Analisis Model Heisenberg Untuk Bahan Antiferromagnet Dengan Kekisi Segitiga Anisotropik (Semnas MIPA 2009)

(1)

)7-28/0-$)45!61)9'%:+"$%0-$).+(+"%);#(<-2-"0-1)=>)4+%)?@@A

!"!#$%$%&'()#&+$%",-.&/"0/1&,!+!"&!"0$2--('!."0&

)*".!"&1*1$%$&&%*.$0$.!&&!"$%(0-(3$1

)4556&)7897:75

B-C#"-0#"%8,)D#,380-$%)7%$%2-1)E8"&%2)7%$%2-1)745!6

9'%:+"$%0-$).+(+"%);#(<-2-"0-!;<=87>

!"#$%&'()(*+$,&-.'"#&/"(0"*1"23&,*),4&1$%$*&$*)(5"22.-$3*")&6$*3&-"-(#(4(& 1"*),4&4"4(0(&0"3()(3$&$*(0.)2.7(4&'(-$*$&)"2'$7$)&4.-7")(0(&(*)"2$40(&$*)$2$&)")$*33$& )"2'"4$)&8'+-"+$0)'+%(FC#8"9:&)")$*33$&)"2'"4$)&1"2(4,)*6$&8'+G0)'+-"+$0)'+%(FC#8"9&'$*& 4.7#(*3&$*)$2&2$*)$(;

/$0(# & 6$*3 & '(7"2.#"% & -"*,*+,44$* & 1$%<$ & (*)"2$40( & )")$*33$ & )"2'"4$)& 1"2(4,)*6$ & ="*'"2,*3 & -"*(*34$)4$* & 4")"2$),2$* & 8#"&+"%'(9 & '$#$- & -.'"# & /"(0"*1"23& ,*),4&1$%$*&)"20"1,);&>*)"2$40(&(*(&-"*,2,*4$*&4")$4)"2$),2$*&8&%$#"&+"%'(9&7$'$&5$0"& )2$*0(0(&$*)$2$&5$0"&?""#&'"*3$*&5$0"&07(2$#&6$*3&'(1$*34()4$*&.#"%&4.-7")(0(&$*)$2$& (*)"2$40(&4.7#(*3&$*)$2&2$*)$(&'"*3$*&(*)"2$40(&)")$*33$&)"2'"4$);

17=7&>?5@A@&0(0)"-&)"252,0)2$0(:&$*)(5"22.-$3*")

3*")!+/#/!"

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

E$+($* & )".2")(4 & -"*3"*$( & 0(0)"- & )"252,0)2$0( & 7$'$ & 1$%$* & $*)(5"22.-$3*")(4 & 7"2)$-$ & 4$#(& '(#$4,4$* & 7$'$ & 0(0)"- & 4"4(0( & 0"3()(3$ & '"*3$* & -"*33,*$4$* & -.'"# & >0(*3 & 8G$**("2: & HIJK9;& C"*.-"*$ & (*( & 0"=$2$ & "407"2(-"*)$# & )"2$-$)( & ,*),4 & & 1$%$* & $*)(5"22.-$3*")(4 & 0"7"2)( & L0DL,L#M& 8L.#'"$: &+0H)-/;:&DKKN9&'$*&4"#,$23$&1$%$*&0,7"24.*',4).2&.23$*(4&!B8OPA!B!!C9DQ&8R"2(*.&+0H ) -/H:&HIII9;

A$#$-&-$4$#$%&(*(&$4$*&'()(*+$,&0(0)"-&)"252,0)2$0(&7$'$&-.'"#&/"(0"*1"23&,*),4&1$%$*& $*)(5"22.-$3*")(4 & '"*3$* & 4"4(0( & 0"3()(3$ & $*(0.)2.7(4 & 6$*3 & '(1$*34()4$* & .#"% & 4.-7")(0( & $*)$2$& (*)"2$40( & )")$*33$& )"2'"4$) & 7$'$& 2$*)$( & 07(*& '"*3$*& (*)"2$40( & $*)$2B2$*)$( & '$* & (*)"2$40( & )")$*33$& )"2'"4$)&1"2(4,)*6$&0"7$*+$*3&2$*)$(&07(*;&R").'"&6$*3&'(3,*$4$*&$'$#$%&'"*3$*&-"*"2$74$*&)".2(& 3"#.-1$*3&07(*&#(*"$2&7$'$&-.'"#&/"(0"*1"23&07(*&0")"*3$%;

'()*#&+*$%*",*-.

