2002 London NIRT: Fe 2002 London NIRT: Fe 8 8 EPR EPR linewidth data linewidth data 0 10 20 30 40 50 0 50 100 150 200 250 2 0 -2 -4 -6 -8 -10 0 20 40 60 80 100 120 140 A bsorption (arb.units) EPR linew idth (m illitesla) T em perature (kelvin) 8 to 7 5 to 4 10 to 9 7 to 6 4 to 3 9 to 8 6 to 5 3 to 2 0.0 0.5 1.0 to to to to M agnetic field (tesla) T = 10 K 64 G Hz 68 G Hz 89 G Hz 100 G Hz 109 G Hz 113 G Hz 133 G Hz 141 G Hz Spin projection (M S ) • M M S dependence of dependence of Gaussian widths is due Gaussian widths is due to to D D -strain -strain • Energies Energies M M S 2 , , therefore energy therefore energy differences differences M M S • D = 0.6% = 0.6% • D D -strain -strain disorder; disorder; multiple environments multiple environments • S. Hill, S. Maccagnano, K. Park, S. Hill, S. Maccagnano, K. Park, R. M. Achey, J. M. North and N. S. R. M. Achey, J. M. North and N. S. Dalal, Phys. Rev. B Dalal, Phys. Rev. B 65 65 , 224410 , 224410 (2002). (2002). • Temperature dependence Temperature dependence of Gaussian widths is of Gaussian widths is due to intermolecular due to intermolecular spin-spin interactions spin-spin interactions (dipolar and exchange) (dipolar and exchange) 117 GHz 89 GHz
2002 London NIRT: Fe 8 EPR linewidth data. M S dependence of Gaussian widths is due to D -strain Energies M S 2 , therefore energy differences M S s D = 0.6% D -strain disorder; multiple environments. 89 GHz. 117 GHz. - PowerPoint PPT Presentation
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2002 London NIRT: Fe2002 London NIRT: Fe88 EPR linewidth data EPR linewidth data
0 10 20 30 40 50
0
50
100
150
200
250
2 0 -2 -4 -6 -8 -100
20406080
100120140
Abs
orpt
ion
(arb
. uni
ts)
EPR
line
wid
th (
mil
lites
la)
Temperature (kelvin)
8 to 7 5 to 4 10 to 9 7 to 6 4 to 3 9 to 8 6 to 5 3 to 2
•S. Hill, S. Maccagnano, K. Park, R. M. Achey, J. S. Hill, S. Maccagnano, K. Park, R. M. Achey, J. M. North and N. S. Dalal, Phys. Rev. B M. North and N. S. Dalal, Phys. Rev. B 6565, 224410 , 224410 (2002).(2002).
•Temperature dependence Temperature dependence of Gaussian widths is due of Gaussian widths is due to intermolecular spin-spin to intermolecular spin-spin interactions (dipolar and interactions (dipolar and exchange)exchange)
117 GHz89 GHz
field//field//zz
z, S4-axis
Bz
2( )s s B sm D m g Bm E
•Magnetic dipole transitions (ms = ±1) - note frequency scale!
•S. Hill, S. Maccagnano, K. Park, R. M. Achey, J. S. Hill, S. Maccagnano, K. Park, R. M. Achey, J. M. North and N. S. Dalal, Phys. Rev. B M. North and N. S. Dalal, Phys. Rev. B 6565, 224410 , 224410 (2002).(2002).
•Temperature dependence Temperature dependence of Gaussian widths is due of Gaussian widths is due to intermolecular spin-spin to intermolecular spin-spin interactions (dipolar and interactions (dipolar and exchange)exchange)
117 GHz89 GHz
Attempts to model this behaviorAttempts to model this behavior(spin-spin interactions)(spin-spin interactions)
-40
-30
-20
-10
0
10
0 5 10 15 20 25 30
-40
-30
-20
-10
0
10 to 9 9 to 8 8 to 7 7 to 6 6 to 5 5 to 4 4 to 3 3 to 2
f = 116.9 GHz
10 to 9 9 to 8 8 to 7 7 to 6 6 to 5 5 to 4 4 to 3 3 to 2
EPR
Lin
eshi
ft (
mill
itesl
a)
Temperature (kelvin)
•Kyungwha Park, M.A. Novotny, N.S. Dalal, S. Hill, Kyungwha Park, M.A. Novotny, N.S. Dalal, S. Hill, P.A. Rikvold, Phys. Rev. B P.A. Rikvold, Phys. Rev. B 6565, 14426 (2002)., 14426 (2002).
•Kyungwha Park, M.A. Novotny, N.S. Dalal, S. Hill, Kyungwha Park, M.A. Novotny, N.S. Dalal, S. Hill, P.A. Rikvold, Phys. Rev. B (In press, October 2002); P.A. Rikvold, Phys. Rev. B (In press, October 2002); cond-mat/0204481.cond-mat/0204481.
