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Magnetism of V monolayers on Fe(1 0 0) and Cr(1 0 0)
Vacuum 54 (1999) 137 — 141
Magnetism of V monolayers on Fe(1 0 0) and Cr(1 0 0) S.V. Man’kovsky*, V.T. Cherepin Institute for Metal Physics of the N.A.S. of Ukraine, 36 Vernadsky Blvd., UA-252680 Kiev-142, Ukraine
Abstract The magnetic ordering in a V monolayer on the (1 0 0)Fe and (1 0 0)Cr substrates was investigated using the ab initio spin-polarised electronic structure calculations. Two stable states for the V/Fe(1 0 0) system were found with magnetic moments of !1.46 and !0.97 k in the V monolayer which couple antiferromagnetically with Fe. The total energy calculations show that the state with the V magnetic moment of !0.97 k would be the ground state of this system. For the V/Cr(1 0 0) system two stable states with antiferromagnetic coupling of the V and Cr layers (!1.11 and !0.23 k in V layer) and two states with ferromagnetic coupling and V magnetic moment of 0.05 and 0.62 k were found. The state with !0.23 k V magnetic moment is the most stable. Analysis of the results of calculations show a key role of the interacting overlayer/substrate in stabilising the ground state. 1999 Elsevier Science Ltd. All rights reserved.
1. Introduction The magnetic properties of ultrathin magnetic films on magnetic substrates have been widely investigated throughout the last decade. The phenomenon of enhanced surface magnetism and giant magnetic moments in transition metal films, which is due to the fewer nearest neighbours in the environment of the surface atoms is now well recognised. Moreover, ultrathin films of some transition metals, non-magnetic in the bulk, exhibit ferromagnetic ordering. For example, free monolayers of Ti [1], V [2], Pd [3] were found to be ferromagnetically ordered. However, the magnetic properties of metallic overlayers are significantly influenced by a substrate. The interatomic interaction at the interface may dramatically change the ferromagnetic ordering to in-plane antiferromagnetic (V/Ag(1 0 0) [3], Cr/Fe(1 0 0) and Mn/Fe(1 0 0) [4], etc.), or may induce magnetic moments in nonmagnetic overlayers, as found for Pd/Fe(1 0 0) [5], Ag/Fe(1 0 0) [6], etc. Thus, the influence of the substrate on the magnetic properties of overlayers attracts the attention of investigators. Experimentally, the magnetic moment in V monolayer on bcc Fe (1 0 0) substrate was found to be antiparallel to the Fe magnetisation, and is not greater (by the absolute
* Corresponding author. Tel.: 00380 44 444 320; fax: 00380 44 444 8250; e-mail: [email protected]
value) than !1 k /atom according to the results of Walker and Hopster [7] and is about !0.3 k /atom according to Fuchs et al. [8]. The authors concluded, that this V magnetism is induced by the magnetised Fe substrate. Handshuh and Blu¨gel [9] have shown theoretically, with spin-polarised full-potential linearized-augmented-plane-wave method (FLAPW) calculations of the electronic structure, that the induced V moment in 1V/Fe(1 0 0) system is !0.6 k /atom. The studies of Vega et al. [10] and Mirbt et al. [11] give the V moment of !1.67 and about !1.5 k /atom, respectively. In the present paper, we report the results of spinpolarised calculations of the electronic structure of 1V/Fe(1 0 0) system, which were performed in order to understand the nature of the mentioned discrepancy in the results of the above-mentioned investigations. We report also the results of studies of V overlayer magnetism on the Cr(1 0 0) substrate.
2. Method The ab initio spin-polarised calculations of electronic structure were performed using the FLAPW method. The core states were calculated fully relativistically and the valence states were calculated in scalar-relativistic approximation. The local spin density approximation in the form due to Vosko et al. [12] was employed for the
0042-207X/99/$ — see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 4 2 - 2 0 7 X ( 9 8 ) 0 0 4 4 9 - 7
138
S.V. Man+kovsky, V.T. Cherepin / Vacuum 54 (1999) 137—141
exchange-correlation potential. The grid of 21 k-points in the irreducible wedge of the 2D Bz was used in the iterations and a set of 45 k-points was used in the final iteration. A variational basis set of more than 60 plane waves per atom was used. The calculations were carried out for a five-layer Fe (1 0 0) and Cr(1 0 0) films covered with V monolayers on both sides of the film. The lattice constant of ideal Fe (a "5.416 a.u.) and Cr (a "5.448 a.u.) bcc lattices were used.
