electronic and magnetic properties of pure and doped ...bose.res.in/~mukul/kabir_greece.pdf ·...

Electronic and Magnetic properties of pureand doped manganese clusters

relevance to the III-V semiconductor ferromagnetism

Mukul Kabir

��

Theoretical Condensed Matter GroupS. N. Bose National Centre for Basic Sciences

Salt Lake City, Kolkata - 700 098, INDIA

Mukul Kabir, Bose Centre – p. 1

Group

Prof. Abhijit MookerjeeTheoretical Condensed Matter GroupS. N. Bose National Centre for Basic SciencesSalt Lake City, Kolkata - 700 098, INDIA

Prof. D. G. KanhereDepartment of Physics and Centre for Modeling and SimulationsUniversity of Pune, Pune - 411 007, INDIA


Motivation

How magnetism behaves in the “reduced dimension” and how it evolves to thebulk ???

Several unexpected results have already been reported:

Non-zero magnetic moment in the clusters of nonmagnetic bulk material

Cluster Size NMagn

etic

Mom

ent /

atom

(µ

B/ a

tom

)Rhodium Cluster

Rh clusters Cox et al PRL 71, 923 (1993); PRB 49, 12295 (1994)


Motivation


Several unexpected results have already been reported:�

Non-zero magnetic moment in the clusters of nonmagnetic bulk material

Cluster Size NMagn

etic

Mom

ent /

atom

(µ

B/ a

tom

)Rhodium Cluster

Rh � clusters � Cox et al PRL 71, 923 (1993); PRB 49, 12295 (1994)


Motivation



Enhancement of magnetic moment in the clusters of ferromagnetic bulkmaterials

Fe Cluster

Mag

netic

Mom

ent /

ato

m( µ

B/a

tom

)

Cluster Size N

Fe � clusters � Billas et al. PRL 71, 4067, (1993)


Motivation



Finite magnetic moment in the clusters which is antiferromagnetic as bulk

Mag

netic

Mom

ent /

atom

(µ

B/a

tom

)Mn Cluster

Cluster Size N

Mn � clusters � Knickelbein PRL 82, 5255 (2001); PRB 70, 14424 (2004)


Stern-Gerlach

�

Two methods have been employed to measure cluster magnetism1. Cluster embedded in (rare gas) matrix - cluster-matrix interaction2. Free cluster - Stern-Gerlach experiment

Molecular Beam

L D

2d

X

ZY

magnetic field gradient along zvelocity in the SG magnet along xmass

Cox et al.; de Heer et al.; Knickelbein


Stern-Gerlach

�

Two methods have been employed to measure cluster magnetism1. Cluster embedded in (rare gas) matrix - cluster-matrix interaction2. Free cluster - Stern-Gerlach experiment

Molecular Beam

L D

2d

X

ZY

� � � �� ! � " #$ %�'& ( )+*

� �� magnetic field gradient along z,.- � velocity in the SG magnet along x/ � mass

Cox et al.; de Heer et al.; KnickelbeinMukul Kabir, Bose Centre – p. 6

Mn 0 Clusters

Mag

netic

Mom

ent /

atom

(µ

B/a

tom

)

Mn Cluster

Cluster Size N

Two possible pictures:individual atomic moments are small and ordered ferromagnetically

ORthey remain large but their orientation flips from site to site

Knickelbein PRL 82, 5255 (2001); PRB 70, 14424 (2004)Mukul Kabir, Bose Centre – p. 7

Mn 0 Clusters

1 More features:

0

0.5

1

1.5

2

4 6 8 10 12 14 16 18 20 22

Mag

netic

Mom

ent (

µ B/at

om)

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 (2001); PRB 70, 14424 (2004)


Mn 0 Clusters

1 More features:

0

0.5

1

1.5

2

4 6 8 10 12 14 16 18 20 22

Mag

netic

Mom

ent (

µ B/at

om)

Cluster Size N

Mn Cluster

�

Sudden drop in the magnetic moment at 0 � 23

and

24

!!! WHY ???

