Disorder Promotes Ferromagnetism: Rounding of the Quantum Phase Transition in ${\mathrm{Sr}}_{1-x}{\mathrm{Ca}}_x{\mathrm{RuO}}_3$

The subtle interplay of randomness and quantum fluctuations at low temperatures gives rise to a plethora of unconventional phenomena in systems ranging from quantum magnets and correlated electron materials to ultracold atomic gases. Particularly strong disorder effects have been predicted to occur at zero-temperature quantum phase transitions. Here, we demonstrate that the composition-driven ferromagnetic-to-paramagnetic quantum phase transition in ${\mathrm{Sr}}_{1-x}{\mathrm{Ca}}_x{\mathrm{RuO}}_3$ is completely destroyed by the disorder introduced via the different ionic radii of the randomly distributed Sr and Ca ions. Using a magneto-optical technique, we map the magnetic phase diagram in the composition-temperature space. We find that the ferromagnetic phase is significantly extended by the disorder and develops a pronounced tail over a broad range of the composition $x$. These findings are explained by a microscopic model of smeared quantum phase transitions in itinerant magnets. Moreover, our theoretical study implies that correlated disorder is even more powerful in promoting ferromagnetism than random disorder.

Figure 1

Morphology and magnetic characterization of the composition-spread ${\mathrm{Sr}}_{1-x}{\mathrm{Ca}}_x{\mathrm{RuO}}_3$ epitaxial film. (a) Photographic image of the $10\times 4{\mathrm{mm}}^2$ film with the local concentration $x$ indicated along the composition-spread direction. The large terraces of monoatomic layers in the atomic force microscope image demonstrates the high quality of the film. (b) The contour plot of the remanent magnetization ($M$) over the composition-temperature phase diagram. The dotted mesh is the measured data set used for the interpolation of the surface. The ferromagnetic-paramagnetic phase boundary, $T_C(x)$, derived from the susceptibility and magnetization data (see text for details) is also indicated by the black and white symbols, respectively. (c) Schematic of the magnetism in the tail of the smeared transition. The spins on Sr-rich rare regions (bright islands) form locally ordered “superspins.” Their dynamics freezes due to the coupling to electronic excitations which also tends to align them giving rise to an inhomogeneous long-range ferromagnetic order.

Figure 2

Temperature dependence of (a) the remanent magnetization $M$ and (b) ac susceptibility $\chi$ for selected compositions $x$. The main panel of (b) focuses on the region $x\gtrsim 0.4$, and the inset displays representative susceptibility curves over the full range of $x$. Both the magnetization and susceptibility curves show the continuous suppression of the ferromagnetic phase with increasing $x$ and the broadening of the transition.

Figure 3

The smearing of the quantum phase transition in ${\mathrm{Sr}}_{1-x}{\mathrm{Ca}}_x{\mathrm{RuO}}_3$. (a) The composition dependence of the remanent magnetization $M$ at selected temperatures. The inset shows that the hysteresis in the field loops at $T=4.2\mathrm{K}$ gradually vanishes towards larger $x$ but still present even at $x\approx 0.52$. (b) Semilogarithmic plots of the magnetization and the transition temperature $T_C$ as functions of the control parameter in the tail region. The symbols represent the experimental data while solid lines correspond to the theory which predicts $x_c=0.38$ as the location of the quantum phase transition in the (hypothetical) clean system.

Figure 4

Model calculation of the magnetization-composition ($M\mathrm{\text{−}}x$) curves in the presence of correlated disorder. $M_0$ is the saturation magnetization and $\xi$ is the disorder correlation length measured in lattice constants, i.e., it is the length scale over which the occupations of the unit cells with Sr or Ca atoms are correlated.