magnetic properties of a frustrated nickel cluster with a butterfly structure introduction crystal...
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Magnetic properties of a frustrated nickel cluster with a butterfly structure
IntroductionCrystal structureMagnetic susceptibilityHigh field magnetizationEvaluation of the exchange constantsESREvaluation of the single ion anisotropy constantsTemperature evolution of magnetization process in a pulsed fieldSummary
RIKEN Masayuki HAGIWARA
Outline
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Molecular magnet
Mn12O12(CH3COO)16(H2O)4
Discrete double well structure
Magnetization curves
Mn3+(S=2) 8 ionsMn4+(S=3/2) 4 ions
S=10Quantum tunneling
Mn12-Acetate
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Frustration
Geometrical frustration
?
Triangle latticeTetrahedron
Kagome lattice
Railroad trestle
Antiferromagnetic exchange interactions
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Frustrated molecular magnet
Molecular magnet Frustrated system
Mn12, Fe8, V15 etc. Triangle lattice etc.
Frustrated molecular magnet
[Ni4(-CO3)2(aetpy)8][ClO4]4
aetpy=(2-aminoethyl)-pyridine
Butterfly structure(Diamond structure)
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Experimental
Sample preparation
Apparatus
Slow evaporation method from aquaous solution
Ni(ClO4)6H2O, (2-aminoethyl)-pyridine
vigorously stirring during 24 h
Magnetic susceptibility Static magnetization
SQUID magnetometer MPMS-XL7 at KYOKUGEN
Single crystals chemical analysiscald. 40.26 4.67 12.96 8.20 found 40.17 4.59 12.86 8.20
C H N Cl
High field magnetization Pulse magnet at KYOKUGEN
ESR Home made ESR spectrometer ~50 GHz ABmm network analyzer ~400 GHz 16 T superconducting magnet at RIKEN
FIR laser & pulse magnet ~1.3 THz at KYOKUGEN
Sample preparation & Apparatus
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Unit structure of Ni tetramer
Ni tetramer unit structure of [Ni4(-CO3)2(aetpy)8][ClO4]aetpy=2-aminoethyl-pyridine
a a
[001] projection [110] projection
Body frame
J2 J2
J2J2 J2
J1
J3
Ni
O
C
N
c-axis
a-axis
[1,1,0]a-axis
TetragonalA. Escuer et al., J. Chem. Soc., Dalton Trans., 1998, 3473.
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Crystal structure (packing)
a
a
c
[001]-projection
[110]-projection
Crystal structure (packing) c
a a
Ni O C
Tetragonal Space group P4(2)(1)2
a=14.523(4) A c=16.566(5) A
a-axis
c-axis
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Magnetic susceptibility (H // c)
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
0 50 100 150 200 250 300
Su
scep
tibil
ity
(em
u/m
ol)
T (em
u K
/mo
l)
Temperature (K)
H // c-axisH=1000 Oe
[Ni4(-CO
3)2(aetpy)
8][ClO
4]
Single crystal
Similar resultsfor H // a
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High field magnetization
0.0
0.5
1.0
1.5
2.0
0 10 20 30 40 50 60 70
Mag
netiz
atio
n ( B
/ N
i)
Magnetic field (T)
Single crystalH // c-axisT=1.3 K
H // c-axis
½ and ¾ magnetization plateaus are observed with large hysteresis.The transition field from the ½ plateau to the ¾ plateau for H // a is nearly identical to that for H // c.
0.0
0.5
1.0
1.5
2.0
0 10 20 30 40 50 60
Mag
netiz
atio
n ( B
/ N
i)
Magnetic field (T)
Single crystalH // a-axisT=1.3 K
H // a-axis
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Spin Hamiltonian
H =J1S1S2+J2(S1S3+S1S4+S2S3+S2S4)+J3S3S4+g1BH(S1z+S2
z)+g2BH(S3
z+S4z)+D1{(S1
z)2+(S2z)2)+D2{(S3
z)2+(S4z)2)
J2
J2
J2
J2
J1
J3
S1
S2
S3 S4
D 10, D20, g1=g2=g
SA=S1+S2, SB=S3+S4, ST=SA+SB
H =J1S1S2+J2(S1S3+S1S4+S2S3+S2S4)+J3S3S4+gBH(S1z+S2
z+S3z+S4
z)
H =J12
SA(SA+1)+J22
{ST(ST+1)-SA(SA+1)-SB(SB+1)}+J32
SB(SB+1)+gBHSTz
Assumption because of the similarity of themagnetizations for H // a and H //c.
