Spin order and fluctuations in the EuAl${}_4$ and EuGa${}_4$ topological antiferromagnets: A $\hat{I}¼$SR study

Abstract

We report on systematic muon-spin rotation and relaxation ($\hat{I}¼$SR) studies of the magnetic properties of EuAl${}_4$ and EuGa${}_4$ single crystals at a microscopic level. Transverse-field $\hat{I}¼$SR measurements, spanning a wide temperature range (from 1.5 to 50 K), show clear bulk AFM transitions, with an almost 100% magnetic volume fraction in both cases. Zero-field $\hat{I}¼$SR measurements, covering both the AFM and the paramagnetic (PM) states, reveal internal magnetic fields $B_{\mathrm{int}}(0)=0.33$ T and 0.89 T in EuAl${}_4$ and EuGa${}_4$, respectively. The transverse muon-spin relaxation rate $\hat{I}{»}_{\mathrm{T}}$, a measure of the internal field distribution at the muon-stopping site, shows a contrasting behavior. In EuGa${}_4$, it decreases with lowering the temperature, reaching its minimum at zero temperature, $\hat{I}{»}_{\mathrm{T}}(0)=0.71$ $\hat{I}¼$s${}^{-1}$. In EuAl${}_4$, it increases significantly below $T_{\mathrm{N}}$, to reach 58 $\hat{I}¼$s${}^{-1}$ at 1.5 K, most likely reflecting the complex magnetic structure and the competing interactions in the AFM state of EuAl${}_4$. In both compounds, the temperature-dependent longitudinal muon-spin relaxation $\hat{I}{»}_{\mathrm{L}}(T)$, an indication of the rate of spin fluctuations, diverges near the onset of AFM order, followed by a significant drop at $T<T_{\mathrm{N}}$. In the AFM state, spin fluctuations are much stronger in EuAl${}_4$ than in EuGa${}_4$, while being comparable in the PM state. The evidence of robust spin fluctuations against the external magnetic fields provided by $\hat{I}¼$SR may offer new insights into the origin of the topological Hall effect and the possible magnetic skyrmions in the EuAl${}_4$ and EuGa${}_4$ compounds.

10 pages, 7 figures, accepted by Phys. Rev. B