Neutron spin polarization and spin analysis by triplet DNP spin filter

Thesis

Reference

Neutron spin polarization and spin analysis by triplet DNP spin filter

NIKETIC, Nemanja

Abstract

It has recently been demonstrated that the triplet dynamic nuclear polarization (DNP) can be used to construct an efficient neutron spin filter based on polarized protons. This motivated to drive the development of this type of spin filter to create a broadband neutron beam polarizer and a spin polarization analyzer for magnetic small-angle neutron scattering. The proton spin filter has been implemented for a first time in a neutron spin analysis experiment, which allowed investigation of the magnetization of CuNiFe alloy and distribution of the precipitates within. The polarized protons represent the only alternative to the existing 3He analyzing cells in experiments that require an opaque spin filter for neutron spin analysis. Even though the application of triplet DNP to spin filter neutrons is still under development, high neutron analyzing powers can be achieved. Further development will significantly improve the triplet DNP filter perfomance and allow various applications in future.

NIKETIC, Nemanja. Neutron spin polarization and spin analysis by triplet DNP spin filter. Thèse de doctorat : Univ. Genève, 2017, no. Sc. 5134

URN : urn:nbn:ch:unige-996973

DOI : 10.13097/archive-ouverte/unige:99697

Available at:

http://archive-ouverte.unige.ch/unige:99697

Disclaimer: layout of this document may differ from the published version.

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UNIVERSIT ´E DE GENEV ´E FACULT ´E DES SCIENCES Section de Physique

Department of Quantum Matter Physics Professeur Ch. R¨uegg PAUL SCHERRER INSTITUTE

Laboratory for Scientific Developments and Novel Materials Dr. P. Hautle

Neutron Spin Polarization and Spin Analysis by Triplet DNP Spin Filter

TH `ESE

Pr´esent´e `a la Facult´e des Sciences de l’Universit´e de Gen`eve Pour obtenir le grade de Docteur `es Sciences, mention Physique

par

Nemanja Niketi´c

de

Belgrade (Serbia)

Th`ese N^◦5134

GEN `EVE

Atelier de reproduction de la Section de Physique

2017

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Publications

During the course of this thesis the following papers have been published:

Journal Papers

E.A. P´erigo, D. Mettus, E.P. Gilbert, P. Hautle, N. Niketic, B. van den Brandt, J. Kohlbrecher, P. McGuiness, Z. Fu, A. Michels, ”Magnetic microstructure of a textured Nd–Fe–B sintered magnet characterized by small angle neutron scattering,” Journal of Alloys and Compounds 661(2016) 110.

N. Niketic, B. van den Brandt, W. Th. Wenckebach, J. Kohlbrecher and P. Hautle,

”Polarization analysis in neutron small-angle scattering with a novel triplet dynamic nuclear polarization spin filter”, Journal of Applied Crystallography 48(2015) 1514.

T.R. Eichhorn, N. Niketic, B. van den Brandt, U. Filges, T. Panzner, E. Rantsiou, W.Th. Wenckebach, P. Hautle, ”Proton polarization above 70% by DNP using photo- excited triplet states, a first step towards a broadband neutron spin filter”, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment 754 (2014) 10.

T.R. Eichhorn,N. Niketic, B. van den Brandt, P. Hautle, W.Th. Wenckebach, ”Neutron spin filtering with dynamically polarized protons using photo-excited triplet states”, Journal of Physics: Conference Series 528(2014) 012022.

Conference Papers

N. Niketic, T. R. Eichhorn, B. van den Brandt, J. Kohlbrecher, P. Hautle and W. Th.

Wenckebach. Neutron spin filtering with polarized protons using photo-excited triplet states. PSI Seminar, Villigen, Switzerland (2014), presentation.

N. Niketic, T. R. Eichhorn, B. van den Brandt, P. Hautle and W. Th. Wenckebach. A technically simple broadband neutron spin filter based on dynamically polarized protons using photo-excited triplet states. SPS Annual Meeting, Fribourg, Switzerland (2014), presentation.

N. Niketic, T. R. Eichhorn, B. van den Brandt, J. Kohlbrecher, P. Hautle and W.

Th. Wenckebach. Neutron spin filtering with dynamically polarized protons using photo-excited triplet states. PSI Summer School, Zug, Switzerland (2014), poster.

P. Hautle N. Niketic, B. van den Brandt, J. Kohlbrecher and W. Th. Wenckebach,

”Dynamic Nuclear Polarization using short-lived photo-excited triplet states: experiments and applications”, Proceedings of Science, Bochum 2015.

N. Niketic, T. R. Eichhorn, B. van den Brandt, P. Hautle and W. Th. Wenckebach.

DNP using photo-excited triplet states: above 70% proton spin polarization at moderate magnetic field and temperature. DNP Summer School, Tramelan, Switzerland (2016), poster.

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This thesis work was performed in the Laboratory for Scientific Developments and Novel Materials of the Paul Scherrer Institute in Switzerland.

v

Acknowledgements

It is my pleasure to take this opportunity to express my gratitude to the people who were supporting me and made this thesis possible.

First of all to Christian R¨uegg for accepting me as his PhD student at the University of Geneva and to Michel Kenzelmann for giving me the opportunity to work in the Labora- tory for Scientific Developments and Novel Materials of the Paul Scherrer Institute. My special thanks go to Patrick Hautle, my project supervisor, for giving me motivation and guidance during this research work and with whom I also had many useful discussions during which I deepened my knowledge in Neutron Scattering and Dynamic Nuclear Polarization. During many coffee/tea breaks with Ben van den Brandt I learned about basics of cryogenics, but also I wish to note that his impact on me goes beyond science.

This work was also strongly supported by Tom Wenckebach, whose expertise in Dynamic Nuclear Polarization and ability to transfer knowledge was of invaluable significance. I would also like to thank Joachim Kohlbrecher for introducing me to SANS measurements and for his help and assistance during beam line experiments, it was a pleasure working with him.

My special thanks go to Uwe Filges, the group leader of Neutron Optics and Scientific Computing Group, and Emmanouela Ranitsiou for their help and support while con- ducting McStas simulations. I also wish to thank my fellows, namely Tim Eichhorn my predecessor who introduced me to the experimental techniques that are essential to this project and also to Yifan Quan my successor who has a great potential to continue this research. This research project was also supported by Paul Schurter who always had brilliant ideas how to solve practical problems.

I also wish to thank Jelena Radovanovi´c and Vitomir Milanovi´c, my supervisors during the Bachelor and Master studies, with whom I made my first steps into the world of science.

Finally this work would not be possible without the support of my closest family, my older brothers Marko and Lazar and parents Zorica and Dorde. They were always with me, whether to advise me or to be there to share happiness with them.

PSI Villigen, April 2017 Nemanja Niketi´c

vii

In memory of my father, who was fighting a cancer during the work of this thesis and unfortunately passed away before it was finished.

ix

Abstract

It has recently been demonstrated that the triplet dynamic nuclear polarization (DNP) can be used to construct an efficient neutron spin filter based on polarised protons. This motivated to drive the development of this type of spin filter to create a broadband neutron beam polarizer and a spin polarization analyzer for magnetic small-angle neutron scattering.

The naphthalene protons in a single crystal of naphthalene:pentacene−d₁₄ are routinely polarized via the triplet DNP method above 70%. In triplet DNP the pentacene molecule provides a high electron polarization upon photo-excitation and only moderate magnetic fields near 0.36 T and temperatures not lower than 25 K are required, making this method easy to integrate in neutron beam line experiments. Under these experimental conditions a proton relaxation time of 600 h is achieved.