Uncertainty in the measurement, generally, decreases with size - except at!!! Any Physical Reason ???



Mn 0 Clusters

1 More features:

0

0.5

1

1.5

2

4 6 8 10 12 14 16 18 20 22

Mag

netic

Mom

ent (

µ B/at

om)

Cluster Size N

Mn Cluster

�

Sudden drop in the magnetic moment at 0 � 23

and

24

!!! WHY ???�

Uncertainty in the measurement, generally, decreases with size - except at0 � 5

!!! Any Physical Reason ???



Methodology

1 Density Functional Theory within pseudopotential plane wave method1 We use projector augmented wave method1 Perdew-Bruke-Ernzerhof exchange-correlation functional for spin polarizedGGA1 To locate the ground state geometry, we consider different geometricalstructures1 As well as, all possible spin multiplicities to get the ground state magneticstructure1 Spins are treated collinearly

Vienna ab-initio Simulation Package


pure manganese clusters ...

0.5

1

1.5

2

2.5

3

2 4 6 8 10 12 14 16 18 20B

indi

ng E

nerg

y (e

V/a

tom

)

Cluster Size N

Mn dimer is very weakly bound (van der Walls) dimer.Reason :

lack of hybridization between the half-filled 3d and filled 4s electronshigh promotion energy 2.14 eV

4s2 3d5

4s 3d1 62.14 eV



0.5

1

1.5

2

2.5

3

2 4 6 8 10 12 14 16 18 20B

indi

ng E

nerg

y (e

V/a

tom

)

Cluster Size N�

Mn � dimer is very weakly bound (van der Walls) dimer.Reason :1 lack of hybridization between the half-filled 3d and filled 4s electrons1 high

687 � 3 � 9 � 687 3 � :promotion energy ; 2.14 eV

4s2 3d5

4s 3d1 62.14 eV



0.5

1

1.5

2

2.5

3

2 4 6 8 10 12 14 16 18 20B

indi

ng E

nerg

y (e

V/a

tom

)

Cluster Size N

1

1.5

2

2.5

3

0 0.05 0.1 0.15 0.2

B. E

. (eV

/ato

m)

1/N

(a)

�

Due to the increase in the coordination number with cluster sizeBinding energy increases with cluster size

Extrapolation of the BE with gives the BE for infinitely large cluster(bulk) 2.80 eVExperimental BE value for AF bulk Mn 2.92 eV



0.5

1

1.5

2

2.5

3

2 4 6 8 10 12 14 16 18 20B

indi

ng E

nerg

y (e

V/a

tom

)

Cluster Size N

1

1.5

2

2.5

3

0 0.05 0.1 0.15 0.2

B. E

. (eV

/ato

m)

1/N

(a)

�

Due to the increase in the coordination number with cluster sizeBinding energy increases with cluster size�

Extrapolation of the BE with2 <=

gives the BE for infinitely large cluster(bulk) ; 2.80 eVExperimental BE value for AF bulk Mn ; 2.92 eV



0.5

1

1.5

2

2.5

3

2 4 6 8 10 12 14 16 18 20B

indi

ng E

nerg

y (e

V/a

tom

)

Cluster Size N

1

1.5

2

2.5

3

0 0.05 0.1 0.15 0.2

B. E

. (eV

/ato

m)

1/N

(a)

�

Kinks in the BE curve at 7, 13 and 19



0.5

1

1.5

2

2.5

3

2 4 6 8 10 12 14 16 18 20B

indi

ng E

nerg

y (e

V/a

tom

)

Cluster Size N

1

1.5

2

2.5

3

0 0.05 0.1 0.15 0.2

B. E

. (eV

/ato

m)

1/N

(a)

-1 0 1

5 10 15 20

∆ 2E

N

(b)

�

Kinks in the BE curve at 7, 13 and 19

> � ? @ 0 A � ? @ 0 B 2 A B ? @ 0�C 2 A C D ? @ 0 A

This gives the relative stability of the clusters and we see peaks in the> � ? @ 0 A vs 0 plot at 7, 13 and 19 ——— Why ???

