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Multi-bit magnetic memory using Fe8 high spin molecules
Oren Shafir
Magnetism Group, Physics Department
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Outline
• Preface: memory unit
• Fe8 as a high spin molecule
• Quantum tunneling In Fe8
• Experiments:
– Faraday force magnetometer
– SR
• Discussion
• Summary
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The “memory” of a memory unit
Hysteresis loop
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What do we mean by multi-bit memory?
• Single-bit Memory using the same
measurement one can distinguish between two different
preparation processes.
• Multi-bit Memory using the same
measurement one can distinguish between more than two
preparation processes.
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Memory Unit Evolution
1950 1960 1970 1980 1990 2000 201010
310
410
510
610
710
810
910
1010
1110
1210
1310
1410
1510
1610
1710
1810
1910
20
QTM
Magnetic cores Disk file Magnetic bubble Thin film Optical disk IBM
Ato
ms
per
bit
year
J. Harris and D. Awschalom, Physics World Jan.-1999
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Outline
• Preface: memory unit
• Fe8 as a high spin molecule
• Quantum tunneling In Fe8
• Experiments
– Faraday force magnetometer
– SR
• Discussion
• Summary
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Molecules as magnetic memory
There are some properties that molecules must
have if one wants to use them as magnetic memory:
• Existence of an hysteresis loop (energy barrier between two
magnetization states) = the molecule can “remember”.
• Large interaction between the spins in the molecule (J) = the
molecule acts as a single unit.
• Weak magnetic coupling between the molecules = every molecule
behaves independently.
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[Fe8O2(OH)12(C6H15N3)6]Br7(H2O)Br8H2O
Fe8 Molecule
Iron
Carbon
Nitrogen
Oxygen
Hydrogen
K. Wieghardt, K. Pohl, I. Jibril and G. Huttner, Angew. Chem. Int. Ed. Engl. 23 (1984), 77.
• The magnitude of magnetic interactions between the spins of the ions
is between 20 to 170K.
• The magnetic interactions between the molecules are negligibly
small.
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Single crystal of Fe8
• Single array of nanomagnets
The magnetization is
preferentially oriented parallel to
an axis called the "easy axis“.
Easy axis
Hard axis
Easy axis
Hard axis
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The molecular spin in low temperatures
102522
56 S
M. Ueda & S. Maegawa, J. Phys. Soc. Jpn. 70 (2001)
This was confirmed by a polarized neutron-diffraction experiment.
S=10
(a) is parallel to the easy axis.
(b) is perpendicular to the easy axis.
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Hysteresis loop of Fe8 – Temperature dependence
A. Caneschi et al. JMMM 200, 182 (1999)
• There is a temperature dependence above 0.4K.
• Equally separated steps can be seen at
• The lower the temperature, the wider the hysteresis loop
TnHm 22.0
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Hysteresis loop of Fe8 – sweeping rate dependence
A. Caneschi et al. JMMM 200, 182 (1999)A. Caneschi et al. JMMM 200, 182 (1999)
• Equally separated steps can be seen at
• Fast sweeping rate → wider hysteresis loop
TnHm 22.0
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Outline
• Preface: memory unit
• Fe8 as a high spin molecule
• Quantum tunneling In Fe8 ↔ Multi-bit memory
• Experiments:
– Faraday force magnetometer
– SR
• Discussion
• Summary
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Energy levels with E=0
-D double degenerate
0
Energy levels with E ≠ 0.0
-D-E
-D+E
=2E
1
0
0
up
0
0
1
down
The concept of tunnel splitting: S = 1
0
1
0
middle
2
)cos(1
2
)2cos(1)exp(
2 tEtuptidown
H
The spin will tunnel at a rate given by Δ from up to down .
DE
ED
SSEDS yxz
0
000
0
)( 222H
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D – anisotropic constant (~0.27 K)
E – rhombic parameter (~0.046 K)
The main part of the spin Hamiltonian:
The Hamiltonian of Fe8: S=10
mHgDmmEnergy zB 2)(
Hamiltonian
The tunnel splitting between the two degenerated ground states:
The energy levels are:
where m is the quantum number of the level.
222yxzzBz SSESHgDS H
S
SS D
ES
S
D
8
)!2()!1(
82,
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a) In zero field the two wells are equally populated.
b) An applied magnetic field selectively populates the right well.
c) After removing the field the system returns to equilibrium (thermally).
