stephen hill, saiti datta and sanhita ghosh, nhmfl and florida state university in collaboration...
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Stephen Hill, Saiti Datta and Sanhita Ghosh,NHMFL and Florida State University
In collaboration with:Enrique del Barco, U. Central Florida; Fernando Luis, U. Zaragoza, Spain;Eugenio Coronado and Salvador Cardona-Serra, U. Valencia, Spain
EPR Studies of Quantum Coherent EPR Studies of Quantum Coherent Properties of Rare-Earth SpinsProperties of Rare-Earth Spins
•Where are we coming from?Where are we coming from?•Brief summary of 10 years of EPR studies of molecular magnets Brief summary of 10 years of EPR studies of molecular magnets
•Where are we going?Where are we going?•Simpler molecular magnets with improved functionalitySimpler molecular magnets with improved functionality
•EPR studies of a mononuclear rare-earth (HoEPR studies of a mononuclear rare-earth (Ho3+3+) molecule) molecule•Coherent manipulation of coupled Coherent manipulation of coupled SS, , LL (~ (~JJ) and ) and II (~ (~FF))
•Pure speculationPure speculation (or total nonsense?)(or total nonsense?)
Mn(III)
Mn(IV)
Oxygen
SS = (8 = (8 × 2) – (4 × 2) – (4 × 3/2× 3/2) ) SS = 10 = 10
S S = 3/2= 3/2
S S = 2= 2
The Drosophila of SMMs – MnThe Drosophila of SMMs – Mn1212
SS = 10 = 10
Simplest effective Simplest effective model: uniaxial model: uniaxial anisotropyanisotropy2ˆ ˆ ( 0)zDS D H
"up""up" "down""down"
EE1010
EE99
EE88
EE77
EE1010
EE99
EE88
EE77
EE66
EE55
Spin projection - ms
EE66
EE55
Ene
rgy
Ene
rgy
EE44EE44
smE
2( )s sm D mE
"up""up" "down""down"
EE1010
EE99
EE88
EE77
EE1010
EE99
EE88
EE77
EE66
EE55
Spin projection - ms
EE66
EE55
Ene
rgy
Ene
rgy
EE44EE44
smE
21 discrete 21 discrete mmss levels levels
•Small barrier - Small barrier - DSDS22
•Superparamagnetic at Superparamagnetic at most temperaturesmost temperatures
•Magnetization blocked Magnetization blocked at low temperatures at low temperatures ((TT < 4 K) < 4 K)
E E DS2 10-100 K10-100 K
|D | 0.1 1 K for a typical single molecule magnetThermal activationThermal activation
Magnetic anisotropy Magnetic anisotropy bistability, hysteresis bistability, hysteresisSimplest effective Simplest effective model: uniaxial model: uniaxial anisotropyanisotropy2ˆ ˆ ( 0)zDS D H
2( )s sm D mE
0.14 0.16 0.18 0.20 0.22
-4
-3
-2
-1
log()
1/T (K)
Chak
ov e
t al.,
J. A
m. C
hem
. Soc
. 128
, 697
5 (2
006)
.Re
dler
et a
l, Ph
ys. R
ev. B
80,
094
408
(200
9).
o = 2.0 × 10-9 sUeff = 70 K
AC AC data for [Mn data for [Mn1212OO1212(O(O22CCHCCH22Br)Br)1616(H(H22O)O)44]·Solvent]·Solvent΄ ΄
΄΄
΄
field//field//zz
z, S4-axis
Bz
2( )s s B sm D m g Bm E
•Magnetic dipole transitions (ms = ±1) - note frequency scale!
0 1 2 3 4 5 6 7
< 1
mm
Mn12
-tBuAc
336.3 GHz
30 K 25 K 20 K 15 K 10 K 7 K 5 K 3 K 1.4 K
Nor
mal
ized
tran
smis
sion
(a
rb. u
nits
- o
ffse
t)
Magnetic field (tesla)
2 4 4 42 4 4
ˆ ˆ ˆ ˆ ˆ
55K; 13K; 0.3K
z z
D B CS S S S
S S S
D B C
H•Obtain the axial terms in the z.f.s. Hamiltonian:
Uneven spacingUneven spacingof peaksof peaks
We can measure transverse terms by rotating field into We can measure transverse terms by rotating field into xyxy-plane-plane
What can we learn from single-crystal HFEPR?What can we learn from single-crystal HFEPR?
