The dependence of the energy ylso and the halfwidth Slso of 180" L-domain walls in antiferromagnets on the magnetic field H is calculated for low fields. At H + Ho (Ho is the critical field of the spin-flop transition) the walls expand and their energy yls0 decreases. I n the spin-flop region 90" domain structure appears. yso and 6 , are determined by the value of fourth-order anisotropy constant K,. The calculation of the metastable state ( K , < 0) region shows that its boundaries may be approximated by the astroid at lK21 < Kl only. The wall displacement in the spin-flop region ( K , < 0) and the domain structure at K , > 0 are discussed. The problem of the new magnetic phase nucleation is considered. System of 180" Domains in Low FieldsIt is possible that the formation of the antiferromagnetic domain structure is not related with some dominating mechanism, as in the case of ferromagnets (stray fields). It is simply to assume t h a t i t appears by chance at T, [l]. The ground state of antiferromagnets is degenerated, and domains with different orientation of the antiferromagnetic vector 1 are physically equivalent. Two neighbouring domains that differ by the orientation of 1 demand the formation of a domain wall with the shape determined by the competition between shortrange and long-range interactions. It is evident that in the uniaxial antiferromagnets the system of domains is divided by 180" walls [Z]. We consider the domain structure of uniaxial antiferrornagnets in magnetic fields as a system of L-domains divided by 180" walls. The width and the energy of walls should depend on the temperature T and the magnetic field H . The domain structure is destorted when H i s non-parallel to the crystal axes (along which the vector 1 is oriented a t H = 0 ) .

The influence of antiferromagnetic domain structure on the AF (antiferromagnet) → WF (weak ferromagnet) phase transition is studied. The antiferromagnetic domain structure is considered as a system of antiferromagnetic domains divided by 180° domain walls. AF → WF phase transition occurs by splitting of a 180° wall into two 90° walls and a nucleus of a new phase between 90° walls appears. The structure of the weak ferromagnetic domain wall and its formation from the antiferromagnetic domain structure at the AF → WF phase transition is discussed.

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The application of the elementary excitation theory to the spin system of a ferromagnetic is investigated on the basis of the Heisenberg model. It is found that the spectrum of elementary excitations considered as a gas of quasi-particles, and their distribution function are completely determined by the Hamiltonian of the system. The spectrum of the transverse spin waves and the distribution function both of the transverse and the longitudinal spin waves are calculated by the double-time anticommutator Green's function method. Since the distribution functions have no singularities, it is possible to obtain expressions for the thermodynamic quantities in the form of convergent power series in a small parameter t = TIT,. Expressions