= Solution
Formal ionic counting gives La(III), N(−III), and therefore Re(VI), with a $5d^1$ configuration. An isolated localized $d^1$ center would carry a <saturation magnetic moment> of order $1\mu_{\rm B}$, much larger than the value quoted. It is not a $d^0$ ion made diamagnetic simply by an octahedral <ligand field>.
The spatially extended Re $5d$ orbitals overlap strongly with N $2p$ orbitals. Re–N $\sigma$ interactions raise the $e_g$-derived antibonding states, while $\pi$ interactions mix the $t_{2g}$ states with the nitrogen network. Repetition through corner-sharing <octahedra> turns these combinations into broad <energy bands>. The nominal $d$ <electron> occupies a delocalized, partially filled band rather than an isolated magnetic orbital.
Only <electrons> close to the <Fermi energy> change their occupations appreciably in an applied <magnetic field>. Consequently a <Pauli paramagnetism> has a small, nonzero field-induced <magnetization>:
$$
M\simeq\mu_{\rm B}^2 g(E_F)B
$$
when $g$ is the density of states including both <spin> directions, expressed per formula unit and per unit energy. This band model explains \b[a very small moment without requiring the absence of <electrons> in the Re-derived band]. The reported material has metallic transport and a Pauli-like response.<Preparation of bulk-phase nitride perovskite LaReN3 and topotactic reduction to LaNiO2-type LaReN2 by Simon D. Kloß and others>[Magnetic and transport measurements, Figure 4]{ref}
The description “saturated” in the question should not be interpreted as complete alignment of one localized <spin> per Re: a nearly linear metallic response over a laboratory field range need not be a true fully spin-polarized saturation moment.
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