A big problem with large moleculesA big problem with large molecules
•Full calculation for MnFull calculation for Mn1212 produces matrix of dimension 10 produces matrix of dimension 1088 ×× 10 1088
•Even after major approximation: dimension is 10Even after major approximation: dimension is 1044 × 10 × 1044
•Multiple exchange coupling parameters (Multiple exchange coupling parameters (JJss); anisotropy (LS-); anisotropy (LS-coupling); different oxidation and different symmetry sites.coupling); different oxidation and different symmetry sites.
S = 11
S = 9 S = 10
Mn12
S S = 10= 10
•Matrix dimension 21 × 21Matrix dimension 21 × 21
•JJss irrelevant (apparently)!! irrelevant (apparently)!!
•Ignores (10Ignores (1088 – 21) higher-lying – 21) higher-lying statesstates
SS = 10 = 10
But what is the physical origin of parameters But what is the physical origin of parameters obtained from EPR and other experiments obtained from EPR and other experiments
– – particularly those that cause MQT?particularly those that cause MQT?
To answer this.... To answer this.... ..study simpler molecules..study simpler molecules
Ni4: E.-C. Yang et al., Inorg. Chem. 44, 3836 (2005); A. Wilson et al., PRB 74, R140403 (2006).Mn3: P. Feng et al., Inorg. Chem. 46, 8126 (2008); T. Stamatatos et al., JACS 129, 9484 (2007). Mn6: C. Milios et al., JACS 129, 12505 (2007); R. Inglis et al., Dalton 2009, 3403 (2009).
II4Ni
SS44 symmetry symmetry
(2S + 1)4 = 81
2 2 2ˆ ˆ ˆ ˆ ˆ ˆ ˆij i j i zi i xi yi B i ii j i i
H J s s d s e s s B g s
@
III3Mn
MnIII
(2S + 1)3 = 125
3R
III6Mn
(2S + 1)6 = 15625
CentrosymmetricCentrosymmetric
Ueff = 45K
Ueff = 75K
Ishikawa et al.,
Mononuclear Lanthanide Single Molecule Magnets
Hund’s rule coupling for Ho3+: L = 6, S = 2, J = 8; 5I8
Ground state: mJ = ±5Nuclear spin I = 7/2 (100%)
[(tpaMes)Fe]−
1500 Oe 2.0 K
D = -39.6 cm-1 E = -0.4 cm-1
U = 42 cm-1 τ0 = 2 x 10-9 s
1.7 K
6.0 K
Mononuclear Transition Metal Single Molecule Magnets
Harris,Harmann,Reinhardt,Long
Hund’s rule coupling for Er3+: L = 6, S = 3/2, J = 15/2; 4I15/2
Nuclear spin I = 0, 7/2 (70%, 30%)
Coherent Quantum Dynamics in CaWO4:0.05% Er3+
Bertaina et al., PRL 103, 226402 (2009).Bertaina et al., Nat. Nanotech. 2, 39 (2007).
