Detection of magnetic order in the $S=1\mathrm{}$ chain compound ${\mathrm{LiVGe}}_2{\mathrm{O}}_6$ using implanted spin-polarized muons

The temperature dependence of the internal field in the one-dimensional $S=1\mathrm{}$ chain compound ${\mathrm{LiVGe}}_2{\mathrm{O}}_6$ has been measured using muon-spin rotation. Two muon-spin-precession frequencies are observed, corresponding to two distinct stopping sites. The results demonstrate that ${\mathrm{LiVGe}}_2{\mathrm{O}}_6$ undergoes a second-order phase transition to long-range magnetic order at $T_{\mathrm{N}}=24.5\mathrm{}\mathrm{K}.$ In the paramagnetic regime, we find exponential muon-spin relaxation which is dominated by fluctuations of the ${}^{51}\mathrm{V}$ nuclear moments.