Inelastic Neutron Scattering (INS)

Philip L.W. Tregenna-Piggott

Department of ChemistryUniversity of Bern

Switzerland

Seminar Overview

· Introduction to INS

- Principles and Instrumentation

- Advantages and Disadvantages Over Other Techniques

- Selection Rules for Magnetic INS

· Applications

- Ground State Zero-Field-Splittings of non-Kramers Ions

- Exchange Coupling in Molecular Clusters

The Technique Provides a Measure ofEnergy and Momentum TransferBetween the Neutron and Sample

SampleIncoming Neutrons

Scattered Neutronskr

k ′r

Qr

( )

( )kkQTransferMomentumkk

mTransferEnergy

rrh

rh

hh

′−=

′−=

:

2: 22

2

ω

Schematic of a Time-of-Flight (TOF) INS Spectrometer

One measures the time it takes for neutrons to travel fromthe sample to a position on the detector bank

Incoming “white” neutron beam• Incident energy selection• Scattering by the sample• Final energy selection

From http://www.ill.fr

Schematic of a Triple Axis Spectrometer

Allows the measurement of inelastic excitations at a

given point in reciprocal space

Facility Organisation Location TYPE Description of

Instruments

ILL Institut Laue-

Langevin

Grenoble,

France

High-flux

reactor

http://www.ill.fr/index_sc.html

ISIS Rutherford

Appleton

Laboratory

Oxford, UK Pulsed neutron

facility

http://www.isis.rl.ac.uk/instruments

/index.htm

SINQ Paul Scherrer

Institute

Near Villigen,

Switzerland

Continous

spallation

neutron source.

http://sinq.web.psi.ch/sinq/instrume

nts.html

BENSC Berlin Neutron

Scattering

Centre

Hahn-Meitner-

Institut, Berlin,

Germany

Cold neutron

guides

http://www.hmi.de/bensc//instrume

ntation/instrumentation_en.html

The list is by no means complete. See also:http://www.neutron-eu.net/en/index.php

Principal Facilities for INS in Europe

Variation of INS Intensity with Q, differs for Magnetic and Phonon Transitions

Inte

nsit

y

QIn

tens

ity

Q

Magnetic Transitions Phonon Transitions

In general:

- Ability to detect low energyexcitations limited by the widthof the elastic line

- Momentum transfer increaseswith increasing energy transfer: favours detection of phonon rather than magnetic transitions

- Resolution becomes poorer withincreasing energy transfer

- Practical range of magnetic INS:~0.5 to ~500 cm-1, depending on

sample, and instrument configuration.

In which energy range is INS applicable?

Advantages of INS Over Other Techniques

-Direct Determination of Energy Levels in Zero Magnetic Field

-Change in Intensity and Energy as a Function of Q Carries Useful Information Concerning the Wavefunctions

Disadvantages of INS Over Other Techniques

-Several Grams of Sample Must be Used

-Often Necessary to Use Fully Deuteriated Samples

Neutron Scattering Cross-sectionsof Hydrogen and Deuterium

Coherent Incoherent

Deuterium

Hydrogen

Background due to incoherent scattering from protons often precludes the observation of magnetic transitions

Magnetic Scattering Selection RulesPowdered Sample, Unpolarised Neutron Beam

+++

+++

++

−∝=

iyeyffyeyi

ixexffxexi

izezffzezi

iINS

SgLkSgLk

SgLkSgLk

SgLkSgLk

TkEQI

ψψψψ

ψψψψ

ψψψψ

ˆˆˆˆ

ˆˆˆˆ

ˆˆˆˆ

exp)0(

SL MMSL ,,,Basis

Basler, Tregenna-Piggott, J.A.C.S., 123, 3377 (2001).Carver, Tregenna-Piggott, Inorg. Chem., 42, 5711 (2003).

SMS ,Basis

( )222 ˆˆˆ2exp)0( ififizfiINS sssTkEQI ΨΨΨΨΨΨ −+ ++

−∝=

∆MS = ±1,0 ∆S = ±1,0

Seminar Overview

· Introduction to INS

- Principles and Instrumentation

- Advantages and Disadvantages Over Other Techniques

- Selection Rules for Magnetic INS

· Applications

- Ground State Zero-Field-Splittings of non-Kramers Ions

- Exchange Coupling Parameters in Molecular Clusters

Ground State Zero-Field-Splittings of non-Kramers Ions

Case Studies

1. [Mn(OD2)6]3+

2. [V(OD2)6]3+

3. [Fe(OD2)6]2+

4. [Fe(imidazole)6]2+

5. [Cr(OD2)6]2+

INS is complementary to other spectroscopic techniques, for the characterisation of transition metal complexes. The main advantage of INS is that it affords the direct determination of the low-lying electronic structure in zero magnetic field.

