Stephen Hill, Saiti Datta and Sanhita Ghosh, NHMFL and Florida State University laboration with: Enrique del Barco, U. Central Florida; Fernando Luis, U. Zaragoza, Eugenio Coronado and Salvador Cardona-Serra, U. Valencia, Spain EPR Studies of Quantum Coherent EPR Studies of Quantum Coherent Properties of Rare-Earth Spins Properties of Rare-Earth Spins ere are we coming from? ere are we coming from? • Brief summary of 10 years of EPR studies of molecular magn Brief summary of 10 years of EPR studies of molecular magn ere are we going? ere are we going? • Simpler molecular magnets with improved functionality Simpler molecular magnets with improved functionality R studies of a mononuclear rare-earth (Ho R studies of a mononuclear rare-earth (Ho 3+ 3+ ) molecul ) molecul • Coherent manipulation of coupled Coherent manipulation of coupled S S , , L L (~ (~ J J ) and ) and I I (~ (~ F F ) ) re speculation re speculation (or total nonsense?) (or total nonsense?)
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Stephen Hill, Saiti Datta and Sanhita Ghosh, NHMFL and Florida State University
EPR Studies of Quantum Coherent Properties of Rare-Earth Spins. 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; - PowerPoint PPT Presentation
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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?)
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.
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
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