- Email: [email protected]
Crn(1 1 0) superlattices
ARTICLE IN PRESS
Physica B 403 (2008) 531–534 www.elsevier.com/locate/physb
Theoretical study of magnetism and electronic structure of Fe3/Crn(1 1 0) superlattices Hai-Quan Hua, Heng-Shuai Lia,, Yuan-Xu Wangb, Zhong-Ming Renc a
College of Physics Science and Information Engineering, Liaocheng University, Liaocheng 252059, PR China b College of Physics and Electron, Henan University, Kaifeng 475001, PR China c College of Car and Traffic Engineering, Liaocheng University, Liaocheng 252059, PR China Received 14 January 2007; received in revised form 17 July 2007; accepted 27 August 2007
Abstract The electronic structure and magnetism of Fe3/Crn(1 1 0) (n ¼ 1, 3, 5) superlattices (SL) with varying layer thickness have been studied using the full-potential linearized augmented plane-wave (FLAPW) method within the first-principle formalism. The results show that the ferromagnetic state is the preferable phase in the ground state. The magnetic moments of the Fe layers are slightly modified by the presence of the Cr layers. The Cr magnetic moments alternate direction from layer to layer, and an antiferromagnetic coupling between Fe and Cr at the interfacial layer is seen. The magnetic moments of the Cr layers are suppressed because there is a strong hybridization between d-states of both Fe and Cr atoms. Only a small moment is found in the Cr layer. The Cr moment alignment is determined by a delicate balance between the different magnetic interaction. r 2007 Elsevier B.V. All rights reserved. Keywords: Electronic structure; Magnetism; FLAPW
1. Introduction During the last decade, the magnetic features of the Fe/Cr superlattices (SL) have been intensively studied [1–6], from an experimental as well as a theoretical point of view, for basic research purposes as well as for applications. Depending on the thickness of the intervening Cr layers, the adjacent Fe film order either ferromagnetically (FM), antiferromagnetically (AFM), paramagnetically (PM) or even non-collinearly [7–12], that results in an alternation in the scattering condition for electron transport and thus the magnetoresistance across the SL. The determination of magnetic ordering of Fe/Cr systems is very important for understanding the mechanism of the coupling between Fe layers. To understand the physical origin of the magnetic coupling between two adjacent Fe layers separated by Cr layers, a lot of studies (including first-principle total energy Corresponding author. Tel.: +86 13475895656.
E-mail addresses: [email protected] (H.-Q. Hu), [email protected] (H.-S. Li). 0921-4526/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2007.08.220
local density calculations) have been carried out on the Fe/Cr(0 0 1) SLs. Levy et al. [13] used the augmented spherical wave (ASW) method to study the electronic structure and interlayer magnetic coupling of the Fem/Crn(0 0 1) (m ¼ 3, 4, n ¼ 3, 4, 5) systems. Their results showed that the AFM coupling between the Fe layers can be stabilized except in the (m, n) ¼ (3, 3) case which favors ferromagnetic configuration. Hasegawa and Stoeffler obtained the similar moments or moment distributions of the Fe/Cr SLs by using real-space approaches (the selfconsistent tight-binding (TB) method [14] and the TB method combined with the recursion method [15]). Herman et al. [16] carried out first-principle self-consistent spinpolarized linearized muffin-tin orbital/atomic sphere approximation (LMTO/ASA) and linearized augmented spherical wave methods/atomic sphere approximation (LASW/ASA), calculated the electronic structure based on local spin-density functional theory, and found an alternating sign change in the total energy difference between the AFM and FM configurations depending on the thickness of Cr layers. They noted that their result is inconsistent with experiment. For reconciling the
ARTICLE IN PRESS 532
H.-Q. Hu et al. / Physica B 403 (2008) 531–534
