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