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Evaluation of J1 and J2
J1/kB=28.6 cm-1, J2/kB=7.9 cm-1, g=2.16
The transition fields are independent of J3.
The exchange constants are evaluated from the analyses of magnetization curve.
Evaluated values from susceptibility
H1=40.7 T, H2=69 T g=2.2
J1/kB=41.9 K (29.1 cm-1), J2/kB=9.2 K (6.4 cm-1)
A. Escuer et al., J. Chem. Soc., Dalton Trans., 1998, 3473.
M
HJ1+2J2 2J1+2J2
H1 H2E
~J1-3J2
14 K
0
J3
2J3
J3<0
J3>0
Energydiagram
Expanded(Ferromagnetic)
(Antiferromagnetic)
J3 plus or minus?
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Determination of J3 by fitting
0.0
0.2
0.4
0.6
0.8
1.0
1.2
0 1 2 3 4 5 6 7
T=2.0 K
T=4.2 K
Mag
neti
zati
on (
B/N
i)
Magnetic Field (T)
H // c-axis
J3/k
B=-0.66 0.04 K
g=2.191 0.004
±
±
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
0 50 100 150 200 250 300
Susc
epti
bili
ty (
emu/
mol
)
T (em
u K/m
ol)
Temperature (K)
H // c-axisH=1000 Oe
J1//k
B=49.7 0.5 K
J2/k
B=9.3 0.2 K
J3/k
B=-0.63 0.02 K
g=2.229 0.002
Magnetic susceptibility Magnetization (static)
J3/kB=-0.6 0.7 K (Ferromagnetic)∼ Magnetization is calculated from the lowest singlet, triplet and quintet states.
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ESR spectra (H // c)
0 10 20 30 40 50 60
ES
R s
igna
l (a
rb. u
nits
)
Magnetic field (T)
584.8GHz
655.7GHz
730.5GHz
847.0Hz
977.2Hz
1017.6GHz
1182.0GHz
1623.4GHz
1392.8GHz
H // cT=1.3 K
0 2 4 6 8 10 12 14
ES
R s
igna
ls (
arb.
unit
s)
Magnetic field (T)
H // cT=1.6 K
64.1 GHz
80.1 GHz
113.8 GHz
122.5 GHz
140.0 GHz
161.0 GHz
215.0 GHz
322.7 GHz
441.7 GHz
Static field Pulsed field
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Frequency-field diagram (H // c)
0
500
1000
1500
2000
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
0 10 20 30 40 50 60 70
Freq
uenc
y (G
Hz)
Magnetization (
B /Ni)
Magnetic field (T)
g=2.18, Eg=67.5GHz
g=2.20, Eg=30..7GHz
H // c
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Determination of D value
D/kB= -4.0K , -3.4K
-2000
-1000
0
1000
Ene
rgy
(GH
z)
424038363432302826
Magnetic field (T)
Quintet Septet
1017.6GHz, 4.2K DPPH
41.8T
AB
A B
1000
500
0
-500
Ene
rgy
(GH
z)
14121086420
Magnetic field (T)
AC
B
D
A'
B' C'D'E
E B
AC
D
Blue D1=D2=-3.4KBlack D1=D2=-4.0K
215GHz, 10K
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Magnetic parameter values
g=2.2±0.02J1/kB=41.9±0.5 KJ2/kB=9.2±0.3 KJ3/kB=-0.65±0.05 K
D= -4.0±0.1 K , -3.4±0.1 K
High field magnetization
ESR (static & pulse)
Magnetization & susceptibility
ESR (static & pulse)
We can determine the magnetic parameter values by making a comparison between calculations and various kinds of experiments.
A fine tuning of the parameters is needed.