Specific attention is dedicated to the understanding of light absorption in a naphthalene:pentacene−d₁₄ crystal system. A set of light absorption cross-sections has been determined, which now allows to find an optimum combination of excitation wavelength and pentacene concentration.

The neutron-proton scattering cross-sections were measured and used to estimate a polarizing efficiency of a triplet DNP spin filter. This allows a comparison of our neutron spin filter with the already existing methods. Further, a proof of principle experiment where a triplet DNP spin filter was placed in between focusing/defocusing supermirror system showed that this method is well suited for polarizing high cross-section neutron beams. This has motivated a novel neutron beam line concept where the polarization of a high cross-section neutron beam is provided by a proton spin filter and the corresponding neutron optics.

We have implemented for a first time a proton spin filter in a neutron spin analysis experiment. In this proof of principle experiment we measured the spin dependent scattering signals of a CuNiFe alloy, which were in the excellent agreement with the theoretical model. Further, we were able to extract information on the magnetization of the sample and distribution of the precipitates in CuNiFe alloy.

The polarized protons represent the only alternative to the existing ³He analyzing cells in experiments that require an opaque spin filter for neutron spin analysis. Even though the application of triplet DNP to spin filter neutrons is still under development, high neutron analyzing powers can be achieved. A significant increase in performance can be expected from a more efficient laser source as well as from using crystal orientations that have potentially higher electron polarization. This would then allow the use of larger cross-section crystals, which is essential for neutron spin analysis experiments.

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Abstrait

Il a r´ecemment ´et´e d´emontr´e que la polarisation dynamique nucl´eaire (DNP) en triplet peut ˆetre utilis´ee pour construire un filtre `a spins de neutrons efficace, en utilisant des protons polaris´es. Cette observation a motiv´e le d´eveloppement de ce type de filtre `a spins pour cr´eer un polariseur `a neutrons `a large spectre et un analyseur de polarisation de spin pour la diffusion `a petit angle des neutrons magn´etiques.

Les protons de naphtal`ene dans un monocristal de naphtal`ene:pentac`ene−d<sub>14</sub> sont polaris´es de fa¸con routini`ere `a un pourcentage sup´erieur `a 70% par la m´ethode DNP en triplet. Dans la DNP en triplet, la mol´ecule de pentac`ene fournit une polarisation

´

electronique ´elev´ee lors de la photo-excitation et ne n´ecessite que des champs magn´etiques mod´er´es, environ 0.36 T, et des temp´eratures sup´erieures `a 25 K. Par cons´equent, cette m´ethode est facile `a int´egrer dans des exp´eriences de faisceau de neutrons en ligne. Dans ces conditions exp´erimentales un temps de relaxation protonique de 600 h a ´et´e atteint.

Une attention particuli`ere a ´et´e consacr´ee `a la compr´ehension de l’absorption de la lumi`ere dans le syst`eme cristallin de naphtal`ene:pentac`ene−d₁₄. Un ensemble de sections transversales d’absorption de lumi`ere a ´et´e d´etermin´e, ce qui permet de trouver une combinaison optimale de longueur d’onde d’excitation et de concentration de pentac`ene.

Les sections transversales de diffusion neutron-proton ont ´et´e mesur´ees et utilis´ees pour estimer l’efficacit´e de polarisation d’un filtre `a spins par DNP en triplet. Cela permet la comparaison de notre filtre `a spins de neutrons avec les m´ethodes existantes. En outre, une preuve de principe, o`u un filtre `a spins par DNP en triplet a ´et´e plac´e dans le syst`eme qui consiste en des super-miroirs de mise en/hors focus, a montr´e que cette m´ethode est bien adapt´ee pour polariser les faisceaux de neutrons `a large section. Ce r´esultat a motiv´e la conception d’un nouveau type de faisceau de neutrons en ligne o`u la polarisation du faisceau de neutrons `a large section est fournie par un filtre `a spins de protons et par l’optique neutronique appropri´ee.

Nous avons mis en place pour la premi`ere fois un filtre `a spins de protons dans une exp´erience d’analyse de spins de neutrons. Dans cette exp´erience de preuve de principe, nous avons mesur´e les signaux de diffusion d´ependant du spin d’un alliage CuNiFe, qui concordaient de mani`ere excellente avec le mod`ele th´eorique. En outre, nous avons

´

et´e capables d’extraire des informations sur la magn´etisation de l’´echantillon et sur la distribution des pr´ecipit´es dans l’alliage CuNiFe.

Les protons polaris´es repr´esentent la seule alternative aux cellules de ³He existantes dans des exp´eriences n´ecessitant un filtre `a spins opaque pour l’analyse de spin neu- tronique. Bien que l’application DNP en triplet aux filtres neutroniques soit encore en d´eveloppement, de hautes performances d’analyse des neutrons peuvent d´ej`a ˆetre atteintes.

Une augmentation significative des performances peut ˆetre attendue d’une source laser plus efficace ainsi que d’utilisation des orientations du cristal ayant une polarisation d’´electrons

potentiellement plus ´elev´ee. Cela permettrait l’utilisation de plus grands cristaux, ce qui est essentiel pour les exp´eriences d’analyse de spin neutronique.

