Die vorliegende Dissertation beinhaltet eine umfassende Untersuchung der Entscheidbarkeit und Komplexität der Probleme, die sich durch eine statische Analyse von monadischem Datalog auf endlichen gefärbten Bäumen stellen. Statische Analyse bedeutet hierbei Anfrageoptimierung ohne Blick auf konkrete Instanzen, aber mit Rücksicht auf deren zugrunde liegende Struktur. Im Kern beinhaltet dies die Lösung der drei folgenden Probleme: das Leerheitsproblem (die Frage, ob eine Anfrage auf jeder Instanz ein leeres Ergebnis liefert), das Äquivalenzproblem (die Frage, ob zwei Anfragen auf jeder Instanz das gleiche Ergebnis liefern) und das Query-Containment-Problem (die Frage, ob das Ergebnis der einen Anfrage auf jeder Datenbank im Ergebnis der anderen Anfrage enthalten ist). Von Interesse ist dabei, ob die Fragen für eine gegebene Anfragesprache entscheidbar sind und wenn ja, welche Komplexität ihnen innewohnt. Wir betrachten diese Probleme für monadisches Datalog auf unterschiedlichen Repräsentationen für endliche gefärbte Bäume. Hierbei unterscheiden wir zwischen ungeordneten und geordneten Bäumen, welche die Achsen child bzw. firstchild und nextsibling und deren Erweiterung um die descendant-Achse nutzen. Außerdem unterscheiden wir Alphabete mit und ohne Rang. Monadisches Datalog ist eine Anfragesprache, die in Abhängigkeit vom gewählten Schema die Ausdrucksstärke der monadischen Logik zweiter Stufe (MSO) erreicht und dennoch effizient ausgewertet werden kann. Wir zeigen, dass unter in der Datenbanktheorie üblichen Mengensemantik die drei genannten Probleme für alle Schemata ohne descendant-Achse EXPTIME-vollständig sind und lösbar in 2EXPTIME, falls die descendant-Achse involviert ist. Eine passende untere Schranke wird für fast alle Schemata gezeigt. Unter Multimengensemantik lassen sich die obigen Ergebnisse für das Leerheitsproblem übertragen, während das Query-Containment-Problem für alle betrachteten Schemata unentscheidbar ist. / This thesis provides a comprehensive investigation into the decidability and complexity of the fundamental problems entailed by static analysis of monadic datalog on finite labeled trees. Static analysis is used for optimizing queries without considering concrete database instances but exploiting information about the represented structure. Static analysis relies on three basic decision problems. First, the emptiness problem, whose task is to decide whether a query returns the empty result on every database. Second, the equivalence problem asking if the result of two given queries always coincides on every database. And finally, the query containment problem where it is to decide whether on every database a given query produces a subset of the results of a second given query. We are interested in finding out whether these problems are decidable and, if so, what their complexity is. We consider the aforementioned problems for monadic datalog on different representations of finite labeled trees. We distinguish unordered and ordered trees which use the axis child, as well as the axes firstchild and nextsibling, respectively. An extension of the schemas by the descendant-axis is also considered. Furthermore, we distinguish ranked and unranked labeling alphabets. Depending on the schema, the query language monadic datalog can reach the expressive power of monadic second order logic but remains efficiently evaluable. Under set semantics, we show EXPTIME-completness for all used schemas where the descendant-axis is omitted. If the descendant-axis is involved, we present an algorithm that solves the problem within 2-fold exponential time. A matching lower bound is proven for virtually all schemas. Finally, we prove that the complexity of the emptiness problem of monadic datalog on finite trees under bag semantics is the same as under set semantics. Furthermore, we show that the query containment problem of monadic datalog under bag semantics is undecidable in general.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第18051号 / 理博第3929号 / 新制||理||1567(附属図書館) / 30909 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 石田 憲二, 教授 前野 悦輝, 教授 松田 祐司 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

