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