  We report a comprehensive experimental and theoretical study of the
quasi-one-dimensional quantum magnet CuNCN. Based on magnetization measurements
above room temperature as well as muon spin rotation and electron spin
resonance measurements, we unequivocally establish the localized Cu+2-based
magnetism and the magnetic transition around 70 K, both controversially
discussed in the previous literature. Thermodynamic data conform to the
uniform-spin-chain model with a nearest-neighbor intrachain coupling of about
2300 K, in remarkable agreement with the microscopic magnetic model based on
density functional theory band-structure calculations. Using exact
diagonalization and the coupled-cluster method, we derive a collinear
antiferromagnetic order with a strongly reduced ordered moment of about 0.4
mu_B, indicating strong quantum fluctuations inherent to this
quasi-one-dimensional spin system. We re-analyze the available
neutron-scattering data, and conclude that they are not sufficient to resolve
or disprove the magnetic order in CuNCN. By contrast, spectroscopic techniques
indeed show signatures of long-range magnetic order below 70 K, yet with a
rather broad distribution of internal field probed by implanted muons. We
contemplate the possible structural origin of this effect and emphasize
peculiar features of the microstructure studied with synchrotron powder x-ray
diffraction.
