  We report a high frequency/high magnetic field electron spin resonance
(HF-ESR) spectroscopy study in the sub-THz frequency domain of the two
representatives of the family of magnetic topological insulators
(MnBi$_{2}$Te$_{4}$)(Bi$_{2}$Te$_{3}$)$_{n}$ with $n = 0$ and 1. The HF-ESR
measurements in the magnetically ordered state at a low temperature of $T = 4$
K combined with the calculations of the resonance modes showed that the spin
dynamics in MnBi$_{\text{4}}$Te$_{\text{7}}$ is typical for an anisotropic
easy-axis type ferromagnet (FM) whereas MnBi$_{\text{2}}$Te$_{\text{4}}$
demonstrates excitations of an anisotropic easy-axis type antiferromagnet
(AFM). However, by applying the field stronger than a threshold value $\sim 6$
T we observed in MnBi$_{\text{2}}$Te$_{\text{4}}$ a crossover from the AFM
resonance modes to the FM modes which properties are very similar to the
ferromagnetic response of MnBi$_{\text{4}}$Te$_{\text{7}}$. We attribute this
remarkably unusual effect unexpected for a canonical easy-axis AFM, which,
additionally, can be accurately reproduced by numerical calculations of the
excitation modes, to the closeness of the strength of the AFM exchange and
magnetic anisotropy energies which appears to be a very specific feature of
this compound. Our experimental data evidences that the spin dynamics of the
magnetic building blocks of these compounds, the Mn-based septuple layers
(SLs), is inherently ferromagnetic featuring persisting short-range FM
correlations far above the magnetic ordering temperature as soon as the SLs get
decoupled either by introducing a nonmagnetic quintuple interlayer, as in
MnBi$_{\text{4}}$Te$_{\text{7}}$, or by applying a moderate magnetic field, as
in MnBi$_{\text{2}}$Te$_{\text{4}}$, which may have an effect on the surface
topological band structure of these compounds.