R.'"# & /"(0"*1"23 & -"*6$)$4$* & (*)"2$40( & $*)$2 & 07(*& 7$'$ & )()(4B)()(4& 4"4(0( & 6$*3 & 1"21"'$;& /$-(#).*$*&'$2(&0(0)"-&(*(&'(*6$)$4$*&'"*3$*@

&&&&&&&&&& I!

"

!! "E#!$!J%*!&*!J 8H9

'(-$*$&#!&'$*&#!"&-"2,7$4$*&.7"2$).2&07(*&'$*&E8!&B&!"9&-"2,7$4$*&)")$7$*&),4$2&,*),4&(*)"2$40(& $*)$2$& 07(* &#!& 6$*3 & 1"2$'$ & '( &!& '$*& 07(* &#!"& 6$*3 & 1"2$'$ & '( &!"; &!")$7$* & (*( & 1"20(5$) & 0(-")2(4&

CBHKN

(2)

0"%(*33$&E8!"$%)!9&S&E8!&T&!"9&'$*&1"2*(#$(&*"3$)(5&,*),4&1$%$*&$*)(5"22.-$3*");

A$#$-&-.'"#&(*(:&07(*&'(*6$)$4$*&0"1$3$(&.7"2$).2&U"4).2&6$*3&-"-(#(4(&$2$%&0"1$2$*3& 7$'$&2,$*3&N&'(-"*0(:&0"%(*33$&'$7$)&'(*6$)$4$*&'$#$-&1"*),4&4.-7.*"**6$&0"1$3$(@

&&&&&&&&&&

#

_!

!

*

_!G

G

'

(

*

_!<

'

<

(

*

_!N

N

'

8D9&

'(-$*$&4.-7.*"*&07(*&$4$*&-"-$),%(&2"#$0(&4.-,)$0(&07(*;

/$-(#).*$*&0(0)"-&(*(&'$7$)&+,3$&'(*6$)$4$*&'$#$-&.7"2$).2&4"*$(4$*&'$*&7"*,2,*$*&07(*& 0"1$3$(@

&&&&&&&&&&

I

!

"

!! "

E

#

!

$

!"

%)

H

D

#

*

O

V

*

B_{O J}

(

*

_OB

*

V_{O J}

%(

*

N_O

*

_{O J}N

*$

(

+

P

"

_O

*

O N

8N9

'"*3$*

&&&&&&&&&&

*

O

V

!

*

_OG

(

%*

O <

*

O

B

!

*

O G

$

%*

O

< 8M9

0*(-$&.*#(',!".&%3$"&#$"*!-F$'$&4$0,0&1$%$*&5"22.-$3*")(4&('"$#&8)$*7$&(-7,2()$09&'"*3$*&0,%,&*.#&-,)#$4:&0"-,$& 07(*&$4$*&1"2+$+$2&7$'$&0$),&$2$%&6$*3&'(-(0$#4$*&0"1$3$(&$2$%&VN;&E")(4$&0,%,&-,#$(&'(*$(44$*:& 07(*B07(*&)"20"1,)&-,#$(&1"2.0(#$0(&'(&0"4()$2&$2$%&4")"2$),2$**6$&'$*&0"#$*+,)*6$&-"-1$*34()4$*& 3"#.-1$*3 & 7$'$ & 4"4(0( & -$3*")(4 & 6$*3 & '(0"1,) & 0"1$3$( & 3"#.-1$*3 & 07(*; & W"#.-1$*3 & (*(& )"24,$*)(0$0(&0"1$3$(&,-('#'&6$*3&-"2,7$4$*&7$2)(4"#&4,$0(&1"2)(7"&1.0.*;

A$#$-&)".2(&3"#.-1$*3&07(*:&-.'"#&/"(0"*1"23&'(0"#"0$(4$*&'"*3$*&.7"2$).2&7"*=(7)$$*& '$* & 7"-,0*$%$* & 1.0.* & 6$*3 & '(4"*$# & 0"1$3$( & <$4(#$* & /.#0)"(*BF2(-$4.55 & 6$*3 & '('"5(*(0(4$*& 0"1$3$(&8/.#0)"(*&'$*&F2(-$4.55:&HIMK9@

&&&&&&&&&&

*V_O!