3. Results and discussion 3.1. V(1 ML)/(1 0 0)Fe For study of the stability of the paramagnetic state of a V monolayer on the Fe(1 0 0) substrate the Stoner factor IN(E ) (I is the exchange-correlation integral and $ N(E ) is the density of states (DOS) at the Fermi level) $ was evaluated (Table 1). The exchange-correlation integral, obtained in [2] has been used. Since the Stoner factor for the V overlayer is larger than 1, ferromagnetic ordering in this layer may be expected. Taking into account the above-mentioned discrepancy between theoretical and experimental results, the existence of several magnetic states for the system considered was assumed. Two stable states were found from the calculations for V(1 ML)/(1 0 0)Fe system: one with the magnetic moment of !0.97 k (AFM1) and the other with !1.46 k (AFM2) in the V overlayer. In both states V couples antiferromagnetically with the Fe substrate, and the magnetic moment of the interface Fe layer decreases with respect to the bulk value. The total energy calculations show that the energy of the state AFM1 is less than the energy of the state AFM2 by 22 mRy. Table 2 presents
Table 1 DOS at the E and Stoner factors for V overlayers $ System
N(E ), state/Ry $
IN(E ) $
IV/Fe(1 0 0) IV/Cr(1 0 0)
36.5 33.4
1.20 1.08
Table 2 Layer projected magnetic moments M(in l ) for V(1 ML)/Fe(1 0 0) system and for (1 0 0) V-terminated surface of VFe B2 alloy State
Vacuum
Layers 1
AFM1 AFM2 VFe B2
!0.17 !0.06 0.06
!1.46 !0.97 !0.02
2 1.74 1.70 1.19
3 2.55 2.55 !0.25
4 2.22 2.22 1.07
Fig. 1. Local DOS for the V(1 ML)/Fe(1 0 0) system: in the V monolayer for nonmagnetic state of the system (a); in the V monolayer of the metastable state (b) and layer-by-layer DOS for the stable state (c). Solid lines correspond to majority-spin states, and dotted lines — to minority-spin states.
the layer projected magnetic moments M for both states. It is seen, that their values in the internal Fe layers are equal, and differ only in the interface layers. The value of demagnetisation in the interface Fe layer (M !M )/M , obtained in our calculations is about 0.23 which is in good agreement with the value 0.2, obtained experimentally by Fuchs et al. [8]. Due to the exchange interaction, the Fe majority-spin d-bands drop down below the Fermi level, E , and are $ nearly fully occupied, while the minority-spin states displace up on the energy scale. These result in Fe DOS minimum near the E (Fig. 1b, c). The Fe minority-spin $ d-states overlap with V d-states of the same spin direction, which favours their hybridisation (Figs. 1, 2). Fig. 2 display (for the ground state of the system) highly localised surface (V) states near the Fermi level at the C point and in the C —MM direction, which give rise to the DOS peaks near the E . The average exchange splitting of $ V d-states with opposite spin directions in the ground state is about 0.2 eV.
S.V. Man+kovsky, V.T. Cherepin / Vacuum 54 (1999) 137—141
139
The high localisation degree of localised V states and their large DOS value favour the exchange splitting and the appearance of a second magnetic state with the average exchange splitting of V d-states of about 0.9 eV. As a result, due to higher occupation of V minority-spin d-states drawn down in energy and because of increase of energy distance between the V and Fe minority-spin states, their hybridisation with Fe d-states is diminished. Simultaneously, demagnetisation of the interfacial Fe layer also decreases, as may be seen from the increase of magnetic moment in the interface Fe layer (Table 2). Thus, taking into account that the instability of the paramagnetic state of V monolayer is caused by the localised V states near the Fermi level, a more stable state with smaller magnetic moment (apparently, induced) and larger hybridisation between the V and Fe d-states, suggests, that the hybridisation plays a key role in stabilisation of the AFM1 magnetic state of the considered system. Another picture takes place in the (1 0 0) surface of FeV B2 compound. Although its lattice parameter is slightly greater than that of Fe, the magnetic moment of V surface layer is negligibly small (&0.02 k ). The reason is apparently due to a small exchange splitting of bulk states, which results in coincidence of energy position of the surface V d-states of both spin directions with the bulk d-states and hence to the small localisation of these states, and to the small difference in the degree of hybridisation of V and Fe d-states with opposite spin. 3.2. V(1ML)/Cr(1 0 0)
Fig. 2. Energy band structure for V(1 ML)/Fe(1 0 0) system for majority- (a) and minority-spin states. Solid lines represent the states with more than 70% localisation in vacuum and the surface (V) layer.
