Introduction to

Molecular Magnets

Jason T. Haraldsen

Advanced Solid State II4/17/2007

Basic Molecular Magnets

Mn12-acetate, S = 10 Fe8Br8, S = 10 V15, S = 1/2

[V15As6O42(H2O)]K6[Mn12O12(CH3OO)16(H2O)4].2CH3COOH.4H2O

[(C6H5N3)6Fe8(µ3-O)2(µ2-OH)12]Br7(H2O)Br.8H2O4 Spin-3/2

8 Spin-2 8 Spin-5/215 Spin-1/2

Molecular Magnets:

By Definition

Isolated clusters containing ionic

spins ranging from as few as two

to up to several dozen.

Molecular magnets are not limited

to molecular solids.

No long range order.

S. Nagler et. al. Unpublished

NaCuAsO4, S = 0

Heisenberg Spin-Spin

Exchange Hamiltonian

ij

jiij SSJH

Anisotropic and Zeeman

terms may be added to

give a more complete

description of a given

material.

J > 0 is antiferromagnetic

J < 0 is ferromagnetic

Molecular Magnets:

Theory and Model

Heisenberg Hamiltonian plus anisotropy and Zeeman terms

Molecular Magnets:

Theory and Model

Ising and XY Variations

Molecular Magnets:

DimensionalityHilbert Space

For mixed valance systems

For spin symmetric systems

Examples of how dimensionality increases in systems

Spin-1/2 Dimer

Spin-1/2 Pentamer

Spin-3/2 Pentamer

[Mn12O12(CH3OO)16(H2O)4].2CH3COOH.4H2O

Experimental Techniques

Bulk Quantities

Magnetization

Magnetic Susceptibility

Heat Capacity

Microscopic Quantities

Inelastic Neutron Scattering

Raman Scattering

Infrared Spectroscopy

Magnetization

Examines the overall

magnetic moment.

Steps denote magnetic

spin flips in the material.

J. Schnack et. al. PRB (2006)

Magnetic Susceptibility

Change in magnetization

over change in magnetic

field.

J.T. Haraldsen et. al. PRB (2005)

Heat CapacityThe ability of a material to

store heat as a function of

temperature.

The peak corresponds to

either a cooperative

phase transition or an

anomaly.

J.T. Haraldsen et. al. PRB (2005)

Effects of Dimensionality on

Complexity

J.T. Haraldsen et. al. PRB (2005)

Inelastic Neutron Scattering

)(4

)(

)()()()(

ˆ

2)(

qSd

qS

VVqfqS

q

iaffffbifiba

f

if EEE Excitation Energy

Structure Factor Intensity

Measures the dispersion

relationship of energy

transfer and momentum

transfer.

Tennant et. al, PRL (2005)

Infrared and Raman

Spectroscopy

Not usually thought of when

discussion magnetic transitions.

Activated when a magnetic system

has an anisotropic interaction.

Usually coupled to lattice excitations

through the typically selections rules

of dipole moment (Infrared) and

polarizability (Raman).

T. Room et. al. PRB (2002)

- NaVO

Simplest Molecular Magnet:

Spin 1/2 Dimer

JS

1S

2

-3/4J

1/4J

S = 0

S = 1

E

A

21 SSJH

1

02

1

JE

JE

4

14

3

1

0

The Textbook Dimer:

VO(DPO2)•0.5H2O

Tennant et. al, PRL (2005)

Spin-1/2 vanadium system.

Vanadium ions are arranged

structurally in a lattice.

Magnetic properties show the

presence of an isolated dimer.

Magnetic Susceptibility of

VO(DPO2)•0.5H2O

0 50 100 150 200 250 3000

1

2

3

4

5

Sp

ecifi

c H

eat (

J/K

-mol

)

Temperature (K)

0 50 100 150 200 250 3000

5

10

15

20

VO(DPO4)0.5H

2O

Isolated Dimer Model

Temperature (K)

Mag

netic

Sus

cept

ibili

ty (

10-6 c

m3 /g

)

JJeeZ

4

3

4

1

3

JBA

p eZ

JkNC

2

1

2

223

JBA

molar eZ

gN 4

12)(2

J. W. Johnston et. al., J. Am. Chem. Soc. (1984)

Inelastic Neutron Scattering of

VO(DPO2)•0.5D2O

)(1)()( 0 qAjqfqS D.A. Tennant et. al. PRL (1997)

E = J = 7.86 meVA = 4.37 Å

Predicted Experiment

En

ergy

(m

eV)

En

ergy

(m

eV)

q (Å-1) q (Å-1)

The Textbook Dimer:

VO(DPO2)•0.5H2O

The use of magnetic measurements on

the material of VODPO4 • ½ D2O clarified

the magnetic structure of the material.

Tennant et. al, PRL (2005)

V4+ V4+ V4+

Summary

Molecular magnets are magnetically isolated

clusters that exhibit no long range magnetic

ordering

Many techniques, both bulk and microscopic,

can be used to determine the magnetic

structure.

Magnetic structure is not always obvious from

an examination of the crystal structure.