Contents xiii

Contents

Contents xiii

List of Figures xvii

List of Tables xxv

1 Introduction 1

2 Motivation for Triplet DNP - Naphthalene:Pentacene Crystal System 5

2.1 Introduction . . . 5

2.2 Pentacene Triplet States . . . 5

2.2.1 Optical Excitation of Pentacene Triplet States . . . 6

2.2.2 Magnetic Properties of Pentacene Triplet States . . . 7

2.3 Naphthalene:Pentacene Crystal . . . 11

2.4 Production of Naphthalene:Pentacene Crystals . . . 13

2.4.1 Naphthalene Purification . . . 13

2.4.2 Pentacene Doping . . . 14

2.4.3 Crystal Growth . . . 15

2.4.4 Cutting of Crystals to a Desired Shape . . . 16

2.4.5 Growth Results . . . 18

2.5 Conclusions . . . 20

3 Optical Properties of the Naphthalene:Pentacene Crystal System 21 3.1 Introduction . . . 21

3.2 Theoretical Considerations . . . 21

3.2.1 Light Propagation in Birefringent Crystals - Case of Naphthalene . . 22

3.2.2 Singlet Wavefunctions and Light Absorption . . . 25

3.2.3 Absorption of Polarized Light in a Pentacene Molecule . . . 26

3.2.4 Light Absorption Cross-Section . . . 28

3.3 Optical experiments . . . 31

3.3.1 Experimental Set-up and Procedures . . . 31

3.3.2 Transmission Measurements . . . 32

3.3.3 Evaluation of the Pentacene Absorption Cross-Sections . . . 35

3.4 Conclusions . . . 41

4 The Triplet DNP Apparatus 43 4.1 Introduction . . . 43

4.2 The Triplet DNP Apparatus . . . 43

4.3 The Triplet DNP Experiment . . . 44

4.4 Conclusions . . . 47

5 DNP using Pentacene-d14 - the Solid Effect 49 5.1 Introduction . . . 49

5.2 The Solid Effect Based Techniques - Theory . . . 49

5.2.1 The DNP Hamiltonian . . . 49

5.2.2 The Solid Effect . . . 51

5.2.3 Nuclear Orientation Via Electron Spin Locking (NOVEL) . . . 53

5.2.4 Integrated Solid Effect (ISE) . . . 54

5.3 The Solid Effect Experiments . . . 56

5.3.1 Optimization of the SE . . . 56

5.3.2 Characterization of the Polarization Transfer in the SE . . . 60

5.4 Conclusions . . . 63

6 Neutron Spin Filtering with a Polarized Proton Target 65 6.1 Introduction . . . 65

6.2 Scattering of Slow Neutrons . . . 65

6.2.1 Scattering by a Macroscopic Sample . . . 66

6.2.2 Spin Dependence of the Scattering . . . 67

6.2.3 Coherent and Incoherent Scattering . . . 68

6.3 Neutron Filtering with Polarized Protons . . . 70

6.3.1 Neutron-Proton Scattering in Long Wavelength Range . . . 71

6.3.2 Neutron-Proton Scattering Cross-Sections, General Case . . . 73

6.4 Conclusions . . . 74

7 Polarized Protons as a Broadband Neutron Polarizer 77 7.1 Introduction . . . 77

7.2 Cross-Section Measurements . . . 77

7.2.1 Experimental Set-up . . . 77

7.2.2 Time-of-Flight Measurements . . . 78

7.2.3 Experimental Results . . . 79

7.3 Polarization Dependent Bragg Scattering of Cold Neutrons on Naphthalene Crystal . . . 82

7.4 Application of Neutron Focusing Optics . . . 84

7.5 Conclusions . . . 84

8 Novel Approach for Polarization Analysis in Neutron Small-Angle Scattering 87 8.1 Introduction . . . 87

8.2 Theory of Magnetic Scattering . . . 88

8.3 Experimental Methods . . . 91

8.3.1 Triplet Spin Filter . . . 91

8.3.2 Experimental Arrangement . . . 92

8.3.3 Mode of Operation . . . 92

8.4 Experiment and Results . . . 93

8.4.1 Sample Material . . . 93

8.4.2 SANS Experiments . . . 93

8.5 Naphthalene Background and Crystal Orientation . . . 97

8.6 Conclusions . . . 99

9 Case study: McStas Simulation of New Beam Line With Triplet DNP Polarizer101 9.1 Introduction . . . 101

9.2 Neutron Guides and Supermirror Polarizers . . . 101

9.2.1 Techniques for Neutron Spin Polarization . . . 103

Contents xv

9.3 Design of a Broad Wavelength Neutron Beam Line with a Spin Filter as Primary Polarizer . . . 104 9.3.1 Simulation Results . . . 105 9.4 Conclusions . . . 108

10 Conclusion and Outlook 109

Appendix A. SANS Polarization Analysis Experiment - Beam Line Pictures 113 Appendix B. SANS Polarization Analysis Experiment - Data Analysis 117

Bibliography 121

Appendix C. Curriculum Vitae 129

List of Figures xvii

List of Figures

1.1 Figure of meritQof a³He spin filter optimized for a wavelength of 2 ˚A, for two typical polarization values of a³He cell (dashed and solid line). These are compared to the efficiency of the spin filter based on polarized protons of the equal polarization and two spin filter thicknesses. Definition of Qis given in Chapter 6. Figure is taken from Section 7.2, page 81. . . 2 2.1 Structure of the pentacene molecule with orientation of its axis. . . 6 2.2 Detailed scheme of the electron singlet (Si) and triplet (Tj) levels in a

pentacene molecule, along with relevant transitions between the states. The solid lines indicate radiative transitions, while the dashed lines non-radiative ones. . . 6 2.3 Magnetic field orientation in the molecular frame of reference. The angles

θ and φare defined in text. . . 8 2.4 Plot of the energy of the pentacene triplet sub-levels as a function of the

magnetic field strength. The direction of the magentic field is along the pentacene X-axis (B~||X). . . 9 2.5 Comparison between the normalized high field ESR lines of protonated (red

dashed curve) and deuterated (black solid curve) pentacene in a naphthalene single crystal for X k B. The lines were measured at a temperature of~ T = 100 K with a fixed microwave frequency f = 9.325 GHz, by varying the magnetic field nearB = 0.36 T. . . 10 2.6 Calculated evolution of the ESR signal and polarization of the high field

ESR transition, for pentacene-d₁₄ using the values from Tab. 2.2. . . 11 2.7 The naphthalene crystal unit cell with axes a = 8.24 ˚A, b = 6.00 ˚A and

c= 8.66 ˚A, and an angle between theaand caxis of β = 122.92^◦ [30]. We observe that there are two possible orientations of naphthalene molecules. . 12 2.8 Inside a naphthalene unit cell there exist two orientations for the pentacene

molecule. With its length in the X direction of ∼ 12 ˚A it replaces two naphthalene molecules along the c direction. The angle between the two pentacene Z(Y) axes is 47±3^◦, while the angle between the pentacene X-axis and the c axis of the naphthalene crystal is found to be 10^◦ in the ac-plane. [18]. . . 12 2.9 Zone refinement is a purification procedure - impurities in naphthalene are

driven out of the naphthalene while crystallizing and concentrate in the lower part of the ampoule. . . 13 2.10 The crystal growth ampoule (left) with the pentacene transportation tool.

Tip of the transportation tool (right) has a height of 2 mm and inner di- ameter of Ø 1 mm. A single dose is in the order of 1 mg, perfect for low concentration naphthalene:pentacene crystals. . . 14 2.11 The container filled with silicon oil and glycerol is heated in the upper part

establishing a pronounced vertical temperature gradient. The ampoule with polycrystalline naphthalene:pentacene is moving down and passing through the Liquid state zone, after which a single crystal is formed. . . 15

2.12 Left: A small amount of deuterated pentacene is first deposited on the purified naphthalene. Middle: After liquefaction in the oven a homoge- neous distribution of the pentacene molecules is obtained. Right: Naph- thalene:pentacene single crystal after the growth procedure. Single crystals typically have a length of approximately 5 cm in the vertical direction. . . . 16 2.13 The naphthalene cleavage plane, the ab-plane, with the indicated a axis.

This is the first step in the crystal cut procedure. The diameter of the crystal is about 2 cm. . . 17 2.14 The crystal orientation, where the naphthalene b-axis is vertical and pen-

tacene X-axis is aligned to the external magnetic field B. . . .~ 17 2.15 Typical crystal dimensions are 5×5×5 mm³. Crystals above are ordered

by their pentacene concentration, which ranges from 0.5 to 8×10⁻⁵ mol/mol. 18 2.16 The signature of a perfectly cut crystal. The ESR resonance frequency

as a function of the offset angle between the pentacene X-axis and the magnetic fieldB, where 0~ ^◦ corresponds toXkB. The experimental values~ correspond very well to the theoretical prediction (red) and only at extreme position the two pentacene sites start to split. . . 19 2.17 Proton relaxation as a function of the magnetic field strengthB. The crystal

temperature during the measurements was T = 25 K, except for the crystal NS2 2 which was measured at T = 12.5 K . . . 19 3.1 Index ellipsoid of the naphthalene crystal. It is important to notice that

the sample axes (X_p, b, X) are aligned with the ellipsoid axes (α, β, γ), while the naphthalene a axis lies in the (X, Xp) plane. In this coordinate frame the optical tensor is diagonal. . . 22 3.2 Index ellipsoid of the naphthalene crystal with light propagation direction