The V magnetisation and antiparallel alignment of the V magnetic moment with respect to the Fe one in the ground state is caused by a different degree of hybridisation of majority- and minority-spin states of V and Fe, which occurs for the following reasons. First, as the Fe majority-spin d-states move down in energy and minority-spin d-states move up, the last ones are positioned close to the V d-states. This results in stronger hybridisation of minority-spin d-states of V and Fe in comparison with the majority-spin one. The second reason is that the occupied majority-spin d-states of Fe are more localised near the atoms and this results in a lesser degree of hybridisation with V d-states. These hybridisation features cause also the diminishing of the magnetic moment in the interface Fe layer in comparison with their bulk value.
It is interesting to study the magnetism of the V monolayer on Cr(1 0 0) and compare it with the 1V/Fe(1 0 0) system, because the lattice parameter of bcc Cr is close to the Fe lattice parameter, on the one hand, but the substrate (Cr) is antiferromagnetically ordered, on the other. Moreover, the Fermi level in Cr is positioned in the DOS minimum between the bonding and antibonding states of both spins. For these reasons the V d-states near the Fermi level would be largely localised in the V overlayer, but the difference in degree of hybridisation between the Cr and V d-states for opposite spin directions is significantly less than in the case of V/Fe(1 0 0) system. The Stoner factor analysis indicates the instability of the paramagnetic state of the V overlayer. From the spinpolarised calculations of the electronic structure for the V overlayer on the (1 0 0)Cr substrate four magnetic states for this system were found: two states with antiferromagnetic (AFM1 and AFM2) and two states with ferromagnetic alignment (FM1 and FM2) of V magnetic moment with respect to the one of the substrate. The DOS pictures (Fig. 3a, c) shows the large splitting of V states with opposite spin in AFM2 and FM2 states of the system which result in large V magnetic moments in these states (see Table 3). These states are caused
140
S.V. Man+kovsky, V.T. Cherepin / Vacuum 54 (1999) 137—141 Table 3 The layer projected magnetic moments M (in l ) for V(1 ML)/Cr(1 0 0) ystem for different magnetic states and the energy differences E!E (in mRy) (where E is the ground state) $+ $+ State
Layer
M
AFM1
V (S) Cr (I) V (S) Cr (I) V (S) Cr (I) V (S) Cr (I)
!0.23 0.28 !1.11 0.54 0.05 0.18 0.62 0.07
AFM2 FM1 FM2
E!E
$+
0 70 22 27
Fig. 3. Local DOS for the states with different magnetic moments in the V layer of the V(1 ML)/Cr(1 0 0) system: !1.11 k in the V monolayer (a), 0.05 k in the V monolayer (b), 0.62 k in the V monolayer (c) and layer-by-layer DOS for the stable state (!0.23 k in the V monolayer) (c). Solid lines correspond to majority-spin states, and dotted lines — to minority-spin states.
apparently by the exchange interaction of localised V states near E . The splitting of the opposite-spin states $ in V overlayer in another two states of the system is rather small. The total energy calculations show, that the state with the magnetic moment !0.23 k in V layer (AFM1) has the smallest energy, i.e. it is the ground state. The energy band picture (Fig. 4) shows the surface (V) states at the C point and in the C —M M and C —XM directions. The states in the C —MM direction are located in the gap of Cr states and are largely localised in the V layer. Apparently this enables both ferromagnetic (FM2) and antiferromagnetic (AFM2) ordering in the V layer. The magnetic moments in the V overlayer and in the Cr interface layer and the total energies of these states
Fig. 4. Energy band structure for V(1 ML)/Cr(1 0 0) system for majority- (a) and minority-spin states. Solid lines represent the states with more than 70% localisation in vacuum and surface (V) layer.