calculated results with experiment they presumed that interfacial roughness and impurities effects may play a significant role. Xu and Freeman [17] studied the electronic structures and the magnetism of the Fem/Crn(0 0 1) (m ¼ 1, 3 and n ¼ 1, 3, 5, 7) SLs using the self-consistent linear muffin-tin orbit (LMTO) method with the combined correction term, and found that in the Fem/Crn(0 0 1) systems, when mX3, the FM ordering dominates over the AFM states, whereas when m ¼ 1 the AFM interactions may slightly exceed the FM interaction. But the magnetism of Fe/Cr(1 1 0) has been rarely analyzed. The essential difference between Fe3/Cr1(0 0 1) SL and Fe3/Cr1(1 1 0) SL is the geometry. The geometry affects the electronic structure and the magnetic interaction. Here, we directly calculate the electronic structure and magnetic properties of Fe3/Crn(1 1 0) (n ¼ 1, 3, 5) SL, by using the density functional full-potential linearized augment plane-wave (FLAPW) method [18]. 2. Model and method The FM and AFM configurations of Fe3/Crn SL have been calculated in our work. To study AFM Fe3/Crn structures, we take the double primitive cell as a unit cell, therefore each unit cell contains two formula units. We consider Fe3/Crn(1 1 0) SL with three different thicknesses of Cr layer, namely, Fe3/Cr1, Fe3/Cr3 and Fe3/Cr5, where Fe3/Crn means that three atomic layers of Fe and n atomic layers of Cr are stacked alternatively along the [1 1 0] direction. In forming the Fe3/Crn(1 1 0) SL, we assume the weighted average of the lattice constants of the constituents because both Cr and Fe metals have the same bcc structure and their lattice mismatch is only 0.35% in the lattice constant. The spin-polarized calculations presented in this work are performed within the generalized gradient approximation (GGA) (with Perdew–Burke–Ernzerhof 96 formula [19]) of density functional theory, using the FLAPW method (WIEN2k) [18]. This approach has been successfully applied to determine the electronic and magnetic properties of many transition metal systems [20,21]. The atomic sphere radii Ri=2.25 for both Fe and Cr, respectively. We specify 6.0 Ry as the energy that separates valence from core states. The valence electrons of Fe are 3d64s2, the valence electrons of Cr are 3d54s1. We select 3000 points in the whole Brillouin zone. 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. 3. Results 3.1. Energy differences We can analyze the ground state of Fe3/Crn SL from Table 1. In the three structures the calculated total energies
Table 1 The energy (in Ry) of Fe3/Crn(1 1 0) SL in FM and AFM states Ordering
Fe3Cr1
Fe3Cr3
Fe3Cr5
FM AFM
38954.185111 38953.732276
55768.343563 55767.903419
72582.487049 72582.048029
Table 2 The calculated magnetic moments on Cr and Fe sites of Fe3/Crn(1 1 0) SL
Fe3/Cr1 Fe3/Cr3 Fe3/Cr5
Cri
Crb
Fei
Feb
0.299, 0.302 0.141, 0.140 0.096, 0.095
– 0.050, 0.049 0.095, 0.093, 0.096, 0.092
2.190 2.187 2.181
2.443 2.418 2.354
Subscripts i and b denote interface and bulk-like atoms.
of the FM state are all lower than that of the AFM state. The results indicate that FM state is the preferable phase in the ground state for the model. 3.2. Magnetic moment The calculated magnetic moments on Cr and Fe sites of Fe3/Crn SL are listed in Table 2. In general, we considered the two Cr atoms in the same layer as being of two different types. A test calculation shows that the magnetic moment of Fe is quite insensitive to their environment in all the cases. Therefore, we assume that there is only one type of Fe in one monolayer. It is shown that the magnetic moments of the Fe layers are not significantly affected by the Cr layers, having almost the same magnitude as in bulk bcc Fe (2.2mB). The interface Fe layer is found to have a moment of 2.181–2.190mB per atom, which is roughly the same as that in bulk bcc Fe. On the contrary, the magnetic moments of the interface Cr layers (at most 0.302mB per atom) are suppressed to varying degrees below their values in the spin-density wave (SDW) state found in bulk Cr 0.6mB. In order to understand the mechanism for the Cr moment’s antiparallel alignment in the Fe3/Crn SL, we investigate the magnetic interactions between Cr and Fe atoms as well as between Cr atoms. The magnetic (exchange) field from the large Fe moments induces moderate size moments on the Cr atoms. An important point is that these induced Cr moments align ferromagnetically with respect to each other, cf. for instance the Fe3/Cr1 results in Table 2. However, as we all know, the Cr moments in bcc bulk Cr strongly prefer to align antiferromagnetically. Thus, as a result of this competition, a reduction of the induced Cr magnetic moments is expected due to this antiferromagnetic field. This can be seen clearly from our calculated results in which the Cr moments align antiparallel to neighbor layers. It is apparent that the moment alignment of the