FeFe88Br Br easy axis line position data easy axis line position data•Temperature dependent Temperature dependent shifts are due to competing shifts are due to competing short range ferromagnetic short range ferromagnetic exchange (exchange (JJ = = 7 gauss) 7 gauss) interactions and longer interactions and longer range antiferromagnetic range antiferromagnetic dipolar coupling (dipolar coupling (20 gauss)20 gauss)
•Quantitative agreement Quantitative agreement with simulations taking both with simulations taking both interactions into accountinteractions into account
•First evidence for exchange First evidence for exchange in this widely studied SMMin this widely studied SMM
field//field//zz
z, S4-axis
Bz
2( )s s B sm D m g Bm E
•Magnetic dipole transitions (ms = ±1) - note frequency scale!
0 1 2 3 4 5 6 7
< 1
mm
Mn12
-tBuAc
336.3 GHz
30 K 25 K 20 K 15 K 10 K 7 K 5 K 3 K 1.4 K
Nor
mal
ized
tran
smis
sion
(a
rb. u
nits
- o
ffse
t)
Magnetic field (tesla)
2 4 4 42 4 4
ˆ ˆ ˆ ˆ ˆ
55K; 13K; 0.3K
z z
D B CS S S S
S S S
D B C
H•Obtain the axial terms in the z.f.s. Hamiltonian:
High-frequency EPR dataHigh-frequency EPR data
FeFe88Br (Br (SS = 10) = 10) easy axis linewidth data easy axis linewidth data
0 10 20 30 40 50
0
50
100
150
200
250
2 0 -2 -4 -6 -8 -100
20406080
100120140
Abs
orpt
ion
(arb
. uni
ts)
EPR
line
wid
th (
mil
lites
la)
Temperature (kelvin)
8 to 7 5 to 4 10 to 9 7 to 6 4 to 3 9 to 8 6 to 5 3 to 2
Body-centered tetragonal magnetic latticeBody-centered tetragonal magnetic lattice
[Cu2+]2 dimerJJ'J'
Jf
Each CuEach Cu2+2+ provides a spin-½ provides a spin-½
•Intra-dimer separation: 2.74 Å
•NN inter-dimer distance: 7 Å
•NNN inter-dimer distance: ~10 Å
All All JJss are antiferromagnetic are antiferromagnetic•Intra-dimer J = 4.45 meV (36 cm1)•J' = 0.51 meV (4 cm1)•Jf < J' is frustrating interactiona
bc
•To lowest order, treat as independent spin-½ dimersTo lowest order, treat as independent spin-½ dimers
•[Cu[Cu2+2+]]22 Hamiltonian has perfect cylindrical [ Hamiltonian has perfect cylindrical [UU(1)] symmetry(1)] symmetry
Properties of the isolated dimerProperties of the isolated dimer
TripletTriplet((T T ))
SingletSinglet((SS ))
TT
TT
SS
TT
cB
JB
g
Magnetic field
JJ
1 2ˆ ˆ ˆJH Js s
Heisenberg:Heisenberg:E
nerg
y
Zeeman:Zeeman: 1 2ˆ ˆ ˆZ BH g B s s
1.5 1.6 1.71.7 1.8 1.9 2.0
B//c
Magnetic field (tesla)
B//ab
4.5 K 5 K 5.5 K 6 K 6.5 K 7 K 7.5 K 8 K 8.5 K 9 K
Cav
ity tr
ansm
issi
on (
arb.
uni
ts -
off
set)
Temperature dependence – Low TTemperature dependence – Low T
S.
Seb
astia
n et
al.,
con
d-m
at/0
6062
44.
0 90 180 270 360
-60
-40
-20
0
20
40
60 Center
Shif
t (m
T)
Angle (degrees)
R1 R2
2 212
ˆˆ ; 3cos 1dip zH DS D
Angle dependence – origin of Angle dependence – origin of anisotropyanisotropy
Dipolar interactionDipolar interaction
F.
Mila
, E
uro
Phy
s. J
. B
. 6,
201
(19
98).
T
. G
iam
arch
i & A
. M
. T
svel
ik,
PR
B 5
9, 1
1398
(19
99)
.
Insight from the two leg ladderInsight from the two leg ladder
JJ'
i = 1 2 3 4 5.....
1,ˆ is
2,ˆ is
† †1 1 1eff i i i i i i i
i i i
H t c c c c V n n n K.E.K.E. P.E.P.E. C.P.C.P.
Mobile quasiparticles Mobile quasiparticles dispersion (bandstructure) dispersion (bandstructure)
1.5 1.6 1.71.7 1.8 1.9 2.0
B//c
Magnetic field (tesla)
B//ab
4.5 K 5 K 5.5 K 6 K 6.5 K 7 K 7.5 K 8 K 8.5 K 9 K
Cav
ity tr
ansm
issi
on (
arb.
uni
ts -
off
set)
Temperature dependence – Low TTemperature dependence – Low T
S.
Seb
astia
n et
al.,
con
d-m
at/0
6062
44.
