Magnetic susceptibility of crystals with crossing of their band-contact lines

We theoretically study the orbital magnetic susceptibility produced by electron states near a crossing point of two band-contact lines in a crystal. It is shown that this susceptibility can have an unusual dependence on the Fermi level and can change noticeably with the temperature when the Fermi level is in the vicinity of the crossing point. These features of the magnetic susceptibility can be useful in detecting the crossing points in crystal. The obtained results explain the well-known temperature dependence of the magnetic susceptibility of V${}_3$Si.