Magnetic phase transition in planar antiferromagnets:F19magnetic-resonance experiments inK2MnF4

Nuclear-magnetic-resonance measurements are performed on ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ nuclei in the weakly anisotropic planar antiferromagnet ${\mathrm{K}}_2$Mn${\mathrm{F}}_4$ over the temperature range 4-300 K, which includes the transition temperature $T_N=41.5\mathrm{}$ K. The linewidth contributions due to longitudinal and transverse magnetic fluctuations have been analyzed in detail and compared to the numerical calculations performed for the two-dimensional (2-D) and three-dimensional (3-D) Ising models, and the 3-D Heisenberg model. When $T_N$ is approached from above, the longitudinal contribution to the linewidth of the axial fluorine nuclei diverges critically, in agreement with the 2-D Ising model predictions [$w=2\mathrm{}\nu (1-\eta )=1.5\mathrm{}$]. Conversely, the linewidth of the planar fluorine nuclei, which remains finite as $T\to T_N$, does not exhibit a complete anisotropy in the longitudinal and transverse components, except for a very narrow region of temperatures close to $T_N$. The dramatic influence that the small anisotropy term in the Hamiltonian has on the $\hat{q}\sim 0$ fluctuations (essentially sensed by the axial ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ nuclei), in contrast to the weak influence on the $\hat{q}\sim \frac{\pi }{a}$ fluctuations (sensed by the planar ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ nuclei), is discussed in terms of the dipolar nature of the anisotropy. Arguments are given to justify the $T$ dependence of the planar ${}_{}{}^{19}{}_{}{}^{}\mathrm{F}$ linewidth, which is not satisfactorily described by the current models.