Why is the Characterisation of Integer-SpinTransition Metal Complexes Difficult ?

Kramers Ions are Amenable to Study by Electron Paramagnetic Resonance:

Ener

gy

Magnetic Field

NS

NS

hν

Inte

nsity

Magnetic Field

Ener

gy

Magnetic Field along

hν

D

3D2

2−

11−

0

In Non-Kramers Transition Metal Ions,the Zero-field Splitting is generally large compared to hν:

zr

Values of |D| in S = 2 systems are in the range 2 to 6 cm-1

1

0

inte

nsity

[arb

. uni

ts]

-2 -1 0 1 2energy transfer [meV]

1.4 K

15 K

30 K

I IIα β γα'β'γ'I'II'

D = -4.524(1) cm-1

E = 0.276(1) cm-1

~|2±2>

|2±1>

~|2 0>

I

α

II

β γ

TOF Inelastic Neutron Scattering Spectra of Cs[MnIII(OD2)6](SO4)2⋅6D2O

Basler, Tregenna-Piggott, J.A.C.S., 123, 3377 (2001).

Determination of Ground State Zero-Field-Splittings of non-Kramers Ions using INS

1 meV ~ 8.06554 cm-1

1.

-1200

-1000

-800

-600

-400

-200

0

200

400

600

Ene

rgy

2000180016001400120010008006004002000Trigonal Field / cm-1

Energies of states of the 3T1g term as a function of a positive trigonal

field. λ is set to 100 cm-1.

Spectroscopic Studies of [V(OH2)6]3+ cation

Tanabe-Sugano Diagram for thed2 electronic configuration

Optical Spectroscopy

Electronic Raman

SpectroscopyInelastic Neutron

Scattering

High-Field EPR

States of the d2 electronic configuration in octahedral and trigonal fields

2.

High-Field EPR and Inelastic Neutron Scattering Studies of the [V(OH2)6]3+ cation

Inte

nsity

1086420-2-4-6-8Energy Transfer / cm-1

[C(ND2)3][V(OD2)6][SO4]2T = 5 K

Inelastic Neutron Scattering Spectrum of [V(OH2)6]3+ in

Guanidinium Vanadium Sulphate

Data modelled with an S=1Spin Hamiltonian

D / cm-1 = 4.8713(1)g||= 1.95188(3)g⊥= 1.8662(4)A|| / cm-1 = 0.00988(4)A⊥ / cm-1 = 0.0080(6)

High-Field EPR Spectrum of[V(OH2)6]3+ Doped

Caesium Aluminium Sulphate

Inte

nsity

9.659.609.559.50Field / Tesla

115 GHz B=BzBx=By=0

Tregenna-Piggott et al. Inorg. Chem. 38, 5928, (2001)

2.

Experimental and Theoretical Electronic Raman Profiles of C(NH2)3[VIII(OH2)6](SO4)2

eg

ag

eg

ag

Spichiger, Tregenna-Piggott, Chem. Phys. Lett. 337, 391 (2001)

sMA ,

3A

3E

|0 , 0

|0 , 1

| A , 1

| A , 0

| A , 1

sMA ,

∆

2.

Inte

nsity

(arb

. uni

ts)

43210-1-2-3-4Velocity (mms-1)

4.2K

45K

50K

55K

60K

70K

80K

160K

200K

Inte

nsity

(arb

. uni

ts)-4 -3 -2 -1 0 1 2 3 4

Velocity (mm s-1)

T= 4.2K, H= 0T

T= 4.2K, H= 7T

T= 4.2K, H= 3T

Data Collected and Analysed by Eckhard Bill

Mössbauer Study of Cs[FeII(OH2)6] (PO4)

Shows phase transition beautifully, but does not readilyyield low temperature electronic structure

3.

Inelastic neutron data of CsFe(D2O)6PO4

10 K INS Spectrum of a powdered sample ofCsFe(D2O)6PO4

Simulated spectrum consists of a sum of two spectra, each calculated using an S=2 Spin Hamiltonian with the following parameters:

Species 1:

D=11.999 cm-1E=2.1117 cm-1

Species 2:

D=12.121 cm-1E=1.346 cm-1

Inte

nsity

-3 -2 -1 0 1 2 3Energy transfer [meV]

exp.

sim. 1

sim. 2

sim. 1 + sim. 2 (1:1)

Direct determination of energies of low-lying states by INS

3.

