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LongLong--range range antiferromagneticantiferromagnetic interactions interactions in ZnFein ZnFe22OO44 and CdFeand CdFe22OO44
鄭靜鄭靜
CoContributors Supports碩士畢業生劉晉生 : Initial studies 國科會大學部學生葉學舫 : Diffraction 國家高速電腦中心
2
OutlineOutline
FerritesFerritesDescribing interactionsDescribing interactionsPrevious research worksPrevious research worksWhat and how we can approach these systemsWhat and how we can approach these systemsCalculationalCalculational methodsmethodsQuantitative resultsQuantitative resultsProspectsProspects
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Cubic Cubic SpinelSpinel Ferrite : Ferrite : CompoundsCompounds
MFe2O4 MO‧Fe2O3
FeFe2O4 Fe3O4 magnetite lodestoneCoFe2O4NiFe2O4
ZnFe2O4CdFe2O4
Fe 4s23d6
Co 4s23d7
Ni 4s23d8
Zn 4s23d10
Cd 5s24d10
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Cubic Cubic SpinelSpinel Ferrite : Ferrite : Crystal StructureCrystal Structure
O : FCC
B : Octahedral sites
A : Tetrahedral sites
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Cubic Cubic SpinelSpinel Ferrite : Ferrite : Crystal StructureCrystal Structure
Tetrahedral (A) site
Octahedral (B) site
a
Oxygen FCC
8(MO Fe8(MO Fe22OO33))
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Cubic Cubic SpinelSpinel Ferrite : Ferrite : Magnetic StructureMagnetic Structure
2
3+
3B
+
+B
B site (Fe
B site (
A site5
F
(M )
e 5
)
)µ
µ↑ −
↓ −
normal spinelZnO.Fe2O3CdO.Fe2O3
Fe 4s23d6
3+
3+B
B+
B2+
2
B site (M 2
for
A s
B site (Fe 5 )
ite (Fe
N
+
i )
5 )
µ
µ
µ
↑ −
↓
↑ −
inverse spinelFeO.Fe2O3CoO.Fe2O3NiO.Fe2O3 Ni 4s23d8
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Cubic Cubic SpinelSpinel Ferrite : Ferrite : ZnOZnO..FeFe22OO33
Antiferromagnetic insulators
Frustrated magnetic systemsFrustrated magnetic systems
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( )( )
0
0
0
2 for 1define and
for 12
E E EE SE SJ E E
E E JE E J
↑↑ ↑↓↑↑
↑↓ ↑↓ ↑↑
↑↑
↑↓
≡ +↑↑ ↑ ≡ + ↑↓ ↓ ≡ −≡ −
= −⇒ ⇒
= +0 1 2E = E - JS S
Describing interactionsDescribing interactions
0 0
J ferroE NJJ antiferroE NJ> →↑↑↑↑↑ = −
< →↑↓↑↓↑ = +
K K
K K
112 i i
iH J S S += − ∑
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Describing interactions (continued)Describing interactions (continued)
1 2
1 2
including up to 2nd neighbour interact
(( ) i
)on
E N J JE N J J
↑↑↑↑↑ = − −↑↓↑↓↑ = + −
K K
K K
12 n i i n
n i
H J S S += − ∑ ∑
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Previous researchPrevious research
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Previous research (Continued)Previous research (Continued)ZnFe2O4
TN=10.5K (Konig et al SSC 1970)θCW ≈ +50K (Schiessl et al PRB 1996)θCW ≈ +120K ≈ + 10TN (Kamazawa et al PRB 2003)~ 4.2µB antiferromagnetic J3 (Yamada et al PRB 2002)ferromagnetic J1 for T>TN
CdFe2O4TN ≈ 13K ??? (Kamazawa et al PRB 2004)θCW ≈ -53KJ1 ≈ 5.9meV > 0 antiferromagnetic J1
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What and how we can approach these systemsWhat and how we can approach these systems
The extent of the FeThe extent of the Fe--Fe interactions Fe interactions JJnnthe nththe nth--neighbourneighbour interactionsinteractionsGenerate different configurationsGenerate different configurationsUsing Using IsingIsing model model –– colinearcolinear approachapproachPerform firstPerform first--principles calculationsprinciples calculationsSurprising results?Surprising results?The corresponding analysesThe corresponding analysesProspectsProspects
