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 ${\mathrm{K}}_{2}{\mathrm{Mn}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{x}{\mathrm{F}}_{4}$ 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 $d=2$ systems the transitions to three-dimensional long-range order ($d=3$ 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 $d=3$ LRO in the samples with $x=0.022, 0.028, 0.061, \mathrm{and} 0.125$, we conclude that for $0.022<x<0.028$ the value of ${T}_{c}$ reaches a minimum, and the spin direction changes from the $c$ axis to directions in the $a\ensuremath{-}b$ 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 $x=0.022 \mathrm{and} 0.028$ a spin reorientation to an intermediate direction is found at a temperature ${T}_{R}\ensuremath{\simeq}\frac{1}{2{T}_{c}}$. Information about $d=2$ correlations has been obtained by studying the intensity of scattered neutrons along the line [$\frac{\overline{1}}{\overline{2}}\frac{\overline{1}}{\overline{2}\ensuremath{\zeta}}$] in reciprocal space. These ridge intensities for the $x=0.022 \mathrm{and} 0.028$ samples remain constant for ${T}_{R}<T<{T}_{c}\ensuremath{-}\ensuremath{\Delta}$ ($\ensuremath{\Delta}\ensuremath{\simeq}4$ K), whereas they gradually disappear for $T<{T}_{R}$. In the $x=0.022$ 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 $d=2$ LRO in the $x=0.028$ sample for ${T}_{R}<T<{T}_{c}\ensuremath{-}\ensuremath{\Delta}$ is due to $〈{S}_{z}{S}_{z}〉$, $〈{S}_{y}{S}_{y}〉$, and $〈{S}_{x}{S}_{x}〉$ correlations. The coexistence of $d=3$ LRO and $d=2$ 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 $T<{T}_{R}$. The mismatch mechanism is thereby removed and $d=2$ LRO is transferred into $d=3$ LRO. For the other samples no spin-reorientation is found, since the large majority of the spins are either parallel to [001] (for $x<0.022$) or within the layers (for $x>0.028$). The $x\ensuremath{-}T$ 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 $\ensuremath{\beta}$ is found to display a maximum in the region close to the tetracritical point.
Read full abstract
Nov 15, 1988
Craig D England + 2
Open Access