8 sin exact diagonalization
Spin-1 chain with easy-plane Spin-1 chain with easy-plane anisotropyanisotropy
Antiferromagnetic exchange in a dimer of MnAntiferromagnetic exchange in a dimer of Mn44 SMMs SMMs
mm11
mm22
[Mn[Mn44OO33ClCl44(O(O22CEt)CEt)33(py)(py)33]]
0 1 2 3 4 5
-500
-400
-300
-200
-100
0
100
200
300
400
MS = - 5
/2 to - 3
/2
MS = - 7
/2 to - 5
/2
MS = - 9
/2 to - 7
/2
S = 9/2
Freq
uenc
y (G
Hz)
Magnetic field (tesla)
Monomer Zeeman diagram
D = 0.75(1) KB0
4 = 5 × 10-5 KJ 0.12(1) K
2 0 01 4 4
ˆ ˆ ˆˆz B zz zH DS B O g BS
Wolfgang Wernsdorfer, George Christou, et al., Nature, 2002, 406-409
0.0 0.2 0.4 0.6 0.8 1.0 1.2
-40
-30
-20
Ene
rgy
(K)
Magnetic field (tesla)
( 9/2,9/
2) ( 9/
2, 9/
2)
( 9/2, 7/
2) ( 9/
2, 5/
2)
Antiferromagnetic exchange in a dimer of MnAntiferromagnetic exchange in a dimer of Mn44 SMMs SMMs
1 2 1 2
2 21 2 1 2 1
2
2
1 1 2ˆ ˆ ˆˆ ˆ ˆ ˆ ˆˆ
z z
B
H H H H H
E D m m
JS S JS
g m m Jm m
S
B
mm11
mm22
To zeroth orderTo zeroth order, the exchange generates a bias field , the exchange generates a bias field BBJJ = =
Jm'Jm'/g/g which each spin experiences due to the other spin which each spin experiences due to the other spin within the dimerwithin the dimerWolfgang Wernsdorfer, George Christou, et al., Nature, 2002, 406-409
Look for additional splitting (multiplicity) and Look for additional splitting (multiplicity) and symmetry effects (selection rules) in EPR.symmetry effects (selection rules) in EPR.
Look for additional splitting (multiplicity) and Look for additional splitting (multiplicity) and symmetry effects (selection rules) in EPR.symmetry effects (selection rules) in EPR.
0 1 2 3 4 5 0 1 2 3 4 5 6
(i)(h)
(g)(f)
(e)
(d)
(c)
(b)
(a)
(x)
T
rans
mis
sion
(ar
b. u
nits
- o
ffse
t)
Magnetic field (tesla)
18 K 15 K 10 K 8 K 6 K 4 K 2 K
Jxy
/Jz = 0.3
Jxy
/Jz = 0.6
Jxy
/Jz = 1
Jxy
/Jz = 0
0 1 2 3 4 5 6
(i)(h)(g)(f)
(e)
(c)(b)
(d)
(x)
(a)
Clear evidence for coherent transitions involving both moleculesClear evidence for coherent transitions involving both molecules
JJzz = J = Jxyxy = 0.12(1) K = 0.12(1) K
ExperimentExperiment SimulationSimulation
S. Hill S. Hill et al., Scienceet al., Science 302302, 1015, 1015 (2003) (2003)
11 2 1 2 1 2 1 22
ˆ ˆ ˆ ˆ ˆ ˆˆ ˆ ˆD S S z zH H H JS S J S S S S
f = 145 GHz
D = 0.75(1) KB0
4 = 5 × 10-5 KJ 0.12(1) K
Although most aspects of earlier EPR line width studies on Mn12Ac and Fe8 have been understood in terms of competing exchange and dipolar interactions,20–22 an explanation for the behavior of the ground-state resonance (mS ) -4 to -3 in the present study) has remained elusive for kBT < Δ0. We speculate that this behavior is related to the development of short-range intermolecular magnetic correlations/coherences (either ferro- or antiferromagnetic) which are exchange averaged at higher temperatures.
NiNi44 SMMs SMMs
Inorg. Chem. 47, 1965-1974 (2008).
0 2 4 6 8 10 12-1200
-1000
-800
-600
-400
-200
0
200
400
Freq
uenc
y (G
Hz)
Magnetic field (tesla)
0 1 2 3 4 5 6 7 8 9 10 110
50
100
150
200
250
300
Freq
uenc
y (G
Hz)
Magnetic field (tesla)
15 K
-4 -3 -2 -1 0 1 2 3 4-200
-150
-100
-50
0
50
100
150
200
y = + x + x2 + x3
= -19.0 GHz = -43.5 GHz = 1.04 GHz = -0.401 GHz
zfs
(GH
z)
(m + 1/2)
Experimental zfs 3rd order polynomial fit
Exchange biased S = 4 NiExchange biased S = 4 Ni44 SMM SMM
A. Ferguson et al.,Dalton Trans., 2008, 6409 - 6414, DOI: 10.1039/b807447j
0 1 2 3 4 5 6
Cav
ity tr
ansm
issi
on
(arb
. uni
tso
ffse
t)
Magnetic field (tesla)
8 K 6 K 5 K 4 K 3 K 2 K 1.4 K
Exchange biased S = 4 NiExchange biased S = 4 Ni44 SMM SMM
A. Ferguson et al.,Dalton Trans., 2008, 6409 - 6414, DOI: 10.1039/b807447j