Quantum coherence in an exchange-coupled dimer

of single-molecule magnets

Supported by: NSF, Research Corporation, & University of Florida

PART IPART IIntroduction to single-molecule magnetsIntroduction to single-molecule magnets

•Emphasis on quantum magnetization dynamicsEmphasis on quantum magnetization dynamics

PART IIPART IIMonomeric MnMonomeric Mn44 single-molecule magnets single-molecule magnetsElectron Paramagnetic Resonance technique, with examplesElectron Paramagnetic Resonance technique, with examplesFocus on [MnFocus on [Mn44]]22 dimer dimer

•Quantum mechanical coupling within a dimerQuantum mechanical coupling within a dimer•Evidence for quantum coherence from EPREvidence for quantum coherence from EPR

Stephen Hill and Rachel EdwardsStephen Hill and Rachel EdwardsDepartment of Physics, University of Florida, Gainesville, FL32611Department of Physics, University of Florida, Gainesville, FL32611

Nuria Aliaga-Alcalde, Nicole Chakov and George ChristouNuria Aliaga-Alcalde, Nicole Chakov and George ChristouDepartment of Chemistry, University of Florida, Gainesville, FL32611

PART IPART I

Introduction to single-molecule magnetsIntroduction to single-molecule magnetsEmphasis on their quantum dynamicsEmphasis on their quantum dynamics

MESOSCOPIC MAGNETISMmacroscale nanoscale

permanentmagnets

micronparticles

nanoparticles clusters molecularclusters

Individualspins

S = 1023 1010 108 106 105 104 103 102 10 1

multi - domain single - domain Single molecule nucleation, propagation andannihilation of domain walls

uniform rotation quantum tunneling,quantum interference

-1

0

1

-40 -20 0 20 40

M/M

S

H(mT)

-1

0

1

-100 0 100

M/M

S

H(mT)

-1

0

1

-1 0 1M

/MS

H(T)

Fe8

1K0.1K

0.7K

MnMn1212-ac-ac

FerritinFerritin

1 nm10 nm100 nmsuperparamagnetism

Classical Quantum

size

W. Wernsdorfer, W. Wernsdorfer, Adv. Chem. Phys. Adv. Chem. Phys. 118118, 99-190 (2001), 99-190 (2001); also ; also arXiv/cond-mat/0101104arXiv/cond-mat/0101104..

~1.2 nm

A. J. Tasiopoulos et al., Angew. Chem., in-press.

The first single molecule magnet: Mn12-acetate

[Mn[Mn1212OO1212(CH(CH33COO)COO)1616(H(H22O)O)44]]··2CH2CH33COOHCOOH··4H4H2200

Mn(IV)

Mn(III)

Oxygen

Carbon

S S = 2= 2

S S = 3/2= 3/2

Lis, 1980

•Easy-axis anisotropy due to Jahn-Teller distortion on Mn(III)Easy-axis anisotropy due to Jahn-Teller distortion on Mn(III)

•Crystallizes into a tetragonal structure with SCrystallizes into a tetragonal structure with S44 site site symmetrysymmetry

•Organic ligands ("chicken fat") isolate the moleculesOrganic ligands ("chicken fat") isolate the molecules

R. Sessoli et al. JACS 115, 1804 (1993)

•Ferrimagnetically coupled magnetic ions (Ferrimagnetically coupled magnetic ions (JJintraintra 100 K) 100 K)Well defined giant spin (Well defined giant spin (SS = 10) at low temperatures (T < 35 K) = 10) at low temperatures (T < 35 K)

"up""up" "down""down"

EE1010

EE99

EE88

EE77

EE1010

EE99

EE88

EE77

EE66

EE55

Spin projection - ms

EE66

EE55

Ene

rgy

Ene

rgy

EE44EE44

smE

21 discrete 21 discrete mmss levels levels

Quantum effects at the nanoscale (S = 10)Simplest case: axial Simplest case: axial (cylindrical) crystal field(cylindrical) crystal field

2ˆ ˆ ( 0)zDS D H

Eigenvalues given by:Eigenvalues given by:2( )s sm D mE

•Small barrier - Small barrier - DSDS22

•Superparamagnet at Superparamagnet at ordinary temperaturesordinary temperatures

