconciling the calculated results with experiment, they presumed that the interfacial roughness and the impurities effects might play a significant role. Xu et al.[8] studied the electronic structures and the magnetism of the Fem/Crn(001) (m=1, 3; and n=1, 3, 5, 7) superlattices using the self-consistent linear muffin-tin orbit (LMTO) method with the combined correction term[8], and found that for the Fem/Crn(001) systems containing three (or perhaps more) Fe layers, the FM ordering dominated over the AFM states, whereas for the Fem/Crn(001) systems
Received: November 29, 2006; Revised: January 27, 2007. * Corresponding author. Email: [email protected]. The project was supported by the HI-TECH Research and Development Program of China (2004AA32G090), and the Natural Science Foundation of Shandong Province, China (Y2006A02). Copyright © 2007, Chinese Chemical Society and College of Chemistry and Molecular Engineering, Peking University. Published by Elsevier BV. All rights reserved. Chinese edition available online at www.whxb.pku.edu.cn
Haiquan Hu et al. / Acta Physico-Chimica Sinica, 2007, 23(6): 846-850
containing a single Fe layer the AFM interactions might slightly exceed the FM interactions. These studies are all not accurate enough and the analyses are not explained in detail. In this study, the electronic structures and interlayer magnetic coupling of bcc Fem/Crn(001) (m=3, 4; n=1, 3, 4) superlattices were investigated using the density functional fullpotential linearized augmented plane-wave (FLAPW) method to compare the magnetic properties of Fe/Cr superlattices with different Cr thicknesses[9]. The method of FLAPW was more accurate than other methods. The stable interlayer magnetic coupling (having AFM or FM character) between the two Fe layers separated by Cr layers could be easily determined by comparing their total energies.
1
Method and model
The spin-polarized calculations presented in this study were performed within the generalized gradient approximation (GGA) to density functional theory, using the FLAPW method (WIEN2k)[9]. In this study, the generalized gradient approximation (GGA) (with Perdew-Wang 91 formula[10]) was used to consider the exchange and correlation effects. This approach has been successfully applied to determine the electronic and magnetic properties of many transition metal systems[11,12]. From the calculation, the partial density of states as well as the magnetic moment of each atom in the magnetic unit cell, the electronic band structure throughout the Brillouin zone, and the total energy of a magnetic cell could be found. A common bcc-based structure consisting of m Fe layers and n Cr layers stacked along the (001) direction was constructed to simulate a Fem/Crn(001) superlattices (Fig.1). A weighted average of the lattice constants of the constituents is assumed (i.e., Vegard′s law[13] holds) as in Ref.[8], because both Fe and Cr have the same bcc structure and approximately the same lattice constant (0.287 and 0.288 nm for Fe and Cr, respectively[14]). The thickness of vacuum slab along the z axis is half of the lattice constant. The atomic sphere radii of both Fe and Cr atoms are selected as 2.34 a.u. for all systems. For
both paramagnetic and magnetic (including both AFM and FM) calculations to have the same number of sampling k points in the irreducible wedge of the Brillouin zone, the double primitive cell was considered as a unit cell. Each unit cell contains two formula units. Each layer in the unit cell contains only one atom. In this study, the calculations were started with the iron moments within a layer parallel, and they were aligned ferromagnetically or antiferromagnetically with respect to neighboring iron layers. Initially, the chromium moments were set to zero. After a few iterations, all atomic moments were allowed to relax and determined by selfconsistent iteration. In general, the calculated moments and the absolute value of the total energy increase gradually with increasing number of sampling k points. In this study, a converged ground state was obtained using 3000 k points during self-consistent calculations. These k points correspond to 330, 364, 588 k points in the irreducible Brillouin zone for Fe3/Cr1, Fe3/Cr3, and Fe4/Cr4 systems, respectively. RKmax (RmtKmax, where Kmax is the plane wave cutoff and Rmt is the smallest among all atomic sphere radii), which controls the size of the basis sets in these calculations, is set to be 7.0 to calculate the GGA results. The energy convergence is selected as 0.0001 Ry.