ARTICLE IN PRESS H.-Q. Hu et al. / Physica B 403 (2008) 531–534
7
Cr layers is determined by a delicate balance between these different magnetic interactions on Cr atoms in the Fe3/Crn SL. Density of States (states/eV atom)
In order to understand the nature of the Fe and Cr magnetic moments in the Fe3/Crn SL, we inspect the density of states (DOS) in their paramagnetic structures. The partial d density of states for the paramagnetic Fe3/Cr1(1 1 0) SL is shown in Fig. 1. The interface density of states of both Fe and Cr in Fe3/Crn SL is very close to that of the corresponding pure bcc bulk. For instance the characteristic three-peak feature of pure bcc Fe is seen to remain in the case of Fe3/Cr1 (cf. Figs. 2 and 3). Furthermore, the Fermi energy just lines on the peak of the Fe-d density of states (cf. Fig. 1), indicating clearly that the magnetic instability is basically due to the Fe atoms in the Fe3/Cr1(1 1 0) SL. This result explains the Sellers et al. [22] observations that saturation magnetization of the Fe/Cr(1 1 0) SL has a value, which is nearly equal to the (bulk) saturation magnetization of pure bcc Fe. There is a strong hybridization between the Fe-d and Cr-d states in the present Fe3/Crn SL. As a result a large Cr magnetic moment is not expected in the Fe3/Crn SL. As a matter of fact, the spin-polarized results (cf. Figs. 4 and 5) for Fe3/Cr1(1 1 0) SL show that the spin-up density of states for Cr is nearly compensated by that for spin-down. We find two characters: (1) only a weak ferromagnetic moment of utmost 0.302mB per atom is induced on the Cr atoms; (2) these moments align antiparallel to the nearest neighbor Fe moments.
6 5 4 3 2 1 0 -8
-6
-4
-2
0
2
4
6
8
Energy (eV) Fig. 2. Total density of states (paramagnetic states) for Fe3/Cr1.
7 6 Density of States (states/eV atom)
3.3. Density of states
533
5 4 3 2 1 0
6
-8
Density of States (states/eV atom)
-4
-2
0
2
4
6
8
Energy (eV)
Fei Cri Feb
5
-6
Fig. 3. Total density of states (paramagnetic states) for pure bulk Fe.
4
4. Conclusions 3
2
1
0 -8
-6
-4
-2
0 2 Energy (eV)
4
6
8
Fig. 1. Cr-d and Fe-d spatial (paramagnetic) density of states for Fe3/Cr1. Subscripts i and b denote interface and bulk-like states, respectively.
We calculated the electronic structure and magnetism of Fe3/Crn(1 1 0) SL with varying layer thickness (n ¼ 1, 3, 5) using the full-potential linearized augmented plane-wave (FLAPW) method within the first-principle formalism. The results show that ferromagnetic state is the preferable phase in the ground state. The magnetic moments of the Fe layers are slightly modified by the presence of the Cr layers. The Cr magnetic moments alternate their direction from layer to layer, and an antiferromagnetic coupling between Fe and Cr at the interfacial layer is seen. The magnetic moments of the Cr layers are suppressed because there is a strong hybridization between d-states of both Fe and Cr
ARTICLE IN PRESS H.-Q. Hu et al. / Physica B 403 (2008) 531–534
Density of States (states/eV atom)
534
3.2 3.0 2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0
Acknowledgments Cri Fei Feb
The work was supported by the High Technology Research and Development Program of China under Grant no. 2004AA32G090, the Science Foundation for Distinguished Young Scientist of Shandong Province under Grant no. 02BS050 and the Natural Science Foundation of Shandong Province under Grant no. Y2006A02.
References
-8
-6
-4
-2
0 2 Energy (eV)
4
6
8
Density of states (states/eV atom)
Fig. 4. Cr-d, Fe-d partial (spin up) density of states for Fe3/Cr1. Subscripts i and b denote interface and bulk-like states, respectively.