E E DS2 10-100 K10-100 K

|D | 0.1 1 K for a typical single molecule magnetThermal activationThermal activation

"up""up" "down""down"

EE1010

EE99

EE88

EE77

EE1010

EE99

EE88

EE77

EE66

EE55

Spin projection - ms

EE66

EE55

Ene

rgy

Ene

rgy

EE44EE44

smE

ThermallyThermallyassistedassisted

quantumquantumtunnelingtunneling

Break axial symmetry:Break axial symmetry:2

Tˆ ˆ ˆ

zDS H HT interactions which do not commute with Ŝz

Quantum effects at the nanoscale (S = 10)

EEeffeff < < EE

• mmss notnot good quantum # good quantum #

•Mixing of Mixing of mmss states states

resonant tunneling resonant tunneling (of (of mmss) through barrier) through barrier

•Lower effective barrierLower effective barrier

"up""up" "down""down"

EE1010

EE99

EE88

EE77

EE1010

EE99

EE88

EE77

EE66

EE55

Spin projection - ms

EE66

EE55

Ene

rgy

Ene

rgy

EE44EE44

smE

Pure quantum tunnelingPure quantum tunneling

Strong distortion of the Strong distortion of the axial crystal field:axial crystal field:

•Temperature-independent Temperature-independent quantum relaxation as Tquantum relaxation as T00

•Ground states a mixture of Ground states a mixture of pure "up" and pure "down".pure "up" and pure "down".

"down""down""up""up"

±±1

2{ }

•Ground state degeneracy Ground state degeneracy lifted by transverse lifted by transverse interaction: interaction:

splitting splitting ( (T)n

Tunnel splittingTunnel splitting

Quantum effects at the nanoscale (S = 10)

2T

ˆ ˆ ˆ ˆ

ˆ ˆ ˆ ˆ

z B

x x y y z z

DS g B S

B S B S B S B S

H H

Spin projection - ms

•Applied field represents another source of transverse anisotropy

•Zeeman interaction contains odd powers of Ŝx and Ŝy

Several important points to note:

For now, consider only B//z :(also neglect transverse interactions)

2( )s s B sm D m g Bm E

"down""down""up""up"

•Magnetic quantum tunneling is suppressedMagnetic quantum tunneling is suppressed

•Metastable magnetization is blocked ("down" spins) Metastable magnetization is blocked ("down" spins)

System off resonanceSystem off resonanceX

X

Application of a magnetic field

Application of a magnetic field2

Tˆ ˆ ˆ ˆ

ˆ ˆ ˆ ˆ

z B

x x y y z z

DS g B S

B S B S B S B S

H H

Spin projection - ms

System on resonanceSystem on resonance

•Applied field represents another source of transverse anisotropy.

•Zeeman interaction contains odd powers of Ŝx and Ŝy.

Several important points to note:

For now, consider only B//z :(also neglect transverse interactions)

2( )s s B sm D m g Bm E

"down""down""up""up"

•Resonant magnetic quantum tunneling resumesResonant magnetic quantum tunneling resumes

•Metastable magnetization can relax from "down" to "up" Metastable magnetization can relax from "down" to "up"

Increasing fieldIncreasing field

Hysteresis and magnetization steps

•Friedman, Sarachik, Friedman, Sarachik, Tejada, Ziolo, PRL (1996)Tejada, Ziolo, PRL (1996)

•Thomas, Lionti, Ballou, Thomas, Lionti, Ballou, Gatteschi, Sessoli, Gatteschi, Sessoli, Barbara, Nature (1996)Barbara, Nature (1996)

Mn12-ac

Tunneling "off"Tunneling "off"

Tunneling Tunneling "on""on"

Low temperature H=0 Low temperature H=0 step is an artifactstep is an artifact

This loop represents an This loop represents an ensemble average of the ensemble average of the response of many moleculesresponse of many molecules

PART IIPART II

Quantum Coherence in Exchange-Coupled Quantum Coherence in Exchange-Coupled Dimers of Single-Molecule MagnetsDimers of Single-Molecule Magnets

MnMn44 single molecule magnets single molecule magnets (cubane family)(cubane family)

[Mn4O3Cl4(O2CEt)3(py)3]

•MnMnIIIIII ( (SS = 2) and Mn = 2) and MnIVIV ( (SS = 3/2) ions couple ferrimagnetically to = 3/2) ions couple ferrimagnetically to give an give an extremelyextremely well defined ground state spin of well defined ground state spin of SS = 9/2. = 9/2.

