V. N. Glazkov, Ya V. Rebrov, M. A. Dubovitskii, M. M. Markina, K. V. Zakharov, A. F. Murtazoev, P. S. Berdonosov, A. N. Vasiliev
Nabokoite family compounds ACu$_7$(TeO$_4$)(SO4)$_5$X (A=Na, K, Rb, Cs; X=Cl, Br) host frustrated 2D square kagom'{e} lattice layers decorated by additional inter-layer magnetic ions. We study magnetic order in nabokoites with multi-frequency electron spin resonance spectroscopy and thermodynamic measurement (specific heat, magnetization and dielectric permittivity). Our study reveals that the choice of the low-temperature ground state is qualitatively different in light-alkali-ion (K, Na) and heavy-alkali-ion (Rb, Cs) compounds. Heavy-alkali-ion nabokoites order in conventional collinear antiferromagnetic pattern with easy-axis anisotropy. The parameters of the ordered antiferromagnetic state are very close for all heavy-alkali-ion subfamily. Light-alkali-ion members of nabokoite family demonstrate much more complicated route to the ordered state: firstly, a ferroelectric transition at 25-90K lifts the frustration and thus pre-cooks the low-temperature ordering; secondly, an unusual noncollinear magnetic order develops via two-step phase transition with first transition temperature $T_{c1}\simeq 5-6$K and the second transition at $T_{c2}\simeq 3-4$K. Noncollinear order is evidenced by observation of characteristic non-Larmor antiferromagnetic resonance mode. Spin dynamics of light-alkali-ion nabokoites is characterized by three zero-field magnon gaps and two spin-reorientation fields, the values of magnon gaps and critical fields are quite different for different compounds. The finite-size cluster modeling of pyramidal structural block of nabokoite structure combined suggests that the critical closeness of the nabokoite exchange coupling parameters to the border-line between the different quantum ground state of pyramidal building block of nabokoite structure could be the clue to the choice of qualitatively different ordered state in light- and heavy-alkali-ion nabokoites.