Closedgeometricstructure !!!


non-metallic metallic transition ?

Significant change in the Mn � + H � reaction has been observed at 0 = 16 �non-metallic to metallic transition !!!

0

0.5

1

1.5

2

2.5

2 4 6 8 10 12 14 16 18 20

Spi

n G

aps

(eV

)

Cluster Size N

δ1δ2

4.7

4.8

4.9

5

5.1

5.2

5.3

5.4

5.5

6 8 10 12 14 16 18 20

Ioni

zatio

n P

oten

tial (

eV)

Cluster Size N

Koretsky et al., JCP 106 9810, (1997)

no discontinuity is observed

and argued a certain structural transition at




0

0.5

1

1.5

2

2.5

2 4 6 8 10 12 14 16 18 20

Spi

n G

aps

(eV

)

Cluster Size N

δ1δ2

4.7

4.8

4.9

5

5.1

5.2

5.3

5.4

5.5

6 8 10 12 14 16 18 20

Ioni

zatio

n P

oten

tial (

eV)

Cluster Size N


E � C FHG I J KMLN OPRQS TU T C G I OWV LN OPRQXY U T Z


E � � C F[G I OWV LN OPRQS TU T C G I J KMLN OPQXY U T Z





0

0.5

1

1.5

2

2.5

2 4 6 8 10 12 14 16 18 20

Spi

n G

aps

(eV

)

Cluster Size N

δ1δ2

4.7

4.8

4.9

5

5.1

5.2

5.3

5.4

5.5

6 8 10 12 14 16 18 20

Ioni

zatio

n P

oten

tial (

eV)

Cluster Size N


E � C FHG I J KMLN OPQS TU T C G I OWV LN OPQXY U T Z


E � � C FG I OWV LN OPRQS TU T C G I J KMLN O PQXY U T Z





0

0.5

1

1.5

2

2.5

2 4 6 8 10 12 14 16 18 20

Spi

n G

aps

(eV

)

Cluster Size N

δ1δ2

4.7

4.8

4.9

5

5.1

5.2

5.3

5.4

5.5

6 8 10 12 14 16 18 20

Ioni

zatio

n P

oten

tial (

eV)

Cluster Size N


E � C FHG I J KMLN OPQS TU T C G I OWV LN OPQXY U T Zno discontinuity is observed

E � � C FG I OWV LN OPRQS TU T C G I J KMLN O PQXY U T Z

and argued a certain structural transition at 0 � 2\


magnetic transition ...

0

1

2

3

4

5

2 4 6 8 10 12 14 16 18 20

Mag

netic

Mom

ent (

µ B/a

tom

)Cluster Size N

Theory (GS)Theory (Isomer)

SG Exp.

�

Ferromagnetic coupling of very small clusters 0 ] 6

FM ferrimagnetic transition takes place at



0

1

2

3

4

5

2 4 6 8 10 12 14 16 18 20

Mag

netic

Mom

ent (

µ B/a

tom

)Cluster Size N


SG Exp.

�

Ferromagnetic coupling of very small clusters 0 ] 6

�

FM � ferrimagnetic transition takes place at 0 � ^



0

1

2

3

4

5

2 4 6 8 10 12 14 16 18 20

Mag

netic

Mom

ent (

µ B/a

tom

)Cluster Size N


SG Exp.

�

For most of the clusters, there exist several closely lying isomers withdifferent magnetic solution. For

_ 0` , there are three —

, 0.00 eV , 0.09 eV , 0.19 eV

updown

Large experimental uncertainty in the measured magnetic moment (0.72), is due to the presence of these three isomers in the GS beam.



