Electronic and Magnetic properties of pure and doped manganese clusters
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1 Electronic and Magnetic properties of pure and doped manganese clusters relevance to the IIIV semiconductor ferromagnetism Mukul Kabir Theoretical Condensed Matter Group S. N. Bose National Centre for Basic Sciences Salt Lake City, Kolkata 7 98, INDIA Mukul Kabir, Bose Centre p.
2 Group Prof. Abhijit Mookerjee Theoretical Condensed Matter Group S. N. Bose National Centre for Basic Sciences Salt Lake City, Kolkata 7 98, INDIA Prof. D. G. Kanhere Department of Physics and Centre for Modeling and Simulations University of Pune, Pune 4 7, INDIA Mukul Kabir, Bose Centre p.
3 Motivation How magnetism behaves in the reduced dimension and how it evolves to the bulk??? Mukul Kabir, Bose Centre p.
4 Motivation How magnetism behaves in the reduced dimension and how it evolves to the bulk??? Several unexpected results have already been reported: Mukul Kabir, Bose Centre p.
5 Motivation How magnetism behaves in the reduced dimension and how it evolves to the bulk??? Several unexpected results have already been reported: Nonzero magnetic moment in the clusters of nonmagnetic bulk material Magnetic Moment / atom ( µ B / atom) Rhodium Cluster Cluster Size N Rh clusters Cox et al PRL 7, 923 (993); PRB 49, 2295 (994) Mukul Kabir, Bose Centre p.
6 Motivation How magnetism behaves in the reduced dimension and how it evolves to the bulk??? Several unexpected results have already been reported: Enhancement of magnetic moment in the clusters of ferromagnetic bulk materials Magnetic Moment / atom ( µ /atom) B Fe Cluster Cluster Size N Fe clusters Billas et al. PRL 7, 467, (993) Mukul Kabir, Bose Centre p.
7 Motivation How magnetism behaves in the reduced dimension and how it evolves to the bulk??? Several unexpected results have already been reported: Finite magnetic moment in the clusters which is antiferromagnetic as bulk Magnetic Moment /atom (µ /atom) B Cluster Size N Mn Cluster Mn clusters Knickelbein PRL 82, 5255 (2); PRB 7, 4424 (24) Mukul Kabir, Bose Centre p.
8 SternGerlach Two methods have been employed to measure cluster magnetism. Cluster embedded in (rare gas) matrix clustermatrix interaction 2. Free cluster SternGerlach experiment Mukul Kabir, Bose Centre p.
9 / SternGerlach Two methods have been employed to measure cluster magnetism. Cluster embedded in (rare gas) matrix clustermatrix interaction 2. Free cluster SternGerlach experiment Z Y X Molecular Beam 2d L D % #$ "! )+* ( '&,. magnetic field gradient along z velocity in the SG magnet along x mass Cox et al.; de Heer et al.; Knickelbein Mukul Kabir, Bose Centre p.
10 Mn Clusters Magnetic Moment /atom (µ /atom) B Cluster Size N Mn Cluster Knickelbein PRL 82, 5255 (2); PRB 7, 4424 (24) Mukul Kabir, Bose Centre p.
11 Mn Clusters Magnetic Moment /atom (µ /atom) B Cluster Size N Mn Cluster Two possible pictures: individual atomic moments are small and ordered ferromagnetically OR they remain large but their orientation flips from site to site Knickelbein PRL 82, 5255 (2); PRB 7, 4424 (24) Mukul Kabir, Bose Centre p.
12 Mn Clusters More features: Magnetic Moment (µ B /atom) Cluster Size N Mn Cluster Knickelbein PRL 82, 5255 (2); PRB 7, 4424 (24) Mukul Kabir, Bose Centre p.
13 42 32 Mn Clusters More features: Magnetic Moment (µ B /atom) Cluster Size N Mn Cluster Sudden drop in the magnetic moment at and!!! WHY??? Knickelbein PRL 82, 5255 (2); PRB 7, 4424 (24) Mukul Kabir, Bose Centre p.