with respect to the ground state are presented in Table 3. The correlation between the magnetic moments in the overlayer and the interface Cr layer are seen: the largest value in the interfacial Cr layer corresponds to the largest
S.V. Man+kovsky, V.T. Cherepin / Vacuum 54 (1999) 137—141
value in the overlayer with AFM alignment, and the smallest value in the interfacial Cr layer corresponds to the largest value in the overlayer with FM alignment. This is evidence for a large interaction of the V overlayer with the Cr substrate. However, because of the complicated system considered, more detailed study is needed to clarify the understanding of the role of overlayer/substrate interaction in stabilising the ground state. Several magnetic states for the Cr(1 0 0) and Fe(1 0 0) surfaces covered by V monolayer were found. The states with induced V magnetic moment of !0.23 and !0.97 k on Cr(1 0 0) and Fe(1 0 0) substrates, respectively, were found to be most stable, that is in satisfactory agreement with the results of studies [7—9]. The magnetic moment in the V layer for both systems is caused by the interaction of overlayers with substrates and this interaction has a key role in stabilising the ground states of the systems considered.
141
References [1] Zhu MJ, Bylander DM, Kleinman L. Phys Rev B 1990;42: 2874. [2] Ohnishi S, Fu CL, Frreman AJ. J Magn Magn Mater 1985;50: 161. [3] Blu¨gel S, Drittler B, Zeller R, Dederichs PH. Appl Phys A 1989;49:547. [4] Ruqian Wu, Freeman AJ. Phys Rev B 1995;51:17 131. [5] Rader O, Vescovo E, Redinger J, Blu¨gel S, Carbone C, Eberhardt W, Gudat W. Phys Rev Lett 1994;72:2247. [6] Vescovo E, Rader O, Redinger J, Blu¨gel S, Carbone CW. Phys Rev B 1995;51:12 418. [7] Walker TG, Hopster H. Phys Rev B 1994;49:7687. [8] Fuchs P, Totland K, Landolt M. Phys Rev B 1996;53:9123. [9] Handschuh S, Blu¨gel S. Solid State Commun 1998;105:633. [10] Vega A, Rubio A, Balbas LC, Dorantes-Davia J, Bauarab S, Demangeat C, Mokrani A, Dreisse H. J Appl Phys 1991;69:4544. [11] Mirbt S, Eriksson O, Johansson B, Skriver HL. Phys Rev B 1995;52:15 070. [12] Vosko SW, Wilk L, Nusair M. Can J Phys 1980;58:1200.
Magnetism of V monolayers on Fe(1 0 0) and Cr(1 0 0) S.V. Man’kovsky*, V.T. Cherepin Institute for Metal Physics of the N.A.S. of Ukraine, 36 Vernadsky Blvd., UA-252680 Kiev-142, Ukraine
Abstract The magnetic ordering in a V monolayer on the (1 0 0)Fe and (1 0 0)Cr substrates was investigated using the ab initio spin-polarised electronic structure calculations. Two stable states for the V/Fe(1 0 0) system were found with magnetic moments of !1.46 and !0.97 k in the V monolayer which couple antiferromagnetically with Fe. The total energy calculations show that the state with the V magnetic moment of !0.97 k would be the ground state of this system. For the V/Cr(1 0 0) system two stable states with antiferromagnetic coupling of the V and Cr layers (!1.11 and !0.23 k in V layer) and two states with ferromagnetic coupling and V magnetic moment of 0.05 and 0.62 k were found. The state with !0.23 k V magnetic moment is the most stable. Analysis of the results of calculations show a key role of the interacting overlayer/substrate in stabilising the ground state. 1999 Elsevier Science Ltd. All rights reserved.
