Neutron-scattering study of magnetic-field-induced transitions in a two-component antiferromagnetic system with competing spin anisotropies

Neutron-scattering experiments have been performed on the quasi-two-dimensional antiferromagnet ${\mathrm{K}}_2$ ${\mathrm{Mn}}_{0.978}$ ${\mathrm{Fe}}_{0.022}$ ${\mathrm{F}}_4$ in order to study the coexisting three- and two-dimensional ($d=3\mathrm{}$ and $d=2\mathrm{}$) magnetic order. The measurements were carried out in the temperature range $2 \mathrm{K}<T<\mathrm{}60\mathrm{} \mathrm{K}$, and in external magnetic fields up to $H=50\mathrm{}$ kOe applied perpendicular to the layers, i.e., parallel to the easy axis of magnetization. From temperature scans at constant field, and field scans at constant temperature, we have obtained an $H-T$ phase diagram consisting of four phases, namely, the paramagnetic $P$ phase, the antiferromagnet axial $A$ phase, an antiferromagnetic intermediate $I$ phase, and the spin-flop or planar phase. Coming from the $P$ to the $A$ phase, $d=3\mathrm{}$ and $d=2\mathrm{}$ ordered subsystems coexist, whereas in the $l$ phase the $d=2\mathrm{}$ long-range order (LRO) gradually changes into the $d=3\mathrm{}$ LRO. Upon entering the planar phase all $d=2\mathrm{}$ LRO disappears and there is no longer a division in two subsystems. After leaving the planar phase the complete spin system remains fully $d=3\mathrm{}$ ordered, as long as the $P$ phase is not reached. The three ordered phases are further characterized by differences in domain structures. The $H-T$ phase diagram can be explained by assuming that in this two-component antiferromagnet with competing spin anisotropies (namely, the axial dipolar anisotropy of the ${\mathrm{Mn}}^{2+}$ and ${\mathrm{Fe}}^{2+}$ ions and the planar single-ion anisotropy of the ${\mathrm{Fe}}^{2+}$ ions) at $H=0\mathrm{}$ a mismatch occurs in the correlations along the $c$ axis between $\mathrm{xy}$ components in $d=2\mathrm{}$ ordered clusters around the ${\mathrm{Fe}}^{2+}$ ions and the $z$ components of the $d=3\mathrm{}$ ordered ${\mathrm{Mn}}^{2+}$ spins in adjacent layers. Applying a sufficiently strong field forces all the moments to lie in the planes and consequently the mismatch in correlation is removed. The observed $H-T$ diagram differs from that...