## ABSTRACT

A large number of the currently known layered metal oxides are characterized by the geometry of cation ordering in magnetically active layers of the honeycomb-type. This structural type is a variant of the organization of a triangular magnetic lattice, but geometric frustration in this case is removed, since the number of spins in a hexagonal cell is doubled in comparison with triangular. At the same time, it is important to note that the causes of frustration can be not only geometric but also have an exchange nature. In this case, frustration arises from the competition of exchange interactions, when the interaction becomes important not only between the nearest neighbours, but also the nearest neighbours or third, etc. It is well known that in the case of the classical Heisenberg model (S = ∞) on a honeycomb-type lattice, taking into account the exchange interaction only between the nearest neighbors J
_{1}, the Néel antiferromagnetic quantum ground state is realized [260] (Fig. 6.1). In the case, however, when the exchange interactions with the next neighbours (second J
_{2} and/or third J
_{3}) play an important role and have an antiferromagnetic nature, frustration arises in the magnetic system, which substantially complicates the general picture of the ground state. Depending on the sign and the magnitude of the J
_{2}/J
_{1} and J
_{3}/J
_{1} ratios, non-trivial spin configurations, such as zigzag 179ordering, stripe, various spiral structures, etc., can occur [261].
2D honeycomb lattice in the Heisenberg model with exchange interactions up to the third order, <italic>J</italic>
<sub>1,2,3</sub>, and the simplest spin-configuration diagrams.
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