Materials in proximity to quantum critical points (QCPs) experience strong fluctuations in the order parameter associated with the transition and often, as a result, display interesting properties. In this dissertation, we have used a variety of experimental probes such as Shubnikov-de Haas quantum oscillations, thermal conductivity and heat capacity, to better understand two such materials — $A_3T_4$Sn$_{13}$ and YFe$_2$Ge$_2$. $A_3T_4$Sn$_{13}$ ($A$ = Ca, Sr; $T$ = Ir, Rh) is a family of quasi-skutterudite superconductors with moderate $T_c$’s between 4 and 8 K. Although the superconductivity is believed to be phonon-mediated with s-wave pairing symmetry, an unusual second-order structural transition makes this material family fascinating to study. Whether this structural transition is a result of three distortions with perpendicular wavevectors resulting in a cubic-to-cubic transformation, or each wavevector acting independently giving rise to cubic-to-tetragonal transformations and formation of twinned domains is a disputed issue. We have measured quantum oscillations in the resistivity of Sr3Ir4Sn13 and compared it to density functional theory (DFT) calculations for both scenarios. Our results strongly suggest that the former interpretation is correct. The structural transition temperature $T^*$ in $A_3T_4$Sn$_{13}$ can be suppressed to zero by tuning with physical or chemical pressure. In (Ca$_x$Sr$_{1−x}$)$_3$Rh$_4$Sn$_13$, the quantum critical point can be accessed purely by chemical substitution at x ~ 0.9. In the vicinity of the QCP, we expect large fluctuations of the order parameter at low temperatures, which for a structural transition could manifest as a structural disorder. We have measured thermal conductivity at temperatures much lower than $T_c$ and found that it is well described by a single power law with suppressed exponents near the QCP. The heat capacity, however, remains ~ $T^3$. After excluding conventional phonon scattering mechanisms, we propose the possibility of intrinsic quasi-static spatial disorder that is related to the structural QCP. YFe$_2$Ge$_2$ is closely linked to the “122” family of iron-based superconductors like KFe$_2$As$_2$, although it has a significantly lower $T_c$ ~ 1 K. It has a rather three-dimensional Fermi surface which closely resembles that of KFe$_2$As$_2$ in the pressure-induced collapsed tetragonal phase. YFe$_2$Ge$_2$ is in proximity to several types of magnetic order which are predicted by DFT calculations to have lower energy than the non-spin polarised case. Even though YFe$_2$Ge$_2$ is non-magnetic, its superconductivity could be strongly affected by magnetic fluctuations. Through a collaboration with researchers at the University of Waterloo, we have measured the thermal conductivity of YFe$_2$Ge$_2$ down to millikelvin temperatures and up to 2.5 T in field. Our results suggest that YFe$_2$Ge$_2$ is a nodal superconductor. This result could assist in the explanation of the unconventional superconductivity in iron-based superconductors.

This thesis reports light-scattering experiments and visual investigations close to the critical point, in the solvophobic systems, 3-methylpyridine (3MP) + heavy water (D2O) + sodium bromide (NaBr) and methyl ethyl ketone (MEK) + water (W) + secondary butyl alcohol (sBA). The system 3MP + D2O + NaBr was chosen in order to throw more light on the reported crossover from mean-field to Ising-type of critical behaviour shown by this system and to investigate the existence of a mean-field tricritical point in it at an NaBr weight fraction of X = 0.1700, two issues that have been the subject of an intense scientific debate in recent years. The system MEK + W + sBA is the result of our search for a system, other than, the well known 3-methylpyridine (3MP) + water (W) + heavy water (HW) + potassium iodide (KI), in which a quadruple critical point (QCP) can potentially be realized. In addition to this the thesis provides exhaustive details regarding the design, fabrication, and characterization, of a microkelvin thermostat in which a temperature stability of the order of a few microkelvin is achievable despite its relatively simple thermal design. The thesis is organized into 6 Chapters. Chapter 1 provides an introduction to the field of critical phenomena in liquid mixtures. The critical phenomena observed in various systems such as simple fluids, ionic fluids, polymer blends and polymer solutions, and micellar and microemulsion systems, are discussed in brief. Particular attention has been paid to the investigations by various researchers, into, the crossover from Ising to mean-field critical behaviour in electrolyte and polymer solutions, and in amphiphilic systems. Recent theoretical attempts at modeling ionic