$\beta$-Mn-type family alloys ${\mathrm{Mn}}_{3}TX$ ($T=\text{Co}$, Rh, and Ir; $X=\text{Si}$ and Ge) have a three-dimensional antiferromagnetic (AF) corner-shared triangular network, i.e., the hyperkagome lattice. The antiferromagnet ${\mathrm{Mn}}_3\mathrm{RhSi}$ shows magnetic short-range order over a wide temperature range of approximately 500 K above the Néel temperature $T_{\mathrm{N}}$ of 190 K. In this family of compounds, as the lattice parameter decreases, the long-range magnetic ordering temperature decreases. ${\mathrm{Mn}}_3\mathrm{CoSi}$ has the smallest lattice parameter and the lowest $T_{\mathrm{N}}$ in the family. The quantum critical point (QCP) from AF to the quantum paramagnetic state is expected near a cubic lattice parameter of 6.15 $\AA$. Although the Néel temperature of ${\mathrm{Mn}}_3\mathrm{CoSi}$ is only 140 K, the emergence of the quantum critical behavior in ${\mathrm{Mn}}_3\mathrm{CoSi}$ is discussed. We study how the magnetic short-range order appears in ${\mathrm{Mn}}_3\mathrm{CoSi}$ by using neutron scattering, $\mu \mathrm{SR}$, and bulk characterization such as specific heat capacity. According to the results, the neutron scattering intensity of the magnetic short-range order in ${\mathrm{Mn}}_3\mathrm{CoSi}$ does not change much at low temperatures from that of ${\mathrm{Mn}}_3\mathrm{RhSi}$, although the $\mu \mathrm{SR}$ short-range order temperature of ${\mathrm{Mn}}_3\mathrm{CoSi}$ is largely suppressed to 240 K from that of ${\mathrm{Mn}}_3\mathrm{RhSi}$. Correspondingly, the volume fraction of the magnetic short-range order regions, as shown by the initial asymmetry drop ratio of $\mu \mathrm{SR}$ above $T_{\mathrm{N}}$, also becomes small. Instead, the electronic-specific heat coefficient $\gamma$ of ${\mathrm{Mn}}_3\mathrm{CoSi}$ is the largest in this ${\mathrm{Mn}}_{3}T\mathrm{Si}$ system, possibly due to the low-energy spin fluctuation near the quantum critical point.

• Received 14 September 2023
• Accepted 18 December 2023

DOI:https://doi.org/10.1103/PhysRevResearch.6.013144

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Published by the American Physical Society