Spin order and fluctuations in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>EuAl</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi mathvariant="normal">EuGa</mml:mi><mml:mn>4</mml:mn></mml:msub></mml:math> topological antiferromagnets: A <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>μ</mml:mi><mml:mi>SR</mml:mi></mml:math> study

Abstract

${\mathrm{EuAl}}_{4}$ and ${\mathrm{EuGa}}_{4}$ are two candidate materials for studying the interplay between correlated-electron phenomena, topological spin textures, and topologically nontrivial bands. Both compounds crystallize in a centrosymmetric tetragonal ${\mathrm{BaAl}}_{4}$-type structure (space group $I4/mmm$) and show antiferromagnetic (AFM) order below ${T}_{\mathrm{N}}=15.6$ and 16.4 K, respectively. Here, we report on systematic muon-spin rotation and relaxation ($\ensuremath{\mu}\mathrm{SR}$) studies of the magnetic properties of ${\mathrm{EuAl}}_{4}$ and ${\mathrm{EuGa}}_{4}$ single crystals at a microscopic level. In both cases, transverse-field $\ensuremath{\mu}\mathrm{SR}$ measurements, spanning a wide temperature range (from 1.5 to 50 K), show clear bulk AFM transitions, with an almost 100% magnetic volume fraction. Zero-field $\ensuremath{\mu}\mathrm{SR}$ 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 ${\mathrm{EuAl}}_{4}$ and ${\mathrm{EuGa}}_{4}$, respectively. The transverse muon-spin relaxation rate ${\ensuremath{\lambda}}_{\mathrm{T}}$, a measure of the internal field distribution at the muon-stopping site, shows a contrasting behavior. In ${\mathrm{EuGa}}_{4}$, it decreases with lowering the temperature, reaching its minimum at zero temperature, ${\ensuremath{\lambda}}_{\mathrm{T}}(0)=0.71 \ensuremath{\mu}{\mathrm{s}}^{\ensuremath{-}1}$. In ${\mathrm{EuAl}}_{4}$, it increases significantly below ${T}_{\mathrm{N}}$, to reach 58 $\ensuremath{\mu}{\mathrm{s}}^{\ensuremath{-}1}$ at 1.5 K, most likely reflecting the complex magnetic structure and the competing interactions in the AFM state of ${\mathrm{EuAl}}_{4}$. In both compounds, the temperature-dependent longitudinal muon-spin relaxation ${\ensuremath{\lambda}}_{\mathrm{L}}(T)$, an indication of the rate of spin fluctuations, diverges near the onset of AFM order, followed by a significant drop at $T&lt;{T}_{\mathrm{N}}$. In the AFM state, spin fluctuations are much stronger in ${\mathrm{EuAl}}_{4}$ than in ${\mathrm{EuGa}}_{4}$, while being comparable in the PM state. The evidence of robust spin fluctuations against external magnetic fields provided by $\ensuremath{\mu}\mathrm{SR}$ may offer valuable insights into the origin of the topological Hall effect and the possible magnetic skyrmions in the ${\mathrm{EuAl}}_{4}$ and ${\mathrm{EuGa}}_{4}$ compounds.

Topics & Concepts