Towards mechanomagnetics in elastic crystals: insights from [Cu(acac)$_2$]
We predict that the magnetic properties of \cuacac, an elastically flexible crystal, change dramatically when the crystal is bent. We find that unbent \cuacac\ is an almost perfect Tomonaga-Luttinger liquid. Broken-symmetry density functional calculations reveal that the magnetic exchange interactions along the chains is an order of magnitude larger than the interchain exchange. The geometrically frustrated interchain interactions cannot magnetically order the material at any experimentally accessible temperature. The ordering temperature ($T_N$), calculated from the chain random phase approximation, increases by approximately 24 orders of magnitude when the material is bent. We demonstrate that geometric frustration both suppresses $T_N$ and enhances the sensitivity of $T_N$ to bending. In \cuacac, $T_N$ is extremely sensitive to bending, but remains too low for practical applications, even when bent. Partially frustrated materials could achieve the balance of high $T_N$ and good sensitivity to bending required for practical applications of mechanomagnetic elastic crystals.