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
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
Frustration
Geometrical frustration
?
Triangle latticeTetrahedron
Kagome lattice
Railroad trestle
Antiferromagnetic exchange interactions
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)
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
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.
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
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
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
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.
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?
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.
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
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
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
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.
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
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
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
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
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
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
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
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.
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
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
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