Large anisotropy in the paramagnetic susceptibility of $\mathrm{Sr}\mathrm{Ru}{\mathrm{O}}_3$ films

By using the extraordinary Hall effect in $\mathrm{Sr}\mathrm{Ru}{\mathrm{O}}_3$ films we performed measurements of the paramagnetic susceptibility in this itinerant ferromagnet, from $T_c$ $(\sim 150\mathrm{K})$ to $300\mathrm{K}$. These measurements, combined with measurements of magnetoresistance, reveal that the susceptibility, which is almost isotropic at $300\mathrm{K}$, becomes highly anisotropic as the temperature is lowered, diverging along a single crystallographic direction in the vicinity of $T_c$. The results provide a manifestation of the effect of large magnetocrystalline anisotropy in the paramagnetic state of a $4d$ itinerant ferromagnet.

Figure 1

Hall effect with $H=2500\mathrm{Oe}$ applied parallel to the current (along the $\left[1\overline{1}0\right]$ direction) as a function of temperature above $T_c$ $(\simeq 147\mathrm{K})$. The dashed line is a guide to the eye.

Figure 2

EHE at $T=153\mathrm{K}$ divided by the applied field $H$ (circles: $250\mathrm{Oe}$, crosses: $500\mathrm{Oe}$) as a function of the angle $\theta$ between $\mathbf{H}$ and the $b$ direction (see illustration). The dashed curve is the OHE. The solid curve is a fit obtained by assuming certain constant values for the susceptibility along the $a$ and $b$ directions.

Figure 3

Susceptibility along the crystallographic directions [100] $\left({\chi }_a\right)$ and [010] $\left({\chi }_b\right)$ as a function of temperature, on a semilog plot. The values are multiplied by $R_s$, whose temperature dependence is expected to be smooth. The error bars for $R_s{\chi }_a$ reflect an uncertainty of up to 2° in $\theta$. The dashed lines are guides to the eye. The inset shows the ratio ${\chi }_b∕{\chi }_a$ for $165\mathrm{K}<T<300\mathrm{K}$. The solid curve is a fit to $(T-T_{c,a}^{MF})∕(T-T_{c,b}^{MF})$ with $T_{c,a}^{MF}=109\mathrm{K}$, $T_{c,b}^{MF}=150.5\mathrm{K}$.

Figure 4

Magnetoresistance as a function of temperature with a field of $0.5\mathrm{T}$ applied along the different crystallographic directions (the values are normalized to the values at $180\mathrm{K}$). The inset shows the magnetization $\left({\mu }_0{R}_{s}M\right)$ and magnetoresistance $\left(\Delta \rho \right)$ as a function of a field (applied along the $b$ direction, at $T=170\mathrm{K}$). The solid curve is a fit to $\Delta \rho \propto -M^2$.

Figure 5

Deviation of the magnetization from the easy axis as a function of the field which is applied at 60° relative to the easy axis. The solid curve presents the expected behavior with an anisotropy constant of $1.2\times {10}^7\mathrm{erg}∕{\mathrm{cm}}^3$.