HFMF-EPR data of CsFe(D2O)6PO4

HFEPR spectrum (5K, 284.9973 GHz) of a powdered sample of CsFe(D2O)6PO4 fitted using two S=2 Spin Hamiltonians:

Species 1:

D=11.999 cm-1E=2.1117 cm-1gx=2.22,gy=2.22,gz=2.32

Species 2:

D=12.121 cm-1E=1.346 cm-1gx=2.32,gy=2.22,gz=2.32

Inte

nsity

543210Field [Tesla]

*

sim. 1

sim. 2

sim. 1 + sim. 2 (1:1)

exp.

EPR data simulated with zero-field-splitting parametersfrom INS. The EPR experiments then yield the g values

3.

2500

2000

1500

1000

500

0

Ener

gy

2000150010005000Trigonal field [cm-1]

J=1 ground state perturbed by trigonal field:-Model Data with S=1 spin-Hamiltonian

5A1g (D3d) ground term perturbed by trigonal field:- Model Data with S=2 spin-Hamiltonian

4.

States of the 5T2g (Oh) term as a function of the trigonal

field, with λ set to 100 cm-1

Inelastic neutron data for Fe(II)(Imidazole)6(NO3)2In

tens

ity

806040200-20-40Energy Transfer [cm

-1]

1.5K

15K

30K

50K

II' II

80

40

0

Ener

gy [c

m-1

]

I

II II'

I' ae

e

Experimental and calculated Q dependence of the 19.4 cm-1 peak at

various temperatures.

INS spectra (incident wavelength 2.2 Angstrom)of a powdered sample of deuterated

Fe(Im)6(NO3)2 at various temperatures.

1.0

0.8

0.6

0.4

0.2

0.0

Nor

mal

ised

Inte

nsity

543210Momentum transfer Q [Angstrom-1]

1.5K exp. 15K exp. 30K exp. 50K exp. 1.5K calc . 15K calc . 30K calc . 50K calc .

Ground state energies (5A) fitted usingthe ligand field Hamiltonian:

operating in the 5D manifold

π

π λ

− −= + −

−+ ∆ + ⋅

0 3 34 4 4

02

28 10ˆ ( )3 7

14 ˆ ˆ3 5

H Dq Y Y Y

Y L S

4.

Magnetisation data4.

5.5

5.0

4.5

4.0

3.5

3.0

2.5

µ-ef

fect

ive

[Boh

r Mag

neto

ns]

30025020015010050Temperature [K]

exp. calc.

Magnetisation data reproduced using the ligand field Hamiltonian:

operating in the 5D manifold using the parameters obtained from INS.Orbital reduction factor, k = 0.95.

0 3 34 4 4

02

2 8 10ˆ ( )3 7

14 ˆ ˆ3 5

ˆ ˆ( 2 )

H D q Y Y Y

Y L S

k L S B

π

π λ

β

− −= + −

−+ ∆ + ⋅

+

HFMF-EPR data

20

10

0

-10

Ener

gy [c

m-1]

2 4 6 8 10246810B|| [Tesla]B⊥ [Tesla]

a

e

0

⊥

||

15

10

5

0

Ene

rgy

[cm-1

]

1086420Resonant field [Tesla]

|| ⊥

Experimental and calculated resonant field positions for HFMF-EPR.

Calculated energies of the lower three energy levels as a function of field directed parallel and normal to

the three-fold axis.

G. Carver, P.L.W. Tregenna-Piggott, Inorg. Chem. 2003, 42, 5771-5777

4.

Inte

nsity

-8 -6 -4 -2 0 2 4 6 8Energy Transfer (cm-1)

1.5 K

10 K

30 K

75 K

100 K

150 K

200 K

250 K

297 K

αβ βα γγ I IIIII

Inelastic Neutron Scattering Spectra of(ND4)2[CrII(OD2)6](SO4)2

I II

α

β

}~|2±2>

}|2±1>

~|2 0>

γ

Dobe, Tregenna-Piggott,Chem. Phys. Lett.362, 387, (2002)

5.