1. Introduction The magnetic properties of ultrathin magnetic films on magnetic substrates have been widely investigated throughout the last decade. The phenomenon of enhanced surface magnetism and giant magnetic moments in transition metal films, which is due to the fewer nearest neighbours in the environment of the surface atoms is now well recognised. Moreover, ultrathin films of some transition metals, non-magnetic in the bulk, exhibit ferromagnetic ordering. For example, free monolayers of Ti [1], V [2], Pd [3] were found to be ferromagnetically ordered. However, the magnetic properties of metallic overlayers are significantly influenced by a substrate. The interatomic interaction at the interface may dramatically change the ferromagnetic ordering to in-plane antiferromagnetic (V/Ag(1 0 0) [3], Cr/Fe(1 0 0) and Mn/Fe(1 0 0) [4], etc.), or may induce magnetic moments in nonmagnetic overlayers, as found for Pd/Fe(1 0 0) [5], Ag/Fe(1 0 0) [6], etc. Thus, the influence of the substrate on the magnetic properties of overlayers attracts the attention of investigators. Experimentally, the magnetic moment in V monolayer on bcc Fe (1 0 0) substrate was found to be antiparallel to the Fe magnetisation, and is not greater (by the absolute
* Corresponding author. Tel.: 00380 44 444 320; fax: 00380 44 444 8250; e-mail: [email protected]
value) than !1 k /atom according to the results of Walker and Hopster [7] and is about !0.3 k /atom according to Fuchs et al. [8]. The authors concluded, that this V magnetism is induced by the magnetised Fe substrate. Handshuh and Blu¨gel [9] have shown theoretically, with spin-polarised full-potential linearized-augmented-plane-wave method (FLAPW) calculations of the electronic structure, that the induced V moment in 1V/Fe(1 0 0) system is !0.6 k /atom. The studies of Vega et al. [10] and Mirbt et al. [11] give the V moment of !1.67 and about !1.5 k /atom, respectively. In the present paper, we report the results of spinpolarised calculations of the electronic structure of 1V/Fe(1 0 0) system, which were performed in order to understand the nature of the mentioned discrepancy in the results of the above-mentioned investigations. We report also the results of studies of V overlayer magnetism on the Cr(1 0 0) substrate.
2. Method The ab initio spin-polarised calculations of electronic structure were performed using the FLAPW method. The core states were calculated fully relativistically and the valence states were calculated in scalar-relativistic approximation. The local spin density approximation in the form due to Vosko et al. [12] was employed for the
0042-207X/99/$ — see front matter 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 0 4 2 - 2 0 7 X ( 9 8 ) 0 0 4 4 9 - 7
138
S.V. Man+kovsky, V.T. Cherepin / Vacuum 54 (1999) 137—141
exchange-correlation potential. The grid of 21 k-points in the irreducible wedge of the 2D Bz was used in the iterations and a set of 45 k-points was used in the final iteration. A variational basis set of more than 60 plane waves per atom was used. The calculations were carried out for a five-layer Fe (1 0 0) and Cr(1 0 0) films covered with V monolayers on both sides of the film. The lattice constant of ideal Fe (a "5.416 a.u.) and Cr (a "5.448 a.u.) bcc lattices were used.
3. Results and discussion 3.1. V(1 ML)/(1 0 0)Fe For study of the stability of the paramagnetic state of a V monolayer on the Fe(1 0 0) substrate the Stoner factor IN(E ) (I is the exchange-correlation integral and $ N(E ) is the density of states (DOS) at the Fermi level) $ was evaluated (Table 1). The exchange-correlation integral, obtained in [2] has been used. Since the Stoner factor for the V overlayer is larger than 1, ferromagnetic ordering in this layer may be expected. Taking into account the above-mentioned discrepancy between theoretical and experimental results, the existence of several magnetic states for the system considered was assumed. Two stable states were found from the calculations for V(1 ML)/(1 0 0)Fe system: one with the magnetic moment of !0.97 k (AFM1) and the other with !1.46 k (AFM2) in the V overlayer. In both states V couples antiferromagnetically with the Fe substrate, and the magnetic moment of the interface Fe layer decreases with respect to the bulk value. The total energy calculations show that the energy of the state AFM1 is less than the energy of the state AFM2 by 22 mRy. Table 2 presents
Table 1 DOS at the E and Stoner factors for V overlayers $ System
N(E ), state/Ry $
IN(E ) $
IV/Fe(1 0 0) IV/Cr(1 0 0)
36.5 33.4
1.20 1.08
Table 2 Layer projected magnetic moments M(in l ) for V(1 ML)/Fe(1 0 0) system and for (1 0 0) V-terminated surface of VFe B2 alloy State
Vacuum
Layers 1
AFM1 AFM2 VFe B2
!0.17 !0.06 0.06
!1.46 !0.97 !0.02
2 1.74 1.70 1.19
3 2.55 2.55 !0.25
4 2.22 2.22 1.07
Fig. 1. Local DOS for the V(1 ML)/Fe(1 0 0) system: in the V monolayer for nonmagnetic state of the system (a); in the V monolayer of the metastable state (b) and layer-by-layer DOS for the stable state (c). Solid lines correspond to majority-spin states, and dotted lines — to minority-spin states.
