Ferromagnetic resonance in an antiferromagnetic crystal EuSn$_2$As$_2$

TL;DR

This study addresses puzzling ESR spectra in the layered AFM compound $EuSn_2As_2$ by revealing a second, ferromagnetic resonance line arising from planar FM nanodefects. The authors model the material as a metamaterial comprising FM planar inclusions embedded in an AFM matrix, and they validate this picture through detailed ESR measurements across $4.2$–$296$ K, TEM/DFT characterization of defects, and quantitative fits to AFM and FM resonance formulas. They show that the M-line originates from defect-induced FM order with a saturation magnetization $M_{def}^0 \approx 0.135$ T, about an order of magnitude smaller than the bulk AFM magnetization, consistent with a $1/7$ Eu moment per defect unit. The results establish $EuSn_2As_2$ as a natural magnetic metamaterial and suggest planar FM defects may be intrinsic to other layered AFMs, potentially explaining anomalous low-temperature susceptibility in related systems.

Abstract

We report results of electron spin resonance (ESR) measurements in single crystals of EuSn$_2$As$_2$. In the temperature range of antiferromagnetic (AFM) ordering of Eu atoms, $T \leq T_N\approx 24$\,K, the ESR signal splits into two resonance lines, one of which, at high-field (or low-frequency), is the conventional acoustic AFM resonance mode that occurs at temperatures below $T_N$. The lower-field (high-frequency) line, as we have proven here, is the ferromagnetic resonance associated with the presence in the layered AFM crystal of a small amount ($\sim 3\%$) of planar nanodefects with a non-zero ferromagnetic (FM) moment. The existence of ferromagnetic nano-inclusions in the bulk of the antiferromagnetic compound makes EuSn$_2$As$_2$ a peculiar example of a natural magnetic metamaterial. We believe that the planar FM nanodefects are also inherent in other layered AFM compounds, which explains often observed increase in their magnetic susceptibility upon cooling at $T< T_N\rightarrow 0$.

Figures (6)

• Figure 1: (a,b) Crystal lattice structure of EuSn$_2$As$_2$ in the $ac$- and $ab$- planes, respectively. Crimson arrows depict magnetic moments of Eu atoms in the AFM state (adapted from golov_JMMM_2022), (c) SEM image of a typical crystal (field of view $1300 \mu$m wide).
• Figure 2: (a) FFT filtered high-resolution HAADF STEM image of the crystal lattice cross section in the $ac$ plane (adapted from Ref. ESA-defects). The curly bracket marks the 0.79nm thick defect layer with almost missing one row of Sn atoms and with an extra row of Eu atoms; (b)Schematic arrangement of several layers of the lattice in the $ac$ plane: regular lattice (right), and lattice with a defect layer (left); (c)Schematics of the conjectural model of a metamaterial structure with planar defects and of the local magnetic ordering in the AFM state. Red arrows show magnetic moments of Eu atoms. The planar defects are outlined by rectangular frames, where the blue circles with crosses and dots show possible directions of their FM-moments.
• Figure 3: Typical shape of the resonance absorption signal: (a, b) - in the $H\parallel ab$ geometry at two temperatures, and (c, d, e) - in the $H\|c$ geometry at three temperatures. Representative temperatures are above, near and below $T_N \approx 24$K. The shape of the resonance signal in panels (d) and (e) has an inverse asymmetry (compared to the Dyson shape) note:line-shape. Other narrow features noticeable in the resonant absorption spectra in weak fields $H<0.5$T are associated with impurities in the resonator material (sapphire).
• Figure 4: (a) Temperature dependence of the resonance field $H_r$ for $H\|(ab)$. Red solid squares are from our ESR measurements, crossed squares are data extracted from Ref. golov_JMMM_2022 for the A-line. Blue solid squares are the data of present ESR measurements at $f=9.735$ GHz frequency, crossed squares depict results of golov_JMMM_2022 for the M-line. The dash-dotted lines correspond to $g=2.00$ (upper) and $g=2.155$ (lower); (b) Calculated dependences $H_r(T)$ for resonance lines A and M. For A-line it is obtained using Eqs. (1) & (3); for M-line: the solid curve - using Eqs. (4) & (5); dotted line - using Eqs. (4) & (6). (c) Temperature dependence of the width for the A- and M- resonance lines. (d) Temperature dependence of the integral intensity of two ESR signals, obtained by multiplying their amplitude by the square of the width. The straight line is a guide to the eyes.
• Figure 5: Temperature dependence of (a) the resonance field $H_r$ for $H\|c$; (b) the resonance signal width (peak to peak). Various symbols correspond to two lines in the resonance spectrum, for cases when they can be separated. $f=9.735$ GHz.