3.2 3.0 2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0
Cri Fei Feb
-8
-6
-4
-2
0
2
4
6
8
Energy (eV) Fig. 5. Cr-i, Fe-i, Fe-d partial (spin down) density of states for Fe3/Cr1. Subscripts i and b denote interface and bulk-like states, respectively.
atoms. Only a small moment is found in the Cr layer. The Cr moment alignment is determined by a delicate balance between the different magnetic interactions.
[1] J. Unguris, R.J. Cellotta, D.T. Pierce, Phys. Rev. Lett. 67 (1991) 140. [2] P. Weinberger, L. Szunyogh, J. Phys.: Condens. Matter 15 (2003) 5479. [3] E.E. Fullerton, M.J. Conover, J.E. Mattson, C.N. Sowers, S.D. Bader, J. Appl. Phys. 75 (1994) 6461. [4] M. Przybylski, J. Grabowski, M. Rams, K. Tomala, J. Kirschner, J. Appl. Phys. 95 (2004) 597. [5] A. Nefedov, J. Grabis, H. Zabel, Physica B 357 (2005) 22. [6] C. Chesman, C.G. Bezerra, E.L. Albuquerque, A.M. Mariz, Phys. Lett. A 354 (2006) 221. [7] S.S. P’Parkin, N. More, K.P. Roche, Phys. Rev. Lett. 64 (1990) 2304. [8] V.V. Ustinov, N.G. Bebenin, L.N. Romashev, V.I. Minin, M.A. Milyaev, A.R. Del, A.V. Semerikov, Phys. Rev. B 54 (1996) 15958. [9] S.O. Demokritov, C. Bayer, S. Doppe, M. Rickart, J. Fassbender, B. Hillebrands, D.I. Kholin, N.M. Kreines, O.M. Liedke, Phys. Rev. Lett. 90 (2003) 097201. [10] J. Grabowski, M. Przybylski, W. Wulfhekel, M. Rams, J. Kirschner, Vacuum 74 (2004) 279. [11] M. Przybylski, J. Grabowski, W. Wulfhekel, J. Kirschner, Surf. Sci. 566 (2004) 256. [12] D.I. Lobov, M.M. Kirillova, L.N. Romashev, V.V. Ustinov, V.M. Maevskii, A.M. Milyaev, J. Magn. Magn. Mater. 300 (2006) e-359. [13] P.M. Levy, K. Ounadjela, S. Zhang, Y. Wang, C.B. Sommers, A. Fert, J. Appl. Phys. 67 (1990) 5914. [14] H. Hasegawa, Phys. Rev. B 42 (1990) 2368. [15] K. Ounadjela, C.B. Sommers, A. Fert, D. Stoeffler, F. Gautier, V.L. Moruzzi, Europhys. Lett. 15 (1991) 875. [16] F. Herman, J. Sticht, M.V. Schilfgaarde, J. Appl. Phys. 69 (1991) 4783. [17] J.-H. Xu, A.J. Freeman, Phys. Rev. B 47 (1993) 165. [18] P. Blaha, K. Schwarz, G.K. H’Madsen, D. Kvasnicka, J. Luitz, WIEN2k, Vienna University of Technology, 2002. [19] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3965. [20] V.I. Gavrilenko, R. Wu, J. Magn. Magn. Mater. 260 (2003) 330. [21] R.Q. Wu, A.J. Freeman, J. Magn. Magn. Mater. 200 (1991) 498. [22] C. Sellers, Y. Shiroishi, N.K. Jaggj, J.B. Ketterson, J.E. Hilliard, J. Magn. Magn. Mater. 54–57 (1986) 787.
