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В работе описаны семь программ, реализующих численные методы решения нелинейных уравнений теплопроводности. / In the present work seven programs are described that realize numerical methods for solving nonlinear heat equation.

This experimental work focusses on the magnetic thermal conductivity, κ_mag, of the one-dimensional two-leg spin ladder system Sr_14Cu_24O_41 and the spin chain system SrCuO_2. These two S = 1/2 antiferromagnetic Heisenberg compounds possess enormous magnetic contributions to the heat transport which in some cases exceed the phonon contributions by more than one order of magnitude. Despite of intense ongoing experimental and theoretical investigations, the underlying mechanism of the magnetic heat transport remains unclear. The study of κ_mag aims a better understanding of the basic physics which determine mobility, scattering and dissipation of the dispersing magnetic excitations. The most important tool used in this study is to selectively influence the structure and the electronic and magnetic properties of the compounds through doping. For this purpose single crystalline samples were produced using the Traveling Solvent Floating Zone technique, a crucible-free technology, which allows the growth of centimeter sized single crystals of high quality. In particular, the successful growth of large quantities of the hole-free ladders La_4Sr_10Cu_24O_41 allowed the realization of inelastic neutron scattering and, for the first time, the acquisition of the complete magnetic excitation spectrum of the spin ladder, composed not only by the triplon band, but also by the two-triplon continuum, permitting an accurate determination of the coupling constants in this system. The importance of the cyclic-exchange, previously unclear, was asserted. In order to study the scattering mechanisms of the magnetic excitations (triplons) off static defects in the two-leg ladder Sr_14Cu_24O_41, this compound was doped with tiny amounts of Zn. Occupying the Cu site in the ladders, the Zn plays the role of a non-magnetic defect, imposing an upper limit to the mean free path of the triplons. The thermal conductivity of Sr_14Cu_(14−z)Zn_zO_41, with z = 0, 0.125, 0.25, 0.5 and 0.75, shows a strong decrease of both the phononic and magnetic contributions with increasing z value. In particular, the decrease of the magnetic part indicates an increased scattering of the triplons off Zn defects. The analysis of κ_mag, using a kinetic model, allows the extraction of the triplon mean free path l_mag. This quantity was successfully correlated to the mean Zn-Zn distance along the ladders, confirming the validity of the employed kinetic model and corroborating results of previous works. In SrCuO_2, the magnetic contribution to the thermal conductivity appears as a hump-like anomaly on the high-T back of the low-T phonon peak. In order to better separate the magnetic contribution from the phononic background, small amounts of Sr were substituted by the smaller and lighter Ca, leading, on the one hand, to an increased scattering of the phonons and consequently to a suppression of the phononic thermal conductivity. On the other hand, since Ca is isovalent to Sr, no significant changes of the magnetic properties of the system are expected: a magnetic peak belonging to κ_mag should appear. Measurements of the thermal conductivity of Sr_(1−x)Ca_xCuO_2 for x = 0, 0.0125, 0.025, 0.05 and 0.1 show indeed a systematic decrease of the phonon thermal conductivity with increasing x. However, against initial expectations, no magnetic peak appears. Instead, the magnetic thermal conductivity decreases at intermediate and low temperatures with increasing doping level, indicating a strong influence of the Ca dopant on the magnetic system. Surprisingly, no changes of κ_mag occur at higher temperatures, where κ_mag remains constant for all doping levels. To explain this intriguing temperature and doping dependence of κ_mag, three scenarios are proposed. One of the scenarios is based on the phenomenon of mutual spinon and phonon heat transport, the so called spin-phonon-drag mechanism. Another scenario assumes an effective scattering of spinons off Ca defects. In a third scenario, the appearance of a gap in the doped compounds is considered. The obvious effect of the Ca dopant on the magnetic thermal conductivity motivated a more detailed investigation of the doping dependence of electronic and magnetic properties in Sr_(1−x)Ca_xCuO_2. NMR data reveal the presence of a magnetic gap for the x = 0.1 compound. The doping dependent evolution of the specific heat at low-T is consistent with this result. Furthermore, susceptibility data may be explained within a segmentation of the spin chains, which in turn can be also related to the opening of a gap. These results strongly support that the reduction of κ_mag in the Ca doped compounds is related to a smaller number of magnetic excitations participating in the heat transport due to the presence of the gap. A possible reduction of the chain length, as suggested by the susceptibility data, is also consistent with the scenario of a reduced κ_mag due to an increased scattering of magnetic excitations. In spite of these partially consistent results, there are still no clear-cut explanations for the evolution of κ_mag upon doping. In particular, it cannot be completely ruled out that a fraction of the Ca dopant goes into the chains, a point which has to be urgently clarified in order to allow a correct interpretation of the data.

