Electronically Mediated Magnetic Anisotropy in Vibrating Magnetic Molecules

We address the electronically induced anisotropy field acting on a spin moment in a vibrating magnetic molecule located in the junction between ferromagnetic metals. Under weak coupling between the electrons and molecular vibrations, the nature of the anisotropy can be changed from favoring a high spin (easy-axis) magnetic moment to a low spin (easy plane) by applