Quantum fluctuations are of central importance in itinerant ferromagnets; when modeled by a homogeneous electron gas with contact interactions, fluctuations deliver a rich phase diagram featuring a first order ferromagnetic transition preempted by a spin spiral and a paired density wave. In this work we develop the formalism to analyze the effects of fluctuations with a realistic screened Coulomb potential. The finite-ranged interaction suppresses the tricritical point temperature of the first order ferromagnetic transition, bringing theory into line with experiment, while retaining the exotic spin spiral and paired density wave. In an ultracold atomic gas a finite-ranged interaction damps the competing molecular instability, permitting the observation of ferromagnetic correlations.Metallic systems in the vicinity of second order phase transitions display remarkable quantum critical phenomena. 1 However, in several metals 2 quantum criticality gives way to a first order transition, 3-7 or spatially modulated magnetic order, 8-10 or a p-wave superconducting instability. 11-15 A generic phase diagram for many metallic ferromagnets has emerged containing a first order magnetic transition with nearby instabilities into exotic phases. 2 A variety of techniques have emerged to model ferromagnets including analytical treatments of the Hubbard model (for a review see Ref. 16); numerical modeling with density functional theory (DFT) [17][18][19] and dynamical mean field theory 20-22 ; a Stoner model with a modified band structure 23 ; or a homogeneous electron gas (HEG) with fluctuation corrections. [24][25][26][27][28][29][30][31][32][33][34] With several contrasting tools being applied to the system it is unclear whether the emergence of exotic phases are driven solely by electron-electron interactions 16,22,[24][25][26][27][28][30][31][32][33][34] or whether it is essential to also consider electron-ion interactions 18,23 and orbital physics in the form of Hund's rule couplings. 20 One tool to include band structure effects is DFT. Standard implementations are based on a local density approximation (LDA) that neglect gradient terms in the free energy functional. However, gradient terms are vital for electronelectron interactions to drive the spatially modulated magnetic order or p-wave superconductivity observed in experiment. [3][4][5][6][7][8][9][10][11][12][13][14][15] It has been shown that the minimal model of a homogeneous electron gas with contact interactions contains gradient terms that deliver the generic phase diagram seen in many metals around ferromagnetic criticality 2,34 containing a first order transition, 24-28,30 a nearby spin spiral phase, 24,26,27,31 a nematic phase, 32 and a p-wave superconducting instability. 33,34 The analysis develops an effective long wavelength description for just the conduction band electrons. However, there is a significant discrepancy: Experiments typically show a tricritical temperature of T c ≈ 0.02T F 9,10,35 (in Sr 3 Ru 2 O 7 ), whereas this minimal Hamiltonian predict...