Field-Induced Paramagnons at the Metamagnetic Transition of ${\mathrm{Ca}}_{1.8}{\mathrm{Sr}}_{0.2}{\mathrm{RuO}}_4$

The magnetic excitations in ${\mathrm{Ca}}_{1.8}{\mathrm{Sr}}_{0.2}{\mathrm{RuO}}_4$ were studied across the metamagnetic transition and as a function of temperature using inelastic neutron scattering. At low temperature and low magnetic field the magnetic response is dominated by a complex superposition of incommensurate antiferromagnetic fluctuations. Upon increasing the magnetic field across the metamagnetic transition, paramagnon and finally well-defined magnon scattering is induced, partially suppressing the incommensurate signals. The high-field phase in ${\mathrm{Ca}}_{1.8}{\mathrm{Sr}}_{0.2}{\mathrm{RuO}}_4$, therefore, has to be considered as an intrinsically ferromagnetic state stabilized by the magnetic field.

Figure 1

Mapping of the magnetic intensity in the $a^{*}/b^{*}$ plane of reciprocal space around $\mathbf{Q}=(1,0,0)$. Data are taken at $T=2\mathrm{K}$ and at an energy transfer of 2.5 meV. A smooth background is subtracted. The inset shows the same data, but fully symmetrized and corrected for the magnetic form factor $F(\mathbf{Q})$.

Figure 2

Constant energy scans: (a) along $b^{*}$, (b) along the diagonal of the Brillouin zone. The sketch on top illustrates the positions of the incommensurate magnetic signals as described in the text, and the bold arrows are the trajectories of the scans in reciprocal space. The crosses are the weaker $\alpha /\beta$ nesting signal at $(1,0,0)+(\pm 0.3,\pm 0.3,0)$. The lines are fits with Gaussians centered at the positions shown in the sketch.

Figure 3

Temperature dependence of the paramagnon scattering. (a) Constant energy scans at three different temperatures. In (b) we plot the intensity of the (2D) zone center $Q_{\mathrm{FM}}=(0,0,1.6)$ as a function of temperature for 0.4 and 1 meV energy transfer (lines are guides to the eye, 0.4 meV data shifted by $400\frac{{\mu }_B^2}{\mathrm{eV}}$). From the smoothed curves in (b) we estimate the real part of the susceptibility at $\omega =0$ (see text), which is plotted in (c) together with the macroscopic susceptibility (in-plane average) from Ref. 2.

Figure 4

Magnetic scattering for magnetic fields applied along the $b$ axis: (a) Constant energy scans along [100]. Lines assume a superposition of an AFM and a FM contribution [the latter centered at $Q_{\mathrm{FM}}=(0,0,1.6)$], a sketch of these contributions is drawn in (b). (c) Energy scans at the FM position $Q_{\mathrm{FM}}$. The intensities of the FM and AFM contributions fitted to the scans in (a) relative to their values at 0 and 8 T, respectively, are shown in (d) as a function of the field. (e) The field dependence of the low-energy part at $Q_{\mathrm{FM}}$. [Lines in (c) and (e) are guides to the eye.]

Figure 5

(a) Constant energy scans above the MM transition ($B=10\mathrm{T}$, $B\parallel c$) in the same configuration as the scans in Fig. 2. The lines are fits consisting of two contributions: the AFM one was taken to be the same as in Fig. 2a times a variable scale factor $\le 1$; the magnon was added as two Gaussians at symmetric positions, but variable width to account for focusing effects of the spectrometer. In (b) the 2 meV scans at 0 and 6 T are compared. In (c), the fitted peak positions are plotted together with a parabolic dispersion.