High-Field EPR Spectra andSimulations of (ND4)2[CrII(OD2)6](SO4)2

Inte

nsity

(arb

uni

ts)

121086420Field (T)

285GHz

95GHz*

*

Simulation

Simulation

25 K

5 K

Five ParametersRequired to Model the

EPR Data with an S=2 Spin-Hamiltonian. With INS,

the Zero-Field Transitionsare Obtained Directly

5.

-2.4

-2.3

-2.2

-2.1

-2.0

D /

cm-1

25020015010050Temperature / K

0.25

0.20

0.15

0.10

E / c

m-1

25020015010050Temperature / K

Variation of the zero-field-splitting parametersD and E with temperature, obtained by least-squares

refinement of the eigenvalues of:

to the energies of the INS transitions.

( ) [ ]222 ˆˆ131ˆˆ

yxz SSESSSDH −+

+−=

5.

Inte

nsit

y

16 0 001 2 0 008 0 004 00 00Field (G)

1 20 K1 50 K

1 75 K

2 00 K

2 25 K

2 50 K

2 75 K

7K

**

Sim

Variable Temperature X-band EPR Spectra andSimulations of (ND4)2[CrII(OD2)6](SO4)2

5.

2.35

2.30

2.25

2.20

2.15

2.10

2.05

Bon

d Le

ngth

(Å)

30025020015010050Temperature (K)

Cr-O(9)

Cr-O(8)

Cr-O(7)

Variation of Cr-O bond distances with temperature

Cr

Cr

Low Temperature

High Temperature

?

Unable to account for the data using static model

5.

Jahn-Teller Potential Energy Surface of [Cr(OD2)6]2+ in Cubic Symmetry

Cr

CrCr

Qθ

Qε

6

4

2

0

-2

-4

-6

6420-2-4-6 2

000

100

0

100

0

500

500

0 0

0

-500

-500

-500

-500

-100

0

-100

0

-1000

-1000 -1000

-1500 -1500

-1500

-1500 -1500

-1500

-200

0

-2000

-2000

-2000

1500 1500 1000

1000 500 500 0

0

-500 -500

-500

-1000 -1000 -1500

-2000

5.

6

4

2

0

-2

-4

-6

Qθ

-6 -4 -2 0 2 4 6Qε

250

0 2

000

150

0

150

0

100

0

100

0

500

500

0

0

-500

-500 -5

00

-1000

-1000

-1000

-1500

-1500

-1500

-2000

-2000

-2000

-2500

-2500

-3000

Cr

CrCr

Pote

ntia

l ene

rgy

Angular distortion co-ordinate

Calculated Potential Energy Surface of [Cr(OD2)6]2+ in (ND4)2[CrII(OD2)6](SO4)2 at 10 K

Degeneracy of Distorted Configurations Lifted by

Anisotropic Strain

5.

H = H0 + Hph + HJT + Hst

=

1001

τU

−=

1001

θU

=

0110

εU

( ) ( )[ ] ,35.0 3232222 τθεθεθεθω UQQQAQQPPH ph −++++= h

( ) ( )( )εεθθθεεεθθ UQQUQQAUQUQAH JT 22221 +−++=

εεθθ UeUeHst +=

Qθ ~ 2∆z2 – ∆x2 – ∆y2 and Qε ~ ∆x2 – ∆y2.

Hamiltonian for the System

P.L.W. Tregenna-Piggott, Advances in Quantum Chemistry, 144, 461 (2003).

5.

Eigenvalues andEigenvectors

ψψ θQψψ εQ

Cr-OBond Lengths

EPR Spectrum

2exp ifiINS Tk

EI ψµψ ⊥

−∝

INS Spectrum

Timescale ~ 10-14 - 10-13

Timescale < 10-9

Density Matrix Method

Input Rate of Inter-state Relaxation

5.

Theoretical INS Spectra. Orthorhombic Strain and 10Dq Diminish with Increasing Temperature

Inte

nsity

1086420Energy Transfer (cm-1)

1.5 K

10 K

30 K

75 K

100 K

200 K

250 K

297 K

150 K

Inte

nsity

-8 -6 -4 -2 0 2 4 6 8Energy Transfer (cm-1)

1.5 K

10 K

30 K

75 K

100 K

150 K

200 K

250 K

297 K

αβ βα γγ I IIIII

Experiment Theory

5.

2.40

2.35

2.30

2.25

2.20

2.15

2.10

2.05

Bon

d Le

ngth

(Å)

300250200150100500Temperature (K)

Cr-O(7)

Cr-O(8)

Cr-O(9)

Theory Experiment

Theoretical and Experimental Cr-O bond lengths5.