the layer projected magnetic moments M for both states. It is seen, that their values in the internal Fe layers are equal, and differ only in the interface layers. The value of demagnetisation in the interface Fe layer (M !M )/M , obtained in our calculations is about 0.23 which is in good agreement with the value 0.2, obtained experimentally by Fuchs et al. [8]. Due to the exchange interaction, the Fe majority-spin d-bands drop down below the Fermi level, E , and are $ nearly fully occupied, while the minority-spin states displace up on the energy scale. These result in Fe DOS minimum near the E (Fig. 1b, c). The Fe minority-spin $ d-states overlap with V d-states of the same spin direction, which favours their hybridisation (Figs. 1, 2). Fig. 2 display (for the ground state of the system) highly localised surface (V) states near the Fermi level at the C point and in the C —MM direction, which give rise to the DOS peaks near the E . The average exchange splitting of $ V d-states with opposite spin directions in the ground state is about 0.2 eV.
S.V. Man+kovsky, V.T. Cherepin / Vacuum 54 (1999) 137—141
139
The high localisation degree of localised V states and their large DOS value favour the exchange splitting and the appearance of a second magnetic state with the average exchange splitting of V d-states of about 0.9 eV. As a result, due to higher occupation of V minority-spin d-states drawn down in energy and because of increase of energy distance between the V and Fe minority-spin states, their hybridisation with Fe d-states is diminished. Simultaneously, demagnetisation of the interfacial Fe layer also decreases, as may be seen from the increase of magnetic moment in the interface Fe layer (Table 2). Thus, taking into account that the instability of the paramagnetic state of V monolayer is caused by the localised V states near the Fermi level, a more stable state with smaller magnetic moment (apparently, induced) and larger hybridisation between the V and Fe d-states, suggests, that the hybridisation plays a key role in stabilisation of the AFM1 magnetic state of the considered system. Another picture takes place in the (1 0 0) surface of FeV B2 compound. Although its lattice parameter is slightly greater than that of Fe, the magnetic moment of V surface layer is negligibly small (&0.02 k ). The reason is apparently due to a small exchange splitting of bulk states, which results in coincidence of energy position of the surface V d-states of both spin directions with the bulk d-states and hence to the small localisation of these states, and to the small difference in the degree of hybridisation of V and Fe d-states with opposite spin. 3.2. V(1ML)/Cr(1 0 0)
Fig. 2. Energy band structure for V(1 ML)/Fe(1 0 0) system for majority- (a) and minority-spin states. Solid lines represent the states with more than 70% localisation in vacuum and the surface (V) layer.
The V magnetisation and antiparallel alignment of the V magnetic moment with respect to the Fe one in the ground state is caused by a different degree of hybridisation of majority- and minority-spin states of V and Fe, which occurs for the following reasons. First, as the Fe majority-spin d-states move down in energy and minority-spin d-states move up, the last ones are positioned close to the V d-states. This results in stronger hybridisation of minority-spin d-states of V and Fe in comparison with the majority-spin one. The second reason is that the occupied majority-spin d-states of Fe are more localised near the atoms and this results in a lesser degree of hybridisation with V d-states. These hybridisation features cause also the diminishing of the magnetic moment in the interface Fe layer in comparison with their bulk value.
It is interesting to study the magnetism of the V monolayer on Cr(1 0 0) and compare it with the 1V/Fe(1 0 0) system, because the lattice parameter of bcc Cr is close to the Fe lattice parameter, on the one hand, but the substrate (Cr) is antiferromagnetically ordered, on the other. Moreover, the Fermi level in Cr is positioned in the DOS minimum between the bonding and antibonding states of both spins. For these reasons the V d-states near the Fermi level would be largely localised in the V overlayer, but the difference in degree of hybridisation between the Cr and V d-states for opposite spin directions is significantly less than in the case of V/Fe(1 0 0) system. The Stoner factor analysis indicates the instability of the paramagnetic state of the V overlayer. From the spinpolarised calculations of the electronic structure for the V overlayer on the (1 0 0)Cr substrate four magnetic states for this system were found: two states with antiferromagnetic (AFM1 and AFM2) and two states with ferromagnetic alignment (FM1 and FM2) of V magnetic moment with respect to the one of the substrate. The DOS pictures (Fig. 3a, c) shows the large splitting of V states with opposite spin in AFM2 and FM2 states of the system which result in large V magnetic moments in these states (see Table 3). These states are caused
140
S.V. Man+kovsky, V.T. Cherepin / Vacuum 54 (1999) 137—141 Table 3 The layer projected magnetic moments M (in l ) for V(1 ML)/Cr(1 0 0) ystem for different magnetic states and the energy differences E!E (in mRy) (where E is the ground state) $+ $+ State
Layer
M
AFM1
V (S) Cr (I) V (S) Cr (I) V (S) Cr (I) V (S) Cr (I)
!0.23 0.28 !1.11 0.54 0.05 0.18 0.62 0.07
AFM2 FM1 FM2
E!E
$+
0 70 22 27
Fig. 3. Local DOS for the states with different magnetic moments in the V layer of the V(1 ML)/Cr(1 0 0) system: !1.11 k in the V monolayer (a), 0.05 k in the V monolayer (b), 0.62 k in the V monolayer (c) and layer-by-layer DOS for the stable state (!0.23 k in the V monolayer) (c). Solid lines correspond to majority-spin states, and dotted lines — to minority-spin states.