2
Results and discussion
One can analyze the ground state of Fem/Crn systems by comparing the energy difference ΔE (ΔE=EFM−EAFM) of FM and AFM configurations. A negative ΔE indicates that the FM configuration is energetically favored with respect to the AFM configuration, and a positive ΔE indicates that the AFM is energetically favored with respect to the FM configuration. Table 1 shows the calculated total-energy differences between the FM and AFM configurations. Note that for Fe4/Cr4 superlattice, the calculated total-energy difference (ΔE) obtained in this study shows a positive value, 20.055×10−21 J, for Fe3/Cr3 superlattice, the difference is −1.308×10−21 J. So the results indicate that the FM state is the preferable phase in the ground state for the Fe3/Cr3 model, and the AFM configuration is the ground state for Fe4/Cr4 system. This result agrees qualitatively with the finding of both theoretical calculations of Levy[4] and Xu[8] et al. and experimental observations[1]. The quantitative differences between the references and results obtained in this study are assumed to result from the use of Table 1 Total-energy differences ΔE (E, ΔE in 10−21 J) for Fem/Crn(001) superlattices using 3000 k points (m, n)
Fig.1 Schematic description of the model structure for Fem/Crn superlattice used in the calculations (m=3, n=1)
EFM
EAFM
ΔE
ΔE[4]
(3, 1) −474.348
−461.268
−13.08
(3, 3) −429.442
−428.134
−1.308
−5.4497
(4, 4) −610.374
−630.429
20.055
13.0794
ΔE[8] −6.9757
The energy of paramagnetic configuration (EPM) is taken as energy zero. ΔE=EFM−EAFM
Haiquan Hu et al. / Acta Physico-Chimica Sinica, 2007, 23(6): 846-850
Table 2 Calculated magnetic moments (in 10−24 A×m2) for the Fem/Crn(001) superlattices Fei
Feb
FM
18.54
23.55
2.6883
AFM
18.73
22.80
0
FM
18.17
22.16
0.1854
0.1854
AFM
19.00
22.80
1.1124
0
FM
18.73
22.16
1.4832
0.8343
AFM
20.21
22.62
1.7613
0.7416
(m, n)
Ordering
(3, 1) (3, 3) (4, 4)
Cri
Crb
Superscripts i and b stand for interface and bulk like atoms, respectively.
different methods. For the Fe3/Cr1(001) system, the total-energy differences are −13.08×10−21 J, the calculated total energy of the FM state is lower than that of the AFM state, so the FM ordering dominates over the AFM state for the Fe3/Cr1(001) system. The populations of the magnetic moments (in 10−24 A×m2) within each atomic sphere for the Fem/Crn(001) superlattices are listed in Table 2. The overall absolute values of the magnetic moments of the Fe layers are not significantly modified by the presence of the Cr layers. For all the calculated systems, the moment on the center (or bulklike) Fe layer is strongly enhanced compared with that (20.394×10−24 A×m2) of pure bulk bcc Fe. On the other hand, the moments on the interfacial Fe layers are generally reduced with respect to those of the pure bcc Fe. The calculated magnetic moment distribution for the Fem/Crn(001) superlattice obtained in this study agrees with those of Refs.[4,8]. A strong hybridization between the Fe d and Cr d states is considered to be responsible for the moment reduction and will be discussed later in view of the density of states. However, the magnetic moments on the Cr sites are generally much smaller than those of the pure bcc Cr spin density wave (SDW) value (5.562×10−24 A×m2)[15]. In Figs. 2−4, the magnetic moments of the atoms in the magnetic unit cell are plotted. Features that are common to all the three structures are: (1) the moments of the iron atoms at the interfaces are smaller than that for bulk Fe of 20.394×10−24 A×m2, (2) the central Fe atoms moments are greater than the
Fig.2 Magnetic moments (μ) of the atoms in the magnetic
Fig.3 Magnetic moments (μ) of the atoms in the magnetic unit cell for (m, n)=(3, 3) Atoms 1−2, 6−8, and 12−13 are chromium, 3−5 and 9−11 are iron.
bulk values, (3) the moments on the chromium atoms are suppressed to varying degrees below their values in the spin density wave (SDW) state found in bulk Cr of 5.562× 10−24A×m2, (4) the Cr moments alternate direction from layer to layer, (5) the coupling between the Fe and Cr atoms at the interfaces is always antiferromagnetic in the ground state. As is well known, the Fe and Cr moments in their own pure bulk states (i.e., the bcc structure) strongly prefer to align parallel and antiparallel to the first nearest neighbor (nn), respectively. For the Fe/Cr(001) systems, the Fe and Cr moments prefer to stay in their bulk form, i.e., the Fe region is always in the ferromagnetic state whereas the Cr region is in the antiferromagnetic state except in the interfacial region. The totalenergy results show a result of the competition between the nn Cr-Cr and Fe-Fe interactions. For Fe3/Cr1 and Fe3/Cr3 systems the FM dominates over AFM. On the other hand, in the case of Fe4/Cr4, the AFM interactions may surpass the FM interactions. The Cr moments can be understand from the following point. In the Fem/Crn(001) superlattices, the magnetization on the adjacent Fe sites can be viewed as a strong perturbation field for the Cr moments, as a result, the variation of the moments on the Cr sites is thought to depend strongly on the Fe moments ordering (or alignment) and on the coupling between
Fig.4 Magnetic moments (μ) of the atoms in the magnetic
unit cell for (m, n)=(3, 1)
unit cell for (m, n)=(4, 4)
Atoms 1, 5, 9 are chromium, 2–4 and 6–8 are iron.
Atoms 1−4, 9−12, and 17 are chromium, 5−8 and 13−16 are iron.