•This is the monomer from which the dimers are made.This is the monomer from which the dimers are made.

Distorted Distorted cubanecubane

MnIII: 3 × S = 2

MnIV: S = 3/2

SS = = 99//22

C3v symmetry

FairlyFairly typical SMM: exhibits resonant MQT typical SMM: exhibits resonant MQT2 ˆ.ˆˆ ˆ ˆ '.o z TBH DS B g HS H

IB//B//zz

Note: resonant MQT Note: resonant MQT strong at B=0, even strong at B=0, even for half integer spin. for half integer spin.

“u p”“ d o w n ”

B < 0S

( -1 )S -S

11W. Wernsdorfer et al., PRB W. Wernsdorfer et al., PRB 6565, 180403 (2002)., 180403 (2002).22W. Wernsdorfer et al., PRL W. Wernsdorfer et al., PRL 8989, 197201 (2002)., 197201 (2002).•Barrier Barrier 20 20DD 18 K 18 K

•Spin parity effectSpin parity effect11

•Importance of transverse internal fieldsImportance of transverse internal fields11

•Co-tunneling due to inter-SMM exchangeCo-tunneling due to inter-SMM exchange22

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)

Energy level diagram for Energy level diagram for DD < 0 system, B// < 0 system, B//zz2ˆ ˆˆ . .o z BH DS B g S

I

B // z-axis of molecule

Note frequency rangeNote frequency range

Cavity perturbationCavity perturbationCylindrical TE01Cylindrical TE01n n ((QQ ~~ 10104 4 -- 101055))ff = 16 = 16 300 GHz 300 GHzSingle crystal 1 Single crystal 1 × 0.2 × 0.2 mm× 0.2 × 0.2 mm33

T = 0.5 to 300 K, T = 0.5 to 300 K, ooH up to 45 teslaH up to 45 tesla

M. Mola M. Mola et alet al., Rev. Sci. Inst. ., Rev. Sci. Inst. 7171, 186 (2000), 186 (2000)

A u S S

B

•We use a Millimeter-wave Vector We use a Millimeter-wave Vector Network Analyzer (MVNA, ABNetwork Analyzer (MVNA, ABmmmm) as a ) as a spectrometerspectrometer

(now 715 GHz!)(now 715 GHz!)

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)

Energy level diagram for Energy level diagram for DD < 0 system, B// < 0 system, B//zz2ˆ ˆˆ . .o z BH DS B g S

I

B // z-axis of molecule

Note frequency rangeNote frequency range

0.0 1.0 2.0 3.0 4.0 5.0

24 K 18 K 14 K 8 K 6 K 4 K

1/2 to 1/

23/2 to 1/

2

5/2 to 3/

2

7/2 to 5/

2

9/2 to 7/

2f = 138 GHz

C

avity

tran

smis

sion

(ar

b. u

nits

- o

ffse

t)

Magnetic field (tesla)

HFEPR for high symmetry (HFEPR for high symmetry (CC3v3v) Mn) Mn44 cubane cubane

Field // Field // zz-axis of the molecule (-axis of the molecule (±0.5±0.5oo))

[Mn4O3(OSiMe3)(O2CEt)3(dbm)3]

0 1 2 3 4 5

0

50

100

150

S = 9/2

D = 0.484 cm-1

B0

4 = 0.000062 cm-1

gz = 2.00(1)

Freq

uenc

y (G

Hz)

Magnetic field (tesla)

2 0 0 0 2 2 44 4 4

ˆ ˆ ˆ ˆ ˆ ˆ ˆˆ , where o z B zz z z zH DS B O g BS O S S S

Fit to easy axis data - yields diagonal crystal field termsFit to easy axis data - yields diagonal crystal field terms

Core ligands (X): Cl-, Br-, F-

NO3-, N3

-, NCO-

OH-, MeO-, Me3SiO-

Peripheral ligands: (i) carboxylate ligands: -O2CMe, -O2CEt

(ii) Cl-, py, HIm, dbm-, Me2dbm-, Et2dbm-

Routes to incredible # of SMMsRoutes to incredible # of SMMs

Jahn-Teller Jahn-Teller points towards points towards core ligandcore ligand

-40

-30

-20

-10

-1.2 -0.8 -0.4 0 0.4 0.8 1.2

En

erg

y (

K)

