stephen hill, saiti datta and sanhita ghosh, nhmfl and florida state university

Stephen Hill, Saiti Datta and Sanhita Ghosh,NHMFL and Florida State University

In collaboration with:Enrique del Barco, U. Central Florida; Fernando Luis, U. Zaragoza, Spain;Eugenio Coronado and Salvador Cardona-Serra, U. Valencia, Spain

EPR Studies of Quantum Coherent EPR Studies of Quantum Coherent Properties of Rare-Earth SpinsProperties of Rare-Earth Spins

•Where are we coming from?Where are we coming from?•Brief summary of 10 years of EPR studies of molecular magnets Brief summary of 10 years of EPR studies of molecular magnets

•Where are we going?Where are we going?•Simpler molecular magnets with improved functionalitySimpler molecular magnets with improved functionality

•EPR studies of a mononuclear rare-earth (HoEPR studies of a mononuclear rare-earth (Ho3+3+) molecule) molecule•Coherent manipulation of coupled Coherent manipulation of coupled SS, , LL (~ (~JJ) and ) and II (~ (~FF))

•Pure speculationPure speculation (or total nonsense?)(or total nonsense?)

Mn(III)

Mn(IV)

Oxygen

SS = (8 = (8 × 2) – (4 × 2) – (4 × 3/2× 3/2) ) SS = 10 = 10

S S = 3/2= 3/2

S S = 2= 2

The Drosophila of SMMs – MnThe Drosophila of SMMs – Mn1212

SS = 10 = 10

Simplest effective Simplest effective model: uniaxial model: uniaxial anisotropyanisotropy2ˆ ˆ ( 0)zDS D H

"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

2( )s sm D mE

"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

•Small barrier - Small barrier - DSDS22

•Superparamagnetic at Superparamagnetic at most temperaturesmost temperatures

•Magnetization blocked Magnetization blocked at low temperatures at low temperatures ((TT < 4 K) < 4 K)

E E DS2 10-100 K10-100 K

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

Magnetic anisotropy Magnetic anisotropy bistability, hysteresis bistability, hysteresisSimplest effective Simplest effective model: uniaxial model: uniaxial anisotropyanisotropy2ˆ ˆ ( 0)zDS D H

2( )s sm D mE

0.14 0.16 0.18 0.20 0.22

-4

-3

-2

-1

log()

1/T (K)

Chak

ov e

t al.,

J. A

m. C

hem

. Soc

. 128

, 697

5 (2

006)

.Re

dler

et a

l, Ph

ys. R

ev. B

80,

094

408

(200

9).

o = 2.0 × 10-9 sUeff = 70 K

AC AC data for [Mn data for [Mn1212OO1212(O(O22CCHCCH22Br)Br)1616(H(H22O)O)44]·Solvent]·Solvent΄ ΄

΄΄

΄

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:

Uneven spacingUneven spacingof peaksof peaks

We can measure transverse terms by rotating field into We can measure transverse terms by rotating field into xyxy-plane-plane

What can we learn from single-crystal HFEPR?What can we learn from single-crystal HFEPR?

A big problem with large moleculesA big problem with large molecules

•Full calculation for MnFull calculation for Mn1212 produces matrix of dimension 10 produces matrix of dimension 1088 ×× 10 1088

•Even after major approximation: dimension is 10Even after major approximation: dimension is 1044 × 10 × 1044

•Multiple exchange coupling parameters (Multiple exchange coupling parameters (JJss); anisotropy (LS-); anisotropy (LS-coupling); different oxidation and different symmetry sites.coupling); different oxidation and different symmetry sites.

S = 11

S = 9 S = 10

Mn12

S S = 10= 10

•Matrix dimension 21 × 21Matrix dimension 21 × 21

•JJss irrelevant (apparently)!! irrelevant (apparently)!!

•Ignores (10Ignores (1088 – 21) higher-lying – 21) higher-lying statesstates

SS = 10 = 10

But what is the physical origin of parameters But what is the physical origin of parameters obtained from EPR and other experiments obtained from EPR and other experiments

– – particularly those that cause MQT?particularly those that cause MQT?

To answer this.... To answer this.... ..study simpler molecules..study simpler molecules

Ni4: E.-C. Yang et al., Inorg. Chem. 44, 3836 (2005); A. Wilson et al., PRB 74, R140403 (2006).Mn3: P. Feng et al., Inorg. Chem. 46, 8126 (2008); T. Stamatatos et al., JACS 129, 9484 (2007). Mn6: C. Milios et al., JACS 129, 12505 (2007); R. Inglis et al., Dalton 2009, 3403 (2009).