Rabi
Ho3+ – [Xe]4f10
Mononuclear Lanthanide Single Molecule Magnets Based on the Polyoxometalates
[Ln(W5O18)2]9- (LnIII = Tb, Dy, Ho, Er, Tm, and Yb)
~D4d
Hund’s rule coupling for Ho3+: L = 6, S = 2, J = 8; 5I8
= 5/4
AlD
amen
et
al.,
Ho3+ – [Xe]4f10
Mononuclear Lanthanide Single Molecule Magnets Based on the Polyoxometalates
Hund’s rule coupling for Ho3+: L = 6, S = 2, J = 8; 5I8
Ground state: mJ = ±4
AlD
amen
et
al.,
Ho3+ – [Xe]4f10
Mononuclear Lanthanide Single Molecule Magnets Based on the Polyoxometalates
Hund’s rule coupling for Ho3+: L = 6, S = 2, J = 8; 5I8
-10 -8 -6 -4 -2 0 2 4 6 8 10-50
0
50
100
150
200
250
300
350
Ene
rgy
(cm
-1)
J projection - mJ
Ground state: mJ = ±4
AlD
amen
et
al.,
ErEr3+3+ and Ho and Ho3+3+
Exhibit SMMExhibit SMMcharacteristicscharacteristics
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
High(ish) frequency EPR of [Ho0.25Y0.75(W5O18)2]9-
Eight line spectrum due to strong hyperfine coupling to 165Ho nucleus, I = 7/2
Well behaved EPR: nominally forbidden transitions mJ = -4 +4, mI = 0
B//c
High(ish) frequency EPR of [Ho0.25Y0.75(W5O18)2]9-
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 or m
J' = -1/2
mJ = +4 or m
J' = +1/2
mI
+1/2-3/2
-7/2
+3/2+5/2+7/2
-3/2
-7/2F
requ
ency
(G
Hz)
Magnetic Field (tesla)
B//c
Eight line spectrum due to strong hyperfine coupling to 165Ho nucleus, I = 7/2
Well behaved EPR: nominally forbidden transitions mJ = -4 +4, mI = 0
1K = 21GHz
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4
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
Angle-dependent EPR of [Ho0.25Y0.75(W5O18)2]9-
Very strong g-anisotropy associated with transitions mJ = -4 +4Note: hyperfine interaction also exhibits significant anisotropy
-135 -90 -45 0 45
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
Mag
netic
fie
ld (
T)
Angle (degrees)
mI
+7/2 +5/2 +3/2 +1/2 -1/2 -3/2 -5/2 -7/2
Angle-dependent EPR of [Ho0.25Y0.75(W5O18)2]9-
Very strong g-anisotropy associated with transitions mJ = -4 +4Note: hyperfine interaction also exhibits significant anisotropy
( , ) ( ) ( )B IE B g B A m
-135 -90 -45 0 45
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
Mag
netic
fie
ld (
T)
Angle (degrees)
mI
+7/2 +5/2 +3/2 +1/2 -1/2 -3/2 -5/2 -7/2
Angle-dependent EPR of [Ho0.25Y0.75(W5O18)2]9-
Very strong g-anisotropy associated with transitions mJ = -4 +4Note: hyperfine interaction also exhibits significant anisotropy
1( )
( )res IB
hfB A m
g
-135 -90 -45 0 45
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
Mag
netic
fie
ld (
T)
Angle (degrees)
mI
±7/2 ±5/2 ±3/2 ±1/2
2 2 2 2( ) cos sing g g
Angle-dependent EPR of [Ho0.25Y0.75(W5O18)2]9-
Very strong g-anisotropy associated with transitions mJ = -4 +4Note: hyperfine interaction also exhibits significant anisotropy
1
( )resB
hfB
g
-135 -90 -45 0 45
0.4
0.5
0.6
0.7
0.8
Mag
netic
fie
ld (
T)
Angle (degrees)
mI
±7/2 ±5/2 ±3/2 ±1/2
2 2 2 2( ) cos sing g g
Angle-dependent EPR of [Ho0.25Y0.75(W5O18)2]9-
Very strong g-anisotropy associated with transitions mJ = -4 +4Note: hyperfine interaction also exhibits significant anisotropy
1
( )resB
hfB
g
-135 -90 -45 0 45
0.4
0.5
0.6
0.7
0.8
Mag
netic
fie
ld (
T)
Angle (degrees)
mI
±7/2 ±5/2 ±3/2 ±1/2
2 2 2 2( ) cos sing g g
8.545 0.010
0.96 0.1
Note: 1.25J
g
g
g
Angle-dependent EPR of [Ho0.25Y0.75(W5O18)2]9-
Very strong g-anisotropy associated with transitions mJ = -4 +4Note: hyperfine interaction also exhibits significant anisotropy
1
( )resB
hfB
g
-180 -135 -90 -45 0 45 90
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
1.1
Mag
netic
fie
ld (
T)
Angle (degrees)
mI
+7/2 +5/2 +3/2 +1/2 -1/2 -3/2 -5/2 -7/2
Angle-dependent EPR of [Ho0.25Y0.75(W5O18)2]9-
Very strong g-anisotropy associated with transitions mJ = -4 +4Note: hyperfine interaction also exhibits significant anisotropy
Add ( ) IA m
A 53 mT,A 100mT
X-band (9GHz) Electron Spin Echo EPR of [HoxY1-x(W5O18)2]9-
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 or m
J' = -1/2
mJ = +4 or m
J' = +1/2
mI
+1/2-3/2
-7/2
+3/2+5/2+7/2
-3/2
-7/2F
requ
ency
(G
Hz)
Magnetic Field (tesla)
B//c
Recall anisotropic hyperfine interactionLikely neither J or I are good quantum numbers; deal with F = J + I
0 100 200 300
0.1 0.2 0.3 0.4 0.5 0.6 0.7
10
15
20
25
0.00 0.05 0.10 0.15 0.20 0.25
Ech
o am
plitu
de (
arb.
