Criticality in Inhomogeneous Magnetic Systems: Application to Quantum Ferromagnets

Abstract

We consider a φ 4 -theory with a position-dependent distance from the critical point. One realization of this model is a classical ferromagnet subject to non-uniform mechanical stress. We find a sharp phase transition where the envelope of the local magnetization vanishes uniformly. The first-order transition in a quantum ferromagnet also remains sharp. The universal mechanism leading to a tricritical point in an itinerant quantum ferromagnet is suppressed, and in principle one can recover a quantum critical point with mean-field exponents. Observable consequences of these results are discussed.PACS numbers: 75.40.Cx; 75.40.Gb; 05.70.Jk; In standard phase transitions, such as the paramagnetferromagnet transition, or the liquid-gas transition, a homogeneous order parameter (OP; the magnetization in a magnet, or the density difference in a fluid) goes to zero as one crosses from the ordered phase into the disordered one. The OP may vanish continuously, as in the case of a magnet where the transition is second order, or discontinuously, as in the case of a fluid where the transition is first order except at the critical point. An external field may preclude a homogeneous OP. This happens for a fluid in a gravitational field, which produces a position-dependent density profile [1] and in some sense destroys the critical point (see below). Due to the weakness of gravity, this is a very small effect. This raises the question whether qualitatively similar, and maybe quantitatively larger, effects can be achieved in other systems if an external field induces an inhomogeneous OP.We consider one such example, namely, a ferromagnet subject to mechanical stress. We will first discuss a classical Heisenberg magnet, and later generalize to quantum ferromagnets (FMs). Consider a metallic FM in the shape of a circular disk that is bent in the direction perpendicular to the disk plane. This leads to a position dependent mass density [2] and hence, in a metal, to a position dependent electron density and an inhomogeneous chemical potential µ. The FM transition is described by a φ 4 -theory [3], and within a Stoner model the inhomogeneous µ leads to a spatially dependent distance from criticality. Naively, this means that the system can be tuned to criticality only at special positions within the sample, not everywhere at the same time. One might thus expect the transition to become smeared. This is what appears to be found for the liquidgas transition in a gravitational field [4,5,6], which does, however, present a physically different situation [7]. For the FM case we find that the transition remains sharp in a well-defined sense with mean-field critical behavior, even though the magnetization M (x) is position dependent and hence "smeared" in some sense [8,9]. One might expect that M (x) is essentially restricted to a surface layer of fixed width, so that the dimensionality of the system is effectively reduced by one. This is not the case; we find (for a particular model of a sample of linear dimension L) that M (x) is essentia...

Anomalous quantum criticality in an itinerant ferromagnet

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Magnetic order and fluctuations in quasi-two-dimensional planar magnet Sr(Co$_{1-x}$Ni$_x$)$_2$As$_2$

“…Therefore, the absence of a nesting vector does not imply the failure of the RKKY mechanism, but actually suggests that the frustration (either in the real space or reciprocal space) plays a significant role in the formation of a helical magnetic order. In this picture, the Ni-doping induced disorder only affects low energy spin fluctuations, and causes a small change in the effective couplings J c1 and J c2 through the RKKY interactions that stabilize the helical modulation of the magnetic moments near a FM instability 36,37 . While the RKKY interaction induced magnetic frustration may be able to explain the observed helical order, we cannot rule out the possibility that the helical order arises from the Fermi surface nesting not captured by the DMFT calculation.…”

Scaling phenomena driven by inhomogeneous conditions at first-order quantum transitions

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