Magnetic Quantum Tunneling: Insights from Molecules and Magnetic Resonance

1
Magnetic Quantum Tunneling Insights from
Molecules and Magnetic Resonance
PART I Introduction to single-molecule
magnets -Magnetic anisotropy, bistability and
hysteresis -Chemical control of nanoscale
magnetism -Magnetic quantum tunneling (MQT) and
interference PART II Application of
high-field/frequency EPR -Overview of the
technique -EPR as a probe of the symmetry effects
and MQT -Disassembling and reassembling a
single-molecule magnet
Supported by US National Science Foundation,
Research Corporation, NHMFL (IHRP) University
of Florida
2
Nano-scale Single- Molecule Magnets
Magnetic information processing with individual
molecules?
1 Nano- meter
Mn12

• Molecules provide immense control
• Rational design
• Multi-functionality
• Monodisperse arrays

3
Energy
DE K Volume ? local anisotropy
number of spins K ? anisotropy energy
density
DE
4
Energy
DE K Volume ? local anisotropy
number of spins K ? anisotropy energy
density
B
5
The Mn12 single-molecule magnet
High symmetry S4 site symmetry I4 space
group (crystals)
Mn(III)
1 nm
Mn(IV)
Oxygen
Mn12O12(O2CCH2But)16(MeOH)4MeOH
Mn12-acetate (Lis - 1980) Mn12-tBuAc (Murugesu
2005, unpublished)
6
The Mn12 single-molecule magnet
Magnetic anisotropy ? bistability, hysteresis
Mn12O12(O2CCH2But)16(MeOH)4MeOH
First observed in Mn12-acetate Friedman et al.,
PRL (1996) Thomas et al., Nature (1996).

• Ensemble average
• Hysteresis, T lt 4K
• Discrete steps
• Evidence for magnetic quantum tunneling

7
Christou group (U of FL) Angew. Chem. (2004)
8
Molecules provide immense control the future?
Coupled molecules
Mn4O3Cl4(O2CEt)3(py)32
S1
J
Mn42
S2
Mimics two coupled Qbits coherent coupled
dynamics observed by EPR
S. Hill, Science 302, 1015 (2003)
9
The giant spin approximation
S 10
Magnetic anisotropy ? bistability, hysteresis
10
Quantum effects at the nanoscale (S 10)
21 discrete ms levels
Thermal activation
11
Quantum effects at the nanoscale (S 10)
21 discrete ms levels
Thermal activation
12
Quantum effects at the nanoscale (S 10)
Break axial symmetry
HT ? interactions which do not commute with Sz
Thermally assisted quantum tunneling
13
Quantum effects at the nanoscale (S 10)
Strong distortion of the uniaxial anisotropy

• Temperature-independent quantum relaxation as T?0

Tunnel splitting a measure of tunneling rate
14
Evidence for magnetic quantum tunneling (MQT)
Mn30 one of the largest single-molecule magnets
displaying a temperature independent relaxation
rate
W. Wernsdorfer, G. Christou, et al.,
cond-mat/0306303
15
Application of a longitudinal magnetic field
Spin projection - ms
"down"
"up"
Several important points to note

• Applied field represents another source of
  transverse anisotropy.
• Zeeman interaction contains odd powers of Sx and
  Sy (S and S- ).

16
Application of a longitudinal magnetic field
Spin projection - ms
"down"
"up"
Several important points to note

• Applied field represents another source of
  transverse anisotropy.
• Zeeman interaction contains odd powers of Sx and
  Sy (S and S- ).

Increasing field
System on resonance
17
Application of a longitudinal magnetic field
25
Energy (kB)
-25
-50
18
Hysteresis and magnetization steps
Mn12-tBuAc
This hysteresis loop represents an ensemble
average of the response of 1023 molecules
Step height a measure of tunnel splitting (Do),
or MQT probability
First observed Friedman et al., PRL
(1996) (Mn12-acetate) Thomas et al., Nature (1996)
Wernsdorfer, PRL 96, 057208 (2006)
19
Contrasting S 10 systems symmetry is key
z-axis is out of the screen
Wieghardt (1984)
Fe8 S (6 x 5/2) - (2 x 5/2) 10
Mn12-tBuAc, S 10
20
Fe8, S 10
Mn12-tBuAc, S 10
D ? 0.2 K
D ? 0.6 K
D/E ? 5
115 GHz or 5.5 kB
300 GHz or 14.4 kB

• To first-order, HT mixes states with Dms k,
  where k is the power to which S or S- appear in
  HT.

