Emergent topological spin structures in the centrosymmetric cubic perovskite ${\mathrm{SrFeO}}_3$

The skyrmion crystal (SkX) characterized by a triple-$\mathit{q}$ helical spin modulation has been reported to be a unique topological state that competes with the single-$\mathit{q}$ helimagnetic order in noncentrosymmetric materials with Dzyaloshinskii-Moriya (DM) interactions. Here, we report the discovery of a rich variety of multiple-$\mathit{q}$ helimagnetic spin structures in the centrosymmetric cubic perovskite ${\mathrm{SrFeO}}_3$ without DM interactions. On the basis of neutron diffraction measurements, we have identified two types of robust multiple-$\mathit{q}$ spin structures that appear in the absence of external magnetic fields: an anisotropic double-$\mathit{q}$ spin spiral and an isotropic quadruple-$\mathit{q}$ spiral hosting a three-dimensional lattice of topological singularities. The present system not only diversifies the family of SkX host materials but furthermore provides an experimental missing link between centrosymmetric lattices and topological helimagnetic order. It also offers perspectives for integration of SkXs into oxide electronic devices.

Figure 1

(a) Magnetic phase diagram for the applied field direction along [111]. The shaded and the white regions in phase I correspond to states with 12 and 3 domains, respectively. The schematic crystal structure and quadruple-$\mathit{q}$ vectors viewed along [111] are shown on the right-hand side. (b) Double-$\mathit{q}$ spin structure in phase I and (c) quadruple-$\mathit{q}$ spin structure in phase II (the color of each spin corresponds to the spin component along the direction perpendicular to both ${\mathit{q}}_1$ and ${\mathit{q}}_2$ for (b) and that along [111] for (c), respectively). The magnified views around the singular points are shown at the bottom. Note that we adopt ${\mathit{q}}_1$ and ${\mathit{q}}_2$ instead of ${\mathit{q}}_1^{\prime }$ and ${\mathit{q}}_2^{\prime }$ for phase I.

Figure 2

(a) Temperature dependence of integrated intensities of the magnetic scattering along ${\mathit{q}}_i$ ($i=1–4$) measured at zero field after field cooling. The total intensity for ${\mathit{q}}_{1-4}$ is also shown. Magnetic field dependence of the magnetic scattering intensities for (b) phase I at 50 K and (c) phase II at 100 K. The data with solid lines and dashed lines were measured on increasing and decreasing the field along [111], respectively. The data for (b) and (c) were measured after zero-field cooling from room temperature.

Figure 3

(a) Schematic representation describing the crystallographic directions and the azimuthal positions of magnetic scattering peaks in the horizontal configuration for phase I after field cooling (FC). The three red balls indicated by the red square on the gray sphere correspond to the triplet magnetic scattering peaks deviating by $2^{\circ }$ from the [111] direction. (b) SANS data measured at 3 K with the relative rocking angle $\mathrm{\Delta }\omega =0$. The observed magnetic reflection corresponds to the helimagnetic modulation ${\mathit{q}}_{1\left(2\right)}^{\prime }$, which is indicated by the red arrow in the (a). Stereographic projections of magnetic scattering peaks in (c) phase I after field cooling and (d) phase II. The solid and open circles represent the magnetic reflections for the proper-screw and vertical-cycloid-type spin propagations, respectively. (e) and (f) Integrated magnetic scattering profiles around ${\mathit{q}}_1$ parallel to [111]. The peaks in (e) and (g) correspond to the triplet red solid circles and a single blue open circle in the (c), respectively. (g) and (h) Integrated magnetic scattering profiles around ${\mathit{q}}_2$ parallel to $\left[\overline{1}\overline{1}1\right]$. The intensity is normalized by the largest value. The data were collected on heating in zero field after field cooling under a magnetic field of 6.8 T for ${\mathrm{SrFe}}_{0.99}{\mathrm{Co}}_{0.01}{\mathrm{O}}_3$. The data in (b), (e), and (f) were collected with the horizontal configuration, and those in (g) and (h) were collected with the vertical configuration (see Fig. S1 [42]).

Figure 4

(a) The magnetic phase diagram of ${\mathrm{SrFe}}_{0.99}{\mathrm{Co}}_{0.01}{\mathrm{O}}_3$ reproduced from [46], on which the magnetic phase diagram of ${\mathrm{SrFeO}}_3$ is superimposed (the phase boundary of ${\mathrm{SrFeO}}_3$ is shown by dashed lines). The integrated neutron scattering intensities as a function of $\mathrm{\Delta }\omega$ at 3 K and 0.3 T for spin-flip (SF) and non-spin- flip (NSF) geometries are shown in the inset. All the data were collected after field cooling in a magnetic field of 7 T. Temperature dependence of SF and NSF scattering intensities measured on heating at (b) 0.3 T and (c) 7 T. In each case, the applied magnetic field and the incident neutron spin are parallel to [111]. Schematic illustrations of the spiral spin propagation for ${\mathit{q}}_2^{\prime }$ or ${\mathit{q}}_2$ with (d) vertical-cycloid-type (phase I), (e) proper-screw-type (phase II), and (f) horizontal-cycloid-type configurations, where the right-hand side shows the effective spin components for spin-polarized SANS.