0

1

2

3

4

5

2 4 6 8 10 12 14 16 18 20

Mag

netic

Mom

ent (

µ B/a

tom

)Cluster Size N


SG Exp.

�

For most of the clusters, there exist several closely lying isomers withdifferent magnetic solution. For

_ 0` , there are three —

a � � , b ? � 0.00 eV

c � � , b ? � 0.09 eV

d � � , b ? � 0.19 eV

updown

�

Large experimental uncertainty in the measured magnetic moment (0.72efhg 6 D � � ), is due to the presence of these three isomers in the GS beam.Mukul Kabir, Bose Centre – p. 16


0

1

2

3

4

5

2 4 6 8 10 12 14 16 18 20

Mag

netic

Mom

ent (

µ B/a

tom

)Cluster Size N


SG Exp.

�

Sudden drop in the magnetic moment is found at 0 � 23

and

24

For Mn :

Icosahedral Hexagonal Cubooctahedral

3 9 11

= 0.00 eV = 0.89 eV = 1.12 eV



0

1

2

3

4

5

2 4 6 8 10 12 14 16 18 20

Mag

netic

Mom

ent (

µ B/a

tom

)Cluster Size N


SG Exp.

�


and

24

1 For Mn i :

Icosahedral Hexagonal Cubooctahedral

3 � � 9 � � 11 � �

b ?= 0.00 eV

b ?

= 0.89 eV

b ?

= 1.12 eV



0

1

2

3

4

5

2 4 6 8 10 12 14 16 18 20

Mag

netic

Mom

ent (

µ B/a

tom

)Cluster Size N


SG Exp.

�


and

24

For Mn :

Double Icosahedron FCC

21 17

= 0.00 eV = 1.53 eV



0

1

2

3

4

5

2 4 6 8 10 12 14 16 18 20

Mag

netic

Mom

ent (

µ B/a

tom

)Cluster Size N


SG Exp.

�


and

24

1 For Mn j :

Double Icosahedron FCC

21 � � 17 � �

b ?

= 0.00 eV

b ?

= 1.53 eV



0

1

2

3

4

5

2 4 6 8 10 12 14 16 18 20

Mag

netic

Mom

ent (

µ B/a

tom

)Cluster Size N


SG Exp.

�


and

24

This is due to their closed icosahedral geometric structure.

First Icosahedron Double Icosahedron



0

1

2

3

4

5

2 4 6 8 10 12 14 16 18 20

Mag

netic

Mom

ent (

µ B/a

tom

)Cluster Size N


SG Exp.

�


and

24

1 This is due to their closed icosahedral geometric structure.

First Icosahedron Double Icosahedron


k

-electron localization

Localization vs Coordination


k

-electron localization

Localization vs Coordinationl � m npo qsrt @vu A C rw @vu A x �u


summary

�

Intermediate Mn y clusters adopt icosahedral growth pattern

Non-metal metal transition at is not seen, which was predictedfrom the discontinuity in the reaction rate with H . Even there is nostructural transition takes place at N=16.

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 duethe existence of two closely lying isomers (with 7 and 3 ) along withthe ground state (5 ) in the SG beam

Sudden drop in the magnetic moment at and is due to their“closed” icosahedral structure

electrons are more localized for the surface atom than the centralatom due relatively small coordination number

Kabir, Mookerjee and Kanhere (communicated)Mukul Kabir, Bose Centre – p. 21

summary

�

Intermediate Mn y clusters adopt icosahedral growth pattern�

Non-metal � metal transition at

= � 2\

is not seen, which was predictedfrom the discontinuity in the reaction rate with H � . Even there is nostructural transition takes place at N=16.