II4Ni

SS44 symmetry symmetry

(2S + 1)4 = 81

2 2 2ˆ ˆ ˆ ˆ ˆ ˆ ˆij i j i zi i xi yi B i ii j i i

H J s s d s e s s B g s

@

III3Mn

MnIII

(2S + 1)3 = 125

3R

III6Mn

(2S + 1)6 = 15625

CentrosymmetricCentrosymmetric

Ueff = 45K

Ueff = 75K

Ishikawa et al.,

Mononuclear Lanthanide Single Molecule Magnets

Hund’s rule coupling for Ho3+: L = 6, S = 2, J = 8; 5I8

Ground state: mJ = ±5Nuclear spin I = 7/2 (100%)

[(tpaMes)Fe]−

1500 Oe 2.0 K

D = -39.6 cm-1 E = -0.4 cm-1

U = 42 cm-1 τ0 = 2 x 10-9 s

1.7 K

6.0 K

Mononuclear Transition Metal Single Molecule Magnets

Harris,Harmann,Reinhardt,Long

Hund’s rule coupling for Er3+: L = 6, S = 3/2, J = 15/2; 4I15/2

Nuclear spin I = 0, 7/2 (70%, 30%)

Coherent Quantum Dynamics in CaWO4:0.05% Er3+

Bertaina et al., PRL 103, 226402 (2009).Bertaina et al., Nat. Nanotech. 2, 39 (2007).

Rabi

Ho3+ – [Xe]4f10

Mononuclear Lanthanide Single Molecule Magnets Based on the Polyoxometalates

[Ln(W5O18)2]9- (LnIII = Tb, Dy, Ho, Er, Tm, and Yb)

~D4d


= 5/4

AlD

amen

et

al.,

Ho3+ – [Xe]4f10



Ground state: mJ = ±4

AlD

amen

et

al.,

Ho3+ – [Xe]4f10



-10 -8 -6 -4 -2 0 2 4 6 8 10-50

0

50

100

150

200

250

300

350

Ene

rgy

(cm

-1)

J projection - mJ

Ground state: mJ = ±4

AlD

amen

et

al.,

ErEr3+3+ and Ho and Ho3+3+

Exhibit SMMExhibit SMMcharacteristicscharacteristics

0.2 0.4 0.6 0.8

f ~ 50.4 GHz

Tra

nsm

issi

on (

arb.

uni

ts -

off

set)


10 K 8 K 6 K 4 K 2.2 K

High(ish) frequency EPR of [Ho0.25Y0.75(W5O18)2]9-

Eight line spectrum due to strong hyperfine coupling to 165Ho nucleus, I = 7/2

Well behaved EPR: nominally forbidden transitions mJ = -4 +4, mI = 0

B//c

High(ish) frequency EPR of [Ho0.25Y0.75(W5O18)2]9-

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-60

-40

-20

0

20

40

60

mJ = -4 or m

J' = -1/2

mJ = +4 or m

J' = +1/2

mI

+1/2-3/2

-7/2

+3/2+5/2+7/2

-3/2

-7/2F

requ

ency

(G

Hz)

Magnetic Field (tesla)

B//c

Eight line spectrum due to strong hyperfine coupling to 165Ho nucleus, I = 7/2

Well behaved EPR: nominally forbidden transitions mJ = -4 +4, mI = 0

1K = 21GHz

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

f ~ 50.4 GHz T = 3 K

Tra

nsm

issi

on (

arb.

uni

ts -

off

set)


-145 -135 -125 -115 -105 -95 -85 -75 -65 -55 -45 -35 -25 -15 -5 +5 +15 +25 +35 +45

Angle-dependent EPR of [Ho0.25Y0.75(W5O18)2]9-

Very strong g-anisotropy associated with transitions mJ = -4 +4Note: hyperfine interaction also exhibits significant anisotropy

-135 -90 -45 0 45

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

Mag

netic

fie

ld (

T)

Angle (degrees)

mI

+7/2 +5/2 +3/2 +1/2 -1/2 -3/2 -5/2 -7/2



( , ) ( ) ( )B IE B g B A m

-135 -90 -45 0 45

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

Mag

netic

fie

ld (

T)

Angle (degrees)

mI

+7/2 +5/2 +3/2 +1/2 -1/2 -3/2 -5/2 -7/2



1( )

