The current search for room-temperature superconductivity is inspired by the unique properties of the electron-phonon interaction in metal superhydrides. Encouraged by the recently found highest-$T_C$ superconductor fcc-$LaH_{10}$, here we discover several superhydrides of another lanthanide - neodymium. We identify three novel metallic Nd-H phases at pressure range from 85 to 135 GPa: $I4/mmm$-$NdH_4$, $C2/c$-$NdH_7$, $P6_3/mmc$-$NdH_9$, synthesized by laser-heating metal samples in NH3BH3 media for in situ generation of hydrogen. A lower trihydride $Fmbar{3}m$-$NdH_3$ is found at pressures from 2 to 52 GPa. $I4/mmm$-$NdH_4$ and $C2/c$-$NdH_7$ are stable from 135 down to 85 GPa, and $P6_3/mmc$-$NdH_9$ from 110 to 130 GPa. Measurements of the electrical resistance of NdH9 demonstrate a possible superconducting transition at ~4.5 K in $P6_3/mmc$-$NdH_9$. Our theoretical calculations predict that all the neodymium hydrides have antiferromagnetic order at pressures below 150 GPa and represent one of the first discovered examples of strongly correlated superhydrides with large exchange spin-splitting in the electron band structure (> 450 meV). The critical N$e$el temperatures for new neodymium hydrides are estimated using the mean-field approximation as about 4 K ($NdH_4$), 251 K ($NdH_7$) and 136 K ($NdH_9$).
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