~k in the bX plane. Ordinary and extraordinary rays are indicated on the short and long axes of the ellipse that lies in the intersection of the ellipsoid and the plane perpendicular to the vector~k. . . 23 3.3 Sketch of the electric displacement field vector D~_a,b and the electric field

vectorE~_a,b. In case of the naphthalenebaxis vectorsD~_bandE~_b are aligned, while in case of theaaxis vectorsD~_aandE~_aare not aligned along the same direction. The angle between them is ξ. The same angle is between the Poynting vector P~_a and the wavevector~k. . . 24 3.4 Absorption axisY makes the angleδ with the incident light of the polariza-

tion ~q. Direction of the Y axis is determined by the angles θ and φ, while polarization angle is α. . . 30 3.5 Apparatus scheme used for the transmission measurements: a) light source,

b) linear light polarizer, c) glass plate which holds the sample, d) the sam- ple - naphthalene:pentacene single crystal, e) optical fiber which collects transmitted light, f) optical spectrometer. . . 32 3.6 Light propagates in a horizontal direction (~k) with its polarization in the

naphthaleneabplane. After entering the crystal, the incident ray is decom- posed into the ordinary and extraordinary ray. Polarization of the o ray is in the b direction, while polarization of the eray is perpendicular to the b axis and has the angle ξ= 8.4^◦ to theaaxis, see Fig. 3.3. . . 33 3.7 Left - transmission measurements with the light polarization vector~qin the

ab plane. Transmission is obtained for different polarization angles. Right - optical density (Ω = −log₁₀T) as a function of the polarization angle at λ= 597 nm. The fitting function is Eq. (3.36). . . 34

List of Figures xix

3.8 Light propagates along theXdirection with its polarization vector~q in the bXpplane. The transmission is measured as a function of the angle between crystal b axis and the polarization vector ~q. Unlike the ab plane, here we have no deflection of the extraordinary ray. . . 34 3.9 Left - transmission measurements with the light polarization vector~qin the

bX_pplane. Transmission is obtained for different polarization angles. Right - optical density (Ω =−log₁₀T) as a function of the polarization angle at λ= 597 nm. The fitting function is Eq. (3.38). . . 35 3.10 Transmission measurements with light propagating perpendicular to thebX

plane. Comparison between pentacene 0-0 and 0-1 singlet transition. . . 37 3.11 Comparison of the 0-1 transition in two different orientations. Left: X_p

axis is vertical and we observe a shift of the peak in the wavelength. Right:

X axis is vertical and we observe no shift of the peak in the wavelength.

Direction vertical on the two figures indicates the direction of light. . . 39 3.12 Transmission measurements for different temperatures, where light propa-

gates along the baxis (light polarization is in the acplane). . . 40 3.13 The proton polarization gradient observed after 30 min abd 90 min of DNP

via ISE, respectively in a neutron transmission experiment. Crystal TS2 which has a high pentacene concentration was used in this experiment. In this plot the laser light of 515 nm propagates from the left side. The fitted values for the absorption length match the one in Tab. 3.7 within the error bar of the measurements. . . 42 4.1 Laser set-up: the infrared laser light (1030 nm) is first focused (A) to the

LBO crystal (B). After the conversion to the green light (515 nm) the laser beam is recollimated (C). The filtering of infrared light occurs through the reflection of the mirrors that are optimized for visible light. Finally it is coupled to the multimode fiber (D). . . 44 4.2 Triplet DNP set-up: the cryostat with the sample is placed between the

poles of the electromagnet and connected to a⁴He dewar. It has an optical access where a multimode fiber is attached. On the table are the microwave generator, microwave amplifier and the ESR spectrometer. On the left side are the NMR and ISE components. . . 45 4.3 The naphthalene:pentacene-d₁₄ single crystal with cross-section of about

5×6 mm² is mounted on a polychlorotrifluorethylene (PCTFE) holder.

The crystal is then mounted to the insert and placed into the cryostat.

The insert has a cadmium aperture with a cross-section of 3×3 mm², which can be easily increased to 4×4 mm² depending on the size of the naphthalene:pentacene-d₁₄ crystal. . . 45 4.4 The cryostat (left), the corresponding insert (mid): (a) a double helium

inlet, (b) the sinter heat exchanger, (c) fibre coupling stage, (d) two optical windows, (e) micro waves and (f) NMR coaxial lines, (g) the ESR cavity.

ESR cavity (right) - dielectric ring resonator (h), microwave coax line (i) with antenna that can move vertically to match the resonance. A low sensitivity NMR coil (j) is wound on the lower support of the dielectric ring. During the polarization transfer, the external magnetic field is swept in time with the ISE coil (k). This figure is taken from [49]. . . 46 4.5 The electron spin echo signal of d-pentacene in p-naphthalene crystal ob-

tained at 100 K and the magnetic field of|B|~ = 0.36T. . . 46

4.6 Scheme of the ISE sequence. During the application of the microwave pulse the magnetic field needs to be swept in time in order to match the polar- ization transfer condition for all electrons in the ESR line. . . 47 5.1 Effective magnetic field in the rotating frame of reference expressed in terms

of angular frequencies B~_{ef f} =−^~ω_γ^{ef f}

S =−_γ¹

S(ω1S,0, ω0S−ω). . . 50 5.2 Plot of ω_1S/2π as a function of (ω_0S −ω)/2π representing the matching

conditions in the rotating frame. Here we have ω0I/2π = 15 MHz, which corresponds to the typical Larmor frequency of protons in our DNP exper- iments for the external magnetic field strength of 0.35 T. The polarization transfer happens at points A and B, where ω1S/2π= 10 MHz. . . 52 5.3 The NOVEL pulse sequence. It consists of three parts: a π/2 pulse, aπ/2

phase shift and a locking pulse with length tduring which the polarization transfer occurs. . . 53 5.4 Value ofω_1S/2πas a function of (ω_0S−ω)/2π fulfilling the matching condi-

tion (5.9). In a NOVEL experiments the matching condition holds at points A and B where ω1S =ω0I. . . 54 5.5 Value of ω_1S/2π as a function of ˙ω/2π following the matching condition

(5.9). The horizontal arrow is the path of the effective frequency vector during the ISE sweep. The matching condition is met twice, at the points A and B. . . 55 5.6 The microwave power calibration with NOVEL. The Hartman-Hahn condi-

tion is found to be near ω1S/2π = 15 MHz. . . 57 5.7 Sketch of an ESR line before (solid line) and during (dashed line) the polar-

ization transfer via the SE, the irradiated two dips correspond to the angular frequencies ω=ω_0S±

q

ω²_0I−ω_1S² . T op: If the microwave frequency is ap- plied at the center of the ESR line no net polarization is transferred to the protons. Bottom: If the microwave frequency is irradiated off-center the two corresponding electron spin packages have unequal weight and there is a significant polarization transfer to the protons. . . 57 5.8 The Solid Effect polarization transfer as a function of the microwave field

intensity ω_1S at external magnetic field varied near B0 = 0.36 T. Legend indicates the power of the microwave radiation on a scale of the Hartman- Hahn condition (HH). . . 58 5.9 The Solid effect polarization as a function of the microwave field intensity

ω_1S. The optimum intensity is achieved at 87% of the Hartman-Hahn con- dition. The highest spin polarization transfer in this case is obtained for the microwave frequency near (ω−ω_0S)/2π = 12 MHz. . . 59 5.10 Comparison between the SE and ISE in a linear regime of the polarization

build up, where the proton relaxation does not have influence. . . 61 5.11 The microwave pulse during the SE in time and frequency domain. The

zero in the frequency domain corresponds to 4.3 MHz, slightly offset of the ESR line center (see Fig. 5.8). . . 62 5.12 Comparison of the polarization build up via the SE and ISE. It is clear that

the ISE is more efficient. . . 62 6.1 Elastic scattering of a slow neutron by a nucleus. Having much larger wave-

length than the size of nuclei, the neutron will be scattered as a spherical wave. The wavevector of the incident neutron is~k, while the wavevector of the scattered wave is k~⁰. . . 65

