Uniform susceptibility of classical antiferromagnets in one and two dimensions in a magnetic field

We simulated the field-dependent magnetization m(H,T) and the uniform susceptibility of classical Heisenberg antiferromagnets in the chain and square-lattice geometry using Monte Carlo methods. The results confirm the singular behavior of at small T,H: and , where D=3 is the number of spin components, J ₀=zJ, and z is the number of nearest neighbors. A good agreement is achieved in a wide range of temperatures T and magnetic fields H with the first-order 1/D expansion results (D.A. Garanin, J. Stat. Phys. 83, 907 (1996)). Received 20 March 2000     

Magnetization of a chain-like antiferromagnet

The temperature dependence of sublattice magnetizations in a chain-like antiferromagnet is investigated by the spin-wave theory considering kinematical interaction and dynamical interaction. For the latter the biquadratic terms are treated in the mean field approximation. The theory for zero-point spin reduction by Herbert and Ishikawa and Oguchi is extended to finite temperatures following Thermo-Field Dynamics approach by Takahashi. Numerical calculations for KCuF₃ show that the kinematical interaction plays an important role for the spontaneous magnetization, and when the effect of dynamical interaction is taken into account, the results obtained come nearer to the experimental ones.     

Magneto-optics of antiferromagnets

Antiferromagnetic crystals in which crystallographic sites occupied by magnetic ions from various sublattices are not transnationally equivalent and are not associated with each other by a symmetry center can have magneto-optic properties distinct from the properties of other antiferromagnets. In particular, birefringence and dichroism of linear polarized light can be observed which are directly proportional to the magnetic field strength, as well as magnetic rotation and circular dichroism quadratic in the field strength. Both effect—the linear magneto-optic effect and quadratic magnetic gyration — are sensitive to the crystal magnetic symmetry and to reorientation of the antiferromagnetic vector. Both effects reverse their signs when the directions of the magnetic moments of a sublattice are changed. These properties of new magneto-optic effects can be used to study the time-reversed domain structure of antiferromagnets, to define the symmetry of magnetic ordering and to study the magnetic crystal energy spectra by spectroscopic methods. The results of experimental studies of the linear magneto-optic effect and quadratic magnetic rotation in tetragonal antiferromagnetic fluorides of transition metals, manganese-germanium garnet and other antiferromagnets are reported. Experimental results on the domain structure of high symmetric antiferromagnets, the point magnetic symmetry of non-collinear multisublattice antiferromagnetic garnet MnGeG are discussed.     

Superconductivity in antiferromagnets

In a perfect spin up spin down antiferromagnet new B.C.S. electronpairs are being described, which are coupled by only a slightly decreased effective interaction. A repulsive interaction is added by virtual spin wave excitation. Depending on the relative strength, superconductivity may exist in such an antiferromagnet.     

Susceptibility of low-dimensional antiferromagnets

The effect of kinematical interaction in the spin-wave theory on the perpendicular susceptibility of quadratic and chain-like antiferromagnets is examined. Results obtained for the perpendicular susceptibility of quadratic antiferromagnets agree with the experimental values at absolute zero for all spin quantum numbers. Numerical calculation of the perpendicular susceptibility of KCuF₃ is made and a large deviation from that due to the simple spin-wave theory is found, as was noted previously for the magnetization.     

Macroscopic magnetic fields of antiferromagnets

The macroscopic magnetic fields arising in the space outside or in the bulk of an antiferromagnet in the absence of external currents are a result of surface magnetization. The general problem of determining these fields is formulated. It is shown that the field distribution near special lines on the surface is monopolar. An experimental study of the field makes it possible to determine the surface magnetization on the faces of an antiferromagnetic crystal. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 9, 724–728 (10 May 1996)     

Luttinger stripes in antiferromagnets

We propose a model for the physics of stripes in antiferromagnets in which the stripes are described by Luttinger liquids hybridized with antiferromagnetic domains. Using bosonization techniques we study the model in the limit where the magnetic correlation length is larger than the inter-stripe distance and propose an explanation for the commensurate-incommensurate phase transition seen in neutron scattering in the underdoped regime of La₂-_χx Sr_χx Cu O₄. The explanation is based on a phase to anti-phase domain transition in the spin configuration which is associated with the transverse motion of the stripes. Using a non-linear σ model to describe the antiferromagnetic regions we conjecture the crystalization of the stripes in the magnetically ordered phase.     