µ 0 Hz (T)

(1)

(4)(5)(9/2,9/2)

(-9/2,9/2)

(-9/2,-9/2)

(-9/2,7/2)

(9/2,-7/2)

(9/2,-5/2)

(2)(3)

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

D1 = 0.72 K

J = 0.1 K

To zeroth orderTo zeroth order, the exchange generates a bias field , the exchange generates a bias field Jm'Jm'/g/g which each spin experiences due to the other spin within the which each spin experiences due to the other spin within the dimerdimer

[Mn[Mn44OO33ClCl44(O(O22CEt)CEt)33(py)(py)33]]

-1

-0.5

0

0.5

1

-1.2 -0.8 -0.4 0 0.4 0.8 1.2

0.04 K0.3 K0.4 K0.5 K0.6 K0.7 K0.8 K1.0 K

M/M

s

µ0H (T)

0.14 T/s

a

No H = No H = 0 0 tunnelintunnelingg

Wolfgang Wernsdorfer, George Christou, et al., Nature, 2002, 406-409

This scheme in the same spirit as proposals for multi-qubit devices based on quantum dots

D. Loss and D.P. DiVincenzo, Phys. Rev. A 57, 120 (1998).

Systematic control of coupling between SMMs - EntanglementSystematic control of coupling between SMMs - Entanglement

•Zeroth orderZeroth order bias term, bias term, JŜJŜzz11ŜŜzz22, , is diagonal in the is diagonal in the mmzz11,,mmzz22 basis.basis.

•Therefore, Therefore, it does notit does not couple the molecules quantum couple the molecules quantum mechanically, mechanically, i.ei.e. tunneling and EPR involve . tunneling and EPR involve single-spin single-spin rotationsrotations..

•Quantum mechanical coupling caused by the transverse (off-Quantum mechanical coupling caused by the transverse (off-diagonal) parts of the exchange interaction diagonal) parts of the exchange interaction JJxyxy((ŜŜxx11ŜŜxx22 + + ŜŜyy11ŜŜyy22))..

•This term causes the entanglement, This term causes the entanglement, i.ei.e. . it truly mixesit truly mixes mmzz11,,mmzz22 basis statesbasis states, resulting in co-tunneling and EPR , resulting in co-tunneling and EPR transitions involving transitions involving two-spin rotationstwo-spin rotations. .

•CAN WE OBSERVE THIS?CAN WE OBSERVE THIS?

Heisenberg:Heisenberg:JŜJŜ11..ŜŜ22

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 or tunneling symmetry effects (selection rules) in EPR or tunneling experiments.experiments.

0

20

40

60

80

100

120

140

160

180

0 1 2 3 4 5 6

NA11 frequency dependence

(-3 / 2

,-9 / 2

) to (-

1 / 2,-9 / 2

)

(+1 / 2

,-9 / 2

) to (+

3 / 2,-9 / 2

)

(-1 / 2

,-9 / 2

) to (+

1 / 2,-9 / 2

)

Magnetic field (tesla)

Freq

uenc

y (G

Hz)

0 1 2 3 4 5 6

NA11 145 GHz easy axis T-dep

Cav

ity tr

ansm

issi

on (

arb.

uni

ts)

Magnetic field (tesla)

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

0.0 1.0 2.0 3.0 4.0 5.0

24 K 18 K 14 K 8 K 6 K 4 K

1/2 to 1/

23/2 to 1/

2

5/2 to 3/

2

7/2 to 5/

2

9/2 to 7/

2f = 138 GHz

Cav

ity tr

ansm

issi

on (

arb.

uni

ts -

off

set)

Magnetic field (tesla)

0 1 2 3 4 50

50

100

150

S = 9/2

D = 0.484 cm-1

B0

4 = 0.000062 cm-1

gz = 2.00(1)

Freq

uenc

y (G

Hz)

Magnetic field (tesla)

First clues: comparison between monomer and dimer EPR dataFirst clues: comparison between monomer and dimer EPR data

MonomerMonomer

MonomerMonomer-1 / 2

to 1 / 2

Exc

hang

e bi

asE

xcha

nge

bias

[Mn[Mn44OO33ClCl44(O(O22CEt)CEt)33(py)(py)33]]

