Chemistry Reference
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approach.(see.Ref..[79].for.details),.the.following.expression.for.the.total.magnetic.
moment.per.atom.μ
t
.is.obtained
1
3
N
N
(
)
s
t
s
μ
=
1
− ⋅
ν
J N N
⋅
(
−
N
)
.
(11.9)
t
s
t
s
.
where. the. surface. magnetic. moment. μ
s
. can. be. obtained. self-consistently. from. the.
following.expressions:
⎛
⎜
⎞
⎟
1 1
k T g
J N
⎡
⎢
⎤
⎥
s
μ
=
tanh
⋅
⋅
μ
+ ⋅
g h
.
(11.10)
s
s
s
z
B
.
μ
=
tanh( )
ξ
s
1 1
k T g
J N
⎛
⎜
⎞
⎟
s
ξ
=
⋅
⋅
μ
+ ⋅
g h
z
.
(11.11)
s
s
B
.
In.expressions.(11.9).through.(11.11),.
J
s
.indicates.the.average.surface.exchange,.
g
.is.
related.to.the.gyromagnetic.constant,.
h
z
.is.the.effective.ield.in.the.preferred.
z
.direc-
tion,.and.the.constant.ν.is.given.by
3
1 3 2
4 3
/
/
e
m c
e
.
(11.12)
ν
=
λ
2
12
π
.
with
e
.and.
m
e
.indicating.the.charge.and.mass.of.an.electron
c
.the.speed.of.light
∼
.is.a.phenomenological.constant
Figure. 11.7. depicts. a. plot. of. the. magnetic. moment. per. atom. as. a. function. of. the.
particle.size.for.a.typical.gold.nanoparticle..The.results.show.how.this.simple.Ising.
model.reproduces.qualitatively.the.size.dependence.behavior.observed.experimen-
tally.by.Hori.et.al..[63].
We.have.also.performed.studies.aimed.at.understanding.the.origins.of.magnetic.
behavior. in. gold. upon. chemisorption. as. well. as. the. effect. of. different. ligands. on.
the. magnetic. moment.. Using. a. simple. quantum. chemical. model. based. on. inite.
perturbation.theory.(FPT).combined.with.DFT.calculations.on.a.Au.cluster.with.a.
two-layer.slab.of.13.atoms.(9.in.the.irst.layer.and.4.in.the.second.layer),.Gonzalez.
et.al..[80].were.able.to.suggest.ideas.regarding.the.electronic.structure.origin.of.the.
observed.magnetism.in.Au.cluster-ligand.systems.with.different.chemical.linkers.
and. provided. a. theoretical. basis. to. rationalize. the. experimental. observation. indi-
cating. that. magnetism. can. be. induced. in. gold. as. a. result. of. the. chemisorption. of.
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