Mott versus Slater-type metal-insulator transition in Mn-substituted Sr${}_3$Ru${}_2$O${}_7$

We present a temperature-dependent x-ray-absorption (XAS) and resonant elastic x-ray scattering (REXS) study of the metal-insulator transition (MIT) in Sr${}_3$(Ru${}_{1-x}$Mn${}_x$)${}_2$O${}_7$. The XAS results reveal that the MIT drives the onset of local antiferromagnetic correlations around the Mn impurities, a precursor of the long-range antiferromagnetism detected by REXS at $T_{\mathrm{order}}<T_{\mathrm{MIT}}$. This establishes that the MIT is of the Mott type (electronic correlations) as opposed to Slater type (magnetic order). While this behavior is induced by Mn impurities, the $(\frac{1}{4},\frac{1}{4},0)$ order exists for a wide range of Mn concentrations, and points to an inherent instability of Sr${}_3$Ru${}_2$O${}_7$.

Figure 1

(a),(c) Temperature-dependent Mn $L_2$-XAS spectra measured on 5 and 20$\%$ Mn-substituted Sr${}_3$Ru${}_2$O${}_7$ with $\mathbf{E}\parallel \mathbf{c}$. (b),(d) Theoretical $L_2$ spectra calculated with the inclusion of a 1-meV AF exchange field: (b) $H^{\mathrm{ex}}$ 30${}^{\circ }$ away from $c$ axis, $T_{\text{Néel}}=50$ K; (d) $H^{\mathrm{ex}}$ 60${}^{\circ }$ away from $c$ axis, $T_{\text{Néel}}=100$ K. (e) Normalized peak-height ratio $L_2^R\left(T\right)/L_2^R\left(15\right)$ vs temperature for 5, 10, and 20$\%$ Mn substitution; $L_2^R\left(T\right)=[\frac{I_A-I_B}{I_A+I_B}\left(T\right)-\frac{I_A-I_B}{I_A+I_B}\left(295\right)]$ and $I_{A,B}$ is the intensity of peak $A,B$. For 20$\%$ Mn, the modulus of the data is plotted. Inset of (e): dc electrical resistivity data (in logarithmic scale), for the same samples (Ref. 4).

Figure 2

(a) REXS transverse-momentum scan: 10$\%$ Mn rocking curves ($\theta$ scan) for two different azimuthal angles measured at 641 eV and 20 K: $\phi =-5^{\circ }$ corresponds to a $\sim$$(1/4,1/4,l)$ scan probing the $c$-axis component of the order; $\phi ={90}^{\circ }$ corresponds to a $(h,-k,0)$ scan probing the $ab$ in-plane component. (b) REXS longitudinal-momentum scan: 10$\%$ Mn $(\frac{1}{4}+\Delta q,\frac{1}{4}+\Delta q,0)$ scans ($\theta -2\theta$ scan) at 641 eV for different temperatures. (c) Azimuthal-angle dependence of the 10$\%$ Mn $(\frac{1}{4}+\Delta q,\frac{1}{4}+\Delta q,0)$ momentum scan integrated intensity, at Ru $L_2$ (2968 eV) and Mn $L_3$ edges, fitted to the formula $I_{(\frac{1}{4},\frac{1}{4},0)}^{\mathrm{total}}=I_{(\frac{1}{4},\frac{1}{4},0)}^{\pi \to {\sigma }^{\prime }}+I_{(\frac{1}{4},\frac{1}{4},0)}^{\pi \to {\pi }^{\prime }}\propto {\left|\cos \theta \cos \phi \right|}^2+{\left|\sin 2\theta \sin \phi \right|}^2$. Due to the different Mn and Ru scattering angles (${\theta }_{\text{Mn}}=61.6^{\circ }$; ${\theta }_{\text{Ru}}=10.9^{\circ }$), the ratio between $(\pi \to {\sigma }^{\prime })$ and $(\pi \to {\pi }^{\prime })$ scattering signals is also different and the maximum intensity angle is shifted by 90${}^{\circ }$ in $\phi$.

Figure 3

(a) Integrated REXS momentum scans vs temperature (connected symbols) for 5, 7.5, and 10$\%$ Mn, together with transport data (lines), all in log scale and vertically shifted. The REXS intensity is scaled to emphasize $T_{\mathrm{MIT}}$ and $T_{\mathrm{order}}$ temperature difference: $T_{\mathrm{MIT}}$ denotes the onset of the local AF exchange field around Mn impurities, which triggers a metal-insulator transition; $T_{\mathrm{order}}$ is the onset of long-range AF order involving both impurity and Ru host. (b) REXS correlation length vs temperature; no REXS peak was observed on 2.5$\%$ and 20$\%$ Mn samples.

Figure 4

Sr${}_3$(Ru${}_{1-x}$Mn${}_x$)${}_2$O${}_7$ phase diagram: the green line is the MIT phase boundary as seen by transport (Ref. 4) and XAS (Fig. 1), which we interpret as the onset of AF short-range correlations; the red line instead defines the onset of long-range spin order between the Mn impurities via the quasiordered Ru-O host, as detected by REXS (dashed sections are the boundaries suggested by experimental points on either side, although not directly verified). Our results indicate the region between green and red lines to be a Mn-driven disordered AF insulating state.