Physica B 403 (2008) 531–534 www.elsevier.com/locate/physb
Theoretical study of magnetism and electronic structure of Fe3/Crn(1 1 0) superlattices Hai-Quan Hua, Heng-Shuai Lia,, Yuan-Xu Wangb, Zhong-Ming Renc a
College of Physics Science and Information Engineering, Liaocheng University, Liaocheng 252059, PR China b College of Physics and Electron, Henan University, Kaifeng 475001, PR China c College of Car and Traffic Engineering, Liaocheng University, Liaocheng 252059, PR China Received 14 January 2007; received in revised form 17 July 2007; accepted 27 August 2007
Abstract The electronic structure and magnetism of Fe3/Crn(1 1 0) (n ¼ 1, 3, 5) superlattices (SL) with varying layer thickness have been studied using the full-potential linearized augmented plane-wave (FLAPW) method within the first-principle formalism. The results show that the ferromagnetic state is the preferable phase in the ground state. The magnetic moments of the Fe layers are slightly modified by the presence of the Cr layers. The Cr magnetic moments alternate direction from layer to layer, and an antiferromagnetic coupling between Fe and Cr at the interfacial layer is seen. The magnetic moments of the Cr layers are suppressed because there is a strong hybridization between d-states of both Fe and Cr atoms. Only a small moment is found in the Cr layer. The Cr moment alignment is determined by a delicate balance between the different magnetic interaction. r 2007 Elsevier B.V. All rights reserved. Keywords: Electronic structure; Magnetism; FLAPW
1. Introduction During the last decade, the magnetic features of the Fe/Cr superlattices (SL) have been intensively studied [1–6], from an experimental as well as a theoretical point of view, for basic research purposes as well as for applications. Depending on the thickness of the intervening Cr layers, the adjacent Fe film order either ferromagnetically (FM), antiferromagnetically (AFM), paramagnetically (PM) or even non-collinearly [7–12], that results in an alternation in the scattering condition for electron transport and thus the magnetoresistance across the SL. The determination of magnetic ordering of Fe/Cr systems is very important for understanding the mechanism of the coupling between Fe layers. To understand the physical origin of the magnetic coupling between two adjacent Fe layers separated by Cr layers, a lot of studies (including first-principle total energy Corresponding author. Tel.: +86 13475895656.
E-mail addresses: [email protected] (H.-Q. Hu), [email protected] (H.-S. Li). 0921-4526/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2007.08.220
local density calculations) have been carried out on the Fe/Cr(0 0 1) SLs. Levy et al. [13] used the augmented spherical wave (ASW) method to study the electronic structure and interlayer magnetic coupling of the Fem/Crn(0 0 1) (m ¼ 3, 4, n ¼ 3, 4, 5) systems. Their results showed that the AFM coupling between the Fe layers can be stabilized except in the (m, n) ¼ (3, 3) case which favors ferromagnetic configuration. Hasegawa and Stoeffler obtained the similar moments or moment distributions of the Fe/Cr SLs by using real-space approaches (the selfconsistent tight-binding (TB) method [14] and the TB method combined with the recursion method [15]). Herman et al. [16] carried out first-principle self-consistent spinpolarized linearized muffin-tin orbital/atomic sphere approximation (LMTO/ASA) and linearized augmented spherical wave methods/atomic sphere approximation (LASW/ASA), calculated the electronic structure based on local spin-density functional theory, and found an alternating sign change in the total energy difference between the AFM and FM configurations depending on the thickness of Cr layers. They noted that their result is inconsistent with experiment. For reconciling the
ARTICLE IN PRESS 532
H.-Q. Hu et al. / Physica B 403 (2008) 531–534
