Local moment formation and magnetic coupling of Mn guest atoms in Bi$_2$Se$_3$: a low-temperature ferromagnetic resonance study

摘要

We compare the magnetic and electronic configuration of single Mn atoms inmolecular beam epitaxy (MBE) grown Bi$_2$Se$_3$ thin films, focusing onelectron paramagnetic (ferromagnetic) resonance (EPR and FMR, respectively) andsuperconducting quantum interference device (SQUID) techniques. X-raydiffraction (XRD) and electron backscatter diffraction (EBSD) reveal theexpected increase of disorder with increasing concentration of magnetic guestatoms, however, Kikuchi patterns show that disorder consists majorly ofmum-scale 60deg twin domains in the hexagonal Bi$_2$Se$_3$ structure, which arepromoted by the presence of single unclustered Mn impurities. Ferromagnetismbelow T$_C$ ~ (5.4 +/- 0.3) K can be well described by critical scaling lawsM(T) ~ (1-T/T$_C$)$^\beta$ with a critical exponent $\beta$ = (0.34 +/- 0.2)),suggesting 3D Heisenberg class magnetism instead of e.g. 2D-type couplingbetween Mn-spins in van der Waals gap sites. From EPR hyperfine structure datawe determine a Mn$^{2+}$ (d$^5$, S = 5/2) electronic configuration with ag-factor of 2.002 for -1/2 --> +1/2 transitions. In addition, from the strongdependence of the low temperature FMR fields and linewidth on the fieldstrength and orientation with respect to the Bi$_2$Se$_3$ (0001) plane, wederive magnetic anisotropy energies of up to K1 = -3720 erg/cm3 in MBE-grownMn-doped Bi$_2$Se$_3$, reflecting the first order magneto-crystallineanisotropy of an in-plane magnetic easy plane in a hexagonal (0001) crystalsymmetry. Across the ferromagnetic-paramagnetic transition the FMR intensity issuppressed and resonance fields converge the paramagnetic limit of a Mn$^{2+}$(d$^5$, S = 5/2).