Experimental realization
Ms=S Ms=-S
Ms=S
Ms=-S
Ms=S-1 Ms=-S+1
Thermally assisted QT pure QT
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The model and the hysteresis loop
HS Byxz gSSEDS )( 222H
No tunneling
tunneling
M
H
.22.0)( Tng
nDnH
Bm
Ene
rgy
dH/dtmmgμ
π--P
B
mmmm '2
Δexp1
2',
',
Landau Zener model
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Outline
• Preface: memory unit
• Fe8 as a high spin molecule
• Quantum tunneling In Fe8
• Experiments:
– Faraday force magnetometer
– SR
• Discussion
• Summary
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Faraday force magnetometer – Principle of measurement
• Measuring the varying capacitance.
• spatially varying magnetic field → magnetic force
• The restoring force of the springs balances F .
BMF )(
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Faraday force magnetometer – The load cell
sample
Phosphor- Bronze wireThermal
link
screwing
Epoxy (Stycast)
Brass
Cu
Mixingchamber
Vaccumjacet
Thermal link
Superconductingsolenoid magnet
Coaxialwires
center line
The load cell device, displaced from the center of
a solenoid magnet in a dilution refrigerator.
The movable plate is suspended by four wires of phosphor bronze.
dz
dBMaCC z
z 110
a – Calibration constant
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Results - jumps in matching fields
-0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6
15.4881
15.4882
15.4883
15.4884
Capaci
tance
[pF
]
H [Tesla]
The capacitance verses the magnetic field
(dH/dt =0.15 T/min, T =40mK)
The distance between steps is nearly constant
(the arrows are of equal length)
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Sweep rate dependence
Capacitance in arbitrary units for various dHz/dt (at T=40mK). The
vertical dotted lines are at the approximate matching fields Hm≈n×0.21T.
-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0
-3
-2
-1
0
1
2
30.4
0.15
0.1
Cap
acita
nce
[a.u
.]
H [Tesla]
0.03
dHz /dT [T/min]
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Temperature dependence
Capacitance in a.u. for different temperatures (dHz/dt=0.15 [T/min]). The
vertical dotted lines are at the approximate matching fields Hm≈n×0.21T
-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 0.0
-2
0
2
4
Capaci
tance
(a.u
.)
H [Tesla]
T = 30mK T = 200mK T = 500mK T = 700mK T = 4.2K
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Outline
• Preface: memory unit
• Fe8 as a high spin molecule
• Quantum tunneling In Fe8
• Experiments:
– Faraday force magnetometer
– SR
• Discussion
• Summary
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Why measure Fe8 with SR?
We want to measure the magnetization of a few (or one)
molecules
We need a local probe
Moreover, there is an ongoing effort to make Fe8 films →
SR is applicable to films (while most techniques are not).
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SR – Muon Spin Relaxation/Rotation
High energy proton
Carbon atom nucleus
pion
neutrino
muon
sample
Positron detector
positron
From the ISIS website
(ISIS - pulsed neutron and muon source located at the UK)
The muon provides information on the magnetic
environment in its vicinity.
B
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SR experiment setup
• The beam direction || easy axis of Fe8 || applied field.
• Temperature : ~100mK (minimize activation effects).
• The initial polarization of the muons is 50° relative to z.
R
L
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Corrected asymmetry:
)()()(
)()()( tP
tLtR
tLtRtA
Asymmetry
Detected positrons
time difference between the
muon arrival at the sample and
its decay
SR
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1. A strong negative field of -2T that is
parallel to the z axis, polarizes the Fe8
molecules
3. The field is swept back to +50G at
the same rate
same measurementE
nerg
y
The process - three step field cycle:process
0m0m
.1
2. The field is swept to an
intermediate positive value Hi, at
a rate of 4 mT/s
different
process
.2
.3
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0m 0m
Ene
rgy
Illustration of the double well potential in the field cycle
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-0.2-0.10.00.10.2
(a)
Hi=0.1TH
i=0.1T
(d)
-0.2-0.10.00.10.2
(b)
Hi=0.2TH
i=0.2T
Asy
mm
etry
(e)
0 1 2 3 4-0.2-0.10.00.10.2
HolderFe8
(c)
Hi=0.3TH
i=0.3T
Time(msec)
0 1 2 3 4
(f)
Asymmetry
Experiment results• There is a
difference in
amplitude.
• Reproducibility
Hematite
tetAtA
)sin()(
• The solid lines are
the fit to the function:
B .
