The possible antimagnetic rotation in the $N=46$ odd-$A$ isotones ${}^{83}\mathrm{Rb}$ and ${}^{85}\mathrm{Y}$ is investigated using the cranked shell model combined with a particle-number-conserving method. For the positive-parity yrast bands in the two isotones, the angular-momentum alignments are reproduced well. The configurations of high-spin part in both bands are determined as $\pi g_{9/2}\otimes \nu g_{9/2}^{-4}$, by analyzing the occupation probability of each cranked Nilsson orbital near the Fermi surface. The calculated $B\left(E2\right)$ values are small and decrease with the increasing rotational frequency, in agreement with the experiments; meanwhile, the two-shears-like mechanism is exhibited clearly. Therefore, the high-spin parts of the two bands, built on $\pi g_{9/2}\otimes \nu g_{9/2}^{-4}$ configuration, match the criteria of antimagnetic rotation, which is the first time that the antimagnetic rotation is revealed for odd-$A$ nuclei in the $A\approx 80$ mass region.

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• Collective levels
• Electromagnetic transitions
• Nuclear structure & decays
• 59 ≤ A ≤ 89
• Shell model