The standard Doniach phase diagram of Kondo materials or heavy fermion

systems often assumes Kramers-doublet local moments coupled to conduction electrons. On the other hand, there exist a class of materials, where the local moments carry multipolar moments due to their non-Kramers nature. In this talk, I will describe a theory of Kondo materials with multipolar local moments using the example of PrTi₂Al₂₀ and PrV₂Al₂₀ systems. Here the local moments at Pr sites carry quadrupolar and octupolar moments. I will present a general Landau theory for the multipolar ordering in such systems. Further, I will explain how magnetostriction, the length change of the system upon the application of external magnetic field, can be used as a power tool to detect multipolar ordering.

If time permits, I will also describe recent theoretical progress in understanding the multipolar Kondo problem, where new renormalization group fixed points may be found.