| Introduction |
|
vii | |
|
|
|
1 | (41) |
|
|
|
1 | (14) |
|
1.1.1 Spin gap in cesium divanadate |
|
|
3 | (1) |
|
|
|
4 | (5) |
|
1.1.3 Copper trifluoroacetate |
|
|
9 | (6) |
|
|
|
15 | (13) |
|
1.2.1 Trimers of octahedra in rubidium--copper diphosphate |
|
|
18 | (6) |
|
1.2.2 Trimer plaquettes in sodium--copper germanate |
|
|
24 | (4) |
|
|
|
28 | (5) |
|
1.4 Bose--Einstein condensation of magnons |
|
|
33 | (9) |
|
1.4.1 Pigment of the Han Dynasty |
|
|
34 | (1) |
|
1.4.2 Barium--vanadium disilicate |
|
|
35 | (7) |
|
2 Quasi-one dimensional magnetics |
|
|
42 | (64) |
|
2.1 Homogeneous chain of half-integer spins |
|
|
42 | (12) |
|
2.1.1 Rubidium--copper molybdate |
|
|
44 | (1) |
|
|
|
45 | (9) |
|
2.2 A homogeneous chain with competing interactions |
|
|
54 | (29) |
|
2.2.1 Lithium--copper zirconate |
|
|
56 | (2) |
|
2.2.2 Isostructural cuprates of lithium and sodium |
|
|
58 | (8) |
|
2.2.3 Rubidium--copper--aluminium phosphate |
|
|
66 | (6) |
|
2.2.4 Cesium--copper vanadium-diphosphate |
|
|
72 | (6) |
|
2.2.5 Bismuth--iron selenite--oxochloride |
|
|
78 | (5) |
|
2.3 Alternating chain of half-integer spins |
|
|
83 | (5) |
|
2.4 A homogeneous chain of integer spins |
|
|
88 | (9) |
|
2.5 Spin--Peierls transition |
|
|
97 | (4) |
|
2.6 Orbital mechanism of dimerization of the spin chain |
|
|
101 | (5) |
|
|
|
106 | (18) |
|
3.1 Spin ladders with an odd number of legs |
|
|
106 | (2) |
|
3.2 Spin ladders with an even number of legs: A spin liquid with an energy gap in the spectrum of magnetic excitations |
|
|
108 | (4) |
|
3.3 Charge mechanism of dimerization of the spin ladder |
|
|
112 | (3) |
|
3.4 Combinations of spin chains and spin ladders |
|
|
115 | (2) |
|
|
|
117 | (7) |
|
4 Quasi-two dimensional magnets with a square lattice |
|
|
124 | (14) |
|
|
|
124 | (2) |
|
4.2 The Berezinsky--Kosterlitz--Thouless transition |
|
|
126 | (3) |
|
|
|
129 | (9) |
|
5 Quasi-two dimensional magnetics with a triangular lattice |
|
|
138 | (40) |
|
5.1 Geometrical frustration |
|
|
138 | (13) |
|
5.1.1 Lithium--nickel tellurate |
|
|
142 | (5) |
|
5.1.2 Barium--cobalt antimonide |
|
|
147 | (2) |
|
|
|
149 | (2) |
|
5.2 BKT transition in two-dimensional magnetic materials with a triangular lattice |
|
|
151 | (27) |
|
5.2.1 Chiral and non-chiral polymorphs of manganese antimonate |
|
|
153 | (14) |
|
5.2.2 Lithium--iron antimonate |
|
|
167 | (11) |
|
6 Quasi-two dimensional magnets with a honeycomb magnetic lattice |
|
|
178 | (41) |
|
6.1 Frustration due to the competition of exchange interactions |
|
|
178 | (3) |
|
|
|
181 | (1) |
|
6.3 Experimental realization of Kitaev's model |
|
|
182 | (8) |
|
6.4 BKT transition in the honeycomb lattice |
|
|
190 | (2) |
|
6.5 Antimonates and tellurates of transition metals |
|
|
192 | (27) |
|
|
|
201 | (10) |
|
|
|
211 | (8) |
|
7 Quasi-two-dimensional magnets with triangular motifs in the structure |
|
|
219 | (64) |
|
7.1 Frustration of exchange interactions in the lattice of kagome and in diamond chains |
|
|
219 | (38) |
|
7.1.1 Herbertsmithite and vesignieite |
|
|
221 | (2) |
|
7.1.2 The combination of kagome and triangular layers in quasi-2D cobaltites |
|
|
223 | (14) |
|
|
|
237 | (11) |
|
|
|
248 | (9) |
|
7.2 Plateau of magnetization in the lattice of diamond chains |
|
|
257 | (9) |
|
7.3 Shastry--Sutherland lattice |
|
|
266 | (4) |
|
7.4 Potassium carbonate--manganese vanadate |
|
|
270 | (5) |
|
7.5 Sodium--nickel phosphate hydroxide |
|
|
275 | (8) |
| Conclusion |
|
283 | (2) |
| References |
|
285 | (16) |
| Index |
|
301 | |