calculated results with experiment they presumed that interfacial roughness and impurities effects may play a significant role. Xu and Freeman [17] studied the electronic structures and the magnetism of the Fem/Crn(0 0 1) (m ¼ 1, 3 and n ¼ 1, 3, 5, 7) SLs using the self-consistent linear muffin-tin orbit (LMTO) method with the combined correction term, and found that in the Fem/Crn(0 0 1) systems, when mX3, the FM ordering dominates over the AFM states, whereas when m ¼ 1 the AFM interactions may slightly exceed the FM interaction. But the magnetism of Fe/Cr(1 1 0) has been rarely analyzed. The essential difference between Fe3/Cr1(0 0 1) SL and Fe3/Cr1(1 1 0) SL is the geometry. The geometry affects the electronic structure and the magnetic interaction. Here, we directly calculate the electronic structure and magnetic properties of Fe3/Crn(1 1 0) (n ¼ 1, 3, 5) SL, by using the density functional full-potential linearized augment plane-wave (FLAPW) method [18]. 2. Model and method The FM and AFM configurations of Fe3/Crn SL have been calculated in our work. To study AFM Fe3/Crn structures, we take the double primitive cell as a unit cell, therefore each unit cell contains two formula units. We consider Fe3/Crn(1 1 0) SL with three different thicknesses of Cr layer, namely, Fe3/Cr1, Fe3/Cr3 and Fe3/Cr5, where Fe3/Crn means that three atomic layers of Fe and n atomic layers of Cr are stacked alternatively along the [1 1 0] direction. In forming the Fe3/Crn(1 1 0) SL, we assume the weighted average of the lattice constants of the constituents because both Cr and Fe metals have the same bcc structure and their lattice mismatch is only 0.35% in the lattice constant. The spin-polarized calculations presented in this work are performed within the generalized gradient approximation (GGA) (with Perdew–Burke–Ernzerhof 96 formula [19]) of density functional theory, using the FLAPW method (WIEN2k) [18]. This approach has been successfully applied to determine the electronic and magnetic properties of many transition metal systems [20,21]. The atomic sphere radii Ri=2.25 for both Fe and Cr, respectively. We specify 6.0 Ry as the energy that separates valence from core states. The valence electrons of Fe are 3d64s2, the valence electrons of Cr are 3d54s1. We select 3000 points in the whole Brillouin zone. 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. 3. Results 3.1. Energy differences We can analyze the ground state of Fe3/Crn SL from Table 1. In the three structures the calculated total energies
Table 1 The energy (in Ry) of Fe3/Crn(1 1 0) SL in FM and AFM states Ordering
Fe3Cr1
Fe3Cr3
Fe3Cr5
FM AFM
38954.185111 38953.732276
55768.343563 55767.903419
72582.487049 72582.048029
Table 2 The calculated magnetic moments on Cr and Fe sites of Fe3/Crn(1 1 0) SL
Fe3/Cr1 Fe3/Cr3 Fe3/Cr5
Cri
Crb
Fei
Feb
0.299, 0.302 0.141, 0.140 0.096, 0.095
– 0.050, 0.049 0.095, 0.093, 0.096, 0.092
2.190 2.187 2.181
2.443 2.418 2.354
Subscripts i and b denote interface and bulk-like atoms.
of the FM state are all lower than that of the AFM state. The results indicate that FM state is the preferable phase in the ground state for the model. 3.2. Magnetic moment The calculated magnetic moments on Cr and Fe sites of Fe3/Crn SL are listed in Table 2. In general, we considered the two Cr atoms in the same layer as being of two different types. A test calculation shows that the magnetic moment of Fe is quite insensitive to their environment in all the cases. Therefore, we assume that there is only one type of Fe in one monolayer. It is shown that the magnetic moments of the Fe layers are not significantly affected by the Cr layers, having almost the same magnitude as in bulk bcc Fe (2.2mB). The interface Fe layer is found to have a moment of 2.181–2.190mB per atom, which is roughly the same as that in bulk bcc Fe. On the contrary, the magnetic moments of the interface Cr layers (at most 0.302mB per atom) are suppressed to varying degrees below their values in the spin-density wave (SDW) state found in bulk Cr 0.6mB. In order to understand the mechanism for the Cr moment’s antiparallel alignment in the Fe3/Crn SL, we investigate the magnetic interactions between Cr and Fe atoms as well as between Cr atoms. The magnetic (exchange) field from the large Fe moments induces moderate size moments on the Cr atoms. An important point is that these induced Cr moments align ferromagnetically with respect to each other, cf. for instance the Fe3/Cr1 results in Table 2. However, as we all know, the Cr moments in bcc bulk Cr strongly prefer to align antiferromagnetically. Thus, as a result of this competition, a reduction of the induced Cr magnetic moments is expected due to this antiferromagnetic field. This can be seen clearly from our calculated results in which the Cr moments align antiparallel to neighbor layers. It is apparent that the moment alignment of the
