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
TL;DR: In this article, 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.
Abstract: 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 ${|\frac{T}{{T}_{N}}\ensuremath{-}1|}_{3}\ensuremath{\le}2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$.
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TL;DR: In this article, a review of the theoretical and experimental results obtained on simple magnetic model systems on magnetic lattices of dimensionality 1, 2, and 3 is presented, with particular attention paid to the approximation of these model systems in real crystals, viz how they can be realized or be expected to exist in nature.
Abstract: “…. For the truth of the conclusions of physical science, observation is the supreme Court of Appeal….” (Sir Arthur Eddington, The Philosophy of Physical Science.) In this paper we shall review the theoretical and experimental results obtained on simple magnetic model systems. We shall consider the Heisenberg, XY and Ising type of interaction (ferro and antiferromagnetic), on magnetic lattices of dimensionality 1, 2 and 3. Particular attention will be paid to the approximation of these model systems in real crystals, viz. how they can be realized or be expected to exist in nature. A large number of magnetic compounds which, according to the available experimental information, meet the requirements set by one or the other of the various models are considered and their properties discussed. Many examples will be given that demonstrate to what extent experiments on simple magnetic systems support theoretical descriptions of magnetic ordering phenomena and contribute to their understanding. It will a...
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TL;DR: In this article, the crystal chemistry of the oxides of the general formula A 2 B O 4 with particular reference to the stability of the K 2 NiF 4 structure and the relations between the different structures exhibited by this family of oxides is discussed.
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TL;DR: A generalized homogeneous function (GHF) as mentioned in this paper is defined as a function that can be scaled with respect to any of its arguments, such that the critical subspace becomes higher dimensional.
Abstract: A function $f({x}_{1}, {x}_{2},\dots{}, {x}_{n})$ is a generalized homogeneous function (GHF) if we can find numbers ${a}_{1}, {a}_{2}, \dots{}, {a}_{n}$ such that for all values of the positive number $\ensuremath{\lambda}$, $f({\ensuremath{\lambda}}^{{a}_{1}}{x}_{1}, {\ensuremath{\lambda}}^{{a}_{2}}{x}_{2}, \dots{}, {\ensuremath{\lambda}}^{{a}_{n}}{x}_{n})={\ensuremath{\lambda}}^{{a}_{f}}f({x}_{1}, {x}_{2}, \dots{}, {x}_{n})$. We organize the properties of GHFs in four theorems. These are used to systematically examine the consequences of various scaling hypotheses. An advantage of this approach is that the same formalism may be used to treat thermodynamic functions, static correlation functions, dynamic correlation functions, and "universality." The simple case of thermodynamic scaling (two independent variables) is first generalized to static and dynamic correlation functions (three and four variables), and then to scaling with a parameter (for which the critical subspace becomes higher dimensional). In this last case, where a second GHF hypothesis is made, the necessity of crossover lines is demonstrated. The assumption of homogeneity is clearly separated from any extra assumptions that may also be called scaling (or "strong scaling"), but are independent of and different from that of homogeneity. One practical insight gained from the present approach is that all experimentally measured exponents are expressible as the ratio of two scaling powers, ${a}_{f}$ (which refers to the function) and ${a}_{j}$ (which refers to the path of approach to the critical point). A second practical advantage is that, since a GHF can be scaled with respect to any of its arguments, one can immediately write a variety of scaling functions for each type of scaling hypothesis. The GHF approach thereby permits data to be plotted in a variety of convenient fashions, and is found to facilitate computation of the relevant scaling functions (in particular, the GHF approach led directly to the recent calculation of the Heisenberg model scaling function by Milos\ifmmode \breve{}\else \u{}\fi{}evi\ifmmode \acute{c}\else \'{c}\fi{} and Stanley).
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TL;DR: In this article, the exchange interaction between the spins within the c-plane is found to be the Heisenberg type with about one percent XY-like anisotropy and j / k = 10.0 K.
Abstract: It has been found that K 2 CuF 4 is ferromagnetic below 6.25 K. The two-dimensionality of this compound as expected from its K 2 NiF 4 type structure is strongly supported by magnetic and specific heat measurements. The torque as well as zero field NMR measurements suggest that the c -plane is an easy plane, in which the spins are very weakly bounded to the direction of a -axis. On the assumption that this magnetic system to be purely two-dimensional, the exchange interaction J between the spins within the c -plane is found to be the Heisenberg type with about one percent XY-like anisotropy and j / k =10.0 K is obtained from the series expansion analysis of the high temperature susceptibility as well as linear dependence of the low temperature specific heat. The transition at 6.25 K may be caused by inter-layer exchange interaction. The exchange field between the adjacent layers is expected at least larger than 400 Oe.
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