criticality have also been cited and summarized. A brief discussion on the various types of special critical points and multicritical points that are observed in multicomponent liquid mixtures and other condensed matter systems has been provided. The appealing possiblity of the presence of multicritical points in ionic fluids leading to crossover behaviour is also discussed. The chapter ends with a statement on the goals of this thesis. Chapter 2 describes the instrumentation and other aspects of the experimental techniques used for the light-scattering studies reported in this thesis. Details about the thermal instrumentation such as the water bath and the silicone-oil bath used for the visual investigation experiments and the metal thermostat used for the light-scattering experiments have been provided. The important design considerations relating to the achievement of a high degree of temperature stability (Formula) have been elucidated clearly. The modifications made to the design of the light-scattering thermostat, that enables achievement of a temperature stability of ± 2.5 mK at temperatures 19 ≤ T ≤ 24°C has been discussed. A section has been devoted to the description of the calibration of the temperature sensors we used in our experiments. The light-scattering instrumentation has been discussed in depth. The difficulties associated with the light-scattering techniques when it is used as a tool to study critical phenomena have been detailed. This is followed by a description of the method we used in correcting our light-scattering data for double-scattering effects. A description of the sample cells used for visual investigations and light-scattering experiments along with the sample filling and cleaning procedures followed by us has been described. Chapter 3 deals with the first of the three important problems discussed in this thesis. The chapter is aimed at investigating the crossover behaviour of the solvo-phobic system 3-methylpyridine (3MP)+ water (H2O) + sodium bromide (NaBr), by means of light-scattering studies on the strongly motivated and non-trivial system of 3-methylpyridine (3MP) + heavywater (D2O) + sodium bromide (NaBr). The replacement of H2O by D2O in 3MP + D2O + NaBr, is expected to accentuate the crossover behaviour reportedly displayed by 3MP + H2O + NaBr, and thereby, provide conclusive evidence regarding the existence or otherwise of a crossover between the Ising- and the mean-field-types of critical behaviour in this system. The chapter begins with a detailed literature survey on the topic of the crossover behaviour shown by the system 3MP + H2O + NaBr. We also provide a survey of the effect of the iso-topic H→D substitution on the critical behaviour of binary and quasibinary systems. Through an argument based on small-angle neutron scattering (SANS) studies and the Kirkwood-Buff integrals (KBIs), a strong and cogent motivation is established, which proves that, if the reported crossover behaviour in 3MP + H2O + NaBr is assumed to be correct, then the system 3MP + D2O + NaBr should display not just the same crossover behaviour as shown by the undeuterated system 3MP + H2O + NaBr, but, in addition, also a more pronounced dependence of the crossover temperature on the concentration of NaBr in the mixture than that seen in 3MP + H2O + NaBr. This approach to understand the crossover behaviour of 3MP + H2O + NaBr, has not been used by any of the previous investigators. The coexistence curve data for the system 3MP + D2O + NaBr are obtained at six different values of the NaBr weight fractions viz. X = 0, 0.0250, 0.0800, 0.1200, 0.1500, and 0.1800. The closed-loop immiscibility loop obtained for X = 0, agrees well with the reported phase diagram for 3MP + D2O in the literature. A comparison between the lower-critical lines obtained for the deuterated and the undeuterated system has been provided. Within error bars, no perceptible dip was observed in the critical line at X = 0.1700 in the case of the system 3MP + D2O + NaBr. Hence, our study does not indicate the presence of a mean-field tricritical point that has been reported at X = 0.1700 in the system 3MP + H2O + NaBr. A large section of Chapter 3 is devoted to the results and discussions of our extensive light-scattering experiments on the system 3MP + D2O + NaBr. The experiments were performed on 13 different samples of 3MP + D2O + NaBr with NaBr weight fractions in the range of 0 ≤ X ≤ 0.1900. The choice of the X values were