Background: Detailed spectroscopy of neutron-rich odd-$A$ Cu isotopes is of great importance for studying the shell evolution in the region of $78\mathrm{Ni}$. While there is experimental information on excited states in $69-73,77,79\mathrm{Cu}$ isotopes, the information concerning $75\mathrm{Cu}$ is very limited.

Purpose: Experimentally observed single-particle, core-coupling, and proton-hole intruder states in $75\mathrm{Cu}$, will complete the systematics of these states in the chain of isotopes.

Method: Excited states in $75\mathrm{Cu}$ were populated in the $\beta$ decay of $75\mathrm{Ni}$ isotopes. The Ni nuclei were produced by the in-flight fission of $238U$ projectiles, and were separated, identified, and implanted in a highly segmented Si detector array for the detection of the $\beta$-decay electrons. The $\beta$-delayed $\gamma$ rays were detected in a HPGe cluster array. Monte Carlo shell model calculations were performed using the A3DA interaction built on the $pf{g}_{9/2}{d}_{5/2}$ model space for both neutrons and protons.

Results: A level scheme of $75\mathrm{Cu}$ was built up to $\approx 4$ MeV by performing a $\gamma \text{−}\gamma$ coincidence analysis. The excited states below 2 MeV were interpreted based on the systematics of neutron-rich odd-$A$ Cu isotopes and the results of the shell model calculations.

Conclusions: The evolution of the single-particle, core-coupling, and proton-hole intruder states in the chain of neutron-rich odd-$A$ Cu isotopes is discussed in the present work, in connection with the newly observed level structure of $75\mathrm{Cu}$.