FM Ferrimagnetic transition takes place at






summary

�



= � 2\

is not seen, which was predictedfrom the discontinuity in the reaction rate with H � . Even there is nostructural transition takes place at N=16.�

FM � Ferrimagnetic transition takes place at

= � ^






summary

�



= � 2\



= � ^

�






summary

�



= � 2\



= � ^

�

Closely lying isomers with different magnetic structure are possible�

Large experimental uncertainty in the magnetic moment of Mn` is duethe existence of two closely lying isomers (with 7 � � and 3 � � ) along withthe ground state (5 � � ) in the SG beam




summary

�



= � 2\



= � ^

�


Large experimental uncertainty in the magnetic moment of Mn` is duethe existence of two closely lying isomers (with 7 � � and 3 � � ) along withthe ground state (5 � � ) in the SG beam�

Sudden drop in the magnetic moment at

= � 2 3

and

24

is due to their“closed” icosahedral structure



summary

�



= � 2\



= � ^

�


Large experimental uncertainty in the magnetic moment of Mn` is duethe existence of two closely lying isomers (with 7 � � and 3 � � ) along withthe ground state (5 � � ) in the SG beam�

Sudden drop in the magnetic moment at

= � 2 3

and

24

is due to their“closed” icosahedral structure� �C electrons are more localized for the surface atom than the centralatom due relatively small coordination number


As doping — motivation

�

Manganese in the semiconductor � Ga {z - Mn- As and Ga z - Mn- Asshow ferromagnetism — dilute magnetic semiconductor (spintronic)materials

Reported wide variation of Curie temperature 50-100K to highest 160K

Samples are prepared by low temperature Molecular beam epitaxygrowth — gives rise to metastable defects

Mn InterstitialsAs antisites (As )Random distribution of MnClustering of Mn

Samples annealed at low (growth) temperature show increase in theCurie temperature

Indeed, even after annealing, clusters of Mn around As have beendetected experimentally

Clustering of Mn is responsible ???

We study Mn As clusters using the same methodology used for pure Mn+ we allow non-collinearity in spins.



�

Manganese in the semiconductor � Ga {z - Mn- As and Ga z - Mn- Asshow ferromagnetism — dilute magnetic semiconductor (spintronic)materials�

Reported wide variation of Curie temperature � 50-100K to highest 160K

Samples are prepared by low temperature Molecular beam epitaxygrowth — gives rise to metastable defects

Mn InterstitialsAs antisites (As )Random distribution of MnClustering of Mn







�


Reported wide variation of Curie temperature � 50-100K to highest 160K�

Samples are prepared by low temperature Molecular beam epitaxygrowth — � gives rise to metastable defects

1 Mn Interstitials1 As antisites (As |�} )1 Random distribution of Mn1 Clustering of Mn







�




1 Mn Interstitials1 As antisites (As |�} )1 Random distribution of Mn1 Clustering of Mn�







�





Samples annealed at low (growth) temperature show increase in theCurie temperature�






�






Indeed, even after annealing, clusters of Mn around As have beendetected experimentally�





�






Indeed, even after annealing, clusters of Mn around As have beendetected experimentally�


�

We study Mn �As clusters using the same methodology used for pure Mn �

+ we allow non-collinearity in spins.


Enhancement in Bonding

�

We ask — whether the clustering of Mn around As are at all energeticallyfavourable or not ?

0.5

1

1.5

2

2.5

0 2 4 6 8 10

Bin

ding

Ene

rgy

(eV

/ato

m)

n

MnnMnnAs

Binding is enhanced substantially due to single As doping in the Mncluster.


Enhancement in Bonding

�

We ask — whether the clustering of Mn around As are at all energeticallyfavourable or not ?

