  It is generally believed that magnetization measurements on sulfur hydride
under high pressure performed in 2015 [1] provided "final convincing evidence
of superconductivity" [2] in that material, in agreement with theoretical
predictions [3,4]. Supported by this precedent, drops in resistance that were
later observed in several other hydrides under high pressure [2,5] have been
generally accepted as evidence of superconductivity without corroborating
evidence from magnetic measurements. In this paper we challenge the original
interpretation that the magnetic measurements on sulfur hydride performed in
2015 were evidence of superconductivity. We point out that a large paramagnetic
contribution to the magnetic susceptibility was detected below Tc and argue
that its temperature dependence rules out the possibility that it would be a
background signal; instead the temperature dependence indicates that the
paramagnetic behavior originated in the sample. We discuss possible
explanations for this remarkable behavior and conclude that standard
superconductors would not show such behavior. We also survey all the other
published data from magnetic measurements on this class of materials and
conclude that they do not provide strong evidence for superconductivity.
Consequently, we call into question the generally accepted view that
conventional superconductivity in hydrogen-rich materials at high temperature
and pressure is a reality, and discuss the implications if it is not.