List of Figures xxi

6.2 Coherent and incoherent cross-section for neutron - proton scattering as a function of the nuclear polarization. . . 70 6.3 Analyzing power (left axis) and transmission (right axis) for different thick-

nesses d of the naphthalene filter with a proton density N = 4.330× 10²²cm⁻³ for a cold neutron beam with a wavelength ofλ= 6 ˚A. . . 72 6.4 Performance of a naphthalene neutron spin filter with a proton spin po-

larization of P = 0.7 (dashed lines) and P = 0.8 (solid lines) for a cold neutron beam with at a wavelength of λ= 6 ˚A. Plotted are the analyzing (polarizing) efficiency (A), total transmission (T) and figure of merit Qas a function of the filter thickness d. . . 73 6.5 Transmissions of the two neutron spin orientations through a naphthalene

filter of 5 mm and 7.5 mm thickness respectively, as function of the proton polarization. Note, their sum divided by 2 gives the transmission of an unpolarized beam plotted in Fig. 6.3 . . . 73 6.6 The absolute value of the polarization cross-section σp as function of the

neutron wavelength. The data points are a compilation of literature values:

black dots and solid line [16], open dot [67] and gray dots [6]. The figure is taken from [10]. The dashed line is to guide the eye. . . 74 7.1 Principal scheme of the experiment used to measure flipping ratios R₊ and

R−. . . 77 7.2 Spectra of neutrons passing through the proton spin filter. We observe a

higher transmission over the whole wavelength spectrum for the neutron spins parallel to the proton polarization (black line). In this measurement the proton polarization relaxed in 24 hours from −44% at the beginning to

−42% at the end of the measurement. . . 78 7.3 Wavelength dependence of the σ₀⁰ cross-section. The fitted value d_f of the

crystal thickness is well within the error bar of the directly measured value dm. . . 80 7.4 Wavelength dependence of the scattering cross-sectionsσ⁰₀,σ₀^P andσ_p. The

values for σ_p are taken from [9]. The lines are to guide the eye. . . 80 7.5 Figures of merit between two methods used for the neutron spin filtering:

polarized³He and polarized protons. ³He needs to be optimized for a certain wavelength range, while polarized protons cover a wide spectrum of neutrons. 81 7.6 (a) Orientation of the naphthalene crystal axes and the pentacene X axis

with respect to the incident neutron beam and the applied magnetic field.

The neutron beam faces the bX-plane of the naphthalene:pentacene crys- tal, with the naphthaleneaaxis making angle of 65.62^o to the pentaceneX axis, andcaxis making 10^o to the same axis. (b) Top view of the naphtha- lene:pentacene crystal, with labelled axes, angles and the distances between the crystal planes. . . 82 7.7 Time-of-Flight spectrum of the neutron transmission through a naphthalene

crystal oriented with respect to the beam according to Fig. 7.6. The neutron spin is anti-parallel to the proton polarization. Bragg scattering is observed from the ab-plane (red labels) as well as for thebc-plane (blue labels). . . . 83 7.8 The Bragg conditions for the two crystal planes as a function of the offset

angle from the optimum DNP condition. Positive offset angles correspond to theaand c axes being rotated clockwise (see Fig. 7.6). . . 83 7.9 Experimental scheme of the neutron lenses used in the experiment. . . 84

8.1 Scheme of the experimental set-up with the arrangement of the filter, sample and cryostat (not to scale). . . 92 8.2 Domain structure of the Cu_68at%Ni_24at%Fe_8at% alloy after the preparation.

In this figure the paramagnetic Cu-rich phase (α-phase) is represented as a green matrix in which are embedded ferromagnetic precipitates. The precipitates are of made of Ni/Fe-rich phase (α⁰-phase). . . 94 8.3 Comparison between model calculations and the experimental SANS data

for the four scattering channels taken at a saturating magnetic field of 520 mT. Top row: Scattering intensities resulting from magnetic and nu- clear interaction (8.28,8.29); second row: structure factor S(~q); third row: product of form factor and structure factor;bottom row: experimental data.

As the I⁺⁺ intensity is much higher the others were multiplied by a factor 5 before color coding. . . 95 8.4 Neutron spin flip scattering induced by the CuNiFe sample for different

magnetic fields: a) B=520 mT, b) B=300 mT, c) B=170 mT and d) B=72 mT. . . 98 8.5 Comparison of the scaled backgrounds. Left: case where the Xb plane is

facing the neutron beam - this is the DNP orientation, the measurement was done forλ= 7.5 ˚A. Right: case where theabplane is facing the neutron beam - this is the orientation for the neutron experiments, the measurement was done for λ= 6 ˚A. . . 98 9.1 First row shows the principle of supermirros, while in the second row we

see the influence of additional layers on the increasing reflectivity for the incident neutron angles. Figure is taken from [108]. . . 102 9.2 The neutron source spectra of a planned additional SANS beam line at the

SINQ facility. . . 104 9.3 Scheme of the new beam line, where instead of supermirrors a proton spin

filter (F) is used in conjunction with parabolic F/D mirrors (E and G) to polarize a high cross-section neutron beam. . . 105 9.4 The spatial distribution of the neutrons on the different positions of the

instrument guide (see Fig. 9.3). Simulations are done for λ= 1.6,2,4,6 and 8 ˚A. Note that all columns have the detector size 50×50 mm², except the column F, the proton spin filter, which has the detector size 5×5 mm². Note that the color scale of an each subfigure is individually normalized, therefore only spatial distribution of the neutrons can be compared between them. . . 106 9.5 Comparison of the neutron divergence at the exit of the defocusing neutron

lens. The angular range is±0.35^◦in vertical and horizontal direction. Note that the color scale of an each subfigure is individually normalized, therefore intensities are not to be compared. . . 106 9.6 Comparison between the two beam line concepts at the sample position.

The even columns are the PSD sensors at the sample position, while odd columns are the divergence monitors at the sample position. The PSD monitors cover a range of 20×20 cm², while the divergence monitors show the angle coverage of ±0.1^◦ on the same spatial size. Note that the color scale of each subfigure is individually normalized, therefore only the spatial distribution and the divergence of the neutrons can be compared here. . . . 107

List of Figures xxiii

1 The triplet DNP apparatus installed at the SANS beam line at the contin- uous spallation neutron source SINQ at the Paul Scherrer Institute. The polarized proton spin filter is situated in the cryostat which is placed be- tween the poles of the electromagnet. The laser light for photo-excitation of the pentacene triplet states is guided from the laser located about 10 m away, to the cryostat via a multimode fiber that runs in the blue tube. The ESR, ISE and NMR systems are placed together into a single compact unit. 113 2 Top view of the spin filter installation. The polarized neutron beam prop-

agates from the right towards the detector on the left, with the triplet analyzer placed in between. The electromagnet together with the polarized proton filter (the analyzer) is placed on a table that allows the translation in horizontal and vertical directions as well as the rotation around the cen- ter. It is therefore easy to align the polarized proton filter to the center of the incoming neutron beam. In the spin analysis experiments, the sample of interest is placed on the outside of the cryostat 32 mm before the analyzer.114 3 The high power infrared laser with the corresponding optics is for safety

reasons installed in a place shielded by concrete blocks. The laser beam is coupled to a multimode fiber and guided towards the cryostat. . . 115 1 Concept of the SANS experiment with the polarization analysis. In this

example we show the case where both, the incident neutrons and the ana- lyzer have a positive polarization. The resulting intensity on the detector is labelled asI↑P. . . 117 2 Flow diagram of the data analysis. The RAW files of the four sets of mea-

surements together with the water and background files are the input. From these RAW files the corresponding intensity matrices are formed for each detector pixel. Then the detector dead time and monitor corrections are applied to the intensity matrices, after which each set of measurements is averaged. Having the intensity matrices properly prepared a water and background correction is done. Finally according to equation (2) the scat- tering cross-sections S↑↑, S↑↓, S↓↑ and S↓↓ are determined. In order to fit the theoretical model to the experimental data radial and circular cuts are applied to the scattering cross-sections. . . 119

