Quantum critical behavior of the hyperkagome magnet Mn_{3}CoSi

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