uni
ts)
Pulse length (ns)
B1 (arb. units)
Freq
uenc
y (M
Hz)
Magnetic field (T)
Inte
nsity
(a.
u.)
X-band (9GHz) Electron Spin Echo EPR of [HoxY1-x(W5O18)2]9-
x = 0.25
T = 4.8 K
Impurity
cw EPR
24 ns 120 ns 12 ns200 nst
Hahn echosequence
T1 ~ 1 sT2 ~ 180 ns
Ho-Ho ~ 18År
0 100 200 300 400
180 deg 190 deg 200 deg 210 deg 220 deg 230 deg 240 deg 250 deg 260 degAttenuation : 7 dB
Time (nsec)In
tens
ity (
arb.
uni
ts)
180 195 210 225 240 255
6
7
8
9
10
11
12
Rab
i fre
quen
cy (
MH
z)
Angle (degrees)
X-band (9GHz) Electron Spin Echo EPR of [HoxY1-x(W5O18)2]9-
Rabi oscillations also exhibit the same g-anisotropy
0 100 200 300 400
Inte
nsity
(ar
b. u
nits
)
Magnetic Field (mT)
Echo detected EPR CW
Sample: Ho (25%)T = 4.8 K
X-band (9GHz) Electron Spin Echo EPR of [HoxY1-x(W5O18)2]9-
ESE is TESE is T22 weighted weighted
Ho-Ho ~ 18År
Source of the additional peaks due to strong to 165Ho nuclear spin
Badly behaved EPR: transitions mJ = -4 +4, mI = 0, ±1
0.2 0.4 0.6
-20
0
20
mJ = -4 or m
J' = -1/2
mJ = +4 or m
J' = +1/2
mI
-3/2-5/2
-7/2
-3/2-1/21/2 -5/2
-7/2
Fre
quen
cy (
GH
z)
Magnetic Field (tesla)
X-band (9GHz) Electron Spin Echo EPR of [HoxY1-x(W5O18)2]9-
Schematic:Not an exactCalculation ofspectrum
0 100 200 300 400
ED CW
Inte
nsity
(ar
b. u
nits
- o
ffse
t)
Magnetic Field (mT)
10 % sample 25 % sample
0 100 200 300 400
E4E3E2E1P4
P3
P2P1
ED CWIn
tens
ity (
arb.
uni
ts -
off
set)
Magnetic Field (mT)
E1E2
E3
E4
P1
P2 P3
Ho-Ho ~ 18ÅrHo-Ho ~ 25År
Comparing [HoxY1-x(W5O18)2]9- 10% and 25% samples
Important to recall: ESE is TImportant to recall: ESE is T22 weighted weighted
Comparison of T2 values :
Peak T2 (nsec)
E1 149.71064
P1’ 82.65335
P1 81.23469
E2 123.75861
P2’ 81.08677
P2 80.91722
E3 112.07676
P3’ 82.06742
P3 94.05755
E4 153.39765
Peak T2 (nsec)
E1
P1’
P1 193.89
E2
P2’
P2 146.55
E3
P3’
P3 177.36
E4
10 % sample 25 % sample
Sequence : 12-120-24 Attenuation : 7 dB for 10% sample; 6 dB for 25% sample
Comparing [HoxY1-x(W5O18)2]9- 10% and 25% samples
0 100 200 300 400 500
P4
P3P2
P1
10 dB attenuation
Inte
nsity
(ar
b. u
nits
- o
ffse
t)
Magnetic Field (mT)
12-120-24 12-120-20 12-120-16 12-120-12 8-108-12 8-108-8 4-104-8
25% [HoxY1-x(W5O18)2]9- : splitting of the main (P) peaks
0 100 200 300 400 500
P4
P3P2
P1
Sequence : 12-120-24
Inte
nsity
(ar
b. u
nits
- o
ffse
t)
Magnetic Field (mT)
17dB 15dB 12.5dB 10dB 9dB 8dB 7dB 6dB
25% [HoxY1-x(W5O18)2]9- : splitting of the main (P) peaks
0 100 200 3000
25
50
75
100
125
150
Sequence : 12-120-24Attenuation : 6dB
Inte
nsity
(ar
b. u
nits
) an
d T
2 (ns
)
Magnetic Field (mT)
25% [HoxY1-x(W5O18)2]9- : splitting of the main (P) peaks
Lehmann, Gaita-Arino, Coronado, Loss,
•Coherent nutation of the ground-state magnetic moment deriving from crystal-field effects acting on ~J = ~L + ~S (and ~J + ~I) is not yet well understood.