14 Mn Clusters More features: Magnetic Moment (µ B /atom) Cluster Size N Mn Cluster Sudden drop in the magnetic moment at and!!! WHY??? Uncertainty in the measurement, generally, decreases with size except at!!! Any Physical Reason??? Knickelbein PRL 82, 5255 (2); PRB 7, 4424 (24) Mukul Kabir, Bose Centre p.
15 Methodology Density Functional Theory within pseudopotential plane wave method We use projector augmented wave method PerdewBrukeErnzerhof exchangecorrelation functional for spin polarized GGA To locate the ground state geometry, we consider different geometrical structures As well as, all possible spin multiplicities to get the ground state magnetic structure Spins are treated collinearly Vienna abinitio Simulation Package Mukul Kabir, Bose Centre p.
16 pure manganese clusters... 3 Binding Energy (ev/atom) Cluster Size N Mukul Kabir, Bose Centre p.
17 ; pure manganese clusters... 3 Binding Energy (ev/atom) Cluster Size N Mn dimer is very weakly bound (van der Walls) dimer. Reason : lack of hybridization between the halffilled 3d and filled 4s electrons high promotion energy 2.4 ev : s 2 3d ev 6 4s 3d Mukul Kabir, Bose Centre p.
18 pure manganese clusters... 3 Binding Energy (ev/atom) B. E. (ev/atom) Cluster Size N 3 (a) /N Due to the increase in the coordination number with cluster size Binding energy increases with cluster size Mukul Kabir, Bose Centre p.
19 <= 2 ; ; pure manganese clusters... 3 Binding Energy (ev/atom) B. E. (ev/atom) Cluster Size N 3 (a) /N Due to the increase in the coordination number with cluster size Binding energy increases with cluster size Extrapolation of the BE with gives the BE for infinitely large cluster (bulk) 2.8 ev Experimental BE value for AF bulk Mn 2.92 ev Mukul Kabir, Bose Centre p.
20 pure manganese clusters... 3 Binding Energy (ev/atom) B. E. (ev/atom) Cluster Size N 3 (a) /N Kinks in the BE curve at 7, 3 and 9 Mukul Kabir, Bose Centre p.
21 D B A2 > > pure manganese clusters... Binding Energy (ev/atom) E (b) N B. E. (ev/atom) Cluster Size N (a) /N Kinks in the BE curve at 7, 3 and 9 A C C This gives the relative stability of the clusters and we see peaks in the vs plot at 7, 3 and 9 Why??? Mukul Kabir, Bose Centre p.
22 D B A2 > > pure manganese clusters... Binding Energy (ev/atom) E (b) N B. E. (ev/atom) Cluster Size N (a) /N Kinks in the BE curve at 7, 3 and 9 A C C This gives the relative stability of the clusters and we see peaks in the vs plot at 7, 3 and 9 Why??? Closed geometric structure!!! Mukul Kabir, Bose Centre p.
23 nonmetallic metallic transition? Significant change in the Mn reaction has been observed at nonmetallic to metallic transition!!! + H = 6 Mukul Kabir, Bose Centre p.
24 Z J I E G Z J I G nonmetallic metallic transition? reaction has been observed at = 6 Significant change in the Mn nonmetallic to metallic transition!!! Mukul Kabir, Bose Centre p. + H OPRQ LN OWVI OPRQ KMLN FHG C T TU S C T U YX OP Q KMLN OPRQ LN OWVI F[G T U YX C T TU S C E
25 Z E C T U YX S Z J I T U YX S nonmetallic metallic transition? Significant change in the Mn reaction has been observed at nonmetallic to metallic transition!!! + H = 6 Spin Gaps (ev) δ δ Cluster Size N OP Q LN OWVI OP Q KMLN J I FHG G C T TU OP Q KMLN OPRQ LN OWVI F G G C T TU E C Mukul Kabir, Bose Centre p.
