Uniaxially anisotropic antiferromagnets in a field along the easy axis
Uniaxially anisotropic antiferromagnets in a field along the easy axis are studied with the help of ground state considerations and Monte Carlo simulations. For classical models, the XXZ model as well as variants, we analyze the role of non-collinear spin configurations of biconical or bidirectional type interpolating between the well-known antiferromagnetic and spin-flop structures. Possible experimental applications to layered cuprate antiferromagnets are discussed. Finally, results of quantum Monte Carlo simulations for the S=1/2 XXZ model on a square lattice are presented, and compared with previous findings.
Old and New Results on Multicritical Points
Thirty years after the Liu–Fisher paper on the bicritical and tetracritical points in quantum lattice gases, these multicritical points continue to appear in a variety of new physical contexts. This paper reviews some recent multicritical phase diagrams, which involve, e.g., high-Tc superconductivity and various magnetic phases which may (or may not) coexist with it. One recent example concerns the SO(5) theory, which combines the 3-component antiferromagnetic and the 2-component superconducting order parameters. There, the competition between the isotropic, biconical and decoupled fixed points yields bicritical or tetracritical points. Recalling old results on the subject, it is shown that the decoupled fixed point is stable, implying a tetracritical point, contrary to recent claims, which are critically discussed. Other examples, concerning, e.g., the superconducting versus charge and spin density wave phases are also discussed briefly. In all cases, extensions of old results can be used to correct new claims.
Neutron Scattering Investigation of Phase Transitions and Magnetic Correlations in the Two-Dimensional Antiferromagnets K 2 Ni F 4 , Rb 2 Mn F 4 , Rb 2 Fe F 4
The quasi-elastic magnetic scattering from the planar antiferromagnets ${\mathrm{K}}_{2}$Ni${\mathrm{F}}_{4}$, ${\mathrm{Rb}}_{2}$Mn${\mathrm{F}}_{4}$, ${\mathrm{Rb}}_{2}$Fe${\mathrm{F}}_{4}$ has been studied over a wide range of temperatures both above and below the phase transition. In all three compounds the diffuse scattering above the phase transition takes the form of a ridge rather than a peak, thus giving the first concrete evidence for the two-dimensional nature of the magnetism. At ${T}_{N}$ (97.1, 38.4, 56.3\ifmmode^\circ\else\textdegree\fi{}K, respectively), the crystals undergo sharp phase transitions to long-range order (LRO) in three dimensions. For $0.002\ensuremath{\le}1\ensuremath{-}\frac{T}{{T}_{N}}\ensuremath{\le}0.1$, the sublattice magnetizations in ${\mathrm{K}}_{2}$Ni${\mathrm{F}}_{4}$ and ${\mathrm{Rb}}_{2}$Mn${\mathrm{F}}_{4}$ follow a ${({T}_{N}\ensuremath{-}T)}^{\ensuremath{\beta}}$ law with $\ensuremath{\beta}=0.14 \mathrm{and} 0.16$, respectively. ${\mathrm{Rb}}_{2}$Mn${\mathrm{F}}_{4}$ is found to have two distinct magnetic phases, both with identical ordering within the planes but with different stacking arrangements of the spins between planes; both phases are found to have identical ${T}_{N}'\mathrm{s}$ and $\ensuremath{\beta}'\mathrm{s}$ to within the experimental accuracy of 0.1\ifmmode^\circ\else\textdegree\fi{}K. The sublattice magnetization in ${\mathrm{Rb}}_{2}$Fe${\mathrm{F}}_{4}$ has a rather more complicated behavior, apparently due to magnetostrictive effects. Finally, in the ordered phase in each compound, the three-dimensional magnetic Bragg peaks are accompanied by "diffuse" scattering which is completely two-dimensional in form. These results are discussed in terms of a model in which the phase transition is viewed as being essentially two-dimensional in character, the three-dimensional ordering simply following as a necessary consequence of the onset of LRO with the planes. The systems therefore should have distinct two- and three-dimensional critical regions. The three-dimensional region apparently was not experimentally accessible with 0.1\ifmmode^\circ\else\textdegree\fi{}K temperature control in ${\mathrm{K}}_{2}$Ni${\mathrm{F}}_{4}$ and ${\mathrm{Rb}}_{2}$Mn${\mathrm{F}}_{4}$, indicating that in these compounds ${|\frac{T}{{T}_{N}}\ensuremath{-}1|}_{3}\ensuremath{\le}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$.