Quantum critical points (QCPs) emerge when a 2nd 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 1st 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 FM QCP is buried
within a SDW phase. We establish the presence of quantum tricritical points
(QTCPs) at which both the uniform and finite q susceptibility diverge. The
universal nature of our model suggests that such QTCPs arise naturally from the
interplay between SDW and FM order and exist generally near a buried FM QCP 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
