Stephen Hill NHMFL and Florida State University, Physics Outline of talk: Idea behind the title of this talk Nice recent example: Radical Ferromagnet Mononuclear.

Stephen HillNHMFL and Florida State University, Physics

Outline of talk:

• Idea behind the title of this talk• Nice recent example: Radical Ferromagnet

• Mononuclear nanomagnets based on Lanthanide ions• CW and pulsed EPR studies of Ho system• Coherent quantum tunneling dynamics

EPR Studies of Heavy Atom EPR Studies of Heavy Atom Molecule-Based MagnetsMolecule-Based Magnets

Stephen HillNHMFL and Florida State University, Physics

In collaboration with:

Radical Ferromagnets:Steven Winter and Richard Oakley, U. WaterlooSaiti Datta and Alexey Kovalev (NHMFL Postdocs)

Holmium polyoxometallate:Saiti Datta and Sanhita Ghosh (FSU/NHMFL postdoc/student)Eugenio Coronado and Salvador Cardona-Serra, U. Valencia, SpainEnrique del Barco, U. Central Florida

EPR Studies of Heavy Atom EPR Studies of Heavy Atom Molecule-Based MagnetsMolecule-Based Magnets

Heavy Atom Radical FerromagnetsHeavy Atom Radical Ferromagnets

Record:Tc = 17KHc = 0.15 T

Oak

ley

et a

l., J

AC

S 1

30,

1479

1 (2

008)

; JA

CS

131

, 71

12 (

2009

)

Tryptophan (Trp) radical in azurin, an electron transfer protein

S. Stoll, D. BrittUC Davis

• g tensor characteristic of microenvironment .

• Compare to electronic structure calculations.

• Crucial for systems with small g anisotropy (tryptophans, tetra-pyrroles, e.g., chloro-phylls, and organic photovoltaic materials)Stoll et al., JACS Stoll et al., JACS 132132, 11812 (2010); JACS , 11812 (2010); JACS 131131, 1986 (2009)., 1986 (2009).

Radicals well known to EPR spectroscopists

Radicals well known to EPR spectroscopists

Heavy Atom Radical FerromagnetsHeavy Atom Radical Ferromagnets

Most importantly: huge (record) Most importantly: huge (record) coercive field (1.4 kOe at 2 K)coercive field (1.4 kOe at 2 K)

7.8

8.1

8.4

8.7

9.0

Res

on

ance

fie

ld (

tesl

a)

Record:Tc = 17KHc = 0.15 T

1: HA = 0.8 T2: HA = 0.45 T

Heavy Atom Radical FerromagnetsHeavy Atom Radical Ferromagnets

Record:Tc = 17KHc = 0.15 T

Hubbard Hamiltonian with spin-orbit (Hubbard Hamiltonian with spin-orbit (ss) and hopping () and hopping (hh) perturbations) perturbations

Ishikawa et al.,

Mononuclear Lanthanide Single Molecule Magnets Mononuclear Lanthanide Single Molecule Magnets

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

Axial ligand-field: mJ = ±5I = 7/2 nuclear spin (100%)

Mononuclear Lanthanide Molecular Nanomagnets Based on Polyoxometalates

Mononuclear Lanthanide Molecular Nanomagnets Based on Polyoxometalates

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

~D4d

AlD

amen

et

al.,

AlD

amen

et

al.,

ErEr3+3+ and Ho and Ho3+3+

Exhibit some SMMExhibit some SMMcharacteristicscharacteristics

ErEr3+3+ compound compound

Mononuclear Lanthanide Molecular Nanomagnets Based on Polyoxometalates

Mononuclear Lanthanide Molecular Nanomagnets Based on Polyoxometalates

AlD

amen

et

al.,

0 2 0 0 4 0 4 4 4 0 6 0 4 6 42 2 4 4 4 4 6 6 6 6

ˆ ˆ ˆ ˆ ˆH A r O A r O A r O A r O A r O

D4d (≠ 45o)

