Long-range antiferromagnetic interactions in ZnFe O and CdFe OLong-range antiferromagnetic...
Transcript of Long-range antiferromagnetic interactions in ZnFe O and CdFe OLong-range antiferromagnetic...
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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
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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
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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
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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
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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
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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????
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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
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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
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-5 0-80
-40
0
40
80CFO_nb3
Zn_AFe_B1Fe_B2O
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-5 0-80
-40
0
40
80CFO_nb3u
Zn_AFe_B1Fe_B2O
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-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
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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
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Phase diagram for the 3D electron gasPhase diagram for the 3D electron gas
D. CeperleyNature397_386 (1999)
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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
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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
![Page 37: Long-range antiferromagnetic interactions in ZnFe O and CdFe OLong-range antiferromagnetic interactions in ZnFe2O4 and CdFe2O4 빇쁒 CoContributors Supports 뫓ꑨ늦띾ꗍ뱂껊ꗍ:](https://reader030.fdocument.pub/reader030/viewer/2022040216/5f2ad25f03f7e430be79698b/html5/thumbnails/37.jpg)
37
![Page 38: Long-range antiferromagnetic interactions in ZnFe O and CdFe OLong-range antiferromagnetic interactions in ZnFe2O4 and CdFe2O4 빇쁒 CoContributors Supports 뫓ꑨ늦띾ꗍ뱂껊ꗍ:](https://reader030.fdocument.pub/reader030/viewer/2022040216/5f2ad25f03f7e430be79698b/html5/thumbnails/38.jpg)
38
nn
nnn(111)
nn
![Page 39: Long-range antiferromagnetic interactions in ZnFe O and CdFe OLong-range antiferromagnetic interactions in ZnFe2O4 and CdFe2O4 빇쁒 CoContributors Supports 뫓ꑨ늦띾ꗍ뱂껊ꗍ:](https://reader030.fdocument.pub/reader030/viewer/2022040216/5f2ad25f03f7e430be79698b/html5/thumbnails/39.jpg)
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
![Page 40: Long-range antiferromagnetic interactions in ZnFe O and CdFe OLong-range antiferromagnetic interactions in ZnFe2O4 and CdFe2O4 빇쁒 CoContributors Supports 뫓ꑨ늦띾ꗍ뱂껊ꗍ:](https://reader030.fdocument.pub/reader030/viewer/2022040216/5f2ad25f03f7e430be79698b/html5/thumbnails/40.jpg)
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
![Page 41: Long-range antiferromagnetic interactions in ZnFe O and CdFe OLong-range antiferromagnetic interactions in ZnFe2O4 and CdFe2O4 빇쁒 CoContributors Supports 뫓ꑨ늦띾ꗍ뱂껊ꗍ:](https://reader030.fdocument.pub/reader030/viewer/2022040216/5f2ad25f03f7e430be79698b/html5/thumbnails/41.jpg)
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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)
![Page 42: Long-range antiferromagnetic interactions in ZnFe O and CdFe OLong-range antiferromagnetic interactions in ZnFe2O4 and CdFe2O4 빇쁒 CoContributors Supports 뫓ꑨ늦띾ꗍ뱂껊ꗍ:](https://reader030.fdocument.pub/reader030/viewer/2022040216/5f2ad25f03f7e430be79698b/html5/thumbnails/42.jpg)
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Cubic Cubic SpinelSpinel Ferrite : Ferrite : Magnetic StructureMagnetic Structure
B : Octahedral sites
A : Tetrahedral sites