  Asteroids can be classified into several groups based on their spectral
reflectance. Among these groups, the one belonging to the L-class in the
taxonomic classification based on visible and near-infrared spectra exhibit
several peculiar properties. First, their near-infrared spectrum is
characterized by a strong absorption band interpreted as the diagnostic of a
high content of the FeO bearing spinel mineral. This mineral is one of the main
constituents of Calcium-Aluminum-rich Inclusions (CAI) the oldest mineral
compounds found in the solar system. In polarimetry, they possess an uncommonly
large value of the inversion angle incompatible with all known asteroid
belonging to other taxonomical classes. Asteroids found to possess such a high
inversion angle are commonly called Barbarians based on the first asteroid on
which this property was first identified, (234)~Barbara. In this paper we
present the results of an extensive campaign of polarimetric and spectroscopic
observations of L-class objects. We have derived phase-polarization curves for
a sample of 7 Barbarians, finding a variety of inversion angles ranging between
25 and 30$^{\circ}$. Spectral reflectance data exhibit variations in terms of
spectral slope and absorption features in the near-infrared. We analyzed these
data using a Hapke model to obtain some inferences about the relative abundance
of CAI and other mineral compounds. By combining spectroscopic and polarimetric
results, we find evidence that the polarimetric inversion angle is directly
correlated with the presence of CAI, and the peculiar polarimetric properties
of Barbarians are primarily a consequence of their anomalous composition.