( )res IB

hfB A m

g

-135 -90 -45 0 45

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

Mag

netic

fie

ld (

T)

Angle (degrees)

mI

±7/2 ±5/2 ±3/2 ±1/2

2 2 2 2( ) cos sing g g



1

( )resB

hfB

g

-135 -90 -45 0 45

0.4

0.5

0.6

0.7

0.8

Mag

netic

fie

ld (

T)

Angle (degrees)

mI

±7/2 ±5/2 ±3/2 ±1/2

2 2 2 2( ) cos sing g g



1

( )resB

hfB

g

-135 -90 -45 0 45

0.4

0.5

0.6

0.7

0.8

Mag

netic

fie

ld (

T)

Angle (degrees)

mI

±7/2 ±5/2 ±3/2 ±1/2

2 2 2 2( ) cos sing g g

8.545 0.010

0.96 0.1

Note: 1.25J

g

g

g



1

( )resB

hfB

g

-180 -135 -90 -45 0 45 90

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

Mag

netic

fie

ld (

T)

Angle (degrees)

mI

+7/2 +5/2 +3/2 +1/2 -1/2 -3/2 -5/2 -7/2



Add ( ) IA m

A 53 mT,A 100mT

X-band (9GHz) Electron Spin Echo EPR of [HoxY1-x(W5O18)2]9-

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8-60

-40

-20

0

20

40

60

mJ = -4 or m

J' = -1/2

mJ = +4 or m

J' = +1/2

mI

+1/2-3/2

-7/2

+3/2+5/2+7/2

-3/2

-7/2F

requ

ency

(G

Hz)


B//c

Recall anisotropic hyperfine interactionLikely neither J or I are good quantum numbers; deal with F = J + I

0 100 200 300

0.1 0.2 0.3 0.4 0.5 0.6 0.7

10

15

20

25

0.00 0.05 0.10 0.15 0.20 0.25

Ech

o am

plitu

de (

arb.

uni

ts)

Pulse length (ns)

B1 (arb. units)

Freq

uenc

y (M

Hz)

Magnetic field (T)

Inte

nsity

(a.

u.)


x = 0.25

T = 4.8 K

Impurity

cw EPR

24 ns 120 ns 12 ns200 nst

Hahn echosequence

T1 ~ 1 sT2 ~ 180 ns

Ho-Ho ~ 18År

0 100 200 300 400

180 deg 190 deg 200 deg 210 deg 220 deg 230 deg 240 deg 250 deg 260 degAttenuation : 7 dB

Time (nsec)In

tens

ity (

arb.

uni

ts)

180 195 210 225 240 255

6

7

8

9

10

11

12

Rab

i fre

quen

cy (

MH

z)

Angle (degrees)


Rabi oscillations also exhibit the same g-anisotropy

0 100 200 300 400

Inte

nsity

(ar

b. u

nits

)

Magnetic Field (mT)

Echo detected EPR CW

Sample: Ho (25%)T = 4.8 K


ESE is TESE is T22 weighted weighted

Ho-Ho ~ 18År

Source of the additional peaks due to strong to 165Ho nuclear spin

Badly behaved EPR: transitions mJ = -4 +4, mI = 0, ±1

0.2 0.4 0.6

-20

0

20

mJ = -4 or m

J' = -1/2

mJ = +4 or m

J' = +1/2

mI

-3/2-5/2

-7/2

-3/2-1/21/2 -5/2

-7/2

Fre

quen

cy (

GH

z)



Schematic:Not an exactCalculation ofspectrum

0 100 200 300 400

ED CW

Inte

nsity

(ar

b. u

nits

- o

ffse

t)

Magnetic Field (mT)

10 % sample 25 % sample

0 100 200 300 400

E4E3E2E1P4

P3

P2P1

ED CWIn

tens

ity (

arb.

uni

ts -

off

set)

Magnetic Field (mT)

E1E2

E3

E4

P1

P2 P3

Ho-Ho ~ 18ÅrHo-Ho ~ 25År

Comparing [HoxY1-x(W5O18)2]9- 10% and 25% samples

Important to recall: ESE is TImportant to recall: ESE is T22 weighted weighted

Comparison of T2 values :

Peak T2 (nsec)

E1 149.71064

P1’ 82.65335

P1 81.23469

E2 123.75861

P2’ 81.08677

P2 80.91722

E3 112.07676

P3’ 82.06742

P3 94.05755

E4 153.39765

Peak T2 (nsec)