In dieser Arbeit werden Messungen der elektrischen und thermischen Transportkoeffizienten an einem antiferromagnetisch ordnenden Iridat und FeAs-basierten Hochtemperatursupraleitern vorgestellt und analysiert. Iridate sind Materialien mit starker Spin-Bahn-Kopplung. In dem zweidimensionalen Vertreter Sr_2IrO_4 führt diese Kopplung zu isolierendem Mott-Verhalten mit gleichzeitiger antiferromagnetischer Ordnung der gekoppelten Spin-Bahn-Momente. Somit stellt Sr2IrO4 ein Modellsystem für die Untersuchung magnetischer Anregungen dieser Momente in Iridaten dar. Die Analyse der Wärmeleitfähigkeit von Sr_2IrO_4 liefert erstmals klare Hinweise auf magnetische Wärmeleitung in den Iridaten. Die extrahierte magnetische freie Weglänge gibt Aufschluss über die Streuprozesse der zum Wärmetransport beitragenden Magnonen und lässt Schlüsse über die Anregungen des gekoppelten Spin-Bahnsystems zu. Die FeAs-Hochtemperatursupraleiter haben aufgrund ihrer geschichteten Kristallstruktur einen hauptsächlich zweidimensionalen Ladungstransport. Die Phasendiagramme dieser Materialien setzen sich aus Ordnungsphänomenen zusammen, die Magnetismus, Supraleitung und eine Strukturverzerrung umfassen. Das Hauptaugenmerk richtet sich auf die Reaktion der Transportkoeffizienten mit den sich ausbildenden Phasen in Vertretern der 111- und 122-Familien unter chemischer Dotierung innerhalb und außerhalb der Schichtstruktur. Mithilfe von Widerstand und magnetischer Suszeptibilität lassen sich Phasendiagramme der verschiedenen Supraleiterfamilien konstruieren. In ausgewählten Fällen werden der Hall-Koeffizient und elektrothermische Transporteffekte genutzt, um das Phasendiagramm näher zu erforschen. Der Großteil der Untersuchungen zeigt omnipräsente elektrische Ordnungsphänomene, die als nematische Phase bezeichnet werden. Die Messdaten zeigen, dass die Wärmeleitfähigkeit und der Nernst-Koeffizient dominant von Fluktuationen, die der nematischen Phase vorausgehen, beeinflusst werden. Aus den Ergebnissen der Nernst-Daten an dotiertem BaFe_2As_2 werden Schlüsse über die der nematischen Phase zugrunde liegenden Mechanismen des korrelierten Elektronensystems gezogen.