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ESR spectra (H // a) low frequencyE
SR s
igna
ls (
Arb
.uni
ts)
14121086420Magnetic field (T)
399.9GHz
37.0GHz
329.9GHz
249.1GHz262.7GHz
247.4GHz225.2GHz166.1GHz150.1GHz
137.8GHz142.0GHz
132.6GHz128.6GHz124.2GHz119.3GHz116.0GHz110.0GHz102.2GHz
94.9GHz
81.7GHz
90.8GHz85.0GHz
70.9GHz
75.7GHz73.9GHz
68.1GHz61.6GHz58.8GHz57.2GHz
47.0GHz51.9GHz
42.0GHz
H // aT=1.6 K
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Frequency-field diagram (H // a)1100
1000
900
800
700
600
500
400
300
200
100
0
Fre
que
ncy
(G
Hz)
35302520151050
Magnetic field (T)
g=2.182 g=2.183 g=2.178 g=2.160
g=4.165 g=4.276
H // a
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ES
R s
igna
ls
14121086420
Magnetic field /T
4.2K
10.0K
20.0K
40.0K
H0||c-axis 215.0GHz
ES
R s
igna
ls
14121086420Magnetic field /T
H0||a-axis 1.5K
4.2K
10.0K
20.0K
80.0K
40.0K
166.1GHz
Temperature dependence of the spectra
H // c-axis H // a-axis
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Origins of hysteresis & magnetization
Magnetization behavior depends on the field sweep rate and the magnitude of the energy gap.The magnetization at T=>0 K due to a thermal origin differs from that due to a quantum one.
Thermal origin
Quantum origin
T => 0
Symmetric
H H
M
HH
M
Asymmetric
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Temperature evolution of M curves
0.0
0.5
1.0
1.5
2.0
0 10 20 30 40 50
T=90 mKT=300 mKT=600 mKT=900 mKT=1.3 KT=4.2 K
Mag
netiz
atio
n ( B
/Ni)
Magnetic field (T)
Ascending process
H // c-axis
0.0
0.5
1.0
1.5
2.0
0 10 20 30 40 50
T=90 mKT=300 mKT=600 mKT=900 mKT=1.3 KT=4.2 K
Mag
netiz
atio
n ( B
/Ni)
Magnetic field (T)
Descending process
H // c-axis
Field increasing Field decreasing
Nearly identical behavior below 1.3 Kwith decreasing temperature
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Hysteresis around 40 T
0.0
0.5
1.0
1.5
2.0
0 10 20 30 40 50
Ascending process
Descending processMag
netiz
atio
n ( B
/Ni)
Magnetic field (T)
T=900 mK
H // c-axis
Magnetization in ascending process nearly coincides with that in descending processat 900 mK around 40 T.
0.9
1.0
1.1
1.2
1.3
1.4
1.5
25 30 35 40 45 50
T=90 mKT=90 mKT=300 mKT=300 mKT=600 mKT=600 mKT=900 mKT=900 mKT=1.3 KT=1.3 K
Mag
netiz
atio
n ( B
/Ni)
Magnetic field (T)
H // c-axis
AscendingDescending
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Energy branches vs magnetic field
100 GHz≈4.8 K
-6000
-4000
-2000
0
2000
Ene
rgy
(GH
z)
806040200
Magnetic field (T)
Nonatet Septet Singlet Triplet Quintet
41.8T 66.4T19.5TH1 H2
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Magnetization process in field ascending process
0.0
0.5
1.0
1.5
2.0
0 10 20 30 40 50
T=90 mKT=300 mKT=600 mKT=900 mKT=1.3 KT=4.2 K
Mag
netiz
atio
n ( B
/Ni)
Magnetic field (T)
Ascending process
H // c-axis
E
H~20 T ~41 T
This step is probably caused by“magnetic föhn effect.
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Magnetization process in field descending process
E
H~20 T ~41 T
0.0
0.5
1.0
1.5
2.0
0 10 20 30 40 50
T=90 mKT=300 mKT=600 mKT=900 mKT=1.3 KT=4.2 K
Mag
netiz
atio
n ( B
/Ni)
Magnetic field (T)
Descending process
H // c-axis
Quantum origin
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Summary
1. We performed high field magnetization and ESR experiments on single crystals of the Ni tetramer cluster compound [Ni4(-CO3)2(aetpy)8][ClO4].2. We observed step wise magnetizations with ½ and ¾ magnetization plateaux in a magnetic field up to 70 T.3. We observed several ESR lines with g~2.2 and 4.4.4. All the magnetic parameters including exchange constants as shown in the figure are evaluated: J1/kB=41.9 K (29.1 cm-1), J2/kB=9.2 K (6.4 cm-1) J3/kB= -0.6~0.7 K, D/kB=-3.3 K, D’/kB=-4.0 K
5. We observed interesting temperature dependence of magnetization hysteresis near the second step.
J2
J2
J2
J2
J1
J3
S1
S2
S3 S4
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Acknowledgements
RIKEN Haruhiko Yashiro (HF ESR static)
KYKUGEN, Osaka University Akira Matsuo (HF magnetization)
Shojiro Kimura (HF
ESR pulse) Yasuo Narumi (HF magnetization static magnetization)
Koichi Kindo (Pulse experiments)
Collaborators