Theoretical EPR Spectra as a Function of Temperature:Fast Inter-State Relaxation

ν = 285 GHz

Cr

CrCr

Pote

ntia

l ene

rgy

Angular distortion co-ordinate

5.

Spin-Hamiltonian Parameters of the System Dependon the Experimental Technique Used to Determine Them

5.

Seminar Overview

· Introduction to INS

- Instrumentation

- Advantages and Disadvantages Over Other Techniques

- Selection Rules for Magnetic INS

· Applications

- Ground State Zero-Field-Splittings of non-Kramers Ions

- Exchange Coupling in Molecular Clusters

Exchange Coupling in Molecular Clusters

Case Studies

1. [(NH3)5Cr(OH)Cr(NH3)5]Cl5 · 3H2O

2. [Mn12O12(OAc)16(H2O)4]

3. MnMoO4

INS has played a pivotal role in the elucidation of exchange interactions in molecular clusters. The variation of the energies and intensities of the

transitions with Q, provides a wealth of information that cannot be obtained with other techniques.

Acid Rhodo ComplexBis-µ-hydroxo-pentamine chromium(III)

S = 01

2

3

0– 2 Jab

– 6 Jab

– 12 Jab

E

Hex = – 2 Jab Sa · Sb

W.E. Hatfield et al. 1973

1.

[(NH3)5Cr(OH)Cr(NH3)5]Cl5 · 3H2OLuminescence at 7 K

7B2 S = 3

5A1 S = 2

3B2 S = 11A1 S = 0

ABCD

A

BC

D

4A2 4A2 splitting

first excited state

ground state

5B1 S = 2lowest level of 2E 4A2

Hans U. Güdel and Jim Ferguson, Australian Journal of Chemistry 26(3), 505-11, (1973),

1.

S = 01

2

3

[(ND3)5Cr(OD)Cr(ND3)5]Cl5 · D2OInelastic Neutron Scattering

Hans U. Güdel, Albert Furrer, Molecular Physics 33(5), 1335-44, (1977),

3-ax, λ = 2.34 Å

0– 2 Jab – 13/2 jab

– 6 Jab – 27/2 jab

– 12 Jab – 18/2 jab

E

– 2 Jab = 3.84 ± 0.12 meV+ jab = 0.021 ± 0.023 meV

Hex = – 2 Jab Sa · Sb + jab (Sa · Sb)2

A

B

C

A

B

C

1.

Albert Furrer, Hans U. Güdel Phys. Rev. Lett. 39, 657, (1977),

Variation of Intensity of INS transition Awith Momentum Transfer

Oscillatory behaviour due to interference effects, which are adirect product of metal-metal distance in the cluster

1.

Paramagnetism, Superparamagnetism, and Ferromagnetism

Paramagnet

H = 0 H → H = 0

H

M

Super-paramagnet

H = 0 H → H = 0

H

M

Ferromagnet

H = 0 H → H = 0

H

M

2.

Single Molecule Magnets (SMMs)

⋅ Slow Relaxation of the Magnetisationat Low Temperatures

⋅ Molecular Clusters with Large Spin Ground States and Ising Type Anisotropy

⋅ Intermediate Behaviour Between Classical and Quantum Magnets

2.

The Prototype SMM [Mn12O12(OAc)16(H2O)4]

OAc = acetate

Mn4+

Mn3+

2.

{Mn12O12} core

8 MnIII S = 24 MnIV S = 3/2

⇒ S = 10

The Prototype SMM [Mn12O12(OAc)16(H2O)4]

R. Sessoli et al, J. Am. Chem. Soc. 1993, 115, 1804.

2.

Energy Barrier to Magnetisation Relaxation

Barrier height:

∆ = S2|D|

(integer S)

Mn12: S = 10

D ~ - 0.5 cm-1

∆ = 50 cm-1

H = 0

2.

Slow Magnetisation Relaxation

H = 0

H // easy axis

H = 0

At low temperature...

2.

Resonant Quantum Tunnelling

H = 0

H ≠ 0

H = nD/gµB

magnetisation hysteresis loops

steps due to quantum tunnellingthrough the energy barrier

(D. Gatteschi, R. Sessoli Angew. Chem.Int. Ed., 42, 268 (2003))

2.