Fundamental conservation laws predict a dissipationless transport behavior in one-dimensional S=1/2 spin chains. This truly ballistic heat transport suggests anomalously large life times and mean free paths of the elementary excitations of the spin chain, spinons. Despite this rigorous prediction, in any real system, the transport is dissipative, due to the interaction of spinons with defects and phonons. Nevertheless, a promising large magnetic thermal conductivity \\kappa_{mag} has been observed in a few copper-oxide systems. Characteristic for these cuprate systems is a large exchange interaction J along the spin chain. However, due to the limited number and knowledge of the systems showing a large \\kappa_{mag}, it has been difficult, to identify overarching trends. The goal of this thesis therefore is twofold. First, to test new compounds for the appearance of magnetic heat transport and second, to broaden the understanding of the known compounds by studying the influence of various kinds of impurities. In particular, three families of materials are studied. First, the thermal conductivity \\kappa(T) of the compounds TiOBr and TiOCl is investigated. Below room temperature the compounds undergo two phase transitions T_{c2} and T_{c1}. Above T_{c2} the compounds contain S=1/2 spin chains with J_{Cl}=676 K and J_{Br}=375 K respectively, formed by direct orbital overlap of the Ti-atoms. Below T_{c1} the chains dimerize to form a non-magnetic ground state. The thermal conductivity exhibits pronounced anomalies at T_{c2} and T_{c1} confirming the transitions being of second and first order respectively. Surprisingly, \\kappa(T) appears to be dominated by phonon heat conduction, since no indications of a significant magnetic contribution is found. This is in contrast to the expectation of a spin chain system. In this context possible scenarios to understand the unusual behavior of the thermal conductivity are discussed. Second, two related materials, the single chain Sr_{2}CuO_{3} and the double chain SrCuO_{2} are investigated. In high purity samples huge magnetic heat conductivities and concomitantly, extremely large spinon mean free paths of >0.5 µm for Sr_{2}CuO_{3} and >1 µm for SrCuO_{2} are observed. This demonstrates that \\kappa_{mag} is only limited by extrinsic scattering processes, which is a clear signature of ballistic transport in the underlying spin model. Additionally, various subtle modifications of the spin chain are studied. Due to the large mean free path a pristine picture of the intrinsic incidents is expected. In particular, a chemical pressure is applied to the spin chain by doping SrCuO_{2} with Ca. This has a surprisingly strong effect on \\kappa_{mag}. Furthermore, the influence of magnetic Ni and non-magnetic Mg doping is studied for SrCuO_{2}. While Ni-doping has a large impact on the magnetic thermal conductivity, Mg-doping shows no influence. In order to clarify this surprising behavior, \\kappa_{mag} is compared to measurements of the single chain compound Sr_{2}CuO_{3}. Third, the magnetic thermal conductivity of the spin chain material CaCu_{2}O_{3} doped with non-magnetic Zn impurities is studied. \\kappa_{mag} of the pure compound is linear up to room temperature, which is indicative of a T-independent scattering rate of the magnetic excitations. Both, magnitude and T-dependence of \\kappa_{mag} exhibit a very unusual doping dependence. At moderate Zn-doping the linear temperature dependence of \\kappa_{mag} is preserved and the absolute value of \\kappa_{mag} increases. A slight suppression of \\kappa_{mag} occurs only at high Zn doping, where, surprisingly, the T-dependence of \\kappa_{mag} changes from linearity to one with a higher power of T . In order to clarify this surprising behavior, the results are compared to a detailed study of the g-tensor of the impurities in the material by means of ESR experiments, which reveal a change of the impurity type with increasing Zn-content.

Ce travail de thèse est consacré à la mesure de transport de chaleur par les phonons dans le régime quantique dans des systèmes confinés à très basse température.Le contexte de ce sujet est de soumettre ces systèmes à deux conditions extrêmes : basse température et faibles dimensions et de comprendre les propriétés thermiques fondamentales issues de ces limites.Les échantillons étudiés au cours de cette thèse sont des structures suspendues (membrane ou nanofil) ; elles sont élaborées à partir de nitrure de silicium amorphe (SiN).En abaissant la température, les longueurs caractéristiques des phonons comme le libre parcours moyen ou la longueur d'onde dominante des phonons augmentent. Lorsque ces longueurs caractéristiques dépassent les dimensions latérales du système, la diffusion sur les surfaces (boundary scattering) régira les propriétés thermiques. Dans cette limite de diffusion, le transport des phonons va de la diffusion aux surfaces (régime de Casimir) au régime balistique (limite quantique). Dans ce régime balistique, le courant de chaleur peut être exprimé en utilisant le modèle de Landauer. La conductance thermique est alors exprimée par: K=N_α q T où, N_α est le nombre de modes vibratoires peuplés, q=((π²k_B^2)T)⁄3h est la valeur universelle du quantum de conductance thermique et T est le coefficient de transmission.Dans ce travail, les mesures de