EPR Studies of Heavy Atom Molecule-Based Magnets
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Transcript EPR Studies of Heavy Atom Molecule-Based Magnets
EPR Studies of Heavy Atom
Molecule-Based Magnets
Stephen Hill
NHMFL 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
Molecule-Based Magnets
Stephen Hill
NHMFL and Florida State University, Physics
In collaboration with:
Radical Ferromagnets:
Steven Winter and Richard Oakley, U. Waterloo
Saiti 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, Spain
Enrique del Barco, U. Central Florida
Record:
Tc = 17K
Hc = 0.15 T
Oakley et al., JACS 130, 14791 (2008); JACS 131, 7112 (2009)
Heavy Atom Radical Ferromagnets
Radicals well known to EPR spectroscopists
Tryptophan (Trp) radical in azurin, an electron transfer protein
g-value
2.0040 2.0035 2.0030 2.0025 2.0020 2.0015
gz
f = 695 GHz
S. Stoll, D. Britt
UC Davis
Tryptophan radical EPR
Hydrophobic pocket
Solvent exposed
24.770
gx
gy
24.780
24.790
24.800
Magnetic field (tesla)
Stoll et al., JACS 132, 11812 (2010); JACS 131, 1986 (2009).
• g tensor characteristic of
microenvironment .
• Compare to electronic
structure calculations.
• Crucial for systems with
small g anisotropy
(tryptophans, tetrapyrroles, e.g., chlorophylls, and organic
photovoltaic materials)
Heavy Atom Radical Ferromagnets
Resonance field (tesla)
Record:
Tc = 17K
Hc = 0.15 T
Most importantly: huge (record)
coercive field (1.4 kOe at 2 K)
9.0
8.7
8.4
8.1
7.8
1: HA = 0.8 T
2: HA = 0.45 T
Heavy Atom Radical Ferromagnets
Record:
Tc = 17K
Hc = 0.15 T
Hubbard Hamiltonian with spin-orbit (s) and hopping (h) perturbations
Mononuclear Lanthanide Single Molecule Magnets
Ishikawa et al.,
Hund’s rule coupling for Ho3+:
L = 6, S = 2, J = 8; 5I8
Axial ligand-field: mJ = ±5
I = 7/2 nuclear spin (100%)
Mononuclear Lanthanide Molecular Nanomagnets
Based on Polyoxometalates
[Ln(W5O18)2]9- (LnIII = Tb, Dy, Ho, Er, Tm, and Yb)
AlDamen et al.,
~D4d
Mononuclear Lanthanide Molecular Nanomagnets
Based on Polyoxometalates
Er3+ compound
AlDamen et al.,
Er3+ and Ho3+
Exhibit some SMM
characteristics
Mononuclear Lanthanide Molecular Nanomagnets
Based on Polyoxometalates
AlDamen et al.,
Fits to
cm T &
NMR
D4d (f ≠ 45o)
Hˆ A20 r 2 Oˆ 20 A40 r 4 Oˆ 40 A44 r 4 Oˆ 44 A60 r 6 Oˆ60 A64 r 6 Oˆ64
Mononuclear Lanthanide Molecular Nanomagnets
Based on Polyoxometalates
Hund’s rule coupling for Ho3+: L = 6, S = 2, J = 8; 5I8
gJ = 5/4
Ground state: mJ = ±4
350
-1
Energy (cm )
300
Ho3+:
[Xe]4f10
250
200
150
100
50
0
-50
-8
-6
-4
-2
0
2
4
6
AlDamen et al.,
J projection mJ
0
0 4
0 0 ˆ 00 6 0ˆ ˆ
00
2 2 1ˆ 0
ˆ
ˆ
ˆ
ˆ
O
r O6 6
HH DA
[S2 rz
S SA4 r1
] OB
4 4OA
46 B6 O
3 2