•For Ho, the hyperfine coupling is strong, i.e. the nuclear spin is coherently coupled to the electron spin during nutation.
•A magnetic moment much larger than 1/2 allows spin manipulations in low driving field-vectors (amplitude and direction).
•Rare-earth polyoxometallates are stable outside of a crystal, and may be scalable and addressable on surfaces, e.g. via an STM.
Why do we care?Why do we care?
Variation of t2 versus temperature (4.8K – 9K) at 3 fields (A=0deg):
4 5 6 7 8 990
100
110
120
130
140
150
t2 (
nsec
)
Temperature (K)
645 G 1260 G 1875 G
Data was taken at 10K too, but those plots show huge errors in fitting
4 5 6 7 8 9 10
400
500
600
700
800
900
1000
1100
t1 (
nsec
)
Temperature (K)
Variation of t1 versus temperature (4.8K – 10K) at 1875G (A=0deg):
T1 measurements were also done at 645G and 1260G, but those are not includedin this plot since they do not show the expected variation : some of the plots have significantly large error, I will try to improve the fitting if possible and check if they show better results
0 500 1000 1500 2000
Data: T2180DEG374G_BModel: ExpDec1 Chi^2/DoF = 988043070.97295R^2 = 0.99359 y0 140390.5799 ±4254.70913A1 1815051.63822±18557.49911t1 149.71064 ±2.64064
Inte
nsity
(ar
b. u
nits
)
Time (nsec)
Peak E1
0 500 1000 1500
Inte
nsity
(ar
b. u
nits
)
Time (nsec)
Data: T2180DEG795G_BModel: ExpDec1 Chi^2/DoF = 751697060.45728R^2 = 0.95307 y0 129081.31328 ±3239.56652A1 705238.92155 ±20271.12244t1 81.23469 ±3.87681
Peak P1
0 500 1000 1500
Inte
nsity
(ar
b. u
nits
)
Time (nsec)
Data: T2180DEG1779G_BModel: ExpDec1 Chi^2/DoF = 991631016.50834R^2 = 0.98104 y0 139526.53464 ±3938.27782A1 1156971.50866 ±20793.68362t1 112.07676 ±3.36909
0 500 1000 1500
Inte
nsity
(ar
b. u
nits
)
Time (nsec)
Data: T2180DEG2244G_BModel: ExpDec1 Chi^2/DoF = 1365821331.40121R^2 = 0.98703 y0 143434.68326 ±4467.62435A1 1749519.43461 ±25996.8008t1 94.05755 ±2.32159
Ho 10% sample
Peak E3 Peak P3
0 500 1000 1500 2000
Time (nsec)
Data: T212120246DB_BModel: ExpDec1 Chi^2/DoF = 1193755876.82889R^2 = 0.99522 y0 40860.6835 ±2935.86354A1 2826688.71937 ±18324.7136t1 193.89889 ±2.00646
Inte
nsity
(ar
b. u
nits
)Ho 25% sample
0 500 1000 1500 2000
Inte
nsity
(ar
b. u
nits
)
Time (nsec)
Data: T212120246DB2_BModel: ExpDec1 Chi^2/DoF = 1535776552.72851R^2 = 0.99699 y0 88732.17877 ±4535.64537A1 3458553.82005 ±21582.01422t1 177.35667 ±1.86226
Peak P1 Peak P3