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2 6
2
6
2 6
2 6
2 6
,
2 6
2 6
2 6
, −
−
−
2 6
2 6 ,
,
,
,
,
,
,
,
2 6
≈
a
r X i v : 0 9 1 1 . 3 5 2 5 v 1
[ c o n d - m a t . m t r l - s c i ] 1 8 N o v 2 0 0 9
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−tFM
σ,α
f †iσ,αmjσ,α − tMM
σ,α
m†iσ,αmjσ,α
− tFF
σ,α
f †iσ,αf jσ,α + J
i∈A
Si · f †iασαβf iβ
f m tFM tMM tFF
tFM σ
α 2g 2g
∆̃ = Fe − Mo
t2g ×
Si S
J tFM J tFM
J → ∞
H = tFM
α
(sin(θi2
)f †iαmj↑α − eiφicos(
θi2
)f †iαmj↓α)
+h.c. + tMM
m†iσαmjσα
+tFF
cos(θij/2)(f †iσαf jσα)
+Fe
i
f †iαf iα + Mo
iσα
m†iσαmiσα
mj↓ mj↑
θi, φi θ = 0, φ = 0
S
2 6
2 6
x = 0.4 1
2−x x 6 x =
1
2 6
1
2 6
x =
1
1
3
3 1.5 0.5 6
3 6
3
3
3
2−x x 6
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1
β
2 6 2 6
1
x
,
1
FM AFM −A
1
6 0.5 1.5 6
d
d
2−x x 6
1.5 0.5 6
6 0.5 1.5 6
3+
5+
d d 2g g
2g 2g 2g
2g
2g
x 2g
2g 2g
2g 2g
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0 0.5 1 1.5 2
x
-0.2
-0.1
0
0.1
0.2
0.3
E F M -
E A F M
( e V / f . u . )
GGA
GGA+U
-8 -6 -4 -2 0 2 4
SFMO
-10
-5
0
5
10
-8 -6 -4 -2 0 2 4
LSFMO
-10
-5
0
5
10
-8 -6 -4 -2 0 2 4
L3SFMO
-10
-5
0
5
10
-10 - 8 -6 -4 -2 0 2 4
LFMO
-10
-5
0
5
10
D O S ( s t a t e s / e V / a t o m )
Energy (eV) Energy (eV)
6
0.5
1.5
6
6
0.5 1.5 6
-8 -6 -4 -2 0 2 40
2
4
-8 -6 -4 -2 0 2 40
2
4
-8 -6 -4 -2 0 2 40
2
4
-8 -6 -4 -2 0 2 40
2
4
Fe1
Fe1
Mo1
SFMO LSFMO
L3SFMO LFMO
D O S ( s t a t e s / e V / a t o m )
Energy (eV) Energy (eV)
6 0.5 1.5 6
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FM
Ef
Ef
AFM
f
t2g
x x
-10 -8 -6 -4 -2 0 2 4
-4
-2
0
2
4
D O S
( s t a t e s / e V / a t o m )
Fe
Mo
O
-10 -8 -6 -4 -2 0 2 4 6 8 10
Energy (eV)
0
1
2
3
4
5
6
D O S ( s t a t e s / e V / a t o m )
Fe
Mo
O
Μο1↑
Fe1↑
∆ ∆
0.5 1.5 6
0.375 1.625 6
0.25 1.75 6
0.125 1.875 6
2g 2g
2g 2g
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2g
2g
2g
2g
2g
2g
2g 2g
2g
δ π
t2g↓
2g 2g
%
t2g
t2g
3.04 eV3.09 eV
0.09 eV
0.13 eV
0.63 eV
Fe 3dlevels
Mo−t2glevels
Renormalized
in presencestates
of hybridization
Fe 3dlevels
Mo−t2glevels
Renormalized
in presencestates
of hybridization
t2g
t2g
2.82 eV
2.86 eV
0.33 eV
0.37 eV
0.88 eV
SFMO LFMO
2g
2g
2g
2
× × × × ×
×
J → ∞
× 3
× ×
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2g
2g
xy
yz
xz
xy
yz
xz
xy
yz
xz
∼ x =
0 1 2 3 4
No of conduction electron
-0.05
-0.04
-0.03
-0.02
-0.01
0
E n e r g y d i
f f e r e n c e s i n
u n i t o f t
F M
× ×
2−x x 6
0 1 2 3 4
Number of conduction electrons
0
100
200
300
400
T c ( K
)
c
N
× ×
2−x x 6
∼
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c
c
N
2 6
2−x x 6
x > 1.6
2 6
T c N
T c
0 3
T c
2 6
3+
2g
+5
+5−m m
+3
3+
3+
3+
5+
2 6
3
2g
2g
2 6 2 6
2 6
2g
2g 2g
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́
o
̈o
́i
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