Dynamical magnetic anisotropy in spin--1 molecular systems

We study electronic transport through a deformable spin-1 molecular system in a break junction setup, under the influence of a local vibrational mode. Our study shows that the magnetic anisotropy, which arises due to stretching along the transport axis[Science 328 1370 (2010)], is renormalized by the interactions with vibrations. The coupling induces additional spin--asymmetric hybridizations that contribute to the net molecular anisotropy. We show that the low temperature physics of such device can be described by an anisotropic Kondo model ($J_{\perp} > J_{\parallel}$), with a magnetic anisotropy term, $A_{Net}S_z^2$, negative at zero stretching. A quantum phase transition (QPT) is explored by stretching the molecule, driving $A_{Net}$ into positive values, and changing the character of the device from a non--Fermi--liquid (NFL) to a Fermi liquid (FL) ground state. This transition can be directly observed through the zero--bias conductance, which we find to be finite for negative anisotropy, zero for positive anisotropy, and to reach the unitary limit at $A_{Net} \approx 0$. At that point, an underscreened spin-1 Kondo ground state appears due to the restitution of the spin-1 triplet degeneracy.