guided by the NaBr concentrations at which earlier investigators have done light-scattering experiments on the system 3MP + H2O + NaBr. Detailed light-scattering experiments reveal that the system 3MP + D2O + NaBr shows a simple Ising-type critical behaviour with γ ' 1.24 and ν ' 0.63 over the entire NaBr concentration range 0 ≤ X ≤ 0.1900. The crossover behaviour is predominantly nonmonotonic, and the crossover is completed well outside the critical domain. An analysis in terms of the effective susceptibility exponent (γeff) showed that the crossover behaviour is nonmonotonic for 0 ≤ X ≤ 0.1793 and tends to become monotonic for X > 0.1793. The correlation length amplitude, ξo, has a value of (Formula) for 0.0250 < X ≤ 0.1900, whereas for (Formula). Since isotopic H—> D substitution is not expected to change the critical behaviour of the system, our results shows that the system 3MP + H2O + NaBr should exhibit universal Ising-type critical behaviour that is typical for aqueous solutions. Our search for a new system in which a quadruple critical point (QCP) could possibly be realized forms the subject matter of the Chapter 4 of the thesis. The system methyl ethyl ketone (MEK) + water (W) + secondary butyl alcohol (sBA) is identified as a very promising candidate-system for this purpose. The chapter begins with a brief survey of the various types of multicritical points and special critical points realizable in multicomponent liquid mixtures. The importance of investigating special critical points such as the QCP is motivated. A detailed coexistence surface for MEK + W + sBA was developed by generating the coexistence curves corresponding to five different, but onstant, values of MEK weight fractions XM = 0.0500, 0.1000, 0.1750, 0.2300, and 0.3000, respectively. The complete isobaric coexistence surface (at 1 atm) for the system MEK + W + sBA was visualized in the form of a prismatic phase diagram. The surface is found to display a tunnel-like appearance in the MEK weight fraction range of 0.0500 ≤ XM ≤ 0.1750, with the tunnel being the narrowest at the point (XM,XW,XSBA) = (0.1750, 0.5801, 0.2449), where, xw and XSBA are, respectively, the weight fractions of water and sBA in the mixture. An analysis of the order parameter data showed that MEK + W + sBA shows near Ising-type of critical behaviour near their upper critical solution temperatures, TU's. It was seen that the critical temperature Tc shows a low drift with time (Formula)/day and that the tunnel-like portion in the phase diagram of MEK + W + sBA was very symmetric. These two features make (MEK + W + sBA) a considerably more promising system than (3MP + W + HW + KI )for the realization of the QCP. It may be recalled that 3MP + W + HW + KI is the only system in which QCP studies have been reported so far in literature. The light-scattering investigations in MEK + W + sBA near the lower critical solution temperatures TL are described next. We corrected our light-scattering data for both turbidity as well as double-scattering effects. Our experiments revealed that (MEK + W + sBA) shows near three-dimensional-Ising type of critical behaviour at the lower critical solution temperatures, with the susceptibility exponent (γ) in the range of 1.217 ≤ γ ≤ 1.246. The correlation length amplitudes (ξo) and the critical exponent (ν) of the correlation length (ξ) were in the ranges of 3.536 ≤ ξo ≤ 4.611 A and 0.619 ≤ ν ≤ 0.633, respectively. An analysis in terms of the effective susceptibility exponent (γeff) results in the interesting result, namely that, the critical behaviour of (MEK + W + sBA ) is of the Ising-type for MEK concentrations in the ranges of 0.1000 ≤ XM ≤ 0.1250 and XM ≥ 0.3000; but, for the intermediate range of 0.1750 < XM < 0.3000, the system shows a tendency towards mean-field type of critical behaviour. This behaviour is interesting because both the constituent binary systems of the ternary system (MEK + W + sBA), namely, (MEK + W) and (W + sBA) show Ising-type of critical behaviour. Chapter 5 discusses another crucial objective of this thesis, namely, the fabrication and characterization of a microkelvin thermostat, which has been built for the purpose of performing light-scattering studies exceptionally close to the critical temperature. At the outset, the need for a temperature stability of the order of a few microkelvin for performing reliable critical point phenomena experiments very close to the critical point, is justified and