conductance thermique de nanofils suspendus ont été effectuées jusqu'à très basse température. Une plate-forme de mesure ayant une sensibilité sans précédent a été développée pour mesurer la variation d'énergie inférieure à l'attojoule. Ces nouveaux capteurs permettent de mesurer les propriétés thermiques du guide d'onde de phonon 1D dans le régime quantique du transport de chaleur. Nous montrons que le coefficient de transmission est le facteur dominant qui définit la valeur de conductance thermique. Ce coefficent dépend de la dimension et de la forme des réservoirs ainsi que de la nature du matériau utilisé ce qui rend difficile la mesure du quantum de conductance thermique. Nous montrons que dans toutes les structures de SiN mesurées, le transport thermique pourrait être dominé par des excitations de faible énergie qui existent dans les solides amorphes (a-solides).Le deuxième ensemble important d'expériences concerne la chaleur spécifique. Nous avons étudié les propriétés thermiques de membranes suspendues de SiN très minces que l'on pense être des cavités de phonon 2D. Nous montrons que la dépendance en température de la chaleur spécifique s'écarte du comportement quadratique comme prévu à très basse température. Les modèles pertinents donnant une explication quantitative des résultats sont encore à l'étude. La présence de systèmes à deux niveaux dans les matériaux amorphes pourrait être une explication possible de la valeur absolue élevée de la chaleur spécifique observée. / This PhD entitles Phonon heat transport in the quantum regime is based on the analysis of the thermal properties of confined systems at very low temperature.The context of this subject is putting the systems in two extreme conditions (low temperature and low dimensions) and understand the fundamental thermal properties coming from these limits.The studied samples during this PhD that are suspended structures (membrane or nanowire) are elaborated from amorphous silicon nitride.By lowering the temperature, the phonon characteristic lengths like the mean free path or the phonon dominant wavelength increase. When these characteristic lengths exceed lateral dimensions of the system, the boundary scattering will govern the thermal properties. In the boundary scattering, phonon transport goes from boundary limited scattering (Casimir regime) to ballistics regime (quantum limit). In this ballistic regime, the heat current can be expressed using the Landauer model. The thermal conductance is then expressed as: K=N_α q T where N_α is the number of populated vibrational modes, q=((π²k_B^2)T)⁄3h is the universal value of quantum of thermal conductance, and T is the transmission coefficient.In this work, thermal conductance measurements of suspended nanowires have been performed down to very low temperature. A measurement platform having an unprecedented sensitivity have been developed that can measure a variation of energy smaller than the attojoule. These new sensors allow the measurement of thermal properties of 1D phonon waveguide in the quantum regime of heat transport. We show that the transmission coefficient is the dominant factor that set the thermal conductance value. It depends on the dimension and the shape of the reservoirs, and the nature of the material in use rendering difficult the measurement of the quantum of thermal conductance. We show that in all of the SiN structures, the thermal transport could be dominated by low energy excitations that exist in amorphous solids (a-solids).The second important set of experiments concerns the specific heat. We have studied suspended the thermal properties of very thin SiN membranes that are thought to be 2D phonon cavities. We show that the temperature dependence of the specific heat departs from the quadratic behavior as expected at very low temperature. The true models giving a quantitative explanation of the results is still under consideration. The presence of tunneling two-level systems in amorphous materials could be one possible explanation for the high absolute value of specific heat that has been measured.

Made available in DSpace on 2015-05-14T12:14:21Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1279127 bytes, checksum: 1105a6754e6a3c23ca4d9086f96248a1 (MD5) Previous issue date: 2011-02-25 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / We study two problems involving granular media, the heat transport in viscous granular gases and the mechanical pulse propagation in a granular chains of toroidal ring. To study the heat transport in granular gases, we consider two mechanisms of viscous dissipation during collisions between grains. In the first mechanism, the dissipative force is proportional to the speed of the grain and dissipates not only energy but also momentum. On the other hand, the dissipative force is proportional to the relative velocity of grains and therefore conserves momentum when it dissipates energy. This allows us to explore the role of the conservation of momentum in the heat transport properties of one-dimensional nonlinear systems. We found a thermal conductivity not divergent with or without conservation of momentum. For the system where there is conservation of momentum we obtain the heat flux decreases faster than the energy loss by inelastic dissipation due to shocks, unlike what happens with the momentum conserving