E1

P1’

P1 193.89

E2

P2’

P2 146.55

E3

P3’

P3 177.36

E4

10 % sample 25 % sample

Sequence : 12-120-24 Attenuation : 7 dB for 10% sample; 6 dB for 25% sample

Comparing [HoxY1-x(W5O18)2]9- 10% and 25% samples

0 100 200 300 400 500

P4

P3P2

P1

10 dB attenuation

Inte

nsity

(ar

b. u

nits

- o

ffse

t)

Magnetic Field (mT)

12-120-24 12-120-20 12-120-16 12-120-12 8-108-12 8-108-8 4-104-8

25% [HoxY1-x(W5O18)2]9- : splitting of the main (P) peaks

0 100 200 300 400 500

P4

P3P2

P1

Sequence : 12-120-24

Inte

nsity

(ar

b. u

nits

- o

ffse

t)

Magnetic Field (mT)

17dB 15dB 12.5dB 10dB 9dB 8dB 7dB 6dB


0 100 200 3000

25

50

75

100

125

150

Sequence : 12-120-24Attenuation : 6dB

Inte

nsity

(ar

b. u

nits

) an

d T

2 (ns

)

Magnetic Field (mT)


Lehmann, Gaita-Arino, Coronado, Loss,

•Coherent nutation of the ground-state magnetic moment deriving from crystal-field effects acting on ~J = ~L + ~S (and ~J + ~I) is not yet well understood.

•For Ho, the hyperfine coupling is strong, i.e. the nuclear spin is coherently coupled to the electron spin during nutation.

•A magnetic moment much larger than 1/2 allows spin manipulations in low driving field-vectors (amplitude and direction).

•Rare-earth polyoxometallates are stable outside of a crystal, and may be scalable and addressable on surfaces, e.g. via an STM.

Why do we care?Why do we care?

Variation of t2 versus temperature (4.8K – 9K) at 3 fields (A=0deg):

4 5 6 7 8 990

100

110

120

130

140

150

t2 (

nsec

)

Temperature (K)

645 G 1260 G 1875 G

Data was taken at 10K too, but those plots show huge errors in fitting

4 5 6 7 8 9 10

400

500

600

700

800

900

1000

1100

t1 (

nsec

)

Temperature (K)

Variation of t1 versus temperature (4.8K – 10K) at 1875G (A=0deg):

T1 measurements were also done at 645G and 1260G, but those are not includedin this plot since they do not show the expected variation : some of the plots have significantly large error, I will try to improve the fitting if possible and check if they show better results

0 500 1000 1500 2000

Data: T2180DEG374G_BModel: ExpDec1 Chi^2/DoF = 988043070.97295R^2 = 0.99359 y0 140390.5799 ±4254.70913A1 1815051.63822±18557.49911t1 149.71064 ±2.64064

Inte

nsity

(ar

b. u

nits

)

Time (nsec)

Peak E1

0 500 1000 1500

Inte

nsity

(ar

b. u

nits

)

Time (nsec)

Data: T2180DEG795G_BModel: ExpDec1 Chi^2/DoF = 751697060.45728R^2 = 0.95307 y0 129081.31328 ±3239.56652A1 705238.92155 ±20271.12244t1 81.23469 ±3.87681

Peak P1

0 500 1000 1500

Inte

nsity

(ar

b. u

nits

)

Time (nsec)


0 500 1000 1500

Inte

nsity

(ar

b. u

nits

)

Time (nsec)


Ho 10% sample

Peak E3 Peak P3

0 500 1000 1500 2000

Time (nsec)

Data: T212120246DB_BModel: ExpDec1 Chi^2/DoF = 1193755876.82889R^2 = 0.99522 y0 40860.6835 ±2935.86354A1 2826688.71937 ±18324.7136t1 193.89889 ±2.00646

Inte

nsity

(ar

b. u

nits

)Ho 25% sample

0 500 1000 1500 2000

Inte

nsity

(ar

b. u

nits

)

Time (nsec)

Data: T212120246DB2_BModel: ExpDec1 Chi^2/DoF = 1535776552.72851R^2 = 0.99699 y0 88732.17877 ±4535.64537A1 3458553.82005 ±21582.01422t1 177.35667 ±1.86226

Peak P1 Peak P3

stephen hill, saiti datta and sanhita ghosh, nhmfl and florida state university

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