Publication list .............................................. iii
Contents ........................................................ v
List of Figures ................................................ ix
1 Introduction ............................................... 1
2 Low dimensional quantum magnetism .......................... 4
2.1 Luttinger liquid ........................................... 7
2.2 Magnetic interactions ..................................... 10
2.2.1 Dipolar interaction ................................ 10
2.2.2 Direct exchange .................................... 11
2.2.3 Superexchange ...................................... 12
2.2.4 Dzyaloshinsky-Moriya interaction ................... 14
2.3 Thermodynamics ............................................ 15
2.3.1 Fundamental thermodynamic relations ................ 15
2.3.2 The antiferromagnetic isotropic s = 1/2
Heisenberg chain ................................... 17
2.3.2.1 Specific heat ............................. 18
2.3.2.2 Susceptibility ............................ 18
2.3.2.3 Excitations ............................... 20
2.4 Magnetic frustration ...................................... 21
2.4.1 The J1-J2 s = 1/2 spin chain ........................ 25
2.4.1.1 Physical realization ...................... 25
2.4.1.2 Ground state and field-induced phases ..... 27
2.4.1.3 Thermodynamics ............................ 32
2.4.1.4 Nuclear magnetic resonance ................ 34
3 Experimental techniques ................................... 37
3.1 Nuclear magnetic resonance ................................ 37
3.1.1 Basic principles of NMR ............................ 38
3.1.2 The Bloch equations ................................ 41
3.1.3 Hyperfine interactions ............................. 45
3.1.3.1 The chemical shift ........................ 45
3.1.3.2 The Knight shift .......................... 46
3.1.3.3 Nuclear nuclear interaction ............... 49
3.1.3.4 Electric quadrupole interaction ........... 50
3.1.3.5 Conclusions ............................... 51
3.1.4 Nuclear relaxation ................................. 55
3.1.5 Experimental setup ................................. 57
3.1.5.1 The NMR spectrometer ...................... 58
3.1.5.2 The magnet and the cryostat ............... 59
3.1.5.3 Sample probes and resonance circuits ...... 60
3.1.5.4 Emission and detection of pulses .......... 62
3.2 Macroscopic techniques .................................... 67
3.2.1 Specific heat ...................................... 67
3.2.1.1 The Einstein model ........................ 68
3.2.1.2 The Debye model ........................... 69
3.2.1.3 Electronic specific heat .................. 71
3.2.1.4 Anomalies in the specific heat ............ 72
3.2.1.5 Experimental details ...................... 74
3.2.2 Magnetization measurements ......................... 77
4 The frustrated spin-chain system linarite PbCuSO4(OH)2 .... 80
4.1 History and crystallographic structure .................... 80
4.2 Physical properties of linarite ........................... 83
5 Thermodynamic studies on linarite ......................... 90
5.1 Susceptibility and magnetization .......................... 91
5.1.1 Experimental details ............................... 91
5.1.2 Results ............................................ 92
5.1.2.1 DC susceptibility measurements ............ 92
5.1.2.2 Angular dependent DC susceptibility
measurements .............................. 97
5.1.2.3 Isothermal magnetization measurements ..... 99
5.1.2.4 AC Susceptibility ........................ 103
5.1.3 Theoretical discussion ............................ 105
5.1.3.1 Saturation fields and Curie-Weiss
temperature .............................. 106
5.1.3.2 Spin susceptibility and magnetization
curve .................................... 108
5.1.3.3 Interchain coupling and symmetric
exchange anisotropy for χ(T) ............ 110
5.1.4 Density functional theory: L(S)DA+U ............... 115
5.2 Specific heat and magnetocaloric effect .................. 118
5.2.1 Experimental details .............................. 118
5.2.2 Results ........................................... 118
5.2.2.1 Cross reference: magnetocaloric effect ... 122
5.3 Magnetostriction and thermal expansion ................... 124
5.3.1 Experimental details .............................. 124
5.3.2 Results ........................................... 124
5.4 The magnetic phase diagram of linarite ................... 126
5.5 Linarite in the context of frustrated chain cuprates ..... 130
6 NMR investigations on linarite ........................... 134
6.1 Constitutive NMR experiments in the paramagnetic state ... 135
6.1.1 Experimental details .............................. 135
6.1.2 Results and discussion ............................ 135
6.2 Angular dependent NMR in the paramagnetic state .......... 145
6.2.1 Experimental details .............................. 145
6.2.2 Results ........................................... 146
6.2.3 Model for the NMR shift in the paramagnetic
regime ............................................ 151
6.3 NMR investigations in the magnetic regions of the phase
diagram of linarite ...................................... 161
6.3.1 Experimental details .............................. 161
6.3.2 NMR in phase I .................................... 162
6.3.2.1 Experimental results ..................... 162
6.3.2.2 Elastic neutron scattering experiments
in region I .............................. 166
6.3.2.3 Theoretical modeling to describe region
I by NMR ................................. 169
6.3.3 NMR in region IV .................................. 175
6.3.4 NMR in region III ................................. 178
6.3.5 NMR in region V ................................... 182
6.4 Nuclear spin-lattice relaxation measurements in
PbCuSO4(OH)2 ............................................. 191
7 Conclusion ............................................... 196
A Susceptibility tensors ................................... 199
B Program source codes ..................................... 201
B.l Introduction to programm variables .................. 203
B.2 sequence.py ......................................... 205
B.3 dipole.py ........................................... 209
B.4 clac.py ............................................. 212
B.5 subroutines.py ...................................... 216
B.6 X3D.py .............................................. 223
B.7 X3D_JCYZ.py ......................................... 234
В.8 analyse.py .......................................... 236
References .................................................... 244
Acknowledgements .............................................. 259
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