Resummation of fluctuations near ferromagnetic quantum critical points

Abstract

We present a detailed analysis of the nonanalytic structure of the free energy for the itinerant ferromagnet near the quantum critical point in two and three dimensions. We analyze a model of electrons with an isotropic dispersion interacting through a contact repulsion. A fermionic version of the quantum order-by-disorder mechanism allows us to calculate the free energy as a functional of the dispersion in the presence of homogeneous and spiraling magnetic order. We resum the leading divergent contributions to derive an algebraic expression for the nonanalytic contribution to free energy from quantum fluctuations. Using a recursion which relates subleading divergences to the leading term, we calculate the full T = 0 contribution in d = 3. We propose an interpolating functional form, which allows us to track phase transition lines at temperatures far below the tricritical point and down to T = 0. In d = 2, quantum fluctuations are stronger, and nonanalyticities are more severe. Using a similar resummation approach, we find that despite the different nonanalytic structures, the phase diagrams in two and three dimensions are remarkably similar, exhibiting an incommensurate spiral phase near the avoided quantum critical point.

Ferromagnetic quantum criticality: New aspects from the phase diagram of LaCrGe3

“…LaCrGe 3 is therefore an example of a simple 3d-electrons ferromagnetic system for which a new magnetic phase appears as the Curie temperature is suppressed by pressure. Interestingly, this scenario has been considered recently by several theories [15,[23][24][25][26][27][28][29]. The idea is that particle-hole excitations corresponding to long wavelength correlations lead either to a change of order of the transition to the first order or to a new magnetic phase.…”

Fluctuation-Driven Magnetic Hard-Axis Ordering in Metallic Ferromagnets

“…For λ = 0, the bands decouple and F fl (6) reduces to the expression for the single band case [17,19]. After summation over Matsubara frequencies and resummation of the leading divergencies in temperature to all orders in the magnetization we obtain [21] …”

“…This spatial modulation is associated with deformations of the Fermi surface that enhance the phase space for low energy particle-hole fluctuations. The phase reconstruction can therefore be viewed as a fermionic quantum orderby-disorder effect, which can be studied systematically by self-consistently calculating fluctuations around a whole class of possible broken-symmetry states [19][20][21].The coupling to electronic quantum fluctuations can also have counter-intuitive effects upon the direction of the magnetic order parameter. A notable example is the partially ordered phase of the helimagnet MnSi, in which the spiral ordering vector rotates away from the lattice favored directions [22,23].…”

“…This spatial modulation is associated with deformations of the Fermi surface that enhance the phase space for low energy particle-hole fluctuations. The phase reconstruction can therefore be viewed as a fermionic quantum orderby-disorder effect, which can be studied systematically by self-consistently calculating fluctuations around a whole class of possible broken-symmetry states [19][20][21].…”

Helical glasses near ferromagnetic quantum criticality

“…6 With increasing range of the interaction, λ decreases considerably, leading to an exponential suppression of the tricritical temperature. 6,17 κ is a constant arising from resummation of the leading divergencies 18 and controls where the first-order transition terminates on theT = 0 axis. In the following we use the value κ = 0.001.…”