バタフライ構造を持つニッケル4核錯体の磁性と高周波

Magnetic properties of a frustrated
nickel cluster with a butterfly structure
RIKEN Masayuki HAGIWARA
Outline
Introduction
Crystal structure
Magnetic susceptibility
High field magnetization
Evaluation of the exchange constants
ESR
Evaluation of the single ion anisotropy constants
Temperature evolution of magnetization process in a
pulsed field
Summary

Molecular magnet
Mn12O12(CH3COO)16(H2O)4
Magnetization curves
Mn12-Acetate
Discrete double well structure
Mn3+(S=2) 8 ions S=10
Mn4+(S=3/2) 4 ions
Quantum tunneling
Frustration
Geometrical frustration
Antiferromagnetic exchange interactions
？
Triangle lattice
Tetrahedron
Kagome lattice
Railroad trestle
Frustrated molecular magnet
Molecular magnet
Mn12, Fe8, V15 etc.
Frustrated system
Triangle lattice etc.
Frustrated molecular magnet
Butterfly structure
(Diamond structure)
Sample preparation & Apparatus
Experimental
Sample preparation
Slow evaporation method from aquaous solution vigorously stirring during 24 h
Ni(ClO4)6H2O, (2-aminoethyl)-pyridine
Single crystals
chemical analysis
C
H
N
Cl
cald. 40.26 4.67 12.96 8.20
found 40.17 4.59 12.86 8.20
Apparatus
Magnetic susceptibility
Static magnetization
High field magnetization
ESR
SQUID magnetometer MPMS-XL7
at KYOKUGEN
Pulse magnet
at KYOKUGEN
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
Unit structure of Ni tetramer
Ni tetramer unit structure of [Ni4(-CO3)2(aetpy)8][ClO4]
aetpy=2-aminoethyl-pyridine
c-axis
[1,1,0]
a
a
[001] projection
[110] projection
Ni
J2
J2
J3
O
C
N
a-axis
J2
J1
J2
Body frame
A. Escuer et al., J. Chem. Soc., Dalton Trans., 1998, 3473.
Tetragonal
a-axis
Crystal structure (packing)
Crystal structure (packing)
c
c
a
a
a
[110]-projection
Ni
O
C
Tetragonal
Space group P4(2)(1)2
a
[001]-projection
a=14.523(4) A
c=16.566(5) A
c-axis
a-axis
Magnetic susceptibility (H // c）
5.0
H // c-axis
H=1000 Oe
4.5
1.0
4.0
3.5
[Ni4(-CO3)2(aetpy) 8][ClO 4]
0.5
3.0
Single crystal
2.5
0.0
0
50
100
150
200
T emperature (K)
250
2.0
300
Similar results
for H // a
T (emu K/mol)
Susceptibility (emu/mol)
1.5
High field magnetization
H // c-axis
H // a-axis
2.0
Magnetization ( B / Ni)
Magnetization ( B / Ni)
2.0
1.5
1.0
Single crystal
H // c-axis
T=1.3 K
0.5
0.0
1.5
1.0
Single crystal
H // a-axis
T=1.3 K
0.5
0.0
0
10
20
30
40
50
Magnetic field (T)
60
70
0
10
20
30
40
Magnetic field (T)
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.
50
60
Spin Hamiltonian
Assumption because of the similarity of the
magnetizations for H // a and H //c.
H =J1S1S2+J2(S1S3+S1S4+S2S3+S2S4)+J3S3S4+gBH(S1z+S2z+S3z+S4z)
Evaluation of J1 and J2
The transition fields are independent of J3.
The exchange constants are evaluated
from the analyses of magnetization curve.
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)
Evaluated values from susceptibility
J1/kB=28.6 cm-1, J2/kB=7.9 cm-1, g=2.16
A. Escuer et al., J. Chem. Soc., Dalton Trans., 1998, 3473.
E
Energy
diagram
~ J 1 -3J 2
14 K
0
J3
Expanded
2J 3
J 3 <0 (Ferromagnetic)
J 3 >0 (Antiferromagnetic)
J3 plus or minus?
Determination of J3 by fitting
Magnetic susceptibility
1.2
5.0
H // c-axis
H=1000 Oe
4.0
J1//kB=49.7 0.5 K
J /k =9.3 0.2 K
3.5
J3/kB=-0.630.02 K
3.0
2
B
g=2.229 0.002
2.5
0.0
0
50
100
150
200
250
2.0
300
Temperature (K)
J3/kB=-0.6∼0.7 K (Ferromagnetic)
Magnetization (B /Ni)
1.0
0.5
1.0
4.5
T (emu K/mol)
Susceptibility (emu/mol)
1.5
Magnetization (static)
0.8
T=2.0 K
0.6
T=4.2 K
H // c-axis
0.4
J3/kB=-0.66±0.04 K
g=2.191±0.004
0.2
0.0
0
1
2
3
4
5
6
Magnetic Field (T)
Magnetization is calculated from the
lowest singlet, triplet and quintet states.
7
ESR spectra (H // c)
Pulsed field
Static field
441.7 GHz
1623.4GHz
215.0 GHz
161.0 GHz
140.0 GHz
122.5 GHz
113.8 GHz
H // c
T=1.6 K
80.1 GHz