,

D*

#

H$-O

V

-_O

D*

%

H-D

-_O

*B_O!

,

D* -V_O

#

H$-O

V

-_O

D*

%

H-D

*O N

!*$-O

V

-O

8J9

A"*3$* & -"*3$1$(4$* & (*)"2$40( & $*)$2 & 1.0.*: & 1"*),4 & <$4(#$* & /.#0)"(*BF2(-$4.55 & 7$'$& 7"20$-$$*&8J9&'$7$)&'(*6$)$4$*&'$#$-&1"*),4&#(*"$2&0"1$3$(&@

&&&&&&&&&&

*

V_O

!

,

DX

-

_O

*

O

B

!

,

DX

-

O

V

*

O N

!

*

$

-

O

V

-

O

8Y9

'(-$*$ &-V_{& '$* &}_-_{& -"2,7$4$* & .7"2$).2 & 7"*=(7)$$*& '$* & 7"-,0*$%$* & 1.0.* & '$*& -"-$),%( & $),2$*&} 4.-,)$0(&1.0.*@&Z-:-V_[&S&H;

!"2'$7$)&',$&=$2$&,*),4&-"*"2$74$*&<$4(#$*&/.#0)"(*BF2(-$4.55&7$'$&-.'"#&/"(0"*1"23& 1$%$* & $*)(5"22.-$3*"); & L$2$ & 7"2)$-$ & $'$#$% & '"*3$* & -"*33,*$4$* & *.)$0( & <$4(#$* & & /.#0)"(*B

(3)

)7-28/0-$)45!61)9'%:+"$%0-$).+(+"%);#(<-2-"0-1)=>)4+%)?@@A F2(-$4.55 & 6$*3 & 1"21"'$ & ,*),4 & 0,14"4(0( & 6$*3 & 1"21"'$; & \*),4 & 0,14"4(0( & '"*3$* & 07(* & *$(4:& '(3,*$4$*&7"20$-$$*&8Y9:&0"'$*34$*&,*),4&0,14"4(0(&'"*3$*&07(*&),2,*:&'(3,*$4$*&7"20$-$$*@

&&&&&&&&&&

*

O

V

!

,

]X

C

O

*

O

B

!

,

]X

C

O

V

*

_ON

!

*

$

C

V_O

C

_O

8^9

L$2$&4"',$&$'$#$%&'"*3$*&-"2.)$0(4$*&0,14"4(0(&07(*&),2,*&4"&4"2$*34$&#.4$#&0"%(*33$& 7$'$&4"2$*34$&#.4$#&(*(&0"#,2,%&07(*&1"2$2$%&7$'$&$2$%&VN;&R"#$#,(&2.)$0(&(*(:&7"20$-$$*&8Y9&'$7$)& '()"2$74$* & 7$'$ & 0"#,2,%& 0,14"4(0(; & \*),4& 4"4(0( & 1"21"*),4& 7"20"3(: & )2$*05.2-$0( & 2.)$0( & )"20"1,)& '(*6$)$4$*&0"1$3$(@

&&&&&&&&&&

.

*

_ON

!$

*

_ON

.

*

O

G

!

*

O

G

.

*

O

<

!$

*

O

<

8_9

0"%(*33$

&&&&&&&&&&

.

*

B_O

!

*

_OV

.

*

V_O

!

