Field-induced metastability of the modulation wave vector in a magnetic soliton lattice

We present magnetic-field-induced metastability of the magnetic soliton lattice in a bilayer ruthenate $\mathrm{C}{\mathrm{a}}_3{\left(\mathrm{R}{\mathrm{u}}_{1-x}\mathrm{F}{\mathrm{e}}_x\right)}_2{\mathrm{O}}_7\left(x=0.05\right)$ through single-crystal neutron diffraction study. We show that the incommensurability of the modulation wave vector at zero field strongly depends on the history of magnetic field at low temperature, and that the equilibrium ground state can be achieved by warming above a characteristic temperature $T_{\mathrm{g}}\sim 37\mathrm{K}$. We suggest that such metastability might be associated with the domain wall pinning by the magnetic Fe dopants.

Figure 1

Schematic diagrams of the crystal and magnetic structures of $\mathrm{C}{\mathrm{a}}_3{\left(\mathrm{R}{\mathrm{u}}_{0.95}\mathrm{F}{\mathrm{e}}_{0.05}\right)}_2{\mathrm{O}}_7$. The blue arrow represents the direction of the magnetic field. (a) AFM-b: ferromagnetic bilayers stacked antiferromagnetically along the $c$ axis. (b) CAFM: canted antiferromagnetic structure induced by a magnetic field along the $b$ axis. (c) In-plane view of the magnetic structure at $T<T_{\mathrm{MIT}}$ at $B=0\mathrm{T}$. It has a CM component of AFM-b type [denoted as CM(AFM-b)] and an ICM one forming a magnetic soliton lattice that propagates along the $a$ axis [ICM (soliton lattice)]. The square in magenta denotes one unit cell and the rounded rectangle in orange highlights the domain wall (soliton).

Figure 2

(a), (b) Contour maps of the neutron diffraction intensity of scans along [1 0 0] direction across the magnetic wave vector ${\mathbf{q}}_c=\left(001\right)$ in a magnetic field applied along the $b$ axis at $T=15\mathrm{K}$. The light gray grids denote the measurement fields. (c), (d) Neutron diffraction scans along the [1 0 0] direction across the magnetic Bragg peak ${\mathbf{q}}_c=\left(001\right)$ in the $0_{\uparrow }T$ and $0_{\downarrow }T$ phases (defined in the text) at 1.5 K, respectively. The dark green and orange arrows mark the wave vector of the first-order ICM magnetic Bragg peaks and their third-order harmonics, respectively, while the purple ones mark the CM reflections. Inset shows the zoom-in view of the third-order harmonics at $T=1.5$ and 80 K, respectively, for $B=0_{\uparrow }\mathrm{T}$. The data were taken at CTAX.

Figure 3

(a)–(c) Neutron diffraction scans along [1 0 0] direction across the wave vector ${\mathbf{q}}_c=\left(001\right)$ in the $0_{\uparrow }T$ and $0_{\downarrow }T$ phases (defined in the text) at representative temperatures. The Bragg peaks have been fitted using Gaussian functions (solid curves) as described in the Supplemental Materials. The gray horizontal line indicates the instrument resolution. (d) Incommensurability δ of the primary ICM magnetic wave vector ${\mathbf{q}}_{\mathrm{ic}}=\left(\delta 01\right)$ in the $0_{\uparrow }T$ and $0_{\downarrow }T$ phases measured at different temperatures. The error bars obtained from Gaussian fitting are smaller than the symbol size. The solid curves are guides to the eye. The data were taken at CTAX.

Figure 4

(a) Contour map of the neutron diffraction intensity of scans along [1 0 0] direction over ${\mathbf{q}}_{\mathbf{c}}=\left(001\right)$ while warming up in the metastable $0_{\downarrow }T$ phase. The measurement temperatures are denoted by the light gray grids. (b) Neutron diffraction scans along [1 0 0] direction over ${\mathbf{q}}_c=\left(001\right)$ at representative temperatures. The third-order harmonics of the ICM magnetic reflections are denoted by orange arrows. Inset shows the temperature dependence of the intensity ratio $I_3/I_1$ in the $0_{\downarrow }T$ phase. Note that the measurement procedures of the data shown in Figs. 3 and 4 are different, as described in the text. The data were taken at CTAX.