D = 0.600 cm1, B04 = 6.94 ×103 cm1, B06 = 4.88 ×105 cm1
8
Mononuclear Lanthanide Molecular Nanomagnets
Based on Polyoxometalates
Hund’s rule coupling for Ho3+: L = 6, S = 2, J = 8; 5I8
gJ = 5/4
AlDamen et al.,
Ho3+:
[Xe]4f10
Other relevant details:
•100% I = 7/2 nuclear spin
•Strong hyperfine coupling
•Dilution: [HoxY1-x(W5O18)2]9•Na+ charge compensation
•H2O solvent
0
0 4
0 0 ˆ 00 6 0ˆ ˆ
00
2 2 1ˆ 0
ˆ
ˆ
ˆ
ˆ
O
r O6 6
HH DA
[S2 rz
S SA4 r1
] OB
4 4OA
46 B6 O
3 2
D = 0.600 cm1, B04 = 6.94 ×103 cm1, B06 = 4.88 ×105 cm1
High(ish) frequency EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)
Transmission (arb. units - offset)
Broad 8 line spectrum due to strong hyperfine coupling to Ho nucleus, I = 7/2
f ~ 50.4 GHz
10 K
6K
2.2 K
B//c
0.2
0.4
0.6
Magnetic field (tesla)
8K
4K
0.8
High(ish) frequency EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)
•Nominally (strongly) forbidden transitions: mJ = 4 +4, DmI = 0
•This suggests mixing (tunneling) of mJ states (no EPR for f > 100 GHz)
-5050
mI
mJ = +4
40
Frequency
energy [GHz](GHz)
Next excited level
at least 20-30 cm-1
above
60
-5100
20
1 K = 21 GHz
1 cm-1 = 30 GHz
0
-20
-5150
-40
B//c
+7/2 +5/2
+3/2
3/2
7/2
7/2
3/2
mJ = 4
+1/2
-60
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
-5200
Magnetic Field (tesla)
0
100
200
300
400
500
600
700
800
900
Angle-dependence: [HoxY1-x(W5O18)2]9- single crystal (x = 0.25)
Transmission (arb. units - offset)
•Indicative of strong anisotropy associated with J = 8 ground state
•Note: hyperfine splitting also exhibits significant anisotropy
0.0
f ~ 50.4 GHz
T=3K
-145
-135
-125
-115
-105
-95
-85
-75
-65
-55
-45
-35
-25
-15
-5
+5
+15
+25
+35
+45
0.2
0.4
0.6
0.8
Magnetic field (tesla)
1.0
1.2
Full Matrix Analysis of the Angle-dependence
Hˆ D[Sˆz2 13 S S 1] B40Oˆ40 B60Oˆ60 B B g Sˆ J A I
1.1
Magnetic field (tesla)
7
1.0
/2
0.9
/2
5
3
/2
0.8
1
/2
0.7
1
+ /2
0.6
3
+ /2
0.5
5
+ /2
0.4
7
+ /2
0.3
0.2
gz = 1.06
A = 835 MHz
(0.0278 cm-1)
•Simulations assume
isotropic g
•data do not constrain
gxy so well
•Free ion g = 1.25
-90
-60
-30
0
30
60
90
Angle (degrees)
D = 0.600 cm1, B04 = 6.94 ×103 cm1, B06 = 4.88 ×105 cm1
Ligand field parameters from: AlDamen et al., Inorg. Chem. 48, 3467 (2009)
Standard CW X-band EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)
Multi-frequency studies: does D4d parameterization hold water?
1.5
-5090
-5100
-1
Energy
(cm )
energy [GHz]
1.0
f ~ 9.5 GHz
-5110
0.5
-5120
0.0
-5130
-0.5
-5140
-1.0
-5150
-5160
-1.5
0.0
0
50
0.1
100
0.2
150
200
250
magnetic field [mT]
0.3
300
Magnetic field (tesla)
350
0.4
400
Standard CW X-band EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)
Multi-frequency studies: does D4d parameterization hold water?
