Stephen Hill NHMFL and Florida State University, Physics Outline of talk: Idea behind the title of...
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Transcript of Stephen Hill NHMFL and Florida State University, Physics Outline of talk: Idea behind the title of...
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