List of Tables xxv

List of Tables

2.1 Populations of pentacene triplet sub-levelsTX,TY andTZ at zero field are taken from [18] and for high magnetic field see values in Tab. 2.2. . . 7 2.2 Populations and lifetimes of the triplet states of deuterated pentacene in

naphthalene, of the experimental conditions of T = 100 K, B = 0.36 T and B~ k X. The lifetime of the triplet states of protonated pentacene in naphthalene has been measured with the same apparatus and is taken from [16]. . . 10 3.1 The pentacene concentration obtained from transmission measurements in

two different orientations. The error in these measurements is approxi- mately 10%. Values are given in 10⁻⁵ mol/mol in respect to naphthalene. . 36 3.2 The absorption cross-sections at room temperature at 597 nm, from mea-

surements where the light polarization vector was in the ab plane. The numerical values are given in 10⁻¹⁷cm². . . 36 3.3 The absorption cross-sections at room temperature at 556 nm, from mea-

surements where the light polarization vector was inabplane. The numer- ical values are given in 10⁻¹⁷cm² . . . 38 3.4 The absorption cross-sections at room temperature at 515 nm, from mea-

surements where the light polarization vector was inabplane. The numer- ical values are given in 10⁻¹⁷cm² . . . 38 3.5 Measured values of the Franck-Condon factors obtained from the ratios of

the absorption cross-sections for the 0-1 and 0-2 transition in respect to the 0-0 transition. . . 38 3.6 The optical density for unpolarized light, with its polarization plane in the

ac plane, measured for temperatures down to 20 K for the 602, 556 and 515 nm. Note that these wavelengths do not exactly coincide with the maximums in Fig. 3.12. . . 40 3.7 The absorption lengths in the temperature range 40−60 K for the laser

wavelengths (602, 556 and 515 nm) used in the DNP experiments. The error is in the order of 10%. . . 41 5.1 Parameters used to determine the fraction N⁺ of the ESR line used in the

polarization transfer via the SE. . . 60 8.1 The magnetic properties of Fe and Ni are taken from [97] and

are used to estimate the scattering length densities of the ferromag- netic precipitates Cu_6.7at%Ni_58at%Fe_34.8at% and the paramagnetic matrix Cu_85.5at%Ni_13.6at%Fe_0.9at%. The calculated scattering length density differ- ence ∆η between precipitates and matrix is given for nuclear and magnetic scattering, where the latter is compared to our experimental value given in the last row. . . 94

9.1 Neutron intensities at the sample position (J) with the corresponding polar- ization values obtained with the supermirror polarizer. The ”No polarizer”

and ”With polarizer” intensities are given in 10⁵ cm⁻² s⁻¹. The numerical values for the polarization and the transmission of the V shape supermirror polarizer are from [115]. . . 107 9.2 Neutron polarization intensities at the sample position (J) with the corre-

sponding polarization values obtained with the polarized proton spin fil- ter and focusing/defocusing supermirror system. The ”No polarizer” and

”With polarizer” intensities are given in 10⁵ cm⁻² s⁻¹. The values in the third column are given for the current stage of development - the proton polarization ofPP = 0.71 and the thickness ofd= 4.8 mm, while in the last column we show values that could be expressed after further development - a proton polarization of P_P = 0.80 and thickness ofd= 10 mm. . . 108

Introduction 1

1 Introduction

Modern day research in condensed matter physics employs neutron scattering as a research tool to examine various phenomena. Neutrons are used in elastic and inelastic scattering experiments [1], where the structure and the dynamics of matter systems is investigated.

Their lack of electric charge allows them to penetrate deeply into matter and scatter directly from nuclei. Contrary to X-rays, the neutron scattering cross-section is not pro- portional to the material density and can be very pronounced even for light elements like hydrogen. This has led for example to the development of Neutron Imaging techniques [2]. For the work of this thesis even more important is that the neutron magnetic moment can probe the local magnetic fields inside of materials and provide information about the spatial distribution of spins and energies of magnetic excitations [3].

Polarized neutrons are of a high importance in experiments that investigate magnetic structures, specially in small-angle neutron scattering. Of equal importance is the spin analysis of the scattered neutron beam, which provides information on the neutron spin flip process caused by the local magnetic moment perpendicular to the applied field.

Neutron supermirrors are the standard device to polarize and analyze neutron beams.

Their working principle is rather simple and is based on spin dependent reflection from magnetic materials [4]. Supermirrors require no maintenance, they are easy to set-up and provide a very high polarization for cold neutrons, but become very inefficient below 2

˚A. Further, the restriction in angular acceptance limits their application in neutron spin analysis experiments.

Neutron polarization is also achieved through Bragg reflection from a magnetic single crystal. If the nuclear and magnetic scattering amplitudes are equal, then this leads to the constructive interference of one neutron spin state and destructive interference of the other spin state. These crystals are called Heusler crystals and provide a neutron polarization of about 95%.

Alternatively, polarized nuclei provide a way to build broad-band spin filters with a large acceptance. Optically polarized ³He is often considered the best choice to polarize or analyze wide beams [5]. However its energy-dependent neutron absorption cross-section does not allow to optimise the filter thickness for a broad energy range, see Fig. 1.1. Even more important, the³He filter cell has to be placed in a very homogeneous magnetic field, which makes it difficult to use as an analyzer in an experimental environment with stray magnetic fields, typical for the investigation of magnetic scattering.

Another approach, which overcomes the drawbacks of the ³He, employs dynamically po- larized protons [6]. The strong spin dependence of the neutron-proton scattering cross- section, which is pronounced over a wide range of wavelengths, makes this method an important alternative for designing a broadband neutron spin filter, see Fig. 1.1.

Proton polarization is normally created employing the classical scheme of dynamic nuclear polarization - DNP [7]. One polarizes electron spins by cooling them down to low tem- perature (≈1K) and applying a strong magnetic field (2.5 – 5 T) and then transfers their high thermal equilibrium polarization to the nuclear spins by means of a microwave field.

These stringent conditions can be relieved with a more recent and very promising DNP method that uses optically excited triplet states to achieve high non-equilibrium electron polarization [8]. Here the electron polarization is a result of optical selection rules. In this

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Figure 1.1: Figure of merit Q of a ³He spin filter optimized for a wavelength of 2 ˚A, for two typical polarization values of a³He cell (dashed and solid line). These are compared to the efficiency of the spin filter based on polarized protons of the equal polarization and two spin filter thicknesses. Definition ofQ is given in Chapter 6. Figure is taken from Section 7.2, page 81.

case the requirements for the cryogenic equipment and the magnetic field are significantly relaxed making technically simpler systems with open geometries possible.