1.5
-5090
-5100
-1
Energy
(cm )
energy [GHz]
1.0
f ~ 9.5 GHz
-5110
0.5
-5120
0.0
-5130
-0.5
-5140
-1.0
-5150
-5160
-1.5
0.0
0
50
0.1
100
0.2
150
200
250
magnetic field [mT]
0.3
300
Magnetic field (tesla)
350
0.4
400
Standard CW X-band EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)
ˆ 4 1 B4 S 4 S 4
D4d symmetry approximate → natural to add: B44O
4
2 4
1.5
-5100
~9 GHz tunneling gap - D
1.0
f ~ 9.5 GHz
-1
Energy (cm )
-5110
energy [GHz]
-5120
-5130
-5140
0.5
0.0
f ≠ 45o
-0.5
-5150
-1.0
-5160
-5170
-1.5
0.0
0
50
0.1
100
0.2
150
200
magnetic field [mT]
250
0.3
300
Magnetic field (tesla)
350
0.4
400
Standard CW X-band EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)
0.0
Simulation
Experiment
0.1
0.2
Magnetic field (tesla)
0.3
Parallel mode (B1//B0)
Intensity (arb. units - offset)
Intensity (arb. units - offset)
Standard B1 B0 configuration
0.0
Simulation
Experiment
0.1
0.2
Magnetic field (tesla)
0.3
Pulsed X-band EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)
Echo amplitude (arb. units)
Frequency (MHz)
Rabi oscillations: remarkably long T2
rHo-Ho ~ 18Å
25
20
15
10
T = 4.8 K
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Intensity (arb. units)
B1 (arb. units)
Hahn echo sequence
Echo Intensity
Exponential fit
0
0
200
100
400
600
200
Pulse length (ns)
800
1000
300
T1 ~ 1 s
T2 ~ 140 ns
Pulsed X-band EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)
Rabi oscillations: remarkably long T2
Cr7Ni (S = 1): 0.2mg/mL, T2 ~300 ns @ 5K
Fe4
Ardavan et al., PRL 98, 057201 (2007)
Fe4: 0.5g/mL, 95 GHz and B = 0
Schlegel et al., PRL 101, 147203 (2008)
Fe8: 240 GHz and 4.6 T (kBT ~ 11.5 K)
Echo amplitude (arb. units)
Frequency (MHz)
Takahashi et al., PRL 102, 087603 (2009)
rHo-Ho ~ 18Å
25
20
15
10
S=5
T = 4.8 K
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Intensity (arb. units)
B1 (arb. units)
0
0
T2 ~ 140 ns
Echo Intensity
Exponential fit
200
100
400
600
200
Pulse length (ns)
800
1000
300
Fe8
S = 10
Echo-detected spectrum is T2 weighted
150
135
120
105
90
75
60
EPR Intensity
(arb. units- offset)
T2 (ns)
Pulsed X-band EPR of [HoxY1-x(W5O18)2]9- (x = 0.25)
Spectrum
also
sensitive
to pulse
sequence
Echo intensity
CW spectrum
0
100
200
Magnetic field (tesla)
300
9- (x = 0.25)
Pulsed
X-band
EPR
of
[Ho
Y
(W
O
)
]
x 1-x
5 18 2
-5110
-1
Energy
(cm )
energy [GHz]
Competing anisotropies (TUNNELING):
→ no longer obvious what is parallel/perpendicular
0.50
-5120
0.25
DmI = 0
DmI = ±1
-5130
0.00
-0.25
-5140
-0.50
-0.75
-5150
-1.00
0.0
-5160
0.1
0.2
Magnetic field (tesla)
0.3
1Mohammady
Cancelation resonances → significant reduction in decoherence
-1
Energy
(cm )
energy [GHz]
et al., Phys. Rev. Lett. 105, 067602 (2010)
9- (x = 0.25)
Pulsed
X-band
EPR
of
[Ho
Y
(W
O
)
]
x 1-x
5 18 2
-5110
0.50
-5120
0.25
Bi (I = 9/2) in Si1
Note: excitation bandwidth
Comparable to linewidth
df
0
dB
-5130
0.00
-0.25
-5140
-0.50
-0.75
-5150
-1.00
0.0
-5160
0.1
0.2
Magnetic field (tesla)
0.3
9- (x = 0.25)
Pulsed
X-band
EPR
of
[Ho
Y
(W
O
)
]
x 1-x
5 18 2
-5110
-1
Energy
(cm )
energy [GHz]
COHERENT QUANTUM TUNNELING
0.50
-5120
0.25
Note: excitation bandwidth
Comparable to linewidth
-5130
0.00
-0.25
-5140
-0.50
-0.75
-5150
-1.00
0.0
-5160
0.1
0.2
Magnetic field (tesla)
0.3
Pulsed X-band EPR of [HoxY1-x(W5O18)2]9- (x = 0.1)
Intensity (arb. units - offset)
•Sample not perfectly aligned; shift to consistent with simulations
•Cancelation resonances now stronger than the standard ones!!
•T2 factor of two larger for cancelation resonances
0
T2 ~ 200 ns
rHo-Ho ~ 25Å
Echo detected
CW spectrum
Impurity in
cavity
100
200
300
Magnetic Field (mT)
400
Pulsed X-band EPR: concentration dependence
1.2 s
Coherence time - T2 (ns)
Intensity (arb. units)
Electron-Spin-EchoEnvelope-Modulation
(ESEEM)
ESEEM frequency
Consistent with
Coupling to protons
3
10
T2 x1/ 2
2
0
1
2
3
4
Time (s)
5
6
10
10
-3
10
-2
10
-1
Concentration - x