Néel-Type Skyrmion Lattice in the Tetragonal Polar Magnet ${\mathrm{VOSe}}_2{\mathrm{O}}_5$

The formation of the triangular Skyrmion lattice is found in a tetragonal polar magnet ${\mathrm{VOSe}}_2{\mathrm{O}}_5$. By magnetization and small-angle neutron scattering measurements on the single crystals, we identify a cycloidal spin state at zero field and a Néel-type Skyrmion-lattice phase under a magnetic field along the polar axis. Adjacent to this phase, another magnetic phase of an incommensurate spin texture is identified at lower temperatures, tentatively assigned to a square Skyrmion-lattice phase. These findings exemplify the versatile features of Néel-type Skyrmions in bulk materials, and provide a further opportunity to explore the physics of topological spin textures in polar magnets.

Figure 1

Schematic spin configuration of (a) cycloidal spiral order and (b) a Néel-type Skyrmion under magnetic field ($H$) along the $c$ axis. (c) Crystal structure of ${\mathrm{VOSe}}_2{\mathrm{O}}_5$. Blue, green, and yellow tetragonal pyramids are inequivalent ${\mathrm{VO}}_5$ polyhedra in a unit cell. Small-angle neutron scattering (SANS) pattern for the coaligned single crystals in zero field at 6.2 K ($\pm 0.1\mathrm{K}$), (d) after the ZFC procedure, and (e) after the field-trained process with $H=120\mathrm{Oe}$. $H$ is perpendicular to the incident neutron beam. The incident beam is parallel to the $c$ axis.

Figure 2

(a)–(d) $H$ dependence of $M$, ${\chi }^{\prime }$, and ${\chi }^{\prime \prime }$ under $H//c$ at (a),(b) 7.45 K, and (c),(d) 6.00 K, respectively. Red (blue) circle is for the $H$-increasing (-decreasing) scan. The $H$-increasing scan was performed after the ZFC procedure. (e) Color plot of ${\chi }^{\prime }$ for $H//c$, and the magnetic phase diagram determined by the measurements of $M$, ${\chi }^{\prime }$, and ${\chi }^{\prime \prime }$, where each magnetic phase is indicated as paramagnetic (PM); FM (3-up-1-down type state with $\text{spin}//c$); cycloidal IC-1 (Cyc); incommensurately modulated magnetic order (IC-2) (likely square Skyrmion lattice state, see the text); and triangular Skyrmion lattice state (A). Open circles are the peak in the ${\chi }^{\prime }\text{−}T$ curve; open triangles show the peak in the ${\chi }^{\prime }\text{−}H$ curve; and open squares show the peak in the $(d{\chi }^{\prime }/dH)\text{−}H$ curve. Rescaled $H$ for the phase diagram of the assembled-crystals sample for the SANS investigation is shown on the right ordinate.

Figure 3

(a) SANS pattern for the coaligned single crystals at 7.45 K with $H=25\mathrm{Oe}$ along the $c$ axis. $H$ and the incident neutron beam are parallel with each other and both along the $c$ axis. (b) Schematic illustration of the SANS pattern for (a). Blue, green, and orange circles indicate the respective Bragg spots corresponding to the magnetic orders shown in (c),(d), and (e). Integration sectors for the intensity of magnetic fourfold spots (green region) $I_4$ and SkL (red region) $I_6$. Definition of the azimuth angle ($\varphi$) is also indicated. (c)–(e) Schematics of the SANS pattern for (c),(d), two kinds of domain of triangular SkL and (e) fourfold pattern for multidomain of cycloidal order in the IC-1 phase or for the IC-2 phase. (f),(g) $\varphi$ dependence of integrated intensity for the field-cooling (FC) process with 25 Oe for $H//c$ at (f) 7.45, and (g) 6.00 K (red circle). In (g), the data with 20 Oe for $H//c$ after the ZFC procedure are also plotted by blue circles. The intensity integration is done over the radial $|\overrightarrow{q}|$ range $0.038\le |\overrightarrow{q}|\le 0.056{\mathrm{nm}}^{-1}$ for 7.45 K, and $0.036\le |\overrightarrow{q}|\le 0.053{\mathrm{nm}}^{-1}$ for 6.00 K. The remnant intensity peaks for a super cooled component of the triangular SkL state are indicated by asterisks. (h),(i) Temperature dependence of (h) ${\chi }^{\prime }$, (i) $I_4$, $I_6$, and their ratio $I_6/I_4$ for the field-cooling process with 25 Oe for $H//c$.

Figure 4

(a) SANS pattern for the coaligned single crystals at 6.00 K with 50 Oe for $H//c$. $H$ and the incident neutron beam are parallel to each other and both are along the $c$ axis. (b)–(d) $H$ dependence of (b) ${\chi }^{\prime }$ and ${\chi }^{\prime \prime }$, (c) integrated SANS intensity for the overall detector surface, and (d) the wavelength $\lambda$ of the magnetic modulation. (e),(f) Temperature dependence of the respective data measured in zero field for a cooling (blue circles) scan and a heating scan (red circles): (e) the SANS integrated intensity and ${\chi }^{\prime }$Unhandled Math Content: Z with the ac magnetic field $H_{\text{ac}}$ along the $c$ axis, and (f) $\lambda$ measured by the SANS pattern with the neutron beam parallel to the $c$ axis. (g) Magnetic phase diagram of ${\mathrm{VOSe}}_2{\mathrm{O}}_5$ determined by magnetization measurements with $H//c$. Phase boundaries for the white region ($\sim 4.5\mathrm{K}$, $\sim 30\mathrm{Oe}$) could not be definitely determined by the magnetization measurements. For the definition of each symbol, see the caption for Fig. 2. Red dashed square indicates the $H\text{−}T$ region shown in Fig. 2.