system, indicating that the conservation of momentum has a role relevant. We also implemented an approximation of binary collisions to study the propagation of pulses in a onedimensional chain of O-rings. In particular, we get the analytical results from which the pulse velocity is obtained by simple quadrature. The pulse velocity thus calculated is compared with the velocity obtained by numerical integration of the equations of motion. We study chains with and without precompression, chains precompressed by a constant force at both ends (constant precompression), chains precompressed by gravity (variable precompression). The application of binary collisions approximation for precompressed chains gives us an important generalization of a theory, which until then had been developed for chains without precompression, in other words sonic vacuum state. The velocities calculated using the approximation of binary collisions showed a good agreement with the results obtained from numerical simulations, with relative errors lesser than 8%. / Estudamos dois problemas envolvendo meios granulares, o transporte de calor em gases granulares viscosos e a propagação de pulsos mecânicos em cadeias granulares de anéis toróidais. Para estudar o transporte de calor em gases granulares, consideramos dois mecanismos de dissipação viscosa durante as colisões entre grãos. No primeiro mecanismo, a força dissipativa é proporcional á velocidade do grão e dissipa não apenas energia mas também momentum. No outro, a força dissipativa é proporcional a velocidade relativa dos grãos e portanto conserva momento mesmo quando dissipa energia. Isso nos permite explorar o papel da conservação do momento nas propriedades de transporte de calor desse sistema não linear unidimensional. Encontramos uma condutividade térmica não divergente com ou sem conservação de momento. Para o sistema onde não há conservação do momento obtemos que o fluxo de calor decresce mais rapidamente do que a perda de energia por dissipação devido aos choques inelásticos, diferente do que ocorre no sistema com momento conservado, indicando que a conservação de momento apresenta um papel relevante. Também implementamos uma aproximação de colisões binárias para estudar a propagação de pulsos em uma cadeia de unidimensional de anéis toroidais (O-rings). Em particular, chegamos a resultados analíticos a partir dos quais a velocidade do pulso é obtida por quadratura simples. A velocidade do pulso assim calculada é comparada com a velocidade obtida por integraçãoo numérica das equações de movimento. Estudamos cadeias com e sem precompressão, cadeias precomprimidas por uma força constante nas duas extremidades, (precompressão constante) e cadeias precomprimidas pela gravidade (precompressão variável). A aplicação da aproximação de colisões binárias para cadeias precomprimidas nos dá uma importante generalização de uma teoria que até então só havia sido desenvolvida para cadeias sem precompressão, ou seja, para cadeias em vácuo sônico. As velocidades calculadas usando a aproximação de colisões binárias apresentaram uma boa concordância com os resultados obtidos a partir das simulações numéricas, com erros relativos inferiores a 8%.

In dieser Arbeit werden Messungen der elektrischen und thermischen Transportkoeffizienten an einem antiferromagnetisch ordnenden Iridat und FeAs-basierten Hochtemperatursupraleitern vorgestellt und analysiert. Iridate sind Materialien mit starker Spin-Bahn-Kopplung. In dem zweidimensionalen Vertreter Sr_2IrO_4 führt diese Kopplung zu isolierendem Mott-Verhalten mit gleichzeitiger antiferromagnetischer Ordnung der gekoppelten Spin-Bahn-Momente. Somit stellt Sr2IrO4 ein Modellsystem für die Untersuchung magnetischer Anregungen dieser Momente in Iridaten dar. Die Analyse der Wärmeleitfähigkeit von Sr_2IrO_4 liefert erstmals klare Hinweise auf magnetische Wärmeleitung in den Iridaten. Die extrahierte magnetische freie Weglänge gibt Aufschluss über die Streuprozesse der zum Wärmetransport beitragenden Magnonen und lässt Schlüsse über die Anregungen des gekoppelten Spin-Bahnsystems zu. Die FeAs-Hochtemperatursupraleiter haben aufgrund ihrer geschichteten Kristallstruktur einen hauptsächlich zweidimensionalen Ladungstransport. Die Phasendiagramme dieser Materialien setzen sich aus Ordnungsphänomenen zusammen, die Magnetismus, Supraleitung und eine Strukturverzerrung umfassen. Das Hauptaugenmerk richtet sich auf die Reaktion der Transportkoeffizienten mit den sich ausbildenden Phasen in Vertretern der 111- und 122-Familien unter chemischer Dotierung innerhalb und außerhalb der Schichtstruktur. Mithilfe von Widerstand und magnetischer Suszeptibilität lassen sich Phasendiagramme der verschiedenen Supraleiterfamilien konstruieren. In ausgewählten Fällen werden der Hall-Koeffizient und elektrothermische Transporteffekte genutzt, um das Phasendiagramm näher zu erforschen. Der Großteil der Untersuchungen zeigt omnipräsente elektrische Ordnungsphänomene, die als nematische Phase bezeichnet werden. Die Messdaten zeigen, dass die Wärmeleitfähigkeit und der Nernst-Koeffizient dominant von Fluktuationen, die der nematischen Phase vorausgehen, beeinflusst werden. Aus den Ergebnissen der Nernst-Daten an dotiertem BaFe_2As_2 werden Schlüsse über die der nematischen Phase zugrunde liegenden Mechanismen des korrelierten Elektronensystems gezogen.

