${\mathrm{Ca}}_3{\mathrm{Ru}}_2{\mathrm{O}}_7$ 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.

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• Magnetoelastic effect
• Magnetoresistance
• Magnetostriction
• Pressure effects
• Spin polarization
• Spin-orbit coupling