*

B_O 8I9

1*1$%$&%*.$0$.!&&!"$%(0-(3$1&!"0$2*--('!."*0

A()(*+$,&4"4(0(&0"3()(3$&$*(0.)2.7(4&6$*3&'(),*+,44$*&7$'$&W$-1$2&H;&>*)"2$40(&),4$2&'$2(& )()(4&4"4(0(&)")$*33$&)"2'"4$)&'(*6$)$4$*&.#"%&ED:&(*)"2$40(&),4$2&$*)$2&2$*)$(&07(*&)"2'"4$)&84.7#(*3& $*)$2&2$*)$(9&'(*6$)$4$*&.#"% &EH:&'$*&(*)"2$40(&),4$2&'$2(&)")$*33$&)"2'"4$)&1"2(4,)*6$&'(*6$)$4$*& .#"%&EN;

>*)"2$40(&),4$2 &ED& 1"2,0$%$&-"*6,0,*&7$0$*3$*&07(*&'$#$-&$2$%&6$*3&0"+$+$2&'$*&0$#(*3& 1"2#$<$*$*:&*$-,*&(*)"2$40(&),4$2&EN&$4$*&-"-$40$&0$#$%&0$),&'$2(&7$0$*3$*&07(*&)"20"1,)&,*),4& 0"+$+$2&1"2#$<$*$*&$2$%&'"*3$*&)")$*33$&)"2'"4$)&1"2(4,)*6$;&E.-7")(0(&$*)$2&(*)"2$40(&),4$2&(*(& 0"#$*+,)*6$&-"-(=,&-,*=,#*6$&52,0)2$0(&-$3*")(4;

.79;78&B;&E"4(0(&0"3()(3$&$*(0.)2.7(4;&QH&'$*&QD&-"*6$)$4$*&+$2$4&$*)$2&)()(4&4"4(0(:&EH&-"*6$)$4$*&(*)"2$40(&

),4$2&$*)$2&2$*)$(:&ED&-"*6$)$4$*&(*)"2$40(&),4$2&'"*3$*&)")$*33$&)"2'"4$):&'$*&EN&-"*6$)$4$*&(*)"2$40(&),4$2&

'"*3$*&)")$*33$&)"2'"4$)&1"2(4,)*6$;

(4)

/$-(#).*$*&'$2(&-.'"#&(*(&'(*6$)$4$*&0"1$3$(@

&&&&&&&&&&

I

!

"

_O

E

N

*

O

&

*

O(D# /H(/D%

(

E

D

*

O

&

*

O(/H(/D

(

E

H

*

O

&

*

O(/H

(

E

H

*

O

&

*

O(/D 8HK9

\*),4&-"*'$7$)4$*&4"$'$$*&'$0$2&'$2(&0(0)"-:&07(*&$4$*&'($*33$7&0"1$3$(&U"4).2&4#$0(4&'"*3$*& 7$*+$*3&*&'$*&-"-(*(-4$*&"*"23(*6$;&

A$#$-&4"4(0(&1$#(4:&(*)"2$40(&),4$2*6$&'$7$)&'(*6$)$4$*&0"1$3$(@

&&&&&&&&&&

E

#

&

%!

"

_/

E

#/ %

+

$%&&/

8HH9

'(-$*$&&&-"2,7$4$*&U"4).2&3"#.-1$*3&7$'$&`.*$&O2(##.,(*;&O"2'$0$24$*&1"*),4&4"4(0(*6$:&-$4$& (*)"2$40(&),4$2&'$2(&-.'"#&6$*3&'()(*+$,&-"*3$-1(#&1"*),4

&&&&&&&&&&

E

#

&

%!

E

_N

=.0

#

D

2

_G

(

D

2

_<

%(

E

_D

=.0

#

D

2

_G

(

D

2

_<

%(

E

_H

=.0

#

2

_G

%(

E

_H

=.0

#

2

_<

%

8HD9

X(0)"-&$4$*&-"-(#(4(&"*"23(&)"2"*'$%&4")(4$&2&S&R&6$*3&'(0"1,)&'"*3$*&U"4).2&3"#.-1$*3& 4")"2$),2$*&8#"&+"%'()L-:+):+S0#"9&6$*3&'(7"2.#"%&'"*3$*&-"-(*(-4$*&E82&S&R9@

&&&&&&&&&&

0

E

#

'

%

0

R

_G

!

K &&&&&'$*&&&&&

0

E

#

'

%

0

R

_<

!

K

8HN9

A$2( & 7"20$-$$* & 8HN9 & '(7"2.#"% & 1$%<$ &RG& S &R<& 0"%(*33$ & U"4).2 & 3"#.-1$*3 & 4")"2$),2$*& -"2,7$4$*&0$#$%&0$),&7"*6"#"0$($*&'$2(

&&&&&&&&&&

E

_H

0(*

#

R

_G

%(

E

_D

0(*

#

D

R

_G

%(

D

E

_N

0(*

#

M

R

_G

%!