ARTICLE IN PRESS H.-Q. Hu et al. / Physica B 403 (2008) 531–534
7
Cr layers is determined by a delicate balance between these different magnetic interactions on Cr atoms in the Fe3/Crn SL. Density of States (states/eV atom)
In order to understand the nature of the Fe and Cr magnetic moments in the Fe3/Crn SL, we inspect the density of states (DOS) in their paramagnetic structures. The partial d density of states for the paramagnetic Fe3/Cr1(1 1 0) SL is shown in Fig. 1. The interface density of states of both Fe and Cr in Fe3/Crn SL is very close to that of the corresponding pure bcc bulk. For instance the characteristic three-peak feature of pure bcc Fe is seen to remain in the case of Fe3/Cr1 (cf. Figs. 2 and 3). Furthermore, the Fermi energy just lines on the peak of the Fe-d density of states (cf. Fig. 1), indicating clearly that the magnetic instability is basically due to the Fe atoms in the Fe3/Cr1(1 1 0) SL. This result explains the Sellers et al. [22] observations that saturation magnetization of the Fe/Cr(1 1 0) SL has a value, which is nearly equal to the (bulk) saturation magnetization of pure bcc Fe. There is a strong hybridization between the Fe-d and Cr-d states in the present Fe3/Crn SL. As a result a large Cr magnetic moment is not expected in the Fe3/Crn SL. As a matter of fact, the spin-polarized results (cf. Figs. 4 and 5) for Fe3/Cr1(1 1 0) SL show that the spin-up density of states for Cr is nearly compensated by that for spin-down. We find two characters: (1) only a weak ferromagnetic moment of utmost 0.302mB per atom is induced on the Cr atoms; (2) these moments align antiparallel to the nearest neighbor Fe moments.
6 5 4 3 2 1 0 -8
-6
-4
-2
0
2
4
6
8
Energy (eV) Fig. 2. Total density of states (paramagnetic states) for Fe3/Cr1.
7 6 Density of States (states/eV atom)
3.3. Density of states
533
5 4 3 2 1 0
6
-8
Density of States (states/eV atom)
-4
-2
0
2
4
6
8
Energy (eV)
Fei Cri Feb
5
-6
Fig. 3. Total density of states (paramagnetic states) for pure bulk Fe.
4
4. Conclusions 3
2
1
0 -8
-6
-4
-2
0 2 Energy (eV)
4
6
8
Fig. 1. Cr-d and Fe-d spatial (paramagnetic) density of states for Fe3/Cr1. Subscripts i and b denote interface and bulk-like states, respectively.
We calculated the electronic structure and magnetism of Fe3/Crn(1 1 0) SL with varying layer thickness (n ¼ 1, 3, 5) using the full-potential linearized augmented plane-wave (FLAPW) method within the first-principle formalism. The results show that ferromagnetic state is the preferable phase in the ground state. The magnetic moments of the Fe layers are slightly modified by the presence of the Cr layers. The Cr magnetic moments alternate their direction from layer to layer, and an antiferromagnetic coupling between Fe and Cr at the interfacial layer is seen. The magnetic moments of the Cr layers are suppressed because there is a strong hybridization between d-states of both Fe and Cr
ARTICLE IN PRESS H.-Q. Hu et al. / Physica B 403 (2008) 531–534
Density of States (states/eV atom)
534
3.2 3.0 2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0
Acknowledgments Cri Fei Feb
The work was supported by the High Technology Research and Development Program of China under Grant no. 2004AA32G090, the Science Foundation for Distinguished Young Scientist of Shandong Province under Grant no. 02BS050 and the Natural Science Foundation of Shandong Province under Grant no. Y2006A02.
References
-8
-6
-4
-2
0 2 Energy (eV)
4
6
8
Density of states (states/eV atom)
Fig. 4. Cr-d, Fe-d partial (spin up) density of states for Fe3/Cr1. Subscripts i and b denote interface and bulk-like states, respectively.
3.2 3.0 2.8 2.6 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0
Cri Fei Feb
-8
-6
-4
-2
0
2
4
6
8
Energy (eV) Fig. 5. Cr-i, Fe-i, Fe-d partial (spin down) density of states for Fe3/Cr1. Subscripts i and b denote interface and bulk-like states, respectively.
atoms. Only a small moment is found in the Cr layer. The Cr moment alignment is determined by a delicate balance between the different magnetic interactions.
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