High-spin states in the doubly-odd $^{198}$Bi nucleus have been studied by using the $^{185,187}$Re($^{16}$O, xn) reactions at the beam energy of 112.5 MeV. $gamma-gamma$ coincidence were measured by using the INGA array with 15 Compton suppressed clover HPGe detectors. The observed levels have been assigned definite spin-parity. The high spin structure is grouped into three bands (B1, B2 and B3), of which two (B1 and B2) exhibit the properties of magnetic rotation (MR). Tilted axis cranking calculations were carried out to explain the MR bands having large multi-quasiparticle configurations. The calculated results explain the bands B1 and B2 very nicely, confirming the shears mechanism and suggest a crossing of two MR bands in both the cases. The crossing is from 6-qp to 8-qp in band B1 and from 4-qp to 6-qp in band B2, a very rare finding. A semiclassical model has also been used to obtain the particle-hole interaction strengths for the bands B1 and B2, below the band crossing.
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