Chirality of magnetic excitations in ferromagnetic ${\mathrm{SrRuO}}_3$

Ferromagnetic ${\mathrm{SrRuO}}_3$ was proposed as a candidate material to exhibit an inverted magnon chirality due to a strong impact of spin-orbit coupling and Weyl fermions. By polarized inelastic neutron scattering under magnetic fields we determine the chirality of the ferromagnetic zone-center excitation as a function of temperature. Well in the ferromagnetic phase the excitation is perfectly chiral with the usual (right-handed) sign and only when the spontaneous magnetization is almost completely suppressed the chirality of the zone center magnetic excitations is reduced but does not change sign.

Figure 1

(a) Raw data of constant $\mathbf{Q}$ scans at $\mathbf{Q}=(0,1,1)$ and $\text{T}=10\text{K}$ performed using a horizontal magnetic field of 3.8 T and different flipper configurations. The magnetic signal of the anisotropy gap in the inelastic response can be distinguished from nuclear contributions by the polarization analysis. The inset displays the elastic line for all four flipper configurations. (b) After correction, the magnon signal only appears in the corrected SF1 channel and is fitted with a Gaussian and constant background, while there is no signal visible in the SF2 channel. (c) The spin $\mathbf{S}$ at site $i$ in the excited state precesses around the quantization axis $z$ clockwise. The perpendicular component ${\mathbf{S}}_{\perp }$ follows the right-handed equation of motion derived in the text. (d) The influence of magnetic field direction on the magnon signal is studied by constant $\mathbf{Q}$ scans for two different field directions at 160 K in both spin-flip channels (raw data).

Figure 2

Comparison of all four polarization channels nSFoff, nSFon, SF1, SF2 for various temperatures after applying the correction for finite polarization and flipper efficiency described in the Supplemental Material [35]. [(a)–(h)] The magnon signal in SF1 is fitted with a Gaussian and a constant background. [(i)–(n)] Corrected data around the elastic line. Note that the correction of data can lead to negative intensities, which can be only represented in a linear scale.

Figure 3

Temperature dependence of the magnon gap and the chirality of the magnon: (a) The magnon gap as peak position of the fits of the corrected data in Fig. 2 (black circles) is compared to the field-cooled magnetization at 4 T with field parallel to [0,1,1] direction (red dots). The dashed line designates the finite energy induced by Zeeman splitting [38]. (b) The chiral ratio as the normalized difference of both spin flip channels represents the chiral part of the magnetic scattering and exhibits no pronounced temperature dependence in the ferromagnetic phase but drops above $\sim 200\mathrm{K}$. The chiral ratio is based on corrected data.

Figure 4

At a magnetic field of 1 T polarized INS experiments were only possible above T = 160 K. At this temperature the magnon gap is reduced due to the smaller Zeeman term but the excitation still exhibits a nearly perfect right-handed character, panel (a). Similar to the data at 3.8 T further enhancement of the temperature, panels (b) and (c), leads to an intensity enhancement in channel SF2, which results in a magnetic signal at 200 K that is equally distributed in the two spin-flip channels.