Lattice flexibility in ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$: Control of electrical transport via anisotropic magnetostriction

${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ is a correlated and spin-orbit coupled system with an extraordinary anisotropy. It is both interesting and unique largely because this material exhibits conflicting phenomena that are often utterly inconsistent with traditional precedents, particularly, the quantum oscillations in the nonmetallic state and colossal magnetoresistivity achieved by avoiding a fully spin-polarized state. This work focuses on the relationship between the lattice and transport properties along each crystalline axis and reveals that application of magnetic field, $H$, along different crystalline axes readily $\mathit{stretches}$ or $\mathit{shrinks}$ the lattice in a uniaxial manner, resulting in distinct electronic states. Furthermore, application of modest pressure drastically amplifies the $\mathit{anisotropic}$ magnetoelastic effect, leading to either an occurrence of a robust metallic state at $H\left|\right|\mathrm{hard}$ axis or a reentrance of the nonmetallic state at $H\left|\right|\mathrm{easy}$ axis. ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ presents a rare lattice-dependent magnetotransport mechanism, in which the extraordinary lattice flexibility enables an exquisite control of the electronic state via magnetically stretching or shrinking the crystalline axes, and the spin polarization plays an unconventional role unfavorable for maximizing conductivity. At the heart of the intriguing physics is the anisotropic magnetostriction that leads to exotic states.

Figure 1

(a) The magnetic field dependence of magnetization for the $a, b$, and $c$ axis, $M_{\mathrm{a}}, M_{\mathrm{b}}$, and $M_{\mathrm{c}}$ (solid lines, left scale) and the $c$-axis electrical resistivity ${\rho }_{\mathrm{c}}\left(H\right|\left|a\right), {\rho }_{\mathrm{c}}\left(H\left|\right|b\right)$, and ${\rho }_{\mathrm{c}}\left(H\left|\right|c\right)$ (dashed lines, right scale) [1]. Note that the $a$-axis resistivity ${\rho }_{\mathrm{a}}$ shows the same behavior as ${\rho }_{\mathrm{c}}$ does [10]. (b) The temperature dependence of the $a, b$, and $c$ axis [11] and (c) the thermal expansion coefficient α (blue and red lines, left scale) and the $a$-axis resistivity ${\rho }_{\mathrm{a}}$ (black line, right scale). Insets: Single-crystal ${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ and distorted basal plane of the unit cell. Note that the shaded region in (b) highlights a rapidly changing $c$ axis in the interval 40–48 K.

Figure 2

The magnetic field dependence of magnetostriction $\mathrm{\Delta }L/L$ (a)-(f) for $\mathrm{\Delta }L/L$ ($H\left|\right|a$ axis) and (A)–(F) for $\mathrm{\Delta }L/L$ ($H\left|\right|b$ axis) at six representative temperatures; (x), (y) Schematic illustrations of the magnetostrictive effects on the lattice. Note that $H^{*}$ is marked by the black solid circles, and $H_{\mathrm{c}}$ by the light-gray dashed line.

Figure 3

(a)–(e) The magnetic field dependence of ${\rho }_{\mathrm{c}}\left(H\right)/{\rho }_{\mathrm{c}}\left(0\right)$ (solid lines, left scale) for $H\left|\right|a$ (thick blue lines) and $H\left|\right|b$ (thin red line) and $\mathrm{\Delta }L/L\left(H\left|\right|L\right)$ (dashed lines, right scale) for comparison. Note that the black dashed line is the guide to the eye joining $H^{*}$, and ${\rho }_{\mathrm{c}}\left(H\right)/{\rho }_{\mathrm{c}}\left(0\right)$ for $H\left|\right|b$ is not displayed in (a) and (c) because it remains essentially the same as that in (b).

Figure 4

(a) The temperature dependence of $H^{*}$ for $H\left|\right|a$ axis and $H_{\mathrm{c}}$ for $H\left|\right|b$ axis (Note the two data points in green squares are estimated based on the resistivity [10]). The temperature dependence of the $a$-axis resistivity ${\rho }_{\mathrm{a}}$ (b) at $H=0$ and $P=1\mathrm{bar}$, 5 kbar, 10 kbar, 15 kbar, and 20 kbar, and (c) at $P=20\mathrm{kbar}$ and ${\mu }_{o}H=0$ (black line), 7 T (thin lines), and 14 T (thick lines) for $H\left|\right|a$ axis (blue lines) and $H\left|\right|b$ axis (red lines). Inset: ${\rho }_{\mathrm{a}}$ at $H=0$ and $P=20\mathrm{kbar}$. (d) The magnetic field dependence of ${\rho }_{\mathrm{a}}\left(H\right)/{\rho }_{\mathrm{a}}\left(0\right)$ at $P=20\mathrm{kbar}$ for $H\left|\right|a$ axis (blue line) and $H\left|\right|b$ axis (red line).

Figure 5

A phase diagram for $T_{\mathrm{MI}}$ (thick lines) and $T_{\mathrm{N}}$ (dashed thin lines) as functions of pressure and magnetic field for $H\left|\right|a$ axis (blue lines) and $H\left|\right|b$ axis (red lines) at $P=20\mathrm{kbar}$. The schematic illustrations of the magnetostrictive effects on the orthorhombicity due to $P$ and $H$. Note that PM stands for paramagnetic, M for metal, and NM for nonmetal.