Fits tomT &NMR

Mononuclear Lanthanide Molecular Nanomagnets Based on Polyoxometalates

Mononuclear Lanthanide Molecular Nanomagnets Based on Polyoxometalates

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

0

50

100

150

200

250

300

350

Ene

rgy

(cm

-1)

J projection mJ

Ho3+:[Xe]4f10

Ground state: mJ = ±4

AlD

amen

et

al., 0 2 0 0 4 0 0 6 0

2 2 4 4 6 6ˆ ˆ ˆH A r O A r O A r O

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

2 0 0 0 014 4 6 63

ˆ ˆ ˆˆ [ 1 ]zH D S S S B O B O D = 0.600 cm1, B0

4 = 6.94 ×103 cm1, B06 = 4.88 ×105 cm1

gJ = 5/4

Mononuclear Lanthanide Molecular Nanomagnets Based on Polyoxometalates

Mononuclear Lanthanide Molecular Nanomagnets Based on Polyoxometalates

Ho3+:[Xe]4f10

AlD

amen

et

al., 0 2 0 0 4 0 0 6 0

2 2 4 4 6 6ˆ ˆ ˆH A r O A r O A r O

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

2 0 0 0 014 4 6 63

ˆ ˆ ˆˆ [ 1 ]zH D S S S B O B O D = 0.600 cm1, B0

4 = 6.94 ×103 cm1, B06 = 4.88 ×105 cm1

gJ = 5/4 Other relevant details:Other relevant details:

•100% 100% II = 7/2 nuclear spin = 7/2 nuclear spin•Strong hyperfine couplingStrong hyperfine coupling

•Dilution: [HoDilution: [HoxxYY1-1-xx(W(W55OO1818))22]]9-9-

•NaNa++ charge compensation charge compensation

•HH22O solventO solvent

Mononuclear Lanthanide Molecular Nanomagnets Based on Polyoxometalates

Mononuclear Lanthanide Molecular Nanomagnets Based on Polyoxometalates

0.2 0.4 0.6 0.8

f ~ 50.4 GHz

Tra

nsm

issi

on (

arb.

uni

ts -

off

set)

Magnetic field (tesla)

10 K 8 K 6 K 4 K 2.2 K

B//c

Broad 8 line spectrum due to strong hyperfine coupling to Ho nucleus, I = 7/2

High(ish) frequency EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)High(ish) frequency EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)

0 100 200 300 400 500 600 700 800 900

-5200

-5150

-5100

-5050

magnetic field [mT]

ener

gy [G

Hz]

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

mJ = +4

mI

+1/23/27/2

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

3/27/2

Freq

uenc

y (G

Hz)

Magnetic Field (tesla)

B//c

1 K = 21 GHz1 cm-1 = 30 GHz

•Nominally (strongly) forbidden transitions: Nominally (strongly) forbidden transitions: mmJJ = = 4 4 +4, +4, mmII = 0 = 0

Nex

t ex

cite

d l

evel

Nex

t ex

cite

d l

evel

at l

east

20-

30 c

mat

lea

st 2

0-30

cm

-1-1

abo

veab

ove

•This suggests mixing (tunneling) of This suggests mixing (tunneling) of mmJJ states (no EPR for states (no EPR for ff > 100 GHz) > 100 GHz)

High(ish) frequency EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)High(ish) frequency EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)

0.0 0.2 0.4 0.6 0.8 1.0 1.2

f ~ 50.4 GHz T = 3 K

Tra

nsm

issi

on (

arb.

uni

ts -

off

set)

Magnetic field (tesla)

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

•Indicative of strong anisotropy associated with J = 8 ground state•Note: hyperfine splitting also exhibits significant anisotropy

Angle-dependence: [HoxY1-x(W5O18)2]9- single crystal (x =

0.25)

Angle-dependence: [HoxY1-x(W5O18)2]9- single crystal (x =

0.25)

-90 -60 -30 0 30 60 900.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

Mag

netic

fie

ld (

tesl

a)

Angle (degrees)