K

8HM9

\*),4 & -"*'$7$)4$* & "*"23( & 0(0)"-: & 0"#,2,% & 07(* & '()2$*05.2-$0(4$* & 4" & '$#$- & 4"2$*34$& $=,$*&#.4$#&0"%(*33$&0"#,2,%&07(*&$4$*&0"+$+$2&7$'$&$2$%&N& '(&0")($7&)()(4&4"4(0(;&!2$*05.2-$0(*6$& -"*3$-1(#&1"*),4@

&&&&&&&&&&

*

_OG

!

*

1_OG

*

_O<

!

*

_O1<

=.0

#

'

&

!

%$

*

1_ON

0(*

#

'

&

!

%

*

O

N

!

*

O

1<

0(*

#

'

&

!

%(

*

O

1N

=.0

#

'

&

!

%

8HJ9

X")"#$% & '()2$*05.2-$0(4$* & '"*3$* & 7"20$-$$* & 8HJ9: & /$-(#).*$* & '$2( & 0(0)"- & 0"#$*+,)*6$& '()2$*05.2-$0(4$* & '"*3$* & <$4(#$* & /.#0)"(*BF2(-$4.55 & ,*),4 & -"*"2$74$* & )".2( & 3"#.-1$*3 & 07(*& 7$'$ & 0(0)"-; & \*),4 & -"*'$7$)4$* & /$-(#).*$* & '$#$- & <$4(#$* & 2,$*3 & -.-"*),-: & '(#$4,4$*& )2$*05.2-$0(&C.,2("2&,*),4&4"4(0(&6$*3&'('"5(*(0(4$*&0"1$3$(@

&&&&&&&&&&

-_O! H

,

.

"

2+

$%&&O -₂

-V_O! H

,

.

"

2 +

$%&&O -₂V

8HY9

X"#$*+,)*6$&'(#$4,4$*&)2$*05.2-$0(&O.3.#(,1.U&6$*3&'('"5(*(0(4$*&0"1$3$(@

(5)

)7-28/0-$)45!61)9'%:+"$%0-$).+(+"%);#(<-2-"0-1)=>)4+%)?@@A

&&&&&&&&&&

-

2

!

8

2

(

:

2

$2

V

-

2

V

!

:

2

22(

8

2

$2

V &8H^9

,*),4&-"*'$7$)4$*&/$-(#).*$*&)"2'($3.*$#(0$0(&6$*3&1"21"*),4@

&&&&&&&&&&

I

!

. *

D

E

_R

(

. * E

_R

$

. P *

$

H

D

. P

(

"

2

3

2

#2

2

V

2

(

H

D

%

8H_9

'(-$*$

&&&&&&&&&&

3

₂

!

DX

,

6

₂D

$

P

₂D 8HI9

-"2,7$4$*&2"#$0(&'(07"20(&-$3*.*&'"*3$*&62&'$*&P2&'('"5(*(0(4$*&0"1$3$(@

&&&&&&&&&&

6

₂

!

H

D

E

2

(

H

M

E

R$2

(

H

M

E

R(2

$

E

R

(

H

D

#

P

-

*

%

P

₂

!

H

D

E

2

$

H

M

E

R$2

$

H

M

E

R(2

8DK9

P*"23(&'$0$2&8("#8'&)$0-0+9&'$7$)&'()"*),4$*&4")(4$&-$3*.*&1"#,-&-,*=,#&'$#$-&0(0)"-&8

42

₂V

2

5!

K

9&0"%(*33$

&&&&&&&&&& T_K#P%!. *DE_R(. * E_R$. P *$H

D . P(

H

D

"

232 8DH9

X"'$*34$* & -$3*")(0$0( & 0,14"4(0( & '(7"2.#"% & '"*3$*& -"*,2,*4$*& *(#$( & %$2$7 & 4"$'$$*& '$0$2 & '$2(& /$-(#).*$*&0(0)"-&)"2%$'$7&-"'$*&-$3*")&0"%(*33$&'(7"2.#"%

&&&&&&&&&&

4

*

_O1N

5!$

H

.