0.5

1

1.5

2

2.5

0 2 4 6 8 10

Bin

ding

Ene

rgy

(eV

/ato

m)

n

MnnMnnAs

�

Binding is enhanced substantially due to single As doping in the Mn-

cluster.


energy gains

It can be defined in two ways —�

Energy gain in adding an As atom to a Mn � cluster> � C ~ ? @� �V �� A C � @� �V A C � @ �� A�

Energy gain in adding a Mn atom to a existing Mn As cluster

2

2.5

3

3.5

4

4.5

5

0 2 4 6 8 10

∆1 and

∆2 (e

V)

x

∆1

∆2

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 energeticallyfavourable


energy gains



�

Energy gain in adding a Mn atom to a existing Mn �z As cluster> � � C ~ ? @� �V �� A C � @� �V z �� A C � @� � A �

2

2.5

3

3.5

4

4.5

5

0 2 4 6 8 10

∆1 and

∆2 (e

V)

x

∆1

∆2

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 ( )



energy gains



�


2

2.5

3

3.5

4

4.5

5

0 2 4 6 8 10

∆1 and

∆2 (e

V)

x

∆1

∆2

�

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 (

> �

)



energy gains



�


2

2.5

3

3.5

4

4.5

5

0 2 4 6 8 10

∆1 and

∆2 (e

V)

x

∆1

∆2

�

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 energeticallyfavourable Mukul Kabir, Bose Centre – p. 24

collinear vs noncollinear

� Mn- Mn- As � Mn- Mn- As

Nature M �R� � Nature M �R� � Nature M �� Nature M �R� �

1 — 5 CL 4 6 NCL 12.82 NCL 1.28

2 CL 10 CL 9 7 CL 5 CL 6

3 CL 15 CL 4 8 NCL 6.83 CL 3

4 CL 20 CL 17 9 NCL 5.33 NCL 0.10

5 CL 3 CL 2 10 NCL 5.04 NCL 3.07

Mnj Mn o Mnj As Mn oAs

0 20 40 60 80 100 120 140 160 180

1 2 3 4 5 6 7 8 9 1

2

3

4

5

6

7

8

9

0 20 40 60 80 100 120 140 160 180

1 2 3 4 5 6 7 8 9 10 1

2

3

4

5

6

7

8

9

10

0 20 40 60 80 100 120 140 160 180

1 2 3 4 5 6 7 8 9 10 1

2

3

4

5

6

7

8

9

10

0 20 40 60 80 100 120 140 160 180

2 4 6 8 10

2

4

6

8

10


magnetic coupling

Only in Mn As and Mn As — Mn-Mn coupling is ferromagnetic

Mn As Mn As

9 17

spin density = r t @vu A

- rw @vu A

Spin iso-densityplot

Mn As Mn As

4 7


magnetic coupling

�

Only in Mn �As and Mn �As — Mn-Mn coupling is ferromagnetic

Mn �As Mn �As

9 � � 17 � �

spin density = r t @vu A- rw @vu ASpin iso-density

plot

Mn As Mn As

4 7


magnetic coupling

�

Only in Mn �As and Mn �As — Mn-Mn coupling is ferromagnetic

Mn �As Mn �As

9 � � 17 � �

spin density = r t @vu A- rw @vu ASpin iso-density

plot

Mni As Mn �As

4 � � 7 � �


Exchange coupling

We map the magnetic energy onto a Heisenberg form:� � C ��

For Mn As cluster:


Exchange coupling


For Mn �As cluster: ?t t @�� A C ?t w @ � A � � @�� A F�� t � �� w � B � � t � �� t � Z


Exchange coupling



−60

−50

−40

−30

−20

−10

0

10

20

30

2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7

Exch

ange

Cou

plin

g J

(meV

)

Mn−Mn Separation (rMn−Mn) Å

calculated J


Exchange coupling — RKKY type ???



−60

−50

−40

−30

−20

−10

0

10

20

30

2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7

Exch

ange

Cou

plin

g J

(meV

)

Mn−Mn Separation (rMn−Mn) Å

calculated JJRKKY

For RKKY type interaction � � �� z i � � @ D ¡£¢ ¤ A

� �

oscillates between positive and negative with � favouring FM and AFMsolutions, respectively and dies down as

2 <�� i — a typical RKKY typebehaviour.



But what happens to the exchange coupling when cluster size increases ???