demonstrated. This is followed by an in-depth account of the thermal design of the thermostat and the electronic circuitry used in the temperature controller. The variations in the ambient temperature and the stability of the bridge excitation source are identified and demonstrated to be crucial factors that affect the long-term temperature stability of the thermostat. A simple compensation scheme to nullify the effects of ambient temprature variations on the controller performance is suggested. It is demonstrated that the thermostat gives a temperature stability of (Formula) and ±60−90 µK for 7 − 14 h over a broad range of 25 − 103 °C. A detailed profile of thermal gradients within the sample recess is provided. It is shown that the parameter ∆Teff [i.e., the difference between the maximum (minimum if ∆Teff has a negative value) temperature within the sample recess and the temperature just outside the sample recess] is a more relevant parameter than ∆T (i.e., the temperature difference between the inner and the outer stages) in understanding the behaviour of multistage thermostats. The most important result that emerges from our study is that the thermal gradients and the transient response of the controller, can both be tuned by varying ∆Teff (or by varying ∆T). The best horizontal and vertical thermal gradient performance observed within our thermostat were 250 and 100 µK/mm, respectively, which are observed for a ∆Teff = 4.46 mK. The transient response of the controller is almost invariant for ∆Teff > 0 but it shows a dramatic decrease of almost 50% when ∆Teff < 0. It is seen that, the limit ∆Teff →>• 0, provides the best operating conditions of the thermostat from the standpoints of temperature stability, transient response and gradient performance. An error analysis relevant to the circuitry used by us is provided at the end of the chapter, which clearly indicates the efficacy of the compensations scheme proposed by us to nullify the effects of ambient temperature variations. Chapter 6 summarizes the important results obtained in this thesis. It also presents a range of open problems that need to be explored further in order to fully understand the results that are reported in this thesis, especially, regarding the type of crossover behaviour seen in the systems 3MP + D2O + NaBr and MEK + W + sBA.

This thesis presents a comprehensive study of the magnetic properties and of quantum phase transitions (QPTs) of two different systems which have been investigated by means of low-temperature magnetization measurements. The systems are the heavy-fermion Yb(Rh1-xCox)2Si2 (metallic) and the quantum magnet NiCl2-4SC(NH2)2 (insulator). Although they are very different materials, they share two common properties: magnetism and QPTs. Magnetism originates in Yb(Rh1-xCox)2Si2 from the trivalent state of the Yb3+ ions with effective spin S = 1=2. In NiCl2-4SC(NH2)2, the magnetic Ni2+ ions have spin S = 1. These magnetic ions are located on a body-centered tetragonal lattice in both systems and, in this study, the QPTs are induced by an external magnetic field. In Yb(Rh1-xCox)2Si2 the evolution of magnetism from itinerant in slightly Co-doped YbRh2Si2 to local in YbCo2Si2 is examined analyzing the magnetic moment versus chemical pressure x phase diagram in high-quality single crystals, which indicates a continuous change of dominating energy scale from the Kondo to the RKKY one. The physics of the antiferromagnet YbCo2Si2 can be completely understood. On the other hand, the physics of pure and slightly Co-containing YbRh2Si2 is much more complex, due to the itinerant character of magnetism and the vicinity of the system to an unconventional quantum critical point (QCP). The field-induced AFM QCP in Yb(Rh0.93Co0.07)2Si2 and in pure YbRh2Si2 under a pressure of 1.5GPa is characterized by means of the magnetic Grüneisen ratio. The final part of this thesis describes quantum criticality near the field-induced QCP in NiCl2-4SC(NH2)2 . These results will be compared to the theory of QPTs in Ising and XY antiferromagnets. Since the XY -AFM ordering can be described as BEC of magnons by mapping the spin-1 system into a gas of hardcore bosons, the temperature dependence of the magnetization for a BEC is analytically derived and compared to the results just below the critical field. The remarkable agreement between the BEC theory and experiments in this quantum magnet is one of the most prominent examples of the concept of universality.