#(-

P6K

&T

_K

&P

8DD9

3*',!+!%!"

F#.)&-$3*")(0$0(&)"2%$'$7&2$0(.&(*)"2$40(&),4$2&EHaED&'"*3$*&EN&S&K&8)$*7$&(*)"2$40(&)")$*33$& )"2'"4$) & 1"2(4,)*6$9 & '(),*+,44$* & 7$'$ & 3$-1$2 & D; & ?$-7$4 & 1$%<$ & 7$'$ & 5$0" & 4")"2$),2$* & 07(2$#:& -$3*")(0$0(&-"*=$7$(&-$40(-,-& &4")(4$ &EH& S &ED& '$*&-(*(-,-&4")(4$ &EHaED& S&D&6$*3&-"2,7$4$*& 5$0"&)2$*0(0(&$*)$2$&5$0"&4")"2$),2$*&?""#&'"*3$*&5$0"&4")"2$),2$*&07(2$#;&\*),4&EHaED&b&K:N:&0(0)"-& -,#$( & -"*3$#$-( & 4")$4)"2$),2$* & 8'(0.2'"2"'9; & R$3*")(0$0( & (*( & $4$* & )"2,0 & -"-1"0$2 & '"*3$*& -"*(*34$)*6$&(*)"2$40(&$*)$2&2$*)$(&'$*&-"*=$7$(&*(#$(&)")$7&K:NH&4")(4$ &EHaED& -"*,+,&)$4&%(*33$& 6$*3&-"2,7$4$*&*(#$(&-$3*")(0$0(&,*),4&4"4(0(&1,+,20$*34$2;

(6)

.79;78& C; & F#.) & -$3*")(0$0( & 4"4(0( & 0"3()(3$ & $*(0.)2.7(4 & 1$%$* & $*)(5"22.-$3*") & )$*7$ & 4"%$'(2$* & (*)"2$40(& ),4$2&'"*3$*&)")$*33$&)"2'"4$)&1"2(4,)*6$&8EN&S&K9;

.79;78&D;&F#.)&-$3*")(0$0(&4"4(0(&0"3()(3$&$*(0.)2.7(4&1$%$*&$*)(5"22.-$3*")&'"*3$*&*(#$(&2$0(.&ENaED&S&K:D;

E")(4$& (*)"2$40( & )")$*33$ & )"2'"4$) & 1"2(4,)*6$ & -,#$( & -,*=,#: & 4")$4)"2$),2$*& 6$*3 & )"2+$'(& 7$'$ &EHaED &S&D&0$$) &EN &S&K&1"24,2$*3&8W$-1$2&N9;&R"*(*34$)*6$ &EN& -"*3%(#$*34$*&4")$4)"2$),2$*& 7$'$&)2$*0(0(&5$0"&$*)$2$&5$0"&?""#&'$*&5$0"&07(2$#;&?(#$(&-$3*")(0$0(&-$40(-,-&-$0(%&)")$7&1"2$'$& 7$'$&5$0"&07(2$#&'( &EH& S &ED& *$-,*&'"*3$*&*(#$(&6$*3&#"1(%&1"0$2;&E")$4)"2$),2$*&7$'$ &EHaED& b&K:N& )"2+$'(&,*),4&EH&6$*3&0"-$4(*&4"=(#&4")(4$&*(#$(&EN&-"-1"0$2&6$*3&1"2$2)(&1$%<$&(*)"2$40(&)")$*33$& )"2'"4$)&1"2(4,)*6$&-"-1$*),&-"*(*34$)4$*&4")"2$),2$*&'$2(&2$*)$(&07(*&6$*3&)"24.7"#&#"-$%;

A"*3$*&-"*(*34$)4$*&*(#$(&EN:&-$3*")(0$0(&0(0)"-&$4$*&)"2,0&-"*(*34$)&%(*33$&-"*=$7$(& *(#$(&-$40(-,-&'(-$*$&-$3*")(0$0(&)('$4&#$3(&1"2)$-1$%&'"*3$*&-"-1"0$2*6$&*(#$( &EN& 8W$-1$2& M9;

(7)

)7-28/0-$)45!61)9'%:+"$%0-$).+(+"%);#(<-2-"0-1)=>)4+%)?@@A

.79;78&E;&F#.)&-$3*")(0$0(&4"4(0(&0"3()(3$&$*(0.)2.7(4&1$%$*&$*)(5"22.-$3*")&)"2%$'$7&2$0(.&ENaED&'"*3$*&EHa

ED&S&K:J;

1*%$'3/#!"

