Existence of a tricritical point in the antiferromagnet ${\mathrm{KFe}}_3$(OH)${}_6$(${\mathrm{SO}}_4$)${}_2$ on a kagome lattice

We study the phase diagram in the $H-T$ plane of the potassium jarosite compound ${\mathrm{KFe}}_3$(OH)${}_6$(${\mathrm{SO}}_4$)${}_2$ for the antiferromagnetic $XY$ model with Dzyaloshinskii-Moriya (DM) interaction using the mean-field theory for different values of DM. In our approach, we obtain the tricritical point in the $H-T$ plane and the adjustment has a strong correlation with experimental data.

Figure 1

Phase diagram for the compound potassium jarosite. Solid lines represent second-order transition, while dotted lines represent first-order transition. Open circles and solid circles are the experimental data from Refs. [1] and [2], respectively. TCP is obtained by solving numerically Eqs. (6) and $H_0=16.8T$ [1].

Figure 2

Phase diagram in the $H-T$ plane for kagome lattice: (a) $D/k_B=0.8$ K, (b) $D/k_B=0.5$ K, and (c) $D/k_B=0.1$ K.

Figure 3

Diagram $H-T$ for the square lattice, with $D/J=0.2$. Solid lines represent continuous transition from the determined phase (helical phase) to a paramagnetic phase and the dotted line represents the transition of the first order. The field $H$ is given in units of exchange interaction, $J$.

Figure 4

Spin configurations in triangular and kagome tripartite lattices.

Figure 5

Diagram $H-T$ for triangular lattice, with $D/J=0.08$. The solid line represents the continuous transition from the determined phase (helical phase) to the paramagnetic phase; the trajectory line represents the helical-nonhelical transition [14] and the dotted line represents the transition of the first order. The field of $H$ is given in exchange interaction units, $J$.