This thesis presents a comprehensive study of the magnetic properties and of quantum phase transitions (QPTs) of two different systems which have been investigated by means of low-temperature magnetization measurements. The systems are the heavy-fermion Yb(Rh1-xCox)2Si2 (metallic) and the quantum magnet NiCl2-4SC(NH2)2 (insulator). Although they are very different materials, they share two common properties: magnetism and QPTs. Magnetism originates in Yb(Rh1-xCox)2Si2 from the trivalent state of the Yb3+ ions with effective spin S = 1=2. In NiCl2-4SC(NH2)2, the magnetic Ni2+ ions have spin S = 1. These magnetic ions are located on a body-centered tetragonal lattice in both systems and, in this study, the QPTs are induced by an external magnetic field. In Yb(Rh1-xCox)2Si2 the evolution of magnetism from itinerant in slightly Co-doped YbRh2Si2 to local in YbCo2Si2 is examined analyzing the magnetic moment versus chemical pressure x phase diagram in high-quality single crystals, which indicates a continuous change of dominating energy scale from the Kondo to the RKKY one. The physics of the antiferromagnet YbCo2Si2 can be completely understood. On the other hand, the physics of pure and slightly Co-containing YbRh2Si2 is much more complex, due to the itinerant character of magnetism and the vicinity of the system to an unconventional quantum critical point (QCP). The field-induced AFM QCP in Yb(Rh0.93Co0.07)2Si2 and in pure YbRh2Si2 under a pressure of 1.5GPa is characterized by means of the magnetic Grüneisen ratio. The final part of this thesis describes quantum criticality near the field-induced QCP in NiCl2-4SC(NH2)2 . These results will be compared to the theory of QPTs in Ising and XY antiferromagnets. Since the XY -AFM ordering can be described as BEC of magnons by mapping the spin-1 system into a gas of hardcore bosons, the temperature dependence of the magnetization for a BEC is analytically derived and compared to the results just below the critical field. The remarkable agreement between the BEC theory and experiments in this quantum magnet is one of the most prominent examples of the concept of universality.:1 Introduction 1 2 Theoretical concepts 5 2.1 Ce- and Yb-based 4f-electron systems . . . . . . . . . . . . . . . . 5 2.1.1 Crystalline electric field . . . . . . . . . . . . . . . . . . . . 6 2.2 Heavy-fermion systems . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.1 Fermi liquid theory . . . . . . . . . . . . . . . . . . . . . . . 8 2.2.2 Kondo eff ect . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2.3 RKKY interaction . . . . . . . . . . . . . . . . . . . . . . . 11 2.2.4 Doniach phase diagram . . . . . . . . . . . . . . . . . . . . . 12 2.3 Quantum phase transitions . . . . . . . . . . . . . . . . . . . . . . . 14 2.3.1 Spin density wave scenario . . . . . . . . . . . . . . . . . . . 16 2.3.2 Local quantum critical point scenario . . . . . . . . . . . . . 17 2.3.3 Global phase diagram . . . . . . . . . . . . . . . . . . . . . 18 2.3.4 The Grüneisen ratio . . . . . . . . . . . . . . . . . . . . . . 21 2.4 Spins are almost bosons . . . . . . . . . . . . . . . . . . . . . . . . 22 3 Experimental methods 31 3.1 Magnetization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.1.1 Magnetization measurements . . . . . . . . . . . . . . . . . 32 3.2 Experimental techniques . . . . . . . . . . . . . . . . . . . . . . . . 34 3.2.1 Faraday magnetometer . . . . . . . . . . . . . . . . . . . . . 