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J4
J4
J4
J3
J3
J3
J4
J
188.16BA368.16AB
68.5AA
127.05AA66.97BA126.97AB126.7BB
numberdn (Å)type
12∑ n i i+n
n , iH J S S= −
J2
J3
J2
J2
J2
J1
J1
J1
J1
J
126.0AA
85.5BA165.5AB
43.7AA63.5BA123.5AB
126.0BB
125.2BB
63.0BBnumberdn (Å)type
IsingIsing Model for cubic Model for cubic spinelspinel ferritesferrites
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Three different BThree different B--site site cationcation distributionsdistributions
the only theoretically considered configuration previously
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Ten considered configurationsTen considered configurations
ib1,ib2,ib3−0+ia1,ia2,ia3+0+
FeZnFeInversespinel
nb1,nb2,nb3−+0na1=na2=na3++0
FeFeZnNormalspinel
configurationB2B1Asite
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The nth The nth neighbourneighbour interactionsinteractions12∑ n i i+n
n , iH J S S= −
-6-6-6-3na
+2+2-2+1nb3-2+2+2-1nb2+2-6+2+1nb1J4J3J2J1
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OutlineOutline
FerritesFerritesDescribing interactionsDescribing interactionsPrevious research worksPrevious research worksWhat and how we can approach these systemsWhat and how we can approach these systemsCalculationalCalculational methodsmethodsQuantitative resultsQuantitative resultsProspectsProspects
18
ManyMany--electron systemselectron systems
{ }{ }( )
{ }{ }( )
222 2 22 2 1 1
2 2 2 2ii i j ie i j i
total
Z Z eZ ee r Rm m r r r R R R
E r R
α βαα α
α α α βα α β α
α
≠ ≠
− − ∇ + − ∇ + + + Ψ − − −
= Ψ
∑ ∑ ∑ ∑∑ ∑rh h r
r r rr r r
rr
{ }{ }( ) { }{ }( )2 2
2 1 ( , )2 2
Born-Oppenheimer approximation + Frozen-core approximation
i e ion i ei i j ie i j
e V r r E rm r r
R R Rα αα
α−≠
− ∇ + + Ψ = Ψ −
∑ ∑ ∑∑r rr r r
rrh
r
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Density Functional TheoryDensity Functional Theory
The of a many-electron system under the influence of some external potential is a
Hohenberg and Kohn 1
of the electron dens
96
i
4
ty ( )rρ
ground - state energy
unique functional r
3 3 312
( ) ( )[ ( )] [ ( )] ( ) ( )
[ ( )] : kinetic energy + the rest .... [ ( )]
: the exact form is unknown
extr rE r G r d r d r V r r d rr r
G rG r
ρ ρρ ρ ρ
ρρ
′= + +′−∫ ∫
r rr r r r
r r
r
r
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KohnKohn--Sham Equation : 1965Sham Equation : 1965
22 3( ){ ( ) [ ( )]} ( ) ( )
2 | |ext xc i i irV r d r r r r
m r rρ µ ρ φ ε φ
′′− ∇ + + + =
′−∫r
h r r rvr r
( ), ( )
effV r rρr r
1 4 442 4 4 43
[ ]
222
3
0
2
( )
[ ] [ ] [ ] [ ] ( ) ( )
[ ] : exchange-correlation energy functional...
( )0 subject to the condition ( ) 0
( )
the exact form is unknown
s xc s i i imi i
xc
r
G T E T r r
E
E rr d r
r ρ
ρ ρ ρ ρ φ φ ρ φ
ρ
δ ρδρ
δρ
= + = − ∇ =
= =
∑ ∑
∫
h
r
r r
rr
r
21
OutlineOutline
FerritesFerritesDescribing interactionsDescribing interactionsPrevious research worksPrevious research worksWhat and how we can approach these systemsWhat and how we can approach these systemsCalculationalCalculational methodsmethodsQuantitative resultsQuantitative resultsProspectsProspects
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Numerical results : relative stability (eV/8formu.)Numerical results : relative stability (eV/8formu.)
3.73.73.73.7/1.53.7/1.43.7/1.53.83.93.83.9µ
0.00.90.44.14.95.21.92.72.24.3∆E
ib3ib2ib1ia3ia2ia1nb3nb2nb1naZn
3.73.73.73.83.93.83.83.93.84.0µ
0.01.91.96.97.78.30.81.71.03.5∆E
ib3ib2ib1ia3ia2ia1nb3nb2nb1naCd
The most stable configuration : inverse The most stable configuration : inverse spinelspinel????