26 Z E C T U YX S Z J I \2 T U YX S nonmetallic metallic transition? Significant change in the Mn reaction has been observed at nonmetallic to metallic transition!!! + H = 6 Spin Gaps (ev) δ δ Cluster Size N Ionization Potential (ev) 5.5 Koretsky et al., JCP 6 98, (997) Cluster Size N OP Q KMLN J I FHG G C T TU OP Q LN OWVI no discontinuity is observed E C OPRQ LN OWVI F G G C T TU OP Q KMLN and argued a certain structural transition at Mukul Kabir, Bose Centre p.
27 6 ] magnetic transition... Magnetic Moment (µ B /atom) Theory (GS) Theory (Isomer) SG Exp Cluster Size N Ferromagnetic coupling of very small clusters Mukul Kabir, Bose Centre p.
28 6 ] ^ magnetic transition... Magnetic Moment (µ B /atom) Theory (GS) Theory (Isomer) SG Exp Cluster Size N Ferromagnetic coupling of very small clusters FM ferrimagnetic transition takes place at Mukul Kabir, Bose Centre p.
29 ` _ magnetic transition... Magnetic Moment (µ B /atom) Theory (GS) Theory (Isomer) SG Exp Cluster Size N For most of the clusters, there exist several closely lying isomers with different magnetic solution. For, there are three Mukul Kabir, Bose Centre p.
30 ` _? b d? b c? b a magnetic transition... Magnetic Moment (µ B /atom) Theory (GS) Theory (Isomer) SG Exp Cluster Size N For most of the clusters, there exist several closely lying isomers with different magnetic solution. For, there are three up down,. ev,.9 ev,.9 ev Large experimental uncertainty in the measured magnetic moment (.72 ), is due to the presence of these three isomers in the GS beam. 6 D efhg Mukul Kabir, Bose Centre p.
31 42 32 magnetic transition... Magnetic Moment (µ B /atom) Theory (GS) Theory (Isomer) SG Exp Cluster Size N Sudden drop in the magnetic moment is found at and Mukul Kabir, Bose Centre p.
32 42 32 i? b? b? b magnetic transition... Magnetic Moment (µ B /atom) Theory (GS) Theory (Isomer) SG Exp Cluster Size N Sudden drop in the magnetic moment is found at For Mn : and Icosahedral Hexagonal Cubooctahedral 3 9 =. ev =.89 ev =.2 ev Mukul Kabir, Bose Centre p.
33 42 32 magnetic transition... Magnetic Moment (µ B /atom) Theory (GS) Theory (Isomer) SG Exp Cluster Size N Sudden drop in the magnetic moment is found at and Mukul Kabir, Bose Centre p.
34 42 32 j? b? b magnetic transition... Magnetic Moment (µ B /atom) Theory (GS) Theory (Isomer) SG Exp Cluster Size N Sudden drop in the magnetic moment is found at For Mn : and Double Icosahedron FCC 2 7 =. ev =.53 ev Mukul Kabir, Bose Centre p.
35 42 32 magnetic transition... Magnetic Moment (µ B /atom) Theory (GS) Theory (Isomer) SG Exp Cluster Size N Sudden drop in the magnetic moment is found at and Mukul Kabir, Bose Centre p.
36 42 32 magnetic transition... Magnetic Moment (µ B /atom) Theory (GS) Theory (Isomer) SG Exp Cluster Size N Sudden drop in the magnetic moment is found at and This is due to their closed icosahedral geometric structure. First Icosahedron Double Icosahedron Mukul Kabir, Bose Centre p.