It was recently proved that the triplet DNP method can be used to build a reliably working neutron spin filter [9, 10]. Interesting possibilities for a triplet spin filter are also opened by the recent trend in neutron optics to adapt the neutron beam size with focusing guides to the sample which is often only available in very small size [11]. It is the goal of this thesis to assess and demonstrate the potential of the triplet spin filter technique to build an efficient broad band neutron beam polarizer as well as a polarization analyzer for magnetic small-angle neutron scattering.

Structure of the Thesis

In Chapter 2 we describe details on the optical and the magnetic properties of naph- thalene:pentacene single crystals used for triplet DNP and describe the manufacturing process of this crystal system. InChapter 3a detailed model of light absorption via pla- nar molecules that are built in a birefringent crystal is developed and applied to the case of the naphthalene:pentacene crystal system. The model is used to fit polarized light ab- sorption measurements and extract information on the absorption length at wavelengths of interest. Furthermore on this basis a new and very efficient method for concentration mea- surements of pentacene in naphthalene is developed. Chapter 4describes the triplet DNP apparatus used in this work. InChapter 5we present a theoretical overview of the pulsed DNP techniques using short lived photo-excited triplet states. The experimental analysis of the polarization transfer in case of the Solid Effect in the naphthalene:pentacene-d14

crystal system and its comparison to the Integrated Solid Effect is discussed.

3

Chapter 6 introduces the necessary theoretical frame to describe neutron scattering on polarized protons. The quantities of Transmission T, Analyzing Power A and Figure of MeritQare defined, which can be used with the relevant scattering cross-sections to esti- mate the efficiency of the spin filtering with protons and compare it to other techniques.

Chapter 7 describes the measurement of the neutron-proton scattering cross-sections that largely extend the existing data set and provide the necessary values for the effi- ciency assessment. The successful use of a proton spin filter in conjunction with the focusing/defocusing supermirror system is also shown. In Chapter 8 we present the first use of a neutron spin filter based on polarized protons as an analyzer. We describe the proof of principle experiment in which the triplet DNP system is employed for po- larization analysis in a magnetic small-angle scattering experiment on a CuNiFe alloy.

These successful results motivate further development of the apparatus that will allow a wider range of measurements. Finally in Chapter 9 a novel neutron beam line concept is proposed where a proton spin filter is used as a primary polarizer in conjunction with a focusing/defocusing mirror system. The performance of such a beam line is compared through Monte Carlo simulations to a conventional one that uses supermirrors to polarize neutrons. At the end an overall conclusion is drawn and some future perspectives related to the thesis are highlighted.

Motivation for Triplet DNP - Naphthalene:Pentacene Crystal System 5

2 Motivation for Triplet DNP -

Naphthalene:Pentacene Crystal System

2.1 Introduction

A high nuclear spin polarization can be achieved in solid samples with various schemes, the simplest being the brute force method of high magnetic fields and millikelvin sample temperatures. More elegant and much more efficient are methods of dynamic nuclear polarization (DNP) [7], which can be applied to samples containing a small concentration of spatially immobile unpaired electrons (e.g. paramagnetic centres) in addition to the nuclear spins of interest. On irradiation with microwaves of frequency close to the electron paramagnetic resonance frequency, the polarization of the electron spin system can be transferred to the nearby nuclei, taking advantage of the dipolar interaction between the electron and the nuclear spins.

To obtain high nuclear spin polarizations with DNP three conditions must be fulfilled: (1) the electrons need to be highly polarized, (2) they need to relax rapidly, (3) the nuclei need to relax slowly. Then, the electron spin polarization recovers rapidly and can be used again and again to polarize more and more nuclear spins. In classical DNP these conditions are obtained by lowering the temperature to 1 K or below and raising the magnetic field to 2.5 T or higher (70 GHz ESR frequency) while making a judicious choice for the paramagnetic dopant yielding the electron spin.

There are, however, other methods to achieve the same goal. It was shown by the groups of Wenckebach and Hausser that it is possible to use photo-excited triplet states for DNP [8] with the same efficiency as classical DNP [12]. In this case the electron spins of an aromatic molecule are photo-excited in a triplet state that becomes highly polarized as a result of the selection rules of the optical excitation process. Therefore there is no need for high magnetic fields or low temperatures. The naphthalene:pentacene single crystals are a perfect choice for triplet DNP experiments [13], where pentacene molecules provide electron polarization upon photo-excitation.

In this chapter we give an overview of the optical and magnetic properties of pentacene as well as the influence of deuteration of penetacene molecule on the ESR line and lifetime of the triplet states. The procedure of manufacturing naphthalene:pentacene-d14 single crystals is explained in detail together with the recent improvement in control of pentacene doping. Through optical methods the single crystals are oriented and cut in a desired axis orientation. Finally the quality of the grown crystals was estimated through optical, ESR and NMR measurements.

2.2 Pentacene Triplet States

The electronic structure of aromatic molecules can be described in terms of the 2pz and the three hybrid sp2 orbitals of the carbon atom, which are filled with four valence electrons.

The molecular bonds in aromatic molecules are formed when these orbitals of different carbon atoms overlap. They can form either a σ bond - from the two sp2 orbitals, or a π bond - from the two 2pz orbitals. The electrons forming the π bonds have a higher

energy than the electrons in theσ bonds, therefore theπ electrons are governing the light absorption properties. In case of aromatic molecules we have more than two carbon atoms that are mutually connected with the σ and π bonds. More details can be found in [14]

and references therein.

The electrons in the π bond (and in the σ bond) differ by their spin quantum number and can form either a singlet or a triplet state. The singlet state is labelled with S, while the triplet states are labelled withT_X,T_Y andT_Z, whereX,Y andZ are the axes in the molecular frame of reference (Fig. 2.1). In case of a singlet state, the total spin equals 0, while in a triplet state it is 1. Due to the exchange energy, triplet and singlet states occupy different energy levels, and in case of aromatic molecules, the triplet state has a lower energy than the singlet state of the same level.

Figure 2.1: Structure of the pentacene molecule with orientation of its axis.

2.2.1 Optical Excitation of Pentacene Triplet States

Shining laser light on a pentacene molecule we induce S0 → S1 (singlet−singlet) tran- sition. After excitation a majority of the electrons in the excited state S₁ decay through fluorescence back to the ground stateS₀ in the order of 20 ns [15] (see Fig.2.2).

Figure 2.2: Detailed scheme of the electron singlet (Si) and triplet (Tj) levels in a pentacene molecule, along with relevant transitions between the states. The solid lines indicate radiative transitions, while the dashed lines non-radiative ones.

Another path for the electron decay is via the intermediate triplet states. This is a second order process allowed by the spin-orbit interaction - SOI. The SOI is constant in time and can therefore only induce transitions that conserve energy. The excited triplet state T3

2.2. Pentacene Triplet States 7

of a pentacene molecule has approximately the same energy as the excited singlet state S1 (Fig. 2.2), which makes the transition S1 → T3 possible. This type of transition is calledintersystem crossing - ISC. Once the electrons are in theT₃ state they decay fast to theT1 state via vibrational levels. The energy of theT1 state overlaps with the excited vibrational level of the ground stateS0,v allowing the transitionT1 →S0,v again through the spin orbit interaction. From the higher vibrational levelsS_0,vthe electrons decay back to the ground state S0 under dissipation of heat via the so called dark decay.