35 3.2.1.1 Measurement of the force . . . . . . . . . . . . . . 35 3.2.1.2 Capacitive cell . . . . . . . . . . . . . . . . . . . . 35 3.2.1.3 Design and performance of the cell . . . . . . . . . 37 3.2.1.4 Sensitivity . . . . . . . . . . . . . . . . . . . . . . . 42 3.2.1.5 Background contributions . . . . . . . . . . . . . . 42 3.2.1.6 Calibration . . . . . . . . . . . . . . . . . . . . . . 42 3.2.1.7 Magnets characteristics . . . . . . . . . . . . . . . 44 3.2.1.8 Installation in a dilution refrigerator . . . . . . . . 45 3.2.2 SQUID magnetometer . . . . . . . . . . . . . . . . . . . . . 47 3.3 Magnetization measurements at high pressure . . . . . . . . . . . . 48 3.3.1 Experimental setup for M(H - T) under pressure . . . . . . . 50 4 Yb(Rh1-xCox)2Si2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .51 4.1 Introduction and motivation . . . . . . . . . . . . . . . . . . . . . . 51 4.1.1 The heavy-fermion compound YbRh2Si2 . . . . . . . . . . . 53 4.1.2 The antiferromagnet YbCo2Si2 . . . . . . . . . . . . . . . . 58 4.1.3 Isoelectronic substitution of Co for Rh: Yb(Rh1-xCox)2Si2 . . . .62 4.2 Itinerant vs. local magnetism in Yb(Rh1-xCox)2Si2 . . . . . . . . . 67 4.2.1 Magnetization of Yb(Rh1-xCox)2Si2 with 0 x 0.27 . . . 67 4.2.1.1 YbRh2Si2 and Yb(Rh0.93Co0.07)2Si2 . . . . . . . . . 67 4.2.1.2 Yb(Rh0.88Co0.12)2Si2 . . . . . . . . . . . . . . . . . 71 4.2.1.3 Yb(Rh0.82Co0.18)2Si2 . . . . . . . . . . . . . . . . . 73 4.2.1.4 Yb(Rh0.73Co0.27)2Si2 . . . . . . . . . . . . . . . . . 74 4.2.1.5 Summary . . . . . . . . . . . . . . . . . . . . . . . 78 4.2.2 Magnetization of Yb(Rh1-xCox)2Si2 with x = 0.58 and x = 1 . . . . . 79 4.2.3 Evolution from itinerant to local magnetism . . . . . . . . . 83 4.3 Field-induced QCP in Yb(Rh0.93Co0.07)2Si2 . . . . . . . . . . . . . . 88 4.4 YbRh2Si2 under hydrostatic pressure . . . . . . . . . . . . . . . . . 96 4.4.1 Magnetization vs. field . . . . . . . . . . . . . . . . . . . . . 97 4.4.2 Comparison with 1.28 GPa . . . . . . . . . . . . . . . . . . . 99 4.4.3 Magnetization vs. temperature . . . . . . . . . . . . . . . . 101 4.4.4 Field-induced QCP at 1.5 GPa . . . . . . . . . . . . . . . . 103 4.4.5 The magnetic Grüneisen ratio . . . . . . . . . . . . . . . . . 105 4.5 The magnetic phase diagrams of YbCo2Si2 . . . . . . . . . . . . . . 107 4.5.1 Magnetization vs. temperature . . . . . . . . . . . . . . . . 107 4.5.2 Magnetization vs. fi eld . . . . . . . . . . . . . . . . . . . . . 109 4.5.3 H - T phase diagrams . . . . . . . . . . . . . . . . . . . . 114 4.5.4 Ac-susceptibility . . . . . . . . . . . . . . . . . . . . . . . . 117 4.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 5 NiCl2-4SC(NH2)2 . . . . . . . . . . . . . . . . . . . . . . . .121 5.1 Introduction and motivation . . . . . . . . . . . . . . . . . . . . . . 121 5.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 5.2.1 Magnetization . . . . . . . . . . . . . . . . . . . . . . . . . . 124 5.2.2 Comparison between theory and experiment . . . . . . . . . 126 5.2.3 Magnetic phase diagram . . . . . . . . . . . . . . . . . . . . 129 5.2.4 Speci c heat . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 5.2.5 The magnetic Grüneisen ratio . . . . . . . . . . . . . . . . . 131 5.3 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 6 General conclusions . . . . . . . . . . . . . . . . . . . . . . . .135 Appendix 1 . . . . . . . . . . . . . . . . . . . . . . . .139