37 electron localization k Localization vs Coordination Mukul Kabir, Bose Centre p. 2
38 m l electron localization k Localization vs Coordination u rw A qsrt npo Mukul Kabir, Bose Centre p. 2
39 y summary Intermediate Mn clusters adopt icosahedral growth pattern Kabir, Mookerjee and Kanhere (communicated) Mukul Kabir, Bose Centre p. 2
40 y = \2 summary Intermediate Mn clusters adopt icosahedral growth pattern Nonmetal metal transition at is not seen, which was predicted from the discontinuity in the reaction rate with H. Even there is no structural transition takes place at N=6. Kabir, Mookerjee and Kanhere (communicated) Mukul Kabir, Bose Centre p. 2
41 y = \2 = ^ summary Intermediate Mn clusters adopt icosahedral growth pattern Nonmetal metal transition at is not seen, which was predicted from the discontinuity in the reaction rate with H. Even there is no structural transition takes place at N=6. FM Ferrimagnetic transition takes place at Kabir, Mookerjee and Kanhere (communicated) Mukul Kabir, Bose Centre p. 2
42 y = \2 = ^ summary Intermediate Mn clusters adopt icosahedral growth pattern Nonmetal metal transition at is not seen, which was predicted from the discontinuity in the reaction rate with H. Even there is no structural transition takes place at N=6. FM Ferrimagnetic transition takes place at Closely lying isomers with different magnetic structure are possible Kabir, Mookerjee and Kanhere (communicated) Mukul Kabir, Bose Centre p. 2
43 y = \2 = ^ ` summary Intermediate Mn clusters adopt icosahedral growth pattern Nonmetal metal transition at is not seen, which was predicted from the discontinuity in the reaction rate with H. Even there is no structural transition takes place at N=6. FM Ferrimagnetic transition takes place at Closely lying isomers with different magnetic structure are possible Large experimental uncertainty in the magnetic moment of Mn is due the existence of two closely lying isomers (with 7 and 3 ) along with the ground state (5 ) in the SG beam Kabir, Mookerjee and Kanhere (communicated) Mukul Kabir, Bose Centre p. 2
44 y = \2 = ^ ` = summary Intermediate Mn clusters adopt icosahedral growth pattern Nonmetal metal transition at is not seen, which was predicted from the discontinuity in the reaction rate with H. Even there is no structural transition takes place at N=6. FM Ferrimagnetic transition takes place at Closely lying isomers with different magnetic structure are possible Large experimental uncertainty in the magnetic moment of Mn is due the existence of two closely lying isomers (with 7 and 3 ) along with the ground state (5 ) in the SG beam Sudden drop in the magnetic moment at closed icosahedral structure and is due to their Kabir, Mookerjee and Kanhere (communicated) Mukul Kabir, Bose Centre p. 2
45 y = \2 = ^ ` = summary Intermediate Mn clusters adopt icosahedral growth pattern Nonmetal metal transition at is not seen, which was predicted from the discontinuity in the reaction rate with H. Even there is no structural transition takes place at N=6. FM Ferrimagnetic transition takes place at Closely lying isomers with different magnetic structure are possible Large experimental uncertainty in the magnetic moment of Mn is due the existence of two closely lying isomers (with 7 and 3 ) along with the ground state (5 ) in the SG beam Sudden drop in the magnetic moment at closed icosahedral structure C and is due to their electrons are more localized for the surface atom than the central atom due relatively small coordination number Kabir, Mookerjee and Kanhere (communicated) Mukul Kabir, Bose Centre p. 2