Second magnon in antiferromagnets

Hydrodynamic equations are derived microscopically for Heisenberg antiferromagnets with inclusion of quasimomentum as an almost conserved quantity. For finite external and anisotropy fields, the hydrodynamic quantities are magnetization, energy and momentum density. At small fields, the propagating mode is essentially an oscillation of the local temperature. For high fields it is a wave in the longitudinal magnetization. In the absence of both fields, the staggered magnetization and not the magnetization itself is coupled to momentum and energy. The propagating mode is mainly an energy wave. The propagating part in the staggered magnetization is inversely proportional to the wavelength.     

Broken symmetry in antiferromagnets

We discuss limitations of the conventional ‘broken symmetry’ picture of the Heisenberg antiferromagnet. The exact results on the ground state of the linear chain and of the three-dimensional Hamiltonian do not show a ‘degeneracy of the vacuum’. With the help of a solvable model it is shown that the correlations in the ground state may have the Néel character, as revealed by the neutron experiments, even though the ground state is quite different from the Néel states. There is no Goldstone mode in the linear chain. The spin of the antiferromagnetic spin wave is 1/2. But the physical states have a doublet of the spin waves which could be regarded as degenerate states of spin 1 and spin 0. The fermionic character is suppressed and the bosonic character revealed, as in the decolouring phenomena in quantum field theory. It is plausible that in the three-dimensional case also there is no Goldstone mode.     

Soliton relaxation in antiferromagnets

We study the relaxation two-parameter one-dimensional solitons in antiferromagnets using the phenomenological theory. Allowing for relaxation terms of a relativistic and exchange nature, we set up a system of evolution equations for the constants of the motion of a soliton and calculate the corresponding integral curves, which describe the variation of the soliton parameters in the relaxation process. Zh. éksp. Teor. Fiz. 111, 1633–1650 (May 1997)     

Strongly frustrated random antiferromagnets

A high dimensionality calculation (Weiss like) has been carried out for antiferromagnetism (AFM) in structures with many sublattices. By allowing quenched disorder in the exchange interactions our results clearly exhibit the interplay between the effects of lattice frustration and disorder on the system's properties. For given number of sublattices present, there are several possible phases (ordering of the spins) and as many metastable states in the ergodic phases. It is found that the glassy behavior, and metastability, for multi-sublattices systems is substantially enhanced as compared with simple structures, exhibiting structure dependent de Almeida-Thouless lines. Strongly disordered systems have the long-range AFM ordering, ergodic metastable states and glassy phases intermingled in a non-trivial way. Also, even small fluctuations in the exchange parameters do induce sizeable glassy behavior in structures with many sublattices. Spin glass behavior in apparently non-disordered systems as certain pyrochlores may be accounted for within the present context. Received 9 April 1999 and Received in final form 8 June 1999     

Bipolaronic superconductivity in antiferromagnets

As a model of the cuprate superconductors, we have studied thep hole motion in a planar antiferromagnetic (AFM) background and ac-axis boson field. The indirect coupling between thed spins through thep holes is considered. In a range of the hole concentration, the indirect Cu–Cu interaction enhances the planar AFM coupling though it destroys the weakc-axis AFM order. At higher concentrations, the compensation of thed spins by thep holes occurs. For the strongp-d exchange coupling, thep holes can pair to form small magnetic bipolarons in the enhanced planar AFM background. The in-plane motion of the bipolarons is independent of thec-axis motion assisted by bosons. The superconducting properties of the cuprate superconductors are determined by a 2+1 dimensional bipolaron Hamiltonian. The results obtained from our model are consistent with the observations on the cuprate superconductors.     

Correlation inequalities for antiferromagnets

We prove several correlation inequalities for a class of antiferromagnets with pair interaction and arbitrary fields. To do this we use the Ginibre-Percus method of double variables.