1 2 1 2ˆ ˆˆ ˆ ˆ .D S SH H H JS S

11 2 1 2 1 2 1 2 02

ˆ ˆ ˆ ˆ ˆ ˆˆ ˆ ˆ ˆ ˆD S S z z DH H H JS S J S S S S H H'

Full exchange calculation for the dimerFull exchange calculation for the dimer

}

Isotropic exchangeIsotropic exchangeMonomer HamiltoniansMonomer Hamiltonians

•Apply the field along Apply the field along zz, and neglect the transverse terms in , and neglect the transverse terms in ĤĤSS11 and and ĤĤSS22..

•Then, only off-diagonal terms in Then, only off-diagonal terms in ĤĤDD come from the transverse ( come from the transverse (xx and and yy) part of the exchange interaction, ) part of the exchange interaction, i.e.i.e.

•The zeroth order Hamiltonian (The zeroth order Hamiltonian (ĤĤ00DD) includes the exchange bias.) includes the exchange bias.

•The zeroth order wavefunctions may be labeled according to the The zeroth order wavefunctions may be labeled according to the spin projections (spin projections (mm11 and and mm22) of the two monomers within a dimer, ) of the two monomers within a dimer, i.ei.e..

1 2,m m

•The zeroth order eigenvalues are given byThe zeroth order eigenvalues are given by

2 2 4 40 2 1 2 4 1 2 1 2 1 2D B zE D m m D m m g B m m Jm m

11 2 1 22

ˆ ˆ ˆ ˆH' J S S S S

1 2 1 2

9 92 2

9 7 7 92 2 2 2

9 5 5 9 7 72 2 2 2 2 2

9 3 3 9 7 5 5 72 2 2 2 2 2 2 2

9 9 7 3 3 7 5 51 12 2 2 2 2 2 2 2 2 2

,

9 ,

8 , , ,

7 , , , , ,

6 , , , , , , ,

5 , , , , , , , , ,

M m m m m

M

M

M

M

M

Full exchange calculation for the dimerFull exchange calculation for the dimer

1st order correction1st order correctionlifts degeneracies betweenlifts degeneracies betweenstates where states where mm11 and and mm22

differ by differ by ±±11

•One can consider the off-diagonal part of the exchange (One can consider the off-diagonal part of the exchange (Ĥ'Ĥ') as a ) as a perturbation, or perform a full Hamiltonian matrix diagonalizationperturbation, or perform a full Hamiltonian matrix diagonalization

•Ĥ'Ĥ' preserves the total angular momentum of the dimer, preserves the total angular momentum of the dimer, MM = = mm11 + + mm22..

•Thus, it only causes interactions between levels belonging to a Thus, it only causes interactions between levels belonging to a particular value of particular value of MM. These may be grouped into multiplets, as . These may be grouped into multiplets, as follows...follows...

9 92 21 9 ,

SM

9 7 7 92 2 2 2

9 7 7 92 2 2 2

12 8 , ,

2

13 8 , ,

2

A

S

M

M

9 5 5 9 7 72 2 2 2 2 22

9 5 5 92 2 2 2

7 7 9 5 5 92 2 2 2 2 22

1 14 7 , , 2 ,

2 1 2

15 7 , ,

2

16 7 , , ,

1 2

S

A

S

M

M

M

9 3 3 9 7 5 5 72 2 2 2 2 2 2 22

9 3 3 9 7 5 5 72 2 2 2 2 2 2 22

7 5 5 7 9 3 3 92 2 2 2 2 2 2 22

7 5 5 7 9 3 3 92 2 2 2 2 2 2 22

1 17 6 , , ' , ,

2 1 '

1 17 6 , , ' , ,

2 1 '

1 18 6 , , ' , ,

2 1 '

1 19 6 , , ' , ,

2 1 '

A

S

A

S

M

M

M

M

12

30.472

J

D J

21' 0.578 0.273

8

1st order corrections to the wavefunctions1st order corrections to the wavefunctions

•Ĥ'Ĥ' is symmetric with respect is symmetric with respect to exchange and, therefore, to exchange and, therefore, will only cause 2nd order will only cause 2nd order interactions between states interactions between states having the same symmetry, having the same symmetry, within a multiplet.within a multiplet.