1392.8GHz
ESR signal (arb. units)
ESR signals (arb.units)
322.7 GHz
1182.0GHz
1017.6GHz
977.2Hz
847.0Hz
730.5GHz
H // c
T=1.3 K
655.7GHz
64.1 GHz
584.8GHz
0
2
4
6
8
10
Magnetic field (T)
12
14
0
10
20
30
40
Magnetic field (T)
50
60
Frequency-field diagram (H // c)
2000
3.5
3.0
g=2.18,
Eg=67.5GHz
1500
2.5
g=2.20,
Eg=30..7GHz
2.0
1000
1.5
1.0
500
0.5
0
0
10
20
30
40
50
Magnetic field (T)
60
0.0
70
Magnetization ( B/Ni)
Frequency (GHz)
H // c
Determination of D value
1000
215GHz, 10K
1017.6GHz, 4.2K
1000
E
B'
A
D
C'
D'
C
D
B
A'
0
Energy (GHz)
Energy (GHz)
500
B
E
DPPH
C
A
0
A
-1000
A
B
B
-2000
-500
Black D1=D2=-4.0K
Blue D1=D2=-3.4K
0
2
4
6
41.8T
Quintet
Septet
8
10
Magnetic field (T)
D/kB= -4.0K , -3.4K
12
14
26
28
30
32
34
36
Magnetic field (T)
38
40
42
Magnetic parameter values
ESR (static & pulse)
g=2.2±0.02
J1/kB=41.9±0.5 K High field magnetization
J2/kB=9.2±0.3 K
Magnetization
J3/kB=-0.65±0.05 K
& susceptibility
D= -4.0±0.1 K ,
-3.4±0.1 K
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.
ESR signals (Arb.units)
ESR spectra (H // a)
132.6GHz
128.6GHz
124.2GHz
119.3GHz
116.0GHz
110.0GHz
102.2GHz
94.9GHz
90.8GHz
85.0GHz
81.7GHz
75.7GHz
73.9GHz
70.9GHz
68.1GHz
61.6GHz
58.8GHz
57.2GHz
51.9GHz
47.0GHz
42.0GHz
37.0GHz
0
2
4
6
8
Magnetic field (T)
low frequency
225.2GHz
166.1GHz
150.1GHz
142.0GHz
137.8GHz
399.9GHz
329.9GHz
262.7GHz
249.1GHz
247.4GHz
H // a
T=1.6 K
10
12
14
Frequency-field diagram (H // a)
1100
1000
H // a
Frequency (GHz)
900
800
700
g=4.165
g=4.276
600
500
g=2.182
g=2.183
g=2.178
g=2.160
400
300
200
100
0
0
5
10
15
20
25
Magnetic field (T)
30
35
Temperature dependence of the spectra
H // c-axis
H0||c-axis
H // a-axis
4.2K
215.0GHz
166.1GHz 1.5K
H0||a-axis
10.0K
20.0K
ESR signals
ESR signals
4.2K
10.0K
20.0K
40.0K
40.0K
80.0K
0
2
4
6
8
10
Magnetic field /T
12
14
0
2
4
6
8
10
Magnetic field /T
12
14
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.
Temperature evolution of M curves
Field increasing
Field decreasing
2.0
2.0
Descending process
H // c-axis
1.5
1.0
T=90 mK
T=300 mK
T=600 mK
T=900 mK
T=1.3 K
T=4.2 K
0.5
Magnetization ( B /Ni)
Magnetization ( B /Ni)
Ascending process
H // c-axis
1.5
1.0
T=90 mK
T=300 mK
T=600 mK
T=900 mK
T=1.3 K
T=4.2 K
0.5
0.0
0.0
0
10
20
30
40
50
Magnetic field (T)
with decreasing temperature
0
10
20
30
40
50
Magnetic field (T)
Nearly identical behavior below 1.3 K
Hysteresis around 40 T
1.5
T=900 mK
H // c-axis
1.5
1.4
1.0
Ascending process
0.5
Descending process
Magnetization ( B /Ni)
Magnetization ( B /Ni)
2.0
H // c-axis
1.3
1.2
T=90 mK
T=90 mK
T=300 mK
T=300 mK
T=600 mK
T=600 mK
T=900 mK
T=900 mK
T=1.3 K
T=1.3 K
1.1
Ascending
Descending
1.0
0.9
0.0
0
10
20
30
40
Magnetic field (T)
50
25
30
35
40
45
Magnetic field (T)
Magnetization in ascending process nearly coincides with that in descending process
at 900 mK around 40 T.
50
Energy branches vs magnetic field
Energy (GHz)
2000
100 GHz
≈4.8 K
0
-2000
Nonatet
Septet
Singlet
Triplet
Quintet
-4000
-6000
19.5T
0
20
H1
41.8T
40
Magnetic field (T)
H2
60
66.4T
80
Magnetization process in field
ascending process
This step is probably caused by
“magnetic föhn effect.
2.0
E
Magnetization ( B /Ni)
Ascending process
H // c-axis
1.5
1.0
T=90 mK
T=300 mK
T=600 mK
T=900 mK
T=1.3 K
T=4.2 K
0.5
0.0
0
10
20
30
40
Magnetic field (T)
50
~20 T
~41 T
H
Magnetization process in field
descending process
E
2.0
Quantum origin
Magnetization ( B /Ni)
Descending process
H // c-axis
1.5
1.0
T=90 mK
T=300 mK
T=600 mK
T=900 mK
T=1.3 K
T=4.2 K
0.5
0.0
0
10
20
30
40
Magnetic field (T)
50
~20 T
~41 T
H
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.
Acknowledgements
Collaborators
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)

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