apparently by the exchange interaction of localised V states near E . The splitting of the opposite-spin states $ in V overlayer in another two states of the system is rather small. The total energy calculations show, that the state with the magnetic moment !0.23 k in V layer (AFM1) has the smallest energy, i.e. it is the ground state. The energy band picture (Fig. 4) shows the surface (V) states at the C point and in the C —M M and C —XM directions. The states in the C —MM direction are located in the gap of Cr states and are largely localised in the V layer. Apparently this enables both ferromagnetic (FM2) and antiferromagnetic (AFM2) ordering in the V layer. The magnetic moments in the V overlayer and in the Cr interface layer and the total energies of these states
Fig. 4. Energy band structure for V(1 ML)/Cr(1 0 0) system for majority- (a) and minority-spin states. Solid lines represent the states with more than 70% localisation in vacuum and surface (V) layer.
with respect to the ground state are presented in Table 3. The correlation between the magnetic moments in the overlayer and the interface Cr layer are seen: the largest value in the interfacial Cr layer corresponds to the largest
S.V. Man+kovsky, V.T. Cherepin / Vacuum 54 (1999) 137—141
value in the overlayer with AFM alignment, and the smallest value in the interfacial Cr layer corresponds to the largest value in the overlayer with FM alignment. This is evidence for a large interaction of the V overlayer with the Cr substrate. However, because of the complicated system considered, more detailed study is needed to clarify the understanding of the role of overlayer/substrate interaction in stabilising the ground state. Several magnetic states for the Cr(1 0 0) and Fe(1 0 0) surfaces covered by V monolayer were found. The states with induced V magnetic moment of !0.23 and !0.97 k on Cr(1 0 0) and Fe(1 0 0) substrates, respectively, were found to be most stable, that is in satisfactory agreement with the results of studies [7—9]. The magnetic moment in the V layer for both systems is caused by the interaction of overlayers with substrates and this interaction has a key role in stabilising the ground states of the systems considered.
141
References [1] Zhu MJ, Bylander DM, Kleinman L. Phys Rev B 1990;42: 2874. [2] Ohnishi S, Fu CL, Frreman AJ. J Magn Magn Mater 1985;50: 161. [3] Blu¨gel S, Drittler B, Zeller R, Dederichs PH. Appl Phys A 1989;49:547. [4] Ruqian Wu, Freeman AJ. Phys Rev B 1995;51:17 131. [5] Rader O, Vescovo E, Redinger J, Blu¨gel S, Carbone C, Eberhardt W, Gudat W. Phys Rev Lett 1994;72:2247. [6] Vescovo E, Rader O, Redinger J, Blu¨gel S, Carbone CW. Phys Rev B 1995;51:12 418. [7] Walker TG, Hopster H. Phys Rev B 1994;49:7687. [8] Fuchs P, Totland K, Landolt M. Phys Rev B 1996;53:9123. [9] Handschuh S, Blu¨gel S. Solid State Commun 1998;105:633. [10] Vega A, Rubio A, Balbas LC, Dorantes-Davia J, Bauarab S, Demangeat C, Mokrani A, Dreisse H. J Appl Phys 1991;69:4544. [11] Mirbt S, Eriksson O, Johansson B, Skriver HL. Phys Rev B 1995;52:15 070. [12] Vosko SW, Wilk L, Nusair M. Can J Phys 1980;58:1200.