7/2

5/2

3/2

1/2

+1/2

+3/2

+5/2

+7/2

2 0 0 0 014 4 6 63

ˆ ˆ ˆ ˆˆ [ 1 ]z BH D S S S B O B O B g S J A I &&

D = 0.600 cm1, B04 = 6.94 ×103 cm1, B0

6 = 4.88 ×105 cm1

Full Matrix Analysis of the Angle-dependenceFull Matrix Analysis of the Angle-dependence

Ligand field parameters from: AlDamen et al., Inorg. Chem. 48, 3467 (2009)

gz = 1.06A = 835 MHz (0.0278 cm-1)

•Simulations assume isotropic g

•data do not constrain gxy so well

•Free ion g = 1.25

0 50 100 150 200 250 300 350 400

-5160

-5150

-5140

-5130

-5120

-5110

-5100

-5090

magnetic field [mT]

ener

gy [

GH

z]

0.0 0.1 0.2 0.3 0.4-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

E

nerg

y (c

m-1)

Magnetic field (tesla)

Standard CW X-band EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)Standard CW X-band EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)

Multi-frequency studies: does D4d parameterization hold water?

f ~ 9.5 GHz

0 50 100 150 200 250 300 350 400

-5160

-5150

-5140

-5130

-5120

-5110

-5100

-5090

magnetic field [mT]

ener

gy [

GH

z]

0.0 0.1 0.2 0.3 0.4-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

E

nerg

y (c

m-1)

Magnetic field (tesla)

Standard CW X-band EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)Standard CW X-band EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)

Multi-frequency studies: does D4d parameterization hold water?

f ~ 9.5 GHz

0 50 100 150 200 250 300 350 400-5170

-5160

-5150

-5140

-5130

-5120

-5110

-5100

magnetic field [mT]

ener

gy [

GH

z]

0.0 0.1 0.2 0.3 0.4-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

E

nerg

y (c

m-1)

Magnetic field (tesla)

Standard CW X-band EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)Standard CW X-band EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)

f ~ 9.5 GHz

4 4 4 4 414 4 42

ˆB O B S S D4d symmetry approximate → natural to add:

~9 GHz tunneling gap -

≠ 45o

0.0 0.1 0.2 0.3

Simulation Experiment

Inte

nsity

(ar

b. u

nits

- o

ffse

t)

Magnetic field (tesla)0.0 0.1 0.2 0.3

Simulation Experiment

Inte

nsity

(ar

b. u

nits

- o

ffse

t)

Magnetic field (tesla)

Standard B1 B0 configuration Parallel mode (B1//B0)

Standard CW X-band EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)Standard CW X-band EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)

T1 ~ 1 sT2 ~ 140 ns

Ho-Ho ~ 18År

Pulsed X-band EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)Pulsed X-band EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)

0 100 200 300

0.1 0.2 0.3 0.4 0.5 0.6 0.7

10

15

20

25

E

cho

ampl

itude

(ar

b. u

nits

)

Pulse length (ns)

B1 (arb. units)

Freq

uenc

y (M

Hz)T = 4.8 K

0 200 400 600 800 1000

Echo Intensity Exponential fit

Inte

nsity

(ar

b. u

nits

)

Hahn echo sequence

Rabi oscillations: remarkably long Rabi oscillations: remarkably long TT22

0 100 200 300

0.1 0.2 0.3 0.4 0.5 0.6 0.7

10

15

20

25

Ech

o am

plitu

de (

arb.

uni

ts)

Pulse length (ns)

B1 (arb. units)

Freq

uenc

y (M

Hz)

T = 4.8 K

TT22 ~ 140 ns ~ 140 ns

Ho-Ho ~ 18År

Pulsed X-band EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)Pulsed X-band EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)

0 200 400 600 800 1000

Echo Intensity Exponential fit

Inte

nsity

(ar

b. u

nits

)

Rabi oscillations: remarkably long Rabi oscillations: remarkably long TT22

Fe8

S = 10

Fe4

S = 5

CrCr77Ni (Ni (SS = 1): 0.2mg/mL, = 1): 0.2mg/mL, TT22 ~300 ns @ 5K ~300 ns @ 5KArdavan et al., PRL Ardavan et al., PRL 9898, 057201 (2007), 057201 (2007)

