Disorder Dependence of the Ferromagnetic Quantum Phase Transition

We quantitatively discuss the influence of quenched disorder on the ferromagnetic quantum phase transition in metals, using a theory that describes the coupling of the magnetization to gapless fermionic excitations. In clean systems, the transition is first order below a tricritical temperature $T_{\mathrm{tc}}$. Quenched disorder is predicted to suppress $T_{\mathrm{tc}}$ until it vanishes for residual resistivities ${\rho }_0$ on the order of several $\mu \mathrm{\Omega }\mathrm{cm}$ for typical quantum ferromagnets. We discuss experiments that allow us to distinguish the mechanism considered from other possible realizations of a first-order transition.

Figure 1

Evolution of the phase diagram of a metallic quantum ferromagnet in the space spanned by temperature ($T$), magnetic field ($h$), and the control parameter ($r$) with increasing disorder. Shown are the ferromagnetic (FM) and paramagnetic (PM) phases in the $h=0$ plane, lines of second-order transitions (solid red), the tricritical point (TCP), and surfaces of first-order transitions (“tricritical wings”) that end in quantum critical points (QCP) in the $T=0$ plane. With increasing disorder, the tricritical temperature decreases, the wings shrink, and above a critical disorder strength a QCP is realized in zero field.