We had observed earlier that in the quaternary borocarbide magnetic superco
nductor TmNi2B2C (T-c = 11K, T-N = 1.5 K) quasistatic magnetic correlations
persist well above TN (up to similar to 20 K), which is rather unusual. To
further probe the nature of its spin state, we used magnetically oriented
powder samples of TmNi2B2C and the mu-SR technique. We observe that the qua
sistatic internal held has a well defined direction. The spontaneous muon p
recession signal has three times the amplitude when the c-axis alignment is
perpendicular to the initial muon beam polarization than when parallel. Th
e transverse configuration enhances the oscillatory signal. This has enable
d us to show that the quasistatic magnetic correlations persist even up to
50 K. Furthermore, we find a peak around 7 G in the field dependence of the
longitudinal relaxation, which we attribute to the presence of a level cro
ssing resonance arising from quadrupole levels of the boron nuclei. (C) 199
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