Some New Geometric Phase Effects in Mn 12 Variants
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Transcript of Some New Geometric Phase Effects in Mn 12 Variants
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