46 As doping motivation Manganese in the semiconductor Ga {z Mn z As and Ga Mn As show ferromagnetism dilute magnetic semiconductor (spintronic) materials Mukul Kabir, Bose Centre p. 2
47 As doping motivation Manganese in the semiconductor Ga {z Mn z As and Ga Mn As show ferromagnetism dilute magnetic semiconductor (spintronic) materials Reported wide variation of Curie temperature 5K to highest 6K Mukul Kabir, Bose Centre p. 2
48 As doping motivation Manganese in the semiconductor Ga {z Mn z As and Ga Mn As show ferromagnetism dilute magnetic semiconductor (spintronic) materials Reported wide variation of Curie temperature 5K to highest 6K Samples are prepared by low temperature Molecular beam epitaxy growth gives rise to metastable defects Mn Interstitials As antisites (As Random distribution of Mn Clustering of Mn } ) Mukul Kabir, Bose Centre p. 2
49 As doping motivation Manganese in the semiconductor Ga {z Mn z As and Ga Mn As show ferromagnetism dilute magnetic semiconductor (spintronic) materials Reported wide variation of Curie temperature 5K to highest 6K Samples are prepared by low temperature Molecular beam epitaxy growth gives rise to metastable defects Mn Interstitials As antisites (As Random distribution of Mn Clustering of Mn } ) Samples annealed at low (growth) temperature show increase in the Curie temperature Mukul Kabir, Bose Centre p. 2
50 As doping motivation Manganese in the semiconductor Ga {z Mn z As and Ga Mn As show ferromagnetism dilute magnetic semiconductor (spintronic) materials Reported wide variation of Curie temperature 5K to highest 6K Samples are prepared by low temperature Molecular beam epitaxy growth gives rise to metastable defects Mn Interstitials As antisites (As Random distribution of Mn Clustering of Mn } ) Samples annealed at low (growth) temperature show increase in the Curie temperature Indeed, even after annealing, clusters of Mn around As have been detected experimentally Mukul Kabir, Bose Centre p. 2
51 As doping motivation Manganese in the semiconductor Ga {z Mn z As and Ga Mn As show ferromagnetism dilute magnetic semiconductor (spintronic) materials Reported wide variation of Curie temperature 5K to highest 6K Samples are prepared by low temperature Molecular beam epitaxy growth gives rise to metastable defects Mn Interstitials As antisites (As Random distribution of Mn Clustering of Mn } ) Samples annealed at low (growth) temperature show increase in the Curie temperature Indeed, even after annealing, clusters of Mn around As have been detected experimentally Clustering of Mn is responsible??? Mukul Kabir, Bose Centre p. 2
52 As clusters using the same methodology used for pure Mn As doping motivation Manganese in the semiconductor Ga {z Mn z As and Ga Mn As show ferromagnetism dilute magnetic semiconductor (spintronic) materials Reported wide variation of Curie temperature 5K to highest 6K Samples are prepared by low temperature Molecular beam epitaxy growth gives rise to metastable defects Mn Interstitials As antisites (As Random distribution of Mn Clustering of Mn } ) Samples annealed at low (growth) temperature show increase in the Curie temperature Indeed, even after annealing, clusters of Mn around As have been detected experimentally Clustering of Mn is responsible??? We study Mn + we allow noncollinearity in spins. Mukul Kabir, Bose Centre p. 2
53 Enhancement in Bonding We ask whether the clustering of Mn around As are at all energetically favourable or not? Mukul Kabir, Bose Centre p. 2
54 Enhancement in Bonding We ask whether the clustering of Mn around As are at all energetically favourable or not? 2.5 Binding Energy (ev/atom) Mn n Mn n As n Binding is enhanced substantially due to single As doping in the Mn cluster. Mukul Kabir, Bose Centre p. 2
