Magnetic and neutron scattering experiments on the antiferromagnetic layer-type compoundsK2Mn1−xMxF4(M=Fe,Co)

Substitution of ${\mathrm{Mn}}^{2+}$ in ${\mathrm{K}}_2$Mn${\mathrm{F}}_4$ by ${\mathrm{Fe}}^{2+}$ results in a randomly mixed two-component system with competing spin anisotropies, namely the axial dipolar anisotropy of the ${\mathrm{Mn}}^{2+}$ and ${\mathrm{Fe}}^{2+}$ ions, and the planar crystal-field anisotropy of the ${\mathrm{Fe}}^{2+}$ ions. For increasing amounts of ${\mathrm{Fe}}^{2+}$ the net (axial) anisotropy will initially decrease until it reaches a minimum, whereafter the net (planar) anisotropy increases. Magnetic measurements on single crystals ${\mathrm{K}}_2{\mathrm{Mn}}_{1-x}{\mathrm{Fe}}_x{\mathrm{F}}_4$ with $x=0, 0.008, 0.022$ show indeed a decrease of the value of the spin-flop field with increasing $x$, which is expected for decreasing axial anisotropy. Since in these quasi $d=2\mathrm{}$ systems the transitions to three-dimensional long-range order ($d=3\mathrm{}$ LRO) are induced by the anisotropy, one expects $T_c$ to vary with $x$. From susceptibility data for $x=0.008, 0.019, 0.022, 0.028, 0.061, \mathrm{and} 0.125$, and from neutron-scattering studies of the $d=3\mathrm{}$ LRO in the samples with $x=0.022, 0.028, 0.061, \mathrm{and} 0.125$, we conclude that for $0.022<x<\mathrm{}0.028\mathrm{}$ the value of $T_c$ reaches a minimum, and the spin direction changes from the $c$ axis to directions in the $a-b$ plane, i.e., within the magnetic layers. It is found that $T_c$ in the doped samples is as sharp as in pure ${\mathrm{K}}_2$Mn${\mathrm{F}}_4$. Furthermore, for $x=0.022\mathrm{} \mathrm{and} 0.028$ a spin reorientation to an intermediate direction is found at a temperature $T_R\simeq \frac{1}{2T_c}$. Information about $d=2\mathrm{}$ correlations has been obtained by studying the intensity of scattered neutrons along the line [$\frac{\overline{1}}{\overline{2}}\frac{\overline{1}}{\overline{2}\zeta }$] in reciprocal space. These ridge intensities for the $x=0.022\mathrm{} \mathrm{and} 0.028$ samples remain constant for $T_R<T<\mathrm{}{T}_c-\Delta$ ($\Delta \simeq 4$ K), whereas they gradually disappear for $T<\mathrm{}{T}_R$. In the $x=0.022\mathrm{}$ sample this constant ridge intensity is due to long-range $〈S_x{S}_x〉$ and $〈S_y{S}_y〉$ correlations. Here $x$ and $y$ define the spin components in the magnetic layer. The $d=2\mathrm{}$ LRO in the $x=0.028\mathrm{}$ sample for $T_R<T<\mathrm{}{T}_c-\Delta$ is due to $〈S_z{S}_z〉$, $〈S_y{S}_y〉$, and $〈S_x{S}_x〉$ correlations. The coexistence of $d=3\mathrm{}$ LRO and $d=2\mathrm{}$ LRO can be explained by a mismatch in the correlations along the $c$ axis between ${\mathrm{Fe}}^{2+}$ spins and ${\mathrm{Mn}}^{2+}$ spins in adjacent layers. Since the dipolar anisotropy increases with decreasing temperature, all spins gradually turn to a common orientation for $T<\mathrm{}{T}_R$. The mismatch mechanism is thereby removed and $d=2\mathrm{}$ LRO is transferred into $d=3\mathrm{}$ LRO. For the other samples no spin-reorientation is found, since the large majority of the spins are either parallel to [001] (for $x<\mathrm{}0.022\mathrm{}$) or within the layers (for $x>\mathrm{}0.028\mathrm{}$). The $x-T$ phase diagram obtained from the values of $T_c$ and $T_R$, and from other ordering characteristics, consists of two lines at which either the $z$ or the $\mathrm{xy}$ components order. These two lines cross in a tetracritical point, and encompass an intermediate phase. The critical behavior of the sublattice magnetization appears to depend sensitively on $x$. The critical index $\beta$ is found to display a maximum in the region close to the tetracritical point.