The possible antimagnetic rotation (AMR) of the four negative-parity yrast bands with four $g_{9/2}$ valence proton holes in the isotopes ${}^{103,105,107,109}\mathrm{Pd}$ is systematically investigated by using the cranked shell model with pairing correlations taken into account by a particle-number-conserving treatment. The calculated values of $B(E2$) after backbending agree well with the available experimental data, which display decreasing tendency with the rotational frequency. The two-shears-like mechanism is clearly exhibited in the case of four valence proton holes. Accordingly, we verify the AMR properties of the ${}^{103}\mathrm{Pd}$ negative-parity yrast band recognized previously in the literature, and suggest the negative-parity yrast bands of ${}^{105,107,109}\mathrm{Pd}$ as three new candidates for an AMR band, thereby extending the Pd isotope chain with AMR by four mass units towards the neutron-rich side.

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• Collective levels
• Nuclear structure & decays
• 90 ≤ A ≤ 149
• Shell model