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32(The solid line is a guide to the eye)
Analysis of the results
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
10
20
30
40
50
60
70
B [
Ga
us
s]
Hi [Tesla]
)()(
8
8
iHiH HolderFeHolderFe BBB
• The process:
-2T→ Hi → 50G
.1.2 kGnH n
...2,1,0n
• Matching fields:
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Two different setups
Fe8
Fe8
Silver plate
Muon beam
)a( )b(
In a different experiment the muons stopped in the silver plate
Several Fe8 single
crystals were glued on a
small silver plate.
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-1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8
-0.2
0.0
0.2
0.4
0.6
-15
0
15
30
44
B
[G
ause
]
fu
ll-em
pty
[Mra
d/se
c]
Hi [T]
Analysis of the results – muons hit the silver plate
The resolution is worse, but a full hysteresis loop can be seen .
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Outline
• Preface: memory unit
• Fe8 as a high spin molecule
• Quantum tunneling In Fe8
• Experiments:
– Faraday force magnetometer
– SR
• Discussion
• Summary
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dH/dtmmgμ
π--P
B
mm
'2
Δexp1
2',
W. Wernsdorfer, R. Sessoli, Science 1999, 284, 133.
Comparison to the Landau-Zener model and to previous experiments
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P-10,10
H=0
H=2kG
H=2kG
Flip
1-p-10,9
P-10,9
P-10,9
1-p-10,9
No Flip
Flip No Flip
No FlipFlip
1-p-10,10
For example: 2kG < Hi < 4kG
The probability not to
tunnel -
)1-P-10,10)×(1-P-10,9(2
• The process:
-2T→ Hi → 50G
The probability to stay at m=-10
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Comparison to the Landau-Zener model
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
10
20
30
40
50
60
70
B [
Ga
us
s]
Hi [Tesla]
The agreement between theory and experiment is poor .
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The same process for SmCo
0.0 0.1 0.2 0.3 0.4 0.5 0.6-5
-4
-3
-2
-1
0
1
2
3
4M
[em
u]
Hi [T]
-2T→ Hi → 50G
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
10
20
30
40
50
60
70
B [
Gau
ss]
Hi [Tesla]
SmCo
Fe8
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Outline
• Preface: memory unit
• Fe8 as a high spin molecule
• Quantum tunneling In Fe8
• Experiments:
– Faraday force magnetometer
– SR
• Discussion
• Summary
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Summary
• The qualitative result from the Faraday force magnetometer
demonstrates again the quantum nature of the Fe8 crystals.
• Using the mSR technique, which is also applicable to films, we
observe quantum tunneling of the magnetization (QTM) in the
Fe8 compound.
• We show that Fe8 can “remember” for at least 1/2 hour which
intermediate field was visited. Using Fe8, we can distinguish
between at least six processes by performing the same
measurement.
This warrants Fe8 molecules the candidacy for a
multi-bit magnetic memory.
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Acknowledgments:
Dr. Y. Sheynin, Dr. M. Kapon, Prof. M. Kaftori - for sample
preparation and characterization
Technicians - Leonid Iomin, Mordehay Eilon, Shmuel Hoida
– for their help with the DR
Prof. E. Polturak and Prof. M. Resnikov - for helping with the DR
Prof. S. Maegawa, Dr. M. Ueda - for initial samples, Kyoto
University, Japan
Dr. A. Amato, C. Bains – for SR instrument support, PSI,
Switzerland
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Acknowledgments:
My lab members :
Shahar, Ariel, Meni, Oshri, Rinat, Eva, Lior and
Amit Kanigel
Special thank for Prof. Amit Keren.
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End
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The exchange path ways connecting iron(III) in Fe8
J1= -147K
J2= -173K
J3= -22K
J4= -50K
back
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At temperatures lower than the
magnetic coupling J between
ions inside the molecule, the
spins of the ions are locked,
and the molecules behave like
non -interacting spins.
Blocking Temperature
(a) parallel to the easy axis
(b) perpendicular to the easy axis.
M. Ueda & S. Maegawa, J. Phys. Soc. Jpn. 70 (2001)
T [K]
back
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The effective spin Hamiltonian (without the Zeeman term):
Hamiltonian of Fe8
D. Gatteschi and R. Sessoli, Angew. Chem. Int. Ed. 42, No. 3 (2003), p. 268
back
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What do we mean by multi-bit memory?
• Single-bit Memory using the same measurement one can distinguish between two differentpreparation processes.
• Multi-bit Memory using the same measurement one can distinguish between more than two preparation processes.
