In Situ Control of Diamagnetism by Electric Current in ${\mathrm{Ca}}_3({\mathrm{Ru}}_{1-x}{\mathrm{Ti}}_x{)}_2{\mathrm{O}}_7$

Nonequilibrium steady state conditions induced by a dc current can alter the physical properties of strongly correlated electron systems. In this regard, it was recently shown that dc current can trigger novel electronic states, such as current-induced diamagnetism, which cannot be realized in equilibrium conditions. However, reversible control of diamagnetism has not been achieved yet. Here, we demonstrate reversible in situ control between a Mott insulating state and a diamagnetic semimetal-like state by a dc current in the Ti-substituted bilayer ruthenate ${\mathrm{Ca}}_3({\mathrm{Ru}}_{1-x}{\mathrm{Ti}}_x{)}_2{\mathrm{O}}_7$ ($x=0.5\%$). By performing simultaneous magnetic and resistive measurements, we map out the temperature vs current-density phase diagram in the nonequilibrium steady state of this material. The present results open up the possibility of creating novel electronic states in a variety of strongly correlated electron systems under dc current.

Figure 1

Current-induced diamagnetism in ${\mathrm{Ca}}_3({\mathrm{Ru}}_{1-x}{\mathrm{Ti}}_x{)}_2{\mathrm{O}}_7$ ($x=0.5\%$). Temperature dependence of (a) resistivity and (b) magnetization under various dc currents. The photograph in (a) shows the measured single crystal (sample 1; dimensions of $3.3\times 0.8\times 0.35{\mathrm{mm}}^3$) along with a schematic description of the four-probe configuration. The inset in (b) is an enlarged view of the onset of diamagnetism. The arrows indicate the crossover temperature for diamagnetism $T_{\mathrm{DM}}$.

Figure 2

Temperature vs current-density phase diagram of ${\mathrm{Ca}}_3({\mathrm{Ru}}_{1-x}{\mathrm{Ti}}_x{)}_2{\mathrm{O}}_7$ ($x=0.5\%$). $T_{N1}$, $T_{N2}$, and $T_{\mathrm{MIT}}$ all show negligible changes with current. The antiferromagnetic insulating phase (blue) evolves into a more conducting state (yellow) with increasing current density. At temperatures below 10 K a diamagnetic phase (green) appears for $J>0.1{\mathrm{A}/\mathrm{cm}}^2$ with persisting $\mathrm{AFM}\text{−}b$ ordering. The triangles represent $T_{\mathrm{DM}}$ taken from Fig. 1, while the error bars are evaluated by estimating the real sample temperature due to Joule heating from another test experiment (see Fig. S3).

Figure 3

In situ control of diamagnetism with current in ${\mathrm{Ca}}_3({\mathrm{Ru}}_{1-x}{\mathrm{Ti}}_x{)}_2{\mathrm{O}}_7$ ($x=0.5\%$). (a) Cycling the current between the off and on state induces (b) a change between the high- and low- resistance states and (c) between the positive and negative magnetization (diamagnetic state). Because of the different Joule heating in the two states, sample temperature varied between 2 and 4 K in each cycle (see Fig. S9).

Figure 4

Magnetization vs magnetic field ($M-H$) curves for ${\mathrm{Ca}}_3({\mathrm{Ru}}_{1-x}{\mathrm{Ti}}_x{)}_2{\mathrm{O}}_7$ ($x=0.5\%$) with and without dc current. Both field-up and field-down sweep data are shown. The sudden increase of magnetization with $I=1\mathrm{mA}$ indicates the occurrence of a metamagnetic transition. The inset shows an enlarged view near $M=0$.