FeFe44: 0.5g/mL, 95 GHz and : 0.5g/mL, 95 GHz and BB = 0 = 0Schlegel et al., PRL Schlegel et al., PRL 101101, 147203 (2008), 147203 (2008)

FeFe88: 240 GHz and 4.6 T (: 240 GHz and 4.6 T (kkBBTT ~ 11.5 K) ~ 11.5 K)Takahashi et al., PRL Takahashi et al., PRL 102102, 087603 (2009), 087603 (2009)

607590

105120135150

0 100 200 300

T2 (

ns)

Echo intensity CW spectrum

EPR

Int

ensi

ty(a

rb. u

nits

- of

fset

)

Magnetic field (tesla)

Echo-detected spectrum is TEcho-detected spectrum is T22 weighted weighted

Spectrum Spectrum alsoalsosensitivesensitiveto pulseto pulsesequencesequence

Pulsed X-band EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)Pulsed X-band EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)

0 50 100 150 200 250 300 350 400

-5160

-5150

-5140

-5130

-5120

-5110

-5100

magnetic field [mT]

energ

y [GH

z]

0.0 0.1 0.2 0.3-1.00

-0.75

-0.50

-0.25

0.00

0.25

0.50

Ene

rgy

(cm

-1)

Magnetic field (tesla)

mI = 0mI = ±1

Competing anisotropies (Competing anisotropies (TUNNELINGTUNNELING): ): → → no longer obvious what is parallel/perpendicularno longer obvious what is parallel/perpendicular

Pulsed X-band EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)Pulsed X-band EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)

0df

dB

0 50 100 150 200 250 300 350 400

-5160

-5150

-5140

-5130

-5120

-5110

-5100

magnetic field [mT]

energ

y [GH

z]

0.0 0.1 0.2 0.3-1.00

-0.75

-0.50

-0.25

0.00

0.25

0.50

Ene

rgy

(cm

-1)

Magnetic field (tesla)

Pulsed X-band EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)Pulsed X-band EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)

Cancelation resonances → significant reduction in decoherenceCancelation resonances → significant reduction in decoherence

1 Moh

amm

ady

et a

l., P

hys.

Rev

. Le

tt.

105,

067

602

(201

0)

Bi (I = 9/2) in Si1Note: excitation bandwidthComparable to linewidth

0 50 100 150 200 250 300 350 400

-5160

-5150

-5140

-5130

-5120

-5110

-5100

magnetic field [mT]

energ

y [GH

z]

0.0 0.1 0.2 0.3-1.00

-0.75

-0.50

-0.25

0.00

0.25

0.50

Ene

rgy

(cm

-1)

Magnetic field (tesla)

Pulsed X-band EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)Pulsed X-band EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)

COHERENT QUANTUM TUNNELINGCOHERENT QUANTUM TUNNELING

Note: excitation bandwidthComparable to linewidth

Pulsed X-band EPR of [HoxY1-x(W5O18)2]9- (x = 0.1)Pulsed X-band EPR of [HoxY1-x(W5O18)2]9- (x = 0.1)

0 100 200 300 400

Echo detected CW spectrum

Inte

nsity

(ar

b. u

nits

- o

ffse

t)

Magnetic Field (mT)

Impurity incavity

•Sample not perfectly aligned; shift to consistent with simulationsSample not perfectly aligned; shift to consistent with simulations•Cancelation resonances now stronger than the standard ones!!Cancelation resonances now stronger than the standard ones!!•TT22 factor of two larger for cancelation resonances factor of two larger for cancelation resonances

Ho-Ho ~ 25ÅrT2 ~ 200 ns

0 1 2 3 4 5 6

In

tens

ity (

arb.

uni

ts)

Time (s)

Electron-Spin-Echo-Envelope-Modulation(ESEEM)

10-3 10-2 10-1102

103

Coh

eren

ce ti

me

- T 2

(ns

)

Concentration - x

1.2 1.2 ss

1/ 22T x

Pulsed X-band EPR: concentration dependencePulsed X-band EPR: concentration dependence

ESEEM frequencyESEEM frequencyConsistent with Consistent with Coupling to protonsCoupling to protons