Fundamental conservation laws predict a dissipationless transport behavior in one-dimensional S=1/2 spin chains. This truly ballistic heat transport suggests anomalously large life times and mean free paths of the elementary excitations of the spin chain, spinons. Despite this rigorous prediction, in any real system, the transport is dissipative, due to the interaction of spinons with defects and phonons. Nevertheless, a promising large magnetic thermal conductivity \\kappa_{mag} has been observed in a few copper-oxide systems. Characteristic for these cuprate systems is a large exchange interaction J along the spin chain. However, due to the limited number and knowledge of the systems showing a large \\kappa_{mag}, it has been difficult, to identify overarching trends. The goal of this thesis therefore is twofold. First, to test new compounds for the appearance of magnetic heat transport and second, to broaden the understanding of the known compounds by studying the influence of various kinds of impurities. In particular, three families of materials are studied. First, the thermal conductivity \\kappa(T) of the compounds TiOBr and TiOCl is investigated. Below room temperature the compounds undergo two phase transitions T_{c2} and T_{c1}. Above T_{c2} the compounds contain S=1/2 spin chains with J_{Cl}=676 K and J_{Br}=375 K respectively, formed by direct orbital overlap of the Ti-atoms. Below T_{c1} the chains dimerize to form a non-magnetic ground state. The thermal conductivity exhibits pronounced anomalies at T_{c2} and T_{c1} confirming the transitions being of second and first order respectively. Surprisingly, \\kappa(T) appears to be dominated by phonon heat conduction, since no indications of a significant magnetic contribution is found. This is in contrast to the expectation of a spin chain system. In this context possible scenarios to understand the unusual behavior of the thermal conductivity are discussed. Second, two related materials, the single chain Sr_{2}CuO_{3} and the double chain SrCuO_{2} are investigated. In high purity samples huge magnetic heat conductivities and concomitantly, extremely large spinon mean free paths of >0.5 µm for Sr_{2}CuO_{3} and >1 µm for SrCuO_{2} are observed. This demonstrates that \\kappa_{mag} is only limited by extrinsic scattering processes, which is a clear signature of ballistic transport in the underlying spin model. Additionally, various subtle modifications of the spin chain are studied. Due to the large mean free path a pristine picture of the intrinsic incidents is expected. In particular, a chemical pressure is applied to the spin chain by doping SrCuO_{2} with Ca. This has a surprisingly strong effect on \\kappa_{mag}. Furthermore, the influence of magnetic Ni and non-magnetic Mg doping is studied for SrCuO_{2}. While Ni-doping has a large impact on the magnetic thermal conductivity, Mg-doping shows no influence. In order to clarify this surprising behavior, \\kappa_{mag} is compared to measurements of the single chain compound Sr_{2}CuO_{3}. Third, the magnetic thermal conductivity of the spin chain material CaCu_{2}O_{3} doped with non-magnetic Zn impurities is studied. \\kappa_{mag} of the pure compound is linear up to room temperature, which is indicative of a T-independent scattering rate of the magnetic excitations. Both, magnitude and T-dependence of \\kappa_{mag} exhibit a very unusual doping dependence. At moderate Zn-doping the linear temperature dependence of \\kappa_{mag} is preserved and the absolute value of \\kappa_{mag} increases. A slight suppression of \\kappa_{mag} occurs only at high Zn doping, where, surprisingly, the T-dependence of \\kappa_{mag} changes from linearity to one with a higher power of T . In order to clarify this surprising behavior, the results are compared to a detailed study of the g-tensor of the impurities in the material by means of ESR experiments, which reveal a change of the impurity type with increasing Zn-content.

