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High Resolution Spectroscopy with the Neutron Resonance Spin Echo Method

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High Resolution Spectroscopy with the Neutron Resonance Spin Echo Method High Resolution Spectroscopy with the Neutron Resonance Spin Echo Method vorgelegt von Diplom-Physiker Felix Groitl aus Erlangen von der Fakultät II - Mathematik und Naturwissenschaften der Technischen Universität Berlin zur Erlangung des akademischen Grades Doktor der Naturwissenschaften Dr. rer. nat. genehmigte Dissertation Promotionsausschuss: Vorsitzender: Prof. Dr. M. Kneissl Gutachter: Prof. Dr. D. A. Tennant Gutachter: Prof. Dr. P. Böni Gutachter: Dr. K. Habicht Tag der wissenschaftlichen Aussprache: 18.12.2012 Berlin 2013 D 83 Abstract The first part of this thesis is dedicated to explore new territory for high resolution Neu- tron Resonance Spin Echo (NRSE) spectroscopy beyond measuring lifetimes of elementary excitations. The data analysis of such experiments requires a detailed model for the echo amplitude as a function of correlation time. The model also offers guidance for planning NRSE experiments in terms of a sensible choice of parameters and allows predicting quan- titatively the information content of NRSE spectroscopy for line shape analysis or energy level separation. Major generalizations of the existing formalism, developed in this thesis, allow for violated spin echo conditions, arbitrary local gradient components of the dispersion surface and detuned parameters of the background triple axis spectrometer (TAS) giving rise to important additional depolarizing effects, which have been neglected before. Fur- thermore, the formalism can now be applied to any crystal symmetry class. The model was successfully tested by experiments on phonons in a high quality single crystal of Pb and the results demonstrate the stringent necessity to consider second order depolarization effects. The formalism was subsequently extended to analyze mode doublets. As a major step for- ward, detuning effects for both modes are taken into account here. The model was verified by NRSE measurements on a unique tunable double dispersion setup. The results prove the potential of NRSE spectroscopy to resolve mode doublets with an energy separation smaller than the typical energy resolution of a standard TAS. The second class of NRSE experiments was dedicated to line shape analysis of temperature dependent asymmetric line broadening. Inelastic NRSE spectroscopy was performed on two systems, Cu(NO ) 2.5D O and Sr Cr O . For this purpose high quality single crystals 3 2· 2 3 2 8 of Cu(NO ) 2.5D O were grown in the course of this thesis. As a proof of principle the 3 2· 2 results clearly show that the NRSE method can be used to detect temperature dependent asymmetric line broadening. For the first time this effect was measured with NRSE. The second major part of this thesis was the upgrade of the NRSE option of FLEXX at the BER II neutron source at HZB, Berlin. Redesigned NRSE bootstrap coils allow for a more efficient exploitation of the larger beam cross section, given due to the overall upgrade of FLEXX. Higher accessible coil tilt angles enable measurements on steeper dispersions. The newly designed spectrometer arms result in a more compact instrument, enabling direct beam calibration measurements for the entire accessible wavevector range. In combination with higher coil tilt angles the accessible Q-range in Larmor diffraction geometry is en- hanced. Extensive calibration measurements were performed and the results clearly demon- strate the reliable performance of the new NRSE option, now available for the broader user community at FLEXX. Zusammenfassung Der erste Teil dieser Arbeit erkundet Neuland für die hochauflösende Neutronen Resonanz Spin-Echo (NRSE) Spektroskopie über die Messung von Lebensdauern elementarer Anre- gungen hinaus. Die Datenanalyse solcher Experimente erfordert ein detailliertes Modell der Echoamplitude als Funktion der Korrelationszeit. Das Modell bietet zudem eine Hilfestel- lung für die Experimentplanung in Bezug auf die Wahl der Parameter. Des Weiteren erlaubt es eine quantitative Vorhersage des Informationsgehaltes von NRSE Messungen, z.B. im Be- reich der Linienformanalyse oder der Aufspaltung von Anregungsenergien. Wichtige, in die- ser Arbeit entwickelte Verallgemeinerungen des existierenden Formalismus berücksichtigen Depolarisationseffekte durch Spin-Echo-Bedingungen, die nicht exakt erfüllt sind. Lokale Gradienten der Dispersion mit einer Orientierung, die nicht parallel zum Wellenvektor q sein muss, und geringfügige Abweichungen der Parameter des Dreiachsen-Spektrometers (DAS), welche zu zusätzlichen, zuvor vernachlässigten Depolarisationseffekten führen, wer- den jetzt berücksichtigt. Ferner kann der Formalismus nun auf beliebige Symmetrieklassen angewendet werden. Das Modell wurde erfolgreich mit