Some New Geometric Phase Effects in Mn12 Variants

Jonathan FriedmanEduardo H. da Silva Neto

Michael Foss-FeigAmherst College

Funding: NSF, Research Corporation and Amherst College Dean of Faculty

Christos LampropoulosGeorge ChristouUFL - Chemistry

Nurit AvrahamYuri MyaesoedovHadas ShtrikmanEli ZeldovWeizmann Institute of Science

Mn12 Ac

The Effect of a Transverse Field• The tunneling rate for a particular pair of resonant

levels depends on the transverse field (H┴).

• H┴ increases the tunneling rate and reduces the barrier.

-10-9 9

10

Thermal

Activation

New

Bar

rier

D. A. Garanin and E. M. Chudnovsky, Phys. Rev. B 56, 11 102 (1997)J. R. Friedman, Phys. Rev. B, 57, 10291 (1998)

Interference between Tunneling Paths in Fe8

0 0.2 0.4 0.6 0.8 1 1.2 1.40.1

1

10

Tunn

el s

plitt

ing

²(10

-7 K

)

Magnetic transverse field (T)

M = -10 -> 10

0°

7°

20° 50° 90°

W. Wernsdorfer and R. Sessoli, Science, 1999.

Easy axis

Hard axis

Z

XH

A

B

Solid Angle

Theoretical Prediction: A. Garg., EPL, 1993.

Predicted Interference Effect for Mn12

Park and Garg, PRB, 2002

Two positions of C deduced from X-ray diffraction → induced 2nd order anisotropy

ESR spectrum as a function of azimuthal angle. (Edwards, et al., PRL, 2003)

Solvent Disorder in Mn12Ac

Acetic acid of solvation

Cornia, et al., PRL, 2002

Angle-selected relaxation rate. (del Barco, et al., PRL, 2003)

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

-30 -20 -10 0 10 20 30

2.0 K2.2 K2.4 K2.6 K2.8 K

M (

emu)

H (kOe)

A new SMM - Mn12 tBuAc

• Mn12-tBuAc has less solvent disorder and weaker dipole interactions.

S. Hill et al., J. Appl. Phys. 97 (2005).W. Wernsdorfer et al. Phys. Rev. Lett. 96, 057208 (2006).A.-L. Barra et al., JACS, 129, 10754 (2007).

Mn12-tBuAcMn12-Ac

Sample is rotated to position 1Large component of magnetic field along easy axis

Lower well populated

Sample is rotated to position 2Small component of magnetic field along easy axis

Quasi-exponential decay in magnetization.

Controlling the Relaxation Rate of Mn12-tBuAc with a Transverse Field

Large component of magnetic field transverse to easy axis

position 1 position 2

Applied Magnetic

Field

θ

T = 2.98(3) K HT = 4200 Oe

HL=-500 Oe

Longitudinal Field Rate Distribution

T = 3.21 (3) K HT = 4800 OeON Resonance Relaxation Rate

OFF Resonance Relaxation Rate

-10-9 9

10

Thermal

Activation

T = 3.21 (3) K

Rates on and off resonance

Plateaus indicate dominant tunneling resonance

• Plateaus (much flatter!) in the off-resonance relaxation.

• Steps and plateaus occur at different fields on and off resonance

On-resonance Off-resonance

Predicted Dependence of Relaxation Rate on Transverse Field

D. Garanin, arXiv:0805.0391 HS Bz gDS 2H

On resonance

Off resonance

Now Add Transverse Anisotropy (Fourth Order!)

0.0001

0.001

0.01

0.1

1

0 2000 4000 6000 8000 1 104

1.2 104

HL = 1000

HT (Oe)

T = 3.1 K

HT along hard axis.

)( 4442 SSCgBSDS Bzz HSH

S. Hill et al., J. Appl. Phys. 97, 10M510 (2005)A.-L. Barra et al., JACS, 129, 10754 (2007)

0.0001

0.001

0.01

0.1

1

10

0 2000 4000 6000 8000 1 104

1.2 104

HT (Oe)

m = 4

m = 3

m = 2

0.0001

0.001

0.01

0.1

1

10

0 2000 4000 6000 8000 1 104

1.2 104

HT (Oe)

m = 4

m = 3

m = 2

Calculated Tunnel Splittings

Park and Garg, PRB, 2002

Full Data vs Simulations

400 200 0 200 400

1 .0

0 .5

5 .0

0 .1

10 .0

50 .0

T = 3.21(3) K

Predicted Pressure-Induced Interference Effect

M. S. Foss-Feig and JRF, ArXiv: 0809.2289

• Measured relaxation rate as a function of transverse field in highly symmetric Mn12-tBuAc.• Steps and plateaus in the relaxation rate as a function of transverse field both on and off resonance.• Off-resonance results appear to be a remnant of a geometric-phase interference effect. • Predicted new interference effect induced by uniaxial pressure.

Conclusions