!"#$%&'()(*+$,&4.-7")(0(&(*)"2$40(&$*)$2$&(*)"2$40(&)")$*33$&)"2'"4$):&(*)"2$40(&$*)$2&2$*)$(:& '$*&(*)"2$40(&)")$*33$&)"2'"4$)&1"2(4,)*6$&7$'$&-.'"#&/"(0"*1"23&,*),4&1$%$*&$*)(5"22.-$3*")& '"*3$*&4"4(0(&1"21"*),4&0"3()(3$&$*(0.)2.7(4&6$*3&-"-1$*34()4$*&0(0)"-&)"252,0)$0(&-$3*")(4;

E")(4$&(*)"2$40(&)")$*33$&)"2'"4$)&1"2(4,)*6$&'($1$(4$*:&4.-7")(0(&$*)$2$&(*)"2$40(&'"*3$*& )")$*33$&)"2'"4$)&'$*&(*)"2$40(&$*)$2&2$*)$(&-"*6"1$14$*&4")$4)"2$),2$*&0(0)"-&7$'$&5$0"&)2$*0(0(& $*)$2$&5$0"&?""#&'"*3$*&5$0"&07(2$#;&O"3(),&+,3$&4")(4$&4.7#(*3&$*)$2&2$*)$(&=,4,7&#"-$%;&F$'$& 4.*'(0( & '(-$*$ & 4"',$ & (*)"2$40( & 0$-$ & 4,$): & -$3*")(0$0( & 0(0)"- & -"*+$'( & -$40(-,- & '$* & 0(0)"-& 1"2$'$&7$'$&5$0"&07(2$#;

A"*3$*&%$'(2*6$&(*)"2$40(&)")$*33$&)"2'"4$)&1"2(4,)*6$:&4")$4)"2$),2$*&6$*3&-,*=,#&7$'$& 5$0"&)2$*0(0(&$*)$2$&5$0"&?""#&'$*&5$0"&07(2$#&-"*+$'(&#"*6$7;&E")$4)"2$),2$*&+,3$&'()"-,( &7$'$& 4.7#(*3&$*)$2&2$*)$(&6$*3&0"-$4(*&#"-$%&+(4$&(*)"2$40(&)")$*33$&)"2'"4$)&1"2(4,)*6$&0"-$4(*&4,$):& 0"%(*33$&0"=$2$&,-,-&(*)"2$40(&(*(&="*'"2,*3&-"*(*34$)4$*&4")"2$),2$*&'$2(&0(0)"-;

)!20!-&3/%0!1!

L.#'"$:&c;:&!"**$*):&A;d;:&!6#=`6*04(:&e;:&8DKKN9:&!F<$%S-/)O+:%+L)P:&U.#;&Y_:&%$#;&HNMMDM /.#0)"(*:&!;&'$*&F2(-$4.55:&/;:&8HIMK9:&!F<$%S-/)O+:%+L:&U.#&J_:&%$#;&HKIM

R"2(*.: & f;: & R=E"*`(": & c;/;: & R$20).*: & f;O;: & '$* & L%,*3: & L;/;: & 8HIII9: &E#8"'-/ ) #U ) !F<$%S$V ) W#'&+'$+&)4-00+":&U.#&HH:&%$#;&DIYJ

G$**("2:&W;/;:&8HIJK9:&!F<$%S-/)O+:%+L:&U.#&^I:&%$#;&NJ^

Analisis Model Heisenberg Untuk Bahan Antiferromagnet Dengan Kekisi Segitiga Anisotropik (Semnas MIPA 2009)

!"!#$%$%&'()*#&+*$%*",*-.&/"0/1&,!+!"&!"0$2*--('!."*0&

CBHKN

0

0

K &&&&&'$*&&&&&

0

0

!"!#$%$%&'()#&+$%",-.&/"0/1&,!+!"&!"0$2--('!."0&