55 @ ~ > C energy gains It can be defined in two ways Energy gain in adding an As atom to a Mn cluster A ƒ A C V A C ƒ V Mukul Kabir, Bose Centre p. 2
56 @ ~ > @? ~ C > energy gains It can be defined in two ways Energy gain in adding an As atom to a Mn cluster A ƒ A C A C ƒ V V Energy gain in adding a Mn atom to a existing Mn zas cluster A C ƒ Vz A C ƒ V Mukul Kabir, Bose Centre p. 2
57 @ ~ > @? ~ C > > > energy gains It can be defined in two ways Energy gain in adding an As atom to a Mn cluster A ƒ A C A C ƒ V V Energy gain in adding a Mn atom to a existing Mn zas cluster A C ƒ Vz A C ƒ V and 2 (ev) x Both of the energy gains are positive and the energy gain in adding a As ( ) is larger than the energy gain in adding a Mn ( ) Mukul Kabir, Bose Centre p. 2
58 @ ~ > @? ~ C > > > energy gains It can be defined in two ways Energy gain in adding an As atom to a Mn cluster A ƒ A C A C ƒ V V Energy gain in adding a Mn atom to a existing Mn zas cluster A C ƒ Vz A C ƒ V and 2 (ev) x Both of the energy gains are positive and the energy gain in adding a As ( ) is larger than the energy gain in adding a Mn ( ) Therefore, we conclude Clustering of Mn around As is energetically favourable Mukul Kabir, Bose Centre p. 2
59 Mn o Mn collinear vs noncollinear Mn Nature M Rˆ As Nature M Rˆ Mn Nature M ˆ As Nature M Rˆ 5 CL 4 6 NCL 2.82 NCL.28 2 CL CL 9 7 CL 5 CL 6 3 CL 5 CL 4 8 NCL 6.83 CL 3 4 CL 2 CL 7 9 NCL 5.33 NCL. 5 CL 3 CL 2 NCL 5.4 NCL 3.7 o As Mnj As Mn Mnj Mn Mukul Kabir, Bose Centre p. 2
60 magnetic coupling spin density = rw rt Mukul Kabir, Bose Centre p. 2
61 magnetic coupling Only in Mn As and Mn As MnMn coupling is ferromagnetic Spin isodensity plot Mn 9 As Mn spin density = 7 As rw rt Mukul Kabir, Bose Centre p. 2
62 magnetic coupling Only in Mn As and Mn As MnMn coupling is ferromagnetic Spin isodensity plot Mn 9 As Mn spin density = 7 As rw rt Š As Mni As Mn 4 7 Mukul Kabir, Bose Centre p. 2
63 C Exchange coupling We map the magnetic energy onto a Heisenberg form: ŒŽ Mukul Kabir, Bose Centre p. 2
64 Z t t w t?? Mukul Kabir, Bose Centre p. 2 Exchange coupling We map the magnetic energy onto a Heisenberg form: ŒŽ C As cluster: For Mn š š B š F š t w A t t
65 C Z t š t š?? t w t t Exchange coupling We map the magnetic energy onto a Heisenberg form: ŒŽ For Mn As cluster: B w š F š t A Exchange Coupling J (mev) calculated J Mn Mn Separation (r Mn Mn ) Å Mukul Kabir, Bose Centre p. 2
66 C Z t š t š?? t w t D Ÿ i z ž œ œ 2 Exchange coupling RKKY type??? We map the magnetic energy onto a Heisenberg form: ŒŽ For Mn As cluster: B w š F š t A Exchange Coupling J (mev) calculated J J RKKY Mn Mn Separation (r Mn Mn ) Å For RKKY type interaction A oscillates between positive and negative with favouring FM and AFM solutions, respectively and dies down as a typical RKKY type behaviour. i< Mukul Kabir, Bose Centre p. 2
67 Exchange coupling RKKY type??? But what happens to the exchange coupling when cluster size increases??? Mukul Kabir, Bose Centre p. 3
68 z Exchange coupling RKKY type??? But what happens to the exchange coupling when cluster size increases??? In dilute magnetic semiconductors Ga Mn As, RKKYlike models predict Mukul Kabir, Bose Centre p. 3
69 z #i Exchange coupling RKKY type??? But what happens to the exchange coupling when cluster size increases??? In dilute magnetic semiconductors Ga Mn As, RKKYlike models predict exchange coupling increases with concentration as independent of environment at K Mukul Kabir, Bose Centre p. 3
70 z #i Exchange coupling RKKY type??? But what happens to the exchange coupling when cluster size increases??? In dilute magnetic semiconductors Ga Mn As, RKKYlike models predict exchange coupling increases with concentration as independent of environment at K For Mn As clusters J ij (mev) n Mukul Kabir, Bose Centre p. 3
