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

0.0 0.5 1.0

to to to

to

Magnetic field (tesla)

T = 10 K

64 GHz 68 GHz 89 GHz 100 GHz 109 GHz 113 GHz 133 GHz 141 GHz

Spin projection (MS)

•MMSS dependence of dependence of Gaussian widths is due to Gaussian widths is due to DD-strain-strain

•Energies Energies M MSS22, therefore , therefore

energy differences energy differences M MSS

• DD = 0.6%= 0.6%

•DD-strain -strain disorder; disorder; multiple environmentsmultiple environments

•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!

High-frequency EPR dataHigh-frequency EPR dataS = 10

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

0.0 0.5 1.0

to to to

to

Magnetic field (tesla)

T = 10 K

64 GHz 68 GHz 89 GHz 100 GHz 109 GHz 113 GHz 133 GHz 141 GHz

Spin projection (MS)

•MMSS dependence of dependence of Gaussian widths is due to Gaussian widths is due to DD-strain-strain

•Energies Energies M MSS22, therefore , therefore

energy differences energy differences M MSS

• DD = 0.6%= 0.6%

•DD-strain -strain disorder; disorder; multiple environmentsmultiple environments

•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

0.0 0.5 1.0

to to to

to

Magnetic field (tesla)

T = 10 K

64 GHz 68 GHz 89 GHz 100 GHz 109 GHz 113 GHz 133 GHz 141 GHz

Spin projection (MS)

117 GHz89 GHz

-10

Hill et al., Phys. Rev. B 65, 224410 (2002)

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

[Mn[Mn44OO33ClCl44(O(O22CEt)CEt)33(py)(py)33]] Dimer Zeeman diagram

EPREPR

•Bias should shift the single spin (monomer) EPR Bias should shift the single spin (monomer) EPR transitions.transitions.

D = 0.75(1) KB0

4 = 5 × 10-5 KJ 0.12(1) K

SS11 = = SS22 = = 99//22; multiplicity of levels = (2; multiplicity of levels = (2SS11 + 1) (2 + 1) (2SS22 + 1) = 100 + 1) = 100

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, 7/

2)

( 9/2, 5/

2)

( 9/2,9/

2)

Look for additional splitting (multiplicity) and Look for additional splitting (multiplicity) and symmetry effects (selection rules) in EPR.symmetry effects (selection rules) in EPR.

SS11 = = SS22 = = 99//22; multiplicity of levels = (2; multiplicity of levels = (2SS11 + 1) (2 + 1) (2SS22 + 1) = 100 + 1) = 100

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, 7/

2)

S,A

( 9/2, 5/

2)

S,A

( 9/2,9/

2)

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

0 2 4 6 8 10 12

20K 18K 15K 10K 8K 6K 4K 2K

Cav

ity T

rans

mis

sion

(A

rb. u

nits

, off

set)

Magnetic field (T)

S = 4 MnS = 4 Mn66 SMMs SMMs