This experimental work focusses on the magnetic thermal conductivity, κ_mag, of the one-dimensional two-leg spin ladder system Sr_14Cu_24O_41 and the spin chain system SrCuO_2. These two S = 1/2 antiferromagnetic Heisenberg compounds possess enormous magnetic contributions to the heat transport which in some cases exceed the phonon contributions by more than one order of magnitude. Despite of intense ongoing experimental and theoretical investigations, the underlying mechanism of the magnetic heat transport remains unclear. The study of κ_mag aims a better understanding of the basic physics which determine mobility, scattering and dissipation of the dispersing magnetic excitations. The most important tool used in this study is to selectively influence the structure and the electronic and magnetic properties of the compounds through doping. For this purpose single crystalline samples were produced using the Traveling Solvent Floating Zone technique, a crucible-free technology, which allows the growth of centimeter sized single crystals of high quality. In particular, the successful growth of large quantities of the hole-free ladders La_4Sr_10Cu_24O_41 allowed the realization of inelastic neutron scattering and, for the first time, the acquisition of the complete magnetic excitation spectrum of the spin ladder, composed not only by the triplon band, but also by the two-triplon continuum, permitting an accurate determination of the coupling constants in this system. The importance of the cyclic-exchange, previously unclear, was asserted. In order to study the scattering mechanisms of the magnetic excitations (triplons) off static defects in the two-leg ladder Sr_14Cu_24O_41, this compound was doped with tiny amounts of Zn. Occupying the Cu site in the ladders, the Zn plays the role of a non-magnetic defect, imposing an upper limit to the mean free path of the triplons. The thermal conductivity of Sr_14Cu_(14−z)Zn_zO_41, with z = 0, 0.125, 0.25, 0.5 and 0.75, shows a strong decrease of both the phononic and magnetic contributions with increasing z value. In particular, the decrease of the magnetic part indicates an increased scattering of the triplons off Zn defects. The analysis of κ_mag, using a kinetic model, allows the extraction of the triplon mean free path l_mag. This quantity was successfully correlated to the mean Zn-Zn distance along the ladders, confirming the validity of the employed kinetic model and corroborating results of previous works. In SrCuO_2, the magnetic contribution to the thermal conductivity appears as a hump-like anomaly on the high-T back of the low-T phonon peak. In order to better separate the magnetic contribution from the phononic background, small amounts of Sr were substituted by the smaller and lighter Ca, leading, on the one hand, to an increased scattering of the phonons and consequently to a suppression of the phononic thermal conductivity. On the other hand, since Ca is isovalent to Sr, no significant changes of the magnetic properties of the system are expected: a magnetic peak belonging to κ_mag should appear. Measurements of the thermal conductivity of Sr_(1−x)Ca_xCuO_2 for x = 0, 0.0125, 0.025, 0.05 and 0.1 show indeed a systematic decrease of the phonon thermal conductivity with increasing x. However, against initial expectations, no magnetic peak appears. Instead, the magnetic thermal conductivity decreases at intermediate and low temperatures with increasing doping level, indicating a strong influence of the Ca dopant on the magnetic system. Surprisingly, no changes of κ_mag occur at higher temperatures, where κ_mag remains constant for all doping levels. To explain this intriguing temperature and doping dependence of κ_mag, three scenarios are proposed. One of the scenarios is based on the phenomenon of mutual spinon and phonon heat transport, the so called spin-phonon-drag mechanism. Another scenario assumes an effective scattering of spinons off Ca defects. In a third scenario, the appearance of a gap in the doped compounds is considered. The obvious effect of the Ca dopant on the magnetic thermal conductivity motivated a more detailed investigation of the doping dependence of electronic and magnetic properties in Sr_(1−x)Ca_xCuO_2. NMR data reveal the presence of a magnetic gap for the x = 0.1 compound. The doping dependent evolution of the specific heat at low-T is consistent with this result. Furthermore, susceptibility data may be explained within a segmentation of the spin chains, which in turn can be also related to the opening of a gap. These results strongly support that the reduction of κ_mag in the Ca doped compounds is related to a smaller number of magnetic excitations participating in the heat transport due to the presence of the gap. A possible reduction of the chain length, as suggested by the susceptibility data, is also consistent with the scenario of a reduced κ_mag due to an increased scattering of magnetic excitations. In spite of these partially consistent results, there are still no clear-cut explanations for the evolution of κ_mag upon doping. In particular, it cannot be completely ruled out that a fraction of the Ca dopant goes into the chains, a point which has to be urgently clarified in order to allow a correct interpretation of the data.