•The symmetries of the states are The symmetries of the states are important, both in terms of the energy important, both in terms of the energy corrections due to exchange, and in corrections due to exchange, and in terms of the EPR selection rules.terms of the EPR selection rules.

9 92 2,

40.5

9 72 2,

32.5

9 52 2, 26.5

7 72 2, 24.5

9 32 2, 22.5

7 52 2, 8.5

Exchangebias

Full Exchange

(1) - S

(2) - A(3) - S

(4) - S(5) - A

(6) - S(7) - A & S

(8) - A(9) - S

(a)

(b)(c)

(d)(e)

1st and 2nd order corrections to the energies1st and 2nd order corrections to the energies

Magnetic-dipole interaction is symmetricMagnetic-dipole interaction is symmetric

Matrix elementvery small

0 1 2 3 4 5 6

(7/2,9/

2)(9/

2,9/

2)

(5/2,5/

2)

(+1/2,9/

2)

(3/2,7/

2)

(3/2,9/

2)

(5/2,7/

2)(1/

2,9/

2)

(7/2,7/

2)

(5/2,9/

2)

(7/2,9/

2)

(9/2,9/

2)

Ene

rgy

(K)

Magnetic field (tesla)

Magnetic field dependenceMagnetic field dependence

This figure does not show all levels

•The effect of The effect of Ĥ'Ĥ' is field-independent, because the field does not is field-independent, because the field does not change the relative spacings of levels within a given change the relative spacings of levels within a given MM multiplet. multiplet.

Clear evidence for coherent transitions involving both moleculesClear evidence for coherent transitions involving both molecules

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

9 MHz4.2 4.8 5.4

24 K

18 K

NA11 145 GHz easy axis T-dep

Cav

ity tr

ansm

issi

on (

arb.

uni

ts)

Magnetic field (tesla)

> 1 ns

0 1 2 3 4 5 6

T = 6 K, f = 160 GHz

Abs

orpt

ion

(arb

. uni

ts)

Magnetic field (tesla)

J = 0 J = 0.03 K J = 0.06 K J = 0.1 K J = 0.13 K

Variation of J, considering only the exchange bias

0 1 2 3 4 5 6

T = 6 K, f = 160 GHz

Abs

orpt

ion

(arb

. uni

ts)

Magnetic field (tesla)

J = 0 K J = 0.03 K J = 0.06 K J = 0.1 K J = 0.13 K

Variation of J, considering the full exchange term

• Simulations clearly demonstrate that it is the off diagonal part of the Simulations clearly demonstrate that it is the off diagonal part of the exchange that gives rise to the EPR fine-structure.exchange that gives rise to the EPR fine-structure.

• Thus, EPR reveals the quantum coupling.Thus, EPR reveals the quantum coupling.• Coupled states remain coherent on EPR time scales.Coupled states remain coherent on EPR time scales.

R. Tiron et al., Phys. Rev. Lett. 91, 227203 (2003)Next session: B25.011

Confirmed by hole-digging (minor loop) experimentsConfirmed by hole-digging (minor loop) experiments

Control of exchangeControl of exchange

This scheme is in the same spirit as proposals for multi-qubit devices based on quantum dots

D. Loss and D.P. DiVincenzo, Phys. Rev. A 57, 120 (1998).

"off"

"on"

+

Light

Decoherence – role of nuclear spins

The role of dipolar and hyperfine fields was first The role of dipolar and hyperfine fields was first demonstrated via studies of isotopically substituted demonstrated via studies of isotopically substituted versions of Feversions of Fe88..

[Wernsdorfer et al., Phys. Rev. Lett. [Wernsdorfer et al., Phys. Rev. Lett. 8282, 3903 (1999)], 3903 (1999)]Reduce via nuclear labeling – may require something other Reduce via nuclear labeling – may require something other than Mnthan Mn

Also have to worry about intermolecular interactionsAlso have to worry about intermolecular interactions

Mn4Mn4

Chicken FatChicken Fat

OH OH,

Mn4Mn4

OH OH,

Chicken FatChicken Fat

1.1. Control over magnitude and symmetry of the anisotropy Control over magnitude and symmetry of the anisotropy through the choice of molecule:through the choice of molecule:• Choice of magnetic ion, modifications to molecular core, Choice of magnetic ion, modifications to molecular core,

etc.etc.