21
Application of a transverse magnetic field
Easy
up
down
Medium
Bx
Topological phase like Aharonov-Bohm phase
Hard
Biaxial system Fe8
Possibility of quantum phase interference A.
Garg. Europhys. Lett. 1993, 22205
22
Direct measure of Do in Fe8 Landau-Zener method
Longitudinal field (Bz) sweeps
Static transverse field
Energy/D
Do (10-7 K)
Parity effect
Bx (tesla)
gmBBz/D
P exp(-??o2/2??o?)
Wernsdorfer, Sessoli, Science 284, 133 (1999).
23

• PART II Application of
• high-field/frequency EPR

24
What can we learn from high-field/frequency EPR?
field//z
z, S4-axis
Hz
25
FFF High-frequency, high-field, high-fidelity EPR
Commercial
Only home built NHMFL, UF, plus few others world
wide
26
A. Broad-band, high-frequency

• Quasi-optical setup at University of Florida
• continuous coverage from 8 - 715 GHz
• Sweepable sources and multipliers (Schottkys)
• YIGs (8-18 GHz) Gunns (68-102GHz)
• Associated with vector network analyzer

27
B. High fields
BaCuSi2O6
IHRP
Sebastian et al., cond-mat/0606244 also PRB RC
(in press)

• Instrumentation developed at UF is compatible
  with the DC resistive facility in Tallahassee
• We also have a 17T SC magnet at UF

28
C. High fidelity
Cavities

• TE011 52 GHz (up to 400 GHz)
• (Diameter ? Height 0.3'' ? 0.3'')
• Q 25,000 (TE011, 4.2 K)
• Resolution lt 0.2o (lt 0.1o PPMS)

1st Generation 25 tesla, 4He system
2nd Generation 45 tesla, 3He system
1
3/4
Mola et al., Rev. Sci. Inst. 71, 186
(2000). Takahashi et al., Rev. Sci. Inst. 76,
023114 (2005).
29
Single-crystal, high-field/frequency EPR
How on earth are we going to measure transverse
terms (Do Hz)?
field//z
z, S4-axis
Hz
30
Single-crystal, high-field/frequency EPR
Rotate field in xy-plane and look for symmetry
effects
In high-field limit (gmBB gt DS), ms represents
spin-projection along the applied field-axis
31
Hard-plane rotations for Mn12-acetate
f 51.3 GHz T 15 K
JLTP 140, 119 (2005)
Data for Mn12-acetate in S. Hill et al., PRL 90,
217204 (2003)
32
Determination of transverse crystal-field
interactions
Mn12-acetate
Hard-plane (xy-plane) rotations
33
Determination of transverse crystal-field
interactions
Mn12-acetate
34
Intrinsic disorder lowers the local symmetry
Acetic acid solvent in structure

• 50 of molecules with S4 symmetry (intrinsic
  Mn12 symmetry)
• Remainder have rhombic symmetry 25 and 25 with
  orthogonal hard axes

A. Cornia et al., PRL 89, 257201 (2002) S. Hill
et al., PRL 90, 217204 (2003) E. del Barco et
al., PRL 91, 047203 (2003)
35
(No Transcript)
36
Spin Hamiltonian parameters for Mn12-tBuAc
Spectroscopists Hamiltonian H DSz2 B40Ô40
B44Ô44
Physicists Hamiltonian H DSz2 BSz4 C(S4
S-4)
g// 2 g? 1.94

• D, B40, g// from easy axis data
• B44 from hard plane rotations
• g? from perpendicular data

JAP 97, 10M510 (2005)
37
Why use a giant spin approximation?
Mn12
S 11
S 9

• Full Hilbert space for Mn12 is about 108 108
• Even after major approximation Hilbert space is
  104 104
• Multiple exchange coupling parameters (Js)
  anisotropy (LS-coupling) different oxidation and
  different symmetry sites.

But what is the physical origin of parameters
obtained from EPR and other experiments
particularly those that cause MQT?
38
Lets simplify matters a Ni4 cube
No solvent in the structure!

• Ni ions couple ferro-magnetically giving S 4
• Giant spin matrix is only (2S 1)2 9 x 9

S4 symmetry (like Mn12)
Ni(hmp)(dmb)Cl4
39
Lets simplify matters a Ni4 cube

• NiII ion Hamiltonian matrix is only 3x3!!
• Only 2nd order anisotropy

No solvent in the structure!
S4 symmetry (like Mn12)
How does one get 4th order molecular anisotropy
from 2nd order local anisotropy
40
Take the molecule apart....

• Take advantage of the fact that Ni can be
  exchanged for Zn

Ni0.02Zn0.98(hmp)(dmb)Cl4
8
...measure it...
d -5.30(5) cm-1 e 1.20(1) cm-1 g//
2.30(5) tilt 15o
41
....then put it back together again numerically

• 81 81 matrix
• Reasonably well isolated S 4 state

42
J and the 4th-order anisotropy
2.7 to 3 cm-1
J
J
4th order cause of MQT

• No transverse anisotropy if J is infinite (S an
  exact quantum number)
• 2nd order is symmetry forbidden
• Finite J ? mixing of S 4 into S lt 4 states
  leads to higher order anisotropy

43
Summary

• Single-molecule magnets provide fascinating
  insights into the effects of quantum mechanics on
  magnetism at the nanoscale
• High-field, high-frequency EPR provides a
  powerful tool for probing the quantum properties
  of single-molecule magnets

Students Susumu Takahashi John Lee Jon
Lawrence Tony Wilson Saiti Datta Sung Su
Kim Amalia Betancur- Rodriguez Emmitt Thompson
Collaborators Naresh Dalal (FSU) George Christou
(UF) Dave Hendrickson (UCSD) Andy Kent
(NYU) Laurie Thompson (Memorial U.,
CA) Kyungwha Park (VT) Spyros Perlepes
(Patras, Greece) Motohiro Nakano (Osaka)