In dilute magnetic semiconductors Ga Mn As, RKKY-like models predict

exchange coupling increases with concentration as at 0 K

independent of environment

For Mn As clusters —

−15

−10

−5

0

5

10

15

20

25

1 2 3 4 5 6

J ij (m

eV)

n

Average exchange parameter, decreases with increase in with anexceptional increase for ferromagnetic Mn As

Also has strong environment dependency

As cluster size increases, exchange coupling is no longer RKKY-type



But what happens to the exchange coupling when cluster size increases ???In dilute magnetic semiconductors Ga z - Mn- As, RKKY-like models predict

exchange coupling increases with concentration as at 0 K



−15

−10

−5

0

5

10

15

20

25

1 2 3 4 5 6

J ij (m

eV)

n







�

exchange coupling increases with concentration as � #iat 0 K�



−15

−10

−5

0

5

10

15

20

25

1 2 3 4 5 6

J ij (m

eV)

n







�



For Mn �As clusters —

−15

−10

−5

0

5

10

15

20

25

1 2 3 4 5 6

J ij (m

eV)

n







�




−15

−10

−5

0

5

10

15

20

25

1 2 3 4 5 6

J ij (m

eV)

n

�

Average exchange parameter,

¥�� decreases with increase in � with anexceptional increase for ferromagnetic Mn �As�






�




−15

−10

−5

0

5

10

15

20

25

1 2 3 4 5 6

J ij (m

eV)

n

�

Average exchange parameter,

¥�� decreases with increase in � with anexceptional increase for ferromagnetic Mn �As�


�



Conclusion

�

Due to the 47 �

(of Mn) — 3 ¦i hybridization , binding energy is enhanced� As-atom stabilizes Mn � clusters� Clustering of Mn is energetically favourable around As

Non-collinear treatment of spins are necessary, as both Mn and Mn Asclusters adopt nocollinear magnetic structure for

Mn-Mn coupling is ferromagnetic only for Mn As and Mn As and for allother sizes they are ferrimagnetically coupled

The exchange coupling is anomalous and behave quite differently fromthe RKKY- like predictions.

Mn As and Mn As have high exchange coupling. Therefore, thepresence of Mn As and Mn As clusters in (Ga,Mn)As and (In,Mn)Assamples, would lead to a high Curie temperature.

Whereas, presence of large sized clusters would, eventually, decreaseCurie temperature.

Kabir, Mookerjee, Kanhere physics/0503009


Conclusion

�

Due to the 47 �

(of Mn) — 3 ¦i hybridization , binding energy is enhanced� As-atom stabilizes Mn � clusters� Clustering of Mn is energetically favourable around As�

Non-collinear treatment of spins are necessary, as both Mn � and Mn �Asclusters adopt nocollinear magnetic structure for 0 § \

Mn-Mn coupling is ferromagnetic only for Mn As and Mn As and for allother sizes they are ferrimagnetically coupled






Conclusion

�

Due to the 47 �



�

Mn-Mn coupling is ferromagnetic only for Mn �As and Mn �As and for allother sizes they are ferrimagnetically coupled






Conclusion

�

Due to the 47 �



�

Mn-Mn coupling is ferromagnetic only for Mn �As and Mn �As and for allother sizes they are ferrimagnetically coupled�






Conclusion

�

Due to the 47 �



�

Mn-Mn coupling is ferromagnetic only for Mn �As and Mn �As and for allother sizes they are ferrimagnetically coupled�

The exchange coupling is anomalous and behave quite differently fromthe RKKY- like predictions.�

Mn �As and Mn �As have high exchange coupling. � Therefore, thepresence of Mn �As and Mn �As clusters in (Ga,Mn)As and (In,Mn)Assamples, would lead to a high Curie temperature.� Whereas, presence of large sized clusters would, eventually, decreaseCurie temperature.



Thank You !

I am about to finish my Ph.D. and I am looking for a Post Doc.


electronic and magnetic properties of pure and doped ...bose.res.in/~mukul/kabir_greece.pdf ·...

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