Experimenten an Phononen in einem Pb-Einkristall mit exzellenter Mosaizität überprüft. Die Ergebnisse demonstrieren die Not- wendigkeit, Depolarisationseffekte zweiter Ordnung zu berücksichtigen. Der Formalismus wurde dahingehend erweitert, die Analyse von Anregungsdubletts zu er- möglichen. Dadurch werden nun Dejustageeffekte für beide Anregungen berücksichtigt. Das Modell wurde durch elastische und inelastische NRSE Messungen an einem eigens dafür entwickelten Aufbau, welcher künstlich aufgespaltene Moden realisiert, überprüft. Die Er- gebnisse zeigen das Potenzial der NRSE Spektroskopie, Anregungsdubletts aufzulösen, deren Energieaufspaltung unter der Energieauflösung eines Standard-DAS liegt. Weitere hier durchgeführte NRSE Experimente widmeten sich der Linienformanalyse tem- peraturabhängiger asymmetrischer Linienverbreiterungen. Dafür wurden inelastische NRSE Messungen an Cu(NO ) 2.5D O sowie an Sr Cr O durchgeführt. Hierfür wurden eigens 3 2· 2 3 2 8 hochwertige Cu(NO ) 2.5D O-Einkristalle gezüchtet. Die Ergebnisse zeigen deutlich, dass 3 2· 2 die NRSE Methode in der Lage ist, eine temperaturabhängige asymmetrische Linienverbrei- terung zu bestimmen. Erstmalig wurde dieser Effekt mit NRSE gemessen. Im Zuge dieser Arbeit wurde außerdem die NRSE-Option des kalten Dreiachsen-Spektrome- ters FLEXX an der Neutronenquelle BER II am HZB, Berlin, aufgerüstet. Die dafür neu ge- fertigten NRSE Bootstrap-Spulen erlauben eine effektivere Ausnutzung des größeren Strahl- querschnitts, der durch das FLEXX Upgrade zur Verfügung steht. Höhere erreichbare Spu- lenkippwinkel bieten zusätzlich Zugang zu steileren Dispersionen. Das durch die neu ent- wickelten Spektrometerarme kompaktere Instrument ermöglicht Kalibrationsmessungen im direkten Strahl für den gesamten zugänglichen Wellenvektor-Bereich. In Kombination mit höheren Spulenkippwinkeln wird der zugängliche Q-Bereich in der Larmor Diffraktionsgeo- metrie vergrößert. Umfangreiche Kalibrationsmessungen zeigen deutlich die Zuverlässigkeit und Leistungsfähigkeit der neuen NRSE-Option, die nun einer breiten Nutzerschaft zu Ver- fügung steht. Table of contents 1 Introduction 1 2 NRSE resolution theory 5 2.1 Principle of inelastic neutron spin echo spectroscopy . .... 5 2.2 Principle of neutron resonance spin echo . .. 8 2.2.1 The π-coil................................. 8 2.2.2 NRSE instrument with 4 π-coils .................... 10 2.2.3 Spinechophononfocusing. 12 2.3 ExtendedNRSEresolutionfunction . 16 2.3.1 Generalized spin echo phase - violated spin echo conditions . 17 2.3.2 The τ dependenceofthepolarization. 24 2.3.3 Quantitative description of depolarization due to sample imperfections 28 2.3.4 Quantitative description of depolarization due to curvature of the dis- persionsurface .............................. 31 2.3.5 Quantitative description of depolarization due to sample imperfections andcurvatureofthedispersionsurface . 35 2.3.6 Dispersion surface not coinciding with the center of the TAS resolution ellipsoid.................................. 36 2.3.7 Numericalexamples ........................... 40 2.4 Experimentaltest................................. 43 2.5 Summary ..................................... 46 3 NRSE investigations on split modes 47 3.1 Two modes within the TAS resolution ellipsoid - Simplified NRSE model . 47 3.2 Second dispersion surface within the TAS resolution ellipsoid - General model 51 3.3 Experimental verification . 54 3.3.1 Experimentalsetup............................ 54 3.3.2 Niobium dispersion models . 55 i ii Table of contents 3.3.3 Elastic measurements on split modes . 56 3.3.4 Inelastic measurements on split modes . 61 3.4 Summary ..................................... 67 4 NRSE line shape analysis 69 4.1 Asymmetric line shape of excitations in Cu(NO ) 2.5D O.......... 70 3 2· 2 4.1.1 Properties of Cu(NO ) 2.5D O..................... 70 3 2· 2 4.1.2 Sample deuteration and growth of single crystals . 71 4.1.3 InelasticNRSEmeasurements. 73 4.2 Asymmetric line shape of excitations in Sr3Cr2O8 ............... 82 4.2.1 Properties of Sr3Cr2O8 .......................... 82 4.2.2 InelasticNRSEmeasurements. 84 4.3 Summary ..................................... 88 5 Upgrade of the NRSE option at FLEXX 89 5.1 Bootstrapcoils .................................. 90 5.1.1 B0 coils .................................. 91 5.1.2 Cooling circuit . 94 5.1.3 RFcoils.................................. 95 5.2 Spinechoinstrumentarms............................ 97 5.2.1 Magnetic shielding . 98 5.2.2 Coupling coils . 101 5.2.3 Motorsandencoders ........................... 102 5.3 Calibration of the new NRSE option at FLEXX . 102 5.3.1 Calibration of currents and HF voltage . 103 5.3.2 Spinechocurveandechopoint . 106 5.3.3 Phasestability .............................. 111 5.3.4 Calibration of coil tilt angles . 112 5.4 Summary ..................................... 116 6 Conclusion
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