As the ISC is a second order effect only a fraction of the S₁ states will decay via triplet states. The triplet yield has recently been measured to be in order of 30% for temperatures down to 50K [16]. The ISC efficiency is different for the individual triplet sub-levels and depends on a shape of the molecule [17]. In case of pentacene the selection rules let the triplet sub-level T_Z unpopulated, while transitions to the sub-levels T_Y and T_X are non- zero [18]. This results in a high non-equilibrium population of the triplet sub-levels which makes pentacene a perfect molecule for DNP experiments. Since the pentacene molecule is elongated in the X direction, the matrix element for the S₁ → T_X transition is much larger than the matrix element for theS1 →TY transition. The experimental values are given in Tab. 2.1. The populations N_X,N_Y and N_Z are independent of temperature and magnetic field strength, which relives the experimental conditions, neither high fields nor very low temperatures are required to achieve a high electronic polarization.

State Population T_X 0.91 TY 0.09 T_Z 0.00

Table 2.1: Populations of pentacene triplet sub-levelsTX,TY andTZ at zero field are taken from [18] and for high magnetic field see values in Tab. 2.2.

The same mechanisms that determine the population ofT_X,T_Y andT_Zare also responsible for their decay. Thus, T_X has the shortest, while T_Z the longest lifetime. Overall, the time constants are in the order of tens of µs. Besides the decay, the triplet sub-levels T_X,T_Y and T_Z also thermalize through the spin-lattice relaxation. This process decreases population differences between the triplet sub-levels but has a much longer time constant than the decay process. The DNP experiments require a large number of highly polarized electronic states and it is therefore essential to make an efficient use of the triplet states during their lifetime.

2.2.2 Magnetic Properties of Pentacene Triplet States

Triplet Fine Structure

Due to the dipole-dipole interaction between the electrons in the triplet state, the sub- levels T_X,T_Y and T_Z differ in energy and become non-degenerate even in the absence of an external magnetic field. This is the so called zero field splitting. The Hamiltonian that describes the fine structure of the triplet state is [19],

H_F =D(S_Z² −1

3S(S+ 1)) +E(S_X² −S_Y²) , (2.1) where S_X, S_Y and S_Z are 3×3 matrix representation of spin 1 system on the basis of the molecular principal axes and E = 1381 MHz and D = −42 MHZ are fine structure parameters, experimentally determined by van Strien [18].

Triplet States in the External Magnetic Field

By applying a magnetic field the triplet sub-levels mix and become more separated by the Zeeman interaction. The energy splitting of the triplet sub-levels depends on both the orientation and intensity of the external magnetic field. In the molecular frame (X,Y,Z) the external magnetic field is defined as B~ =B(sinθcosφ,sinθsinφ,cosθ), where θ and φare the polar and the azimuthal angles (see Fig. 2.3).

Figure 2.3: Magnetic field orientation in the molecular frame of reference. The anglesθ andφare defined in text.

The Hamiltonian in the laboratory frame of reference (x, y, z) is given by [19, 20]

HF +HZ =ω0SSz+1 2

D

3(3 cos²θ−1) +Esin²θcos 2φ

(3S_z²−S(S+ 1)) , (2.2) where ω0S = (βBg/~)B0, and the magnetic field is oriented along thez-axis.

High Field Approximation

At sufficiently high magnetic fields, the splitting between the sub-levels is governed by the Zeeman interaction, and we obtain sub-levels which we denote as T−, T0 and T+. These high field eigenstates can be written in the basis of the zero field eigenstates T_X, T_Y and T_Z [19, 20] and in case that the magnetic field B~ is aligned along the pentacene X-axis (B||X) these states are~

T₊=− i

√2T_Y + 1

√2T_Z T0 =TX

T−= i

√

2TY + 1

√ 2TZ .

(2.3)

The population of these sub-levels can be determined by employing Eq. (2.3) and the numerical values in Tab. 2.1. The populations of the triplet sub-levels for X k B~ are N0 ≈0.91 and N+=N− ≈0.045.

2.2. Pentacene Triplet States 9

The frequencies for the two transitions T−↔T0 and T0↔T+ are [19]

ω0±=ω0S±1 2

3E−D

, (2.4)

and their change as the magnetic field increases is given in Fig. 2.4.

Figure 2.4: Plot of the energy of the pentacene triplet sub-levels as a function of the magnetic field strength.

The direction of the magentic field is along the pentaceneX-axis (B||X).~

ESR Transitions

The ESR transitionT0 ↔T+is called the high field and T0 ↔T− the low field transition.

In the following we will analyze the high field transition which is a preferable choice for DNP experiments.

The high field transitions of deuterated and protonated pentacene in the naphthalene host crystal are presented in Fig. 2.5. In case of normal pentacene the hyperfine interaction between the electrons in the triplet states and the hydrogen nuclei of pentacene gives rise to broadening of the triplet ESR line. Deuteration of the pentacene molecule suppresses this interaction and leads to an ESR line that is∼3 times narrower, as we will see below.

Lifetime of Pentacene Triplet States in a Naphthalene Host Crystal

As previously explained, the population of the triplet states is governed by the spin- orbit interaction. The same interaction is responsible for the decay of the triplet states.

Metz and coworkers have shown that the most important mechanism for the non-radiative decay of the triplet T1 state in aromatic molecules is Herzberg-Teller vibronic coupling [21]. Furthermore they show that in case of aromatic molecules the decay rate k_X is governed by C-H bending modes,k_Y mainly by C-C bending modes and k_Z by the both types of bending modes, where kZ << kX +kY. The experimental results of the triplet lifetimes for protonated pentacene in a naphthalene host crystal are found in [18].

The influence of deuteration has been theoretically and experimentally studied in [21–

24]. It was found that triplet lifetimes become longer in case of deuterated pentacene compared to the protonated in case of p-terphenil as a host crystal. The deuteration

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Figure 2.5: Comparison between the normalized high field ESR lines of protonated (red dashed curve) and deuterated (black solid curve) pentacene in a naphthalene single crystal forX kB. The lines were~ measured at a temperature ofT = 100 K with a fixed microwave frequency f = 9.325 GHz, by varying the magnetic field nearB= 0.36 T.

influences mainly the lifetime of theT_X state, while the ones forT_Y andT_Z remain almost unchanged.

In our DNP experiments we use deuterated pentacene inB||X~ orientation and the lifetimes and population of the T0 and T+ states are relevant. According to Eq. (2.3) the lifetime of the T₊ and T₀ sub-levels are

τ(T+) =| hT₊|HSO|S₀i|²

= 1

2(| hT_Y|H_SO|S₀i|²+| hT_Z|H_SO|S₀i|²)

= τ(T_Y) +τ(T_Z) 2 τ(T₀) =τ(T_X) .

(2.5)

We have experimentally determined these values and the results are given in Tab. 2.2.

The lifetime of the sub-levelT0 is easy to measure due to its high population, whereas the lifetime of the T₊ sub-level is harder to obtain. By applying a microwave pulse, which inverts the populations of T0 and T+ before the spin echo pulse, we obtain equally good conditions to measure the lifetime of theT+ sub-level. The measurement results are given in Tab. 2.2.

State Population - pen.-d14 Lifetime[µs] - pen.-d14 Lifetime[µs] - pen.-p14

T0 0.94± 0.01 73± 1 33 ±0.3

T₊ 0.06± 0.01 167± 3 69± 2

Table 2.2: Populations and lifetimes of the triplet states of deuterated pentacene in naphthalene, of the experimental conditions of T = 100 K, B = 0.36 T and B~ k X. The lifetime of the triplet states of protonated pentacene in naphthalene has been measured with the same apparatus and is taken from [16].