2.2. Reduce electronic spin-spin interactions by adding organic Reduce electronic spin-spin interactions by adding organic bulk to the periphery of the SMM, or by diluting with non-bulk to the periphery of the SMM, or by diluting with non-magnetic molecules.magnetic molecules.

3.3. Reduce electron-nuclear cross-relaxation by isotopic Reduce electron-nuclear cross-relaxation by isotopic labeling.labeling.

4.4. Move the tunneling into frequency window where Move the tunneling into frequency window where decoherence may be less severe:decoherence may be less severe:• Achieved with lower spin and lower symmetry Achieved with lower spin and lower symmetry

molecules,molecules,• or with a transverse externally applied field,or with a transverse externally applied field,• or by deliberately engineering-in exchange interactions.or by deliberately engineering-in exchange interactions.

5.5. Move over to antiferromagnetic systems, e.g. the dimer:Move over to antiferromagnetic systems, e.g. the dimer:• Quantum dynamics of the Néel vector - harder to Quantum dynamics of the Néel vector - harder to

observe!observe!

The molecular approach is the The molecular approach is the keykey• Immense control over the magnetic unit Immense control over the magnetic unit

and its coupling to the environmentand its coupling to the environment

What do we currently understand? Quantum tunneling is extremely sensitive to SMM Quantum tunneling is extremely sensitive to SMM

symmetrysymmetry

•Transverse anisotropies provide tunneling matrix Transverse anisotropies provide tunneling matrix elementselements

Magnetization dynamics controlled by nuclear and Magnetization dynamics controlled by nuclear and electron spin-spin interactionselectron spin-spin interactions

•Fluctuations drive SMMs into and out of resonanceFluctuations drive SMMs into and out of resonance

Such interactions represent Such interactions represent unwanted source of unwanted source of decoherencedecoherence

What do we not understand? What are the dominant sources of quantum decoherence?What are the dominant sources of quantum decoherence?

What are typical decoherence times for various quantum What are typical decoherence times for various quantum states based on SMMs which could be useful?states based on SMMs which could be useful?

How can we reduce decoherence?How can we reduce decoherence?

Can we control the spin dynamics coherently?Can we control the spin dynamics coherently?

Pulsed/time-domain EPRPulsed/time-domain EPR

UF PhysicsUF Physics

Rachel EdwardsRachel EdwardsAlexey KovalevAlexey KovalevKonstantin PetukhovKonstantin Petukhov

Susumu TakahashiSusumu TakahashiJon LawrenceJon LawrenceNorman AndersonNorman AndersonTony WilsonTony WilsonCem KirmanCem Kirman

Shaela JonesShaela JonesSara MaccagnanoSara Maccagnano

UF ChemistryUF Chemistry

George ChristouGeorge Christou

Nuria Aliaga-Alcalde Nuria Aliaga-Alcalde Monica SolerMonica SolerNicole ChakovNicole ChakovSumit BhaduriSumit BhaduriMuralee MurugesuMuralee MurugesuAlina VinslavaAlina VinslavaDolos Foguet-AlbiolDolos Foguet-Albiol

UCSD ChemistryUCSD Chemistry

David HendricksonDavid Hendrickson

En-Che YangEn-Che YangEvan RumbergerEvan Rumberger

FSU ChemistryFSU Chemistry

Naresh DalalNaresh Dalal

Micah NorthMicah NorthDavid ZipseDavid ZipseRandy AcheyRandy AcheyChris RamseyChris Ramsey

NYU PhysicsNYU Physics

Andy KentAndy Kent

Enrique del BarcoEnrique del Barco

Many collaborators/students involvedMany collaborators/students involved ...illustrates the interdisciplinary nature of this work...illustrates the interdisciplinary nature of this work

Also:Also: Kyungwha Park (NRL) Kyungwha Park (NRL)Marco Evangelisti (Leiden)Marco Evangelisti (Leiden)Hans Gudel (Bern)Hans Gudel (Bern)Wolfgang Wernsdorfer (Grenoble) Wolfgang Wernsdorfer (Grenoble) Mark Novotny (MS State U)Mark Novotny (MS State U)Per Arne Rikvold (CSIT - FSU)Per Arne Rikvold (CSIT - FSU)