Haiquan Hu et al. / Acta Physico-Chimica Sinica, 2007, 23(6): 846-850
Fig.5 Total density of states (paramagnetic state) for the
Fig.7 Partial density of states (spin-polarized) of the FM
Fem/Crn(001) superlattices with different (m, n)
configuration for the Fe3/Cr3(001) superlattice
(m, n): (a) (3, 1), (b) (3, 3), (c) (4, 4)
(a), (b), Fei d and Cri d are the same as in Fig.6.
Fe and Cr layers. In this study, the density of states (DOS) in their paramagnetic states in Fig.5 was investigated to understand the magnetic behavior of the Fe and Cr atoms in the Fem/Crn(001) superlattices. It is expected that the fundamental features of the total DOS for the Fe/Cr(001) systems will resemble those of their constitutes (i.e., typical of bcc Fe or Cr-like DOS). There are three main features located at approximately −3.5, −2.0, and 0.0 eV, respectively. The spin-dependent DOS of the ground states for Fem/Crn(001) with (m, n)=(3, 1), (3, 3), and (4, 4) are shown in Figs. 6–8. As a characteristic feature, a pervasively strong hybridization between Fe d and Cr d states in the whole energy region from the bottom of the band up to high above Ef is seen. As stated above, the reduction of the interface like Fei and Cri moment is considered to be related to the strong d - d hybridization between the Fe d and Cr d states. It can be observed that the moment of the interface like Fei has a larger value in the AFM configuration of Fe4/Cr4 superlattice than those in FM configuration of Fe3/Cr1 and Fe3/Cr3 super-
Fig.6 Partial density of states (spin-polarized) of the FM configuration for the Fe3/Cr1(001) superlattice (a) and (b) denote spin up and spin down, respectively. Solid and dotted lines denote Fei d and Cri d states, respectively. The superscript i stands for interface like atoms.
Fig.8 Partial density of states (spin-polarized) of the AFM configuration for the Fe4/Cr4(001) superlattice (a), (b), Fei d and Cri d are the same as in Fig.6.
lattices.
3
Conclusions
The results of the first principles FLAPW studies of electronic structure and magnetic properties of both the FM and AFM configurations for Fem/Crn superlattices (m=3, 4; n=1, 3, 4) were presented. The calculated total energy of the FM state was lower than that of the AFM state for Fe3/Cr1 and Fe3/Cr3 superlattices, whereas the energy of the AFM state was lower than that of the FM for Fe4/Cr4 superlattice. For all the calculated systems the moment on the center (or bulklike) Fe layer was strongly enhanced compared with that of pure bulk bcc Fe, but the moments on the interfacial Fe layers were generally reduced. A strong hybridization between the Fe d and Cr d states was considered to be responsible for the moment reduction. The magnetic moments of Cr atoms changed direction from layer to layer. The absolute values of magnetic moments on the Cr sites were generally much smaller than those of the pure bcc Cr spin density wave (SDW) value. An antiferromagnetic coupling existed between Fe and Cr at the interfacial layer.
Haiquan Hu et al. / Acta Physico-Chimica Sinica, 2007, 23(6): 846-850
References 1 Pierce, D. T.; Unguris, J.; Celotta, R. J.; Stiles, M. D. J. Magn. Magn. Mater., 1999, 200: 290 2 Parkin, S. S. P.; More, N.; Roche, K. P. Phys. Rev. Lett., 1990, 4: 2304 3 Zhang, J. F.; Ali, M.; Chen, H. Journal of Southwest China Normal University (Natural Science), 2005, 30: 1061 4 Levy, P. M.; Ounadjela, K.; Zhang, S.; Wang, Y.; Sommers, C. B.; Fert, A. J. Appl. Phys., 1990, 67: 5914 5 Hideo, H. Phys. Rev. B, 1990, 42: 2368 6 Ounadjela, K.; Sommers, C. B.; Fert, A.; Stoeffler, D.; Gautier, F.; Moruzzi, V. L. Europhys. Lett., 1991, 15: 875 7 Herman, F.; Juergen, S.; Mark, V. S. J. Appl. Phys., 1991, 69:
4783 8 Xu, J. H.; Freeman, A. J. Phys. Rev. B, 1993, 47: 165 9 Blaha, P.; Schwarz, K.; Madsen, G. K. H.; Kvasnicka, D.; Luitz, J. WIEN2k, Vienna: Vienna University of Technology, 2002 10 Perdew, J. P.; Wang, Y. Phys. Rev. B, 1992, 45: 13244 11 Gavrilenko, V. I.; Wu, R. J. Magn. Magn. Mater., 2003, 260: 330 12 Wu, R. Q.; Freeman, A. J. J. Magn. Magn. Mater., 1999, 200: 498 13 Cahn, R. W.; Haasen, P. Physical mettallurgy. Amsterdam, NorthHolland, 1983: 178 14 Kittel, C. Introduction to solid state physics. 5th ed. New York: Wiley, 1976: 31 15 Fawcett, E. Rev. Mod. Phys., 1988, 60: 209