SR process
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The eigenvectors and eigenvalues of H0 are:
The spin will tunnel at a rate given by:
zBxB
xBzBzzxxBz hgDhg
hghgDShShgDS
4/2/
2/4/2H
=gBhx known as tunnel splitting
The concept of tunnel splitting: S=1/2
thhg
hh
he zxB
zx
xti 22
22
22
1
001 cos2
1
2
1 H
22zxB hhg
22
22
4/1
1
2
1
,4/1
1
2
1
zxBas
zxBs
hhgDE
hhgDE
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Zener time
hz
02
tunnel
dt
dhg z
Btunnel /0
dt
dhg z
B
0
0 2/
1/20
dt
dhg z
B
dH/dtmmgμ
π--P
B
mmmm '2
Δexp1
2',
',
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Zener Time – Mullen et al
dtdhgdt
dE zB 0lim
/
12
z
/
12
z
Adiabatic limit:
sudden limit:
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Capacitance bridge
3 terminal method
A capacitance bridge with transformer ratio arms.
Basic bridge circuit of AH2550A Capacitance Bridge
magnetometer
X
N
X
N
N
XXXNN N
N
V
V
C
CCVCV
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Dilution refrigerator
Control unit
Inner Vacuum chamber
outer Vacuum chamber
Mixing chamber
magnetometer
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magnetometer
Dilution refrigerator – schematic view
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-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0
15.4880
15.4888
15.4896
15.4904
Cap
acita
nce*
100
[pF
]
H [T]
sweep rate 1.1 sweep rate 1 sweep rate 0.8 sweep rate 0.6 sweep rate 0.5 sweep rate 0.4 sweep rate 0.3 sweep rate 0.2 sweep rate 0.15 sweep rate 0.1 sweep rate 0.03
Changes due to eddy currents
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Pion decay
• Only left-handed neutrinos exist
• Pions have zero spin
• Pions at rest (pp = 0) → Muons have a spin which is
anti-parallel to their momentum SR
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• The muon decays according to:
• The positron is usually energetic enough to travel a
substantial distance before annihilating.
ee
Muon decay
The violation of parity
SR
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0 1 2 3 4 5 6
-0.1
0.0
0.1
-0.1
0.0
0.1
-0.1
0.0
0.1
Time
Ag and mask
(a)
Fe8 and mask
Asy
mm
etry
(c)
(b)
Mask
hematite mask
empty
Fe8
silver
Fe8 as hematite
The asymmetry of a hematite and glue mask (a) is very similar
to mask and Fe8 (b), but different from mask and silver (c).
Therefore, muons in Fe8 do not contribute to the asymmetry.
results
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Comparison to the Landau-Zener model
]/[][106328.7 12 sK
]/[][67170099.0 TKB
]/[][10083.4/[min]][245.0/ 3 sTTdtdH
For -10,10=10-7 K → P-10,10 = 0.02
For -10,9=3×10-7 K → P-10,9 = 0.16
For -10,8=20×10-7 K → P-10,8 = 0.99
dH/dtmmgμ
π--P
B
mm
'2
Δexp1
2',
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Hi
(intermediate field)
The probability not to tunnelN-10 : N10
Hi < ~0.22T1-P-10,100.9776 : 0.0224
~0.22T < Hi < ~0.44T(1-P-10,10)×(1-P-10,9)20.68 : 0.38
~0.44T < Hi < ~0.66T(1-P-10,10)×(1-P-10,9)2×(1-P-10,8)
20 : 1
Comparison to the Landau-Zener model
N-10 - the number of the molecules with spin up
N10 - the number of the molecules with spin down
Starting point - N-10 : N10 = 1:0
illustration
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The simplest model – double well potential
Tunneling in a double well
system:
a) Non-coupling states.
b) Coupling states giving
rise to tunnel splitting, .
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The prediction
(referred to the result in Mn12)
“ These results…also make Mn12ac more appealing for technological applications as it represents a multi- rather than a bi-stable single molecule memory unit. "
A. Caneschi, D. Gatteschi, C. Sangregorio, R. Sessoli, L. Sorace, A. Cornia, M.A. Novak, C. Paulsen, W. WernsdorferJournal of Magnetism and Magnetic Materials Vo. 200 (1999) p. 182-201
“The molecular approach to nanoscale magnetism”
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Summary
• The experimental work:
– Synthesizing Fe8 crystals
– Assembling a dilution refrigerator
– Fraday force magnetometer experiments (Design a
load sensing variable capacitor; operating DR, SC magnet,
capacitance bridge)
– SR experiments
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end