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Inelastic Neutron Scattering (INS)schnack/molmag/... · 2020. 7. 27. · Inelastic neutron data for...
Transcript of Inelastic Neutron Scattering (INS)schnack/molmag/... · 2020. 7. 27. · Inelastic neutron data for...
-
Inelastic Neutron Scattering (INS)
Philip L.W. Tregenna-Piggott
Department of ChemistryUniversity of Bern
Switzerland
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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
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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
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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
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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?
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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
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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
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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
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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
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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.
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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.
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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.
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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.
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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.
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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
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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.
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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.
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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.
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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