Inhomogeneous Magnetic Phases: A Fulde-Ferrell-Larkin-Ovchinnikov-Like Phase in ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathbf{O}}_7$

The phase diagram of ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ contains a metamagnetic transition that bifurcates to enclose an anomalous phase with intriguing properties—a large resistivity with anisotropy that breaks the crystal-lattice symmetry. We propose that this is a magnetic analogue of the spatially inhomogeneous superconducting Fulde-Ferrel-Larkin-Ovchinnikov state. We show—through a Ginzburg-Landau expansion where the magnetization transverse to the applied field can become spatially inhomogeneous—that a Stoner model with electronic band dispersion can reproduce this phase diagram and transport behavior.

Figure 1

The phase diagram of ${\mathrm{Sr}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ as inferred from in-plane transport properties. The green planes correspond to abrupt changes in resistivity as a function of field. Blue shading indicates regions where the in-plane resistivity is anomalously high, becomes highly anisotropic with respect to the in-plane component of the field [11], and shows an anomalous temperature dependence. The phase diagram obtained from magnetic susceptibility [10] shows the same first-order transitions as indicated here in green, but lacks the roof.

Figure 2

(a) Energy contours for a next-nearest neighbor tight-binding model with Fermi surfaces for minority and majority electrons shown in blue and red, respectively, (left). The minority and majority bands are distorted by a spiral modulation with nonzero transverse magnetization and wave vector (right). (b) DOS of minority and majority states with a uniform magnetization (left) and with a spiral distortion (right). In the former, the Fermi surface lies just below a peak in the DOS and in the latter it lies between two split peaks.

Figure 3

Phase diagram for the Ginzburg-Landau theory with possible spin texture. Green sheets represent first-order transitions in $\varphi$. Blue sheets represent continuous transitions into the inhomogeneous phase. The possible spin texture is constructed from four spin helices arranged in a square. The longitudinal magnetization has been suppressed in this picture for emphasis.

Figure 4

The phase diagram rotated into the experimental orientation. The dashed line shows a trajectory through the inhomogeneous region. The inset shows the variation of longitudinal and transverse magnetization through this trajectory.