23
Numerical results : relative stability (Continued)Numerical results : relative stability (Continued)
ia1 ia2 ia3
4.14.14.14.24.24.24.2µ
1.682.682.18.00.14.18.54∆E
ib3ib2ib1nb3nb2nb1naZn
4.14.14.14.24.24.24.2µ
2.814.414.94.00.27.15.76∆E
ib3ib2ib1ia3ia2ia1nb3nb2nb1naCd
Including the onIncluding the on--site Coulomb interactionsite Coulomb interaction
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Numerical results : Numerical results : JJnn ((meVmeV))
-12.4-2.6-39.7PBE+U-12.3-2.7-39.6PBE+U-12.2-3.2-43.7PBE+U-23.6-19.0-220.4PBE4J34J24J1Zn
-6-6-6-3na+2+2-2+1nb3-2+2+2-1nb2+2-6+2+1nb1J4J3J2J1
JJ11*=(nb1*=(nb1--nb2)/2nb2)/2JJ22*=(nb1*=(nb1--nb3)/4nb3)/4
JJ11<0 J<0 J22<0 J<0 J33<0<0
|J|J22|<<|J|<<|J33||
+22.2+9.8+22.0+9.7+21.1+5.0+28.1-126.24J2*4J1*
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Numerical results : Numerical results : JJnn ((meVmeV))
-10.6-2.2-71.1PBE+U-21.8-18.7-275.9PBE4J34J24J1Cd
+18.9-28.9+24.8-188.84J2*4J1*
-12.3-2.7-39.6PBE+U-23.6-19.0-220.4PBE4J34J24J1Zn
+22.0+9.7+28.1-126.24J2*4J1*
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Numerical results : DOS Numerical results : DOS -- effect of Ueffect of U
27
Numerical results : DOS Numerical results : DOS -- effect of Ueffect of U
-8 -6 -4 -2 0 2
E-EF (eV)
N(E
)ZFO_nb3_GGA
Zn_AFe_B1Fe_B2O
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-8 -6 -4 -2 0 2
E-EF (eV)
N(E
)ZFO_nb3_GGA+U
Zn_AFe_B1Fe_B2O
Numerical results : DOS Numerical results : DOS -- effect of Ueffect of U
29
-5 0-80
-40
0
40
80CFO_nb3
Zn_AFe_B1Fe_B2O
30
-5 0-80
-40
0
40
80CFO_nb3u
Zn_AFe_B1Fe_B2O
31
-5 0-80
-40
0
40
80CFO_nb3u
Zn_AFe_B1Fe_B2O
-5 0-80
-40
0
40
80CFO_nb3
Zn_AFe_B1Fe_B2O
Numerical results : DOS Numerical results : DOS -- effect of Ueffect of U
32
Prospects:Prospects:
Diffraction Diffraction –– Low and High TLow and High TJJ11 FeFe--OO--Fe angleFe angleEffect of U Effect of U ---- JJnnDOS DOS –– difference in ZFO and CFOdifference in ZFO and CFOJJnn for AB interactionsfor AB interactions
33
Phase diagram for the 3D electron gasPhase diagram for the 3D electron gas
D. CeperleyNature397_386 (1999)
34
Magnetic properties of BN sheet with defectsMagnetic properties of BN sheet with defects
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Phase diagram for the 3D electron gasPhase diagram for the 3D electron gas
Thank you for your attention!Thank you for your attention!
That is all I have to say about That is all I have to say about ZnFeZnFe22OO44 and CdFeand CdFe22OO44
for the momentfor the moment
37
38
nn
nnn(111)
nn
39-5 0-80
-40
0
40
80ZFO_nb1
Zn_AFe_B1Fe_B2O
-5 0-80
-40
0
40
80ZFO_nb3
Zn_AFe_B1Fe_B2O
40-5 0-80
-40
0
40
80ZFO_ib3
Zn_B1Fe_AFe_B2O
-5 0-80
-40
0
40
80ZFO_nb3
Zn_AFe_B1Fe_B2O
41
nb1 nb2 nb3 ib1 ib3nb1 nb2 nb3 ib1 ib3
0.0
2.0
4.0
6.0PBEPBE+U(2.5)PBE+U(4.5)PW91PW91+U(4.5)
nb1 nb2 nb3 ib1 ib3nb1 nb2 nb3 ib1 ib3
0.0
2.0
4.0
6.0 LDALDA+U(2.5)LDA+U(4.5)PW91PW91+U(4.5)
nb1 nb2 nb3 ib1 ib3nb1 nb2 nb3 ib1 ib3
0.0
2.0
4.0
6.0 CFOPBEPBE+U(2.5)PBE+U(4.5)PW91PW91+U(4.5)
42
Cubic Cubic SpinelSpinel Ferrite : Ferrite : Magnetic StructureMagnetic Structure
B : Octahedral sites
A : Tetrahedral sites