Quantum tricritical points in NbFe2

Quantum critical points (QCPs) emerge when a second-order phase transition is suppressed to zero temperature. In metals the quantum fluctuations at such a QCP can give rise to new phases, including unconventional superconductivity. Whereas antiferromagnetic QCPs have been studied in considerable detail, ferromagnetic (FM) QCPs are much harder to access. In almost all metals FM QCPs are avoided through either a change to first-order transitions or through an intervening spin-density-wave (SDW) phase. Here, we study the prototype of the second case, NbFe2. We demonstrate that the phase diagram can be modelled using a two-order-parameter theory in which the putative FMQCP is buried within a SDW phase. We establish the presence of quantum tricritical points (QTCPs) at which both the uniform and finite wavevector susceptibility diverge. The universal nature of our model suggests that such QTCPs arise naturally from the interplay between SDW and FM order and exist generically near a buried FMQCP of this type. Our results promote NbFe2 as the first example of a QTCP, which has been proposed as a key concept in a range of narrow-band metals, including the prominent heavy-fermion compound YbRh2Si2.