Magnetic Relaxation

10 -4

10 -3

10 -2

10 -1

10 0

10 1

10 2

0 2 4 6 8 10

DCAC

1/T (1/K)τ

(s)

Thermally Activated RelaxationArrhenius Expression: τ = τ0 exp (∆/kT)

Quantum Mechanical Tunnelling

2.

Mn12 - Acetate Inelastic Neutron Scattering

Roland Bircher and Hansueli Güdel, Unpublished ResultsSee also: I. Mirebeau, M. Hennion, H. Casalta, H. Anders, H.U. Gudel, A.V. Ivadova, and A. Caneschi, Phys. Rev. Lett. 83, 628 (1999).

Instrument IN5 (ILL), l = 5.9 Å

2.

[Mn12O12(OCH3COO)16(H2O)4]· 2CH3COOH · 4H2O

Hanspeter Andres, Roland Bircher and Hansueli Güdel

O04 = 35SZ4 – (30S(S+1) – 25)SZ2 + 3S2(S+1)2 – 6S(S+1) O44 = 1/2 (S+4 + S–4)

D = –0.457(2) cm–1

B04 = –2.33(4) 10–5 cm–1

B44 = ±3.0(5) 10–5 cm–1

HZFS = D (SZ2 – 1/3S(S+1)) + B04 O04 + B44 O44

2.

INS Study of MnMoO4• Edge-sharing Mn(II)O6

octahedra → tetramers• Tetramers are connected by

Mo(VI)O4 tetrahedra

Exchange pathways:• within tetramers:

Mn-O-Mn • between tetramers:

Mn-O-Mo-O-Mn

• Ferromagnetic alignment of the spins within the clusters.

• Antiferromagnetic ordering of the clusters at 10.7 K.

3.

TOF INS Spectrum of MnMoO4

• instrument: FOCUS at PSI• incident wavelength: 4.75 Å• temperature: 1.5 K

→ 4 peaks on neutron energy loss side

S. T. Ochsenbein et al, Phys. Rev. B 68, 092410 (2003)

3.

Isotropic quantum mechanical model for the intracluster interactions

S. T. Ochsenbein et al, Phys. Rev. B 68, 092410 (2003)

Exchange Interactions of MnMoO4

103.0

9°

3.6

92

Å

3.417 Å

104.13°

95.73°

Mn1

Mn2

Mn3Mn4 O1

J'

J

J = 0.4 cm-1, J´= -0.15 cm-1 S = 10 Ground state

∑ ⋅−= jiji SSJH 2ˆ

3.

Molecular field model for the intercluster interaction

Exchange Interactions of MnMoO4

Molecular Field at Cluster: gµBHmol = -2Jinter〈Scluster〉z, where z = number of neighbours on opposite sublattice ⇒ Jinter =-0.036 cm-1 (average intercluster interaction)

3.

neut

ron

coun

ts

2.52.01.51.00.50.0-0.5energy transfer (meV)

h = l = 0.5

h = l = 0.6

h = l = 0.7

h = l = 0.8

h = l = 0.9

h = l = 1.0

h = l = 1.1

h = l = 1.2

h = l = 1.3

h = l = 1.4

h = l = 1.5k = 0Measured spectra along (h0h):

Peak positions and intensities vary as a function of the scattering vector Q ⇒

spin wave dispersion

Variation in Energies as a Function of Q3.

Dispersion curves along (h 0 h)

S. T. Ochsenbein, H. U. Güdel, P. S. Häfliger, A. Furrer, B. Trusch, J. Hulliger, work in progress

Dispersion revelations contain detailed informationon the inter-cluster exchange interactions.

3.

AcknowledgementsGround State Zero-Field-Splittings of non-Kramers Ions

Group of Philip L.W. Tregenna-Piggott,Department of Chemistry, University of Bern

Graham Carver → Theory of Vibronic Coupling, Spectroscopy of Imidazole Complexes

Christopher Dobe → Cr(II) Tutton Salt ProjectChristopher Noble → Density Matrix Treatment of

Relaxation in JT SystemsMarkus Thut → INS and EPR Study of Mn(III) hexa-aqua

Exchange Coupling in Molecular ClustersGroup of Hansueli Güdel,

Department of Chemistry, University of Bern

Roland Bircher → INS Studies of Single Molecule MagnetsStefan Ochsenbein → Spin-Wave Dispersion in MnMoO4

Reto Basler → INS Study of Mn(III) hexa-aqua

Funded by the Swiss National Science Foundation