71 z #i Exchange coupling RKKY type??? But what happens to the exchange coupling when cluster size increases??? In dilute magnetic semiconductors Ga Mn As, RKKYlike models predict exchange coupling increases with concentration as independent of environment at K For Mn As clusters J ij (mev) n Average exchange parameter, decreases with increase in exceptional increase for ferromagnetic Mn As Also has strong environment dependency with an Mukul Kabir, Bose Centre p. 3
72 z #i Exchange coupling RKKY type??? But what happens to the exchange coupling when cluster size increases??? In dilute magnetic semiconductors Ga Mn As, RKKYlike models predict exchange coupling increases with concentration as independent of environment at K For Mn As clusters J ij (mev) n Average exchange parameter, decreases with increase in exceptional increase for ferromagnetic Mn As Also has strong environment dependency with an As cluster size increases, exchange coupling is no longer RKKYtype Mukul Kabir, Bose Centre p. 3
73 i 7 Conclusion Due to the 4 (of Mn) 3 hybridization, binding energy is enhanced Asatom stabilizes Mn Clustering of Mn is energetically favourable around As clusters Kabir, Mookerjee, Kanhere physics/539 Mukul Kabir, Bose Centre p. 3
74 i 7 \ Conclusion Due to the 4 (of Mn) 3 hybridization, binding energy is enhanced Asatom stabilizes Mn Clustering of Mn is energetically favourable around As clusters Noncollinear treatment of spins are necessary, as both Mn clusters adopt nocollinear magnetic structure for and Mn As Kabir, Mookerjee, Kanhere physics/539 Mukul Kabir, Bose Centre p. 3
75 i 7 \ Conclusion Due to the 4 (of Mn) 3 hybridization, binding energy is enhanced Asatom stabilizes Mn Clustering of Mn is energetically favourable around As clusters Noncollinear treatment of spins are necessary, as both Mn clusters adopt nocollinear magnetic structure for and Mn As MnMn coupling is ferromagnetic only for Mn other sizes they are ferrimagnetically coupled As and Mn As and for all Kabir, Mookerjee, Kanhere physics/539 Mukul Kabir, Bose Centre p. 3
76 i 7 \ Conclusion Due to the 4 (of Mn) 3 hybridization, binding energy is enhanced Asatom stabilizes Mn Clustering of Mn is energetically favourable around As clusters Noncollinear treatment of spins are necessary, as both Mn clusters adopt nocollinear magnetic structure for and Mn As MnMn coupling is ferromagnetic only for Mn other sizes they are ferrimagnetically coupled As and Mn As and for all The exchange coupling is anomalous and behave quite differently from the RKKY like predictions. Kabir, Mookerjee, Kanhere physics/539 Mukul Kabir, Bose Centre p. 3
77 i 7 \ Conclusion Due to the 4 (of Mn) 3 hybridization, binding energy is enhanced Asatom stabilizes Mn Clustering of Mn is energetically favourable around As clusters Noncollinear treatment of spins are necessary, as both Mn clusters adopt nocollinear magnetic structure for and Mn As MnMn coupling is ferromagnetic only for Mn other sizes they are ferrimagnetically coupled As and Mn As and for all The exchange coupling is anomalous and behave quite differently from the RKKY like predictions. Mn Therefore, the presence of Mn As clusters in (Ga,Mn)As and (In,Mn)As samples, would lead to a high Curie temperature. Whereas, presence of large sized clusters would, eventually, decrease Curie temperature. As and Mn As have high exchange coupling. As and Mn Kabir, Mookerjee, Kanhere physics/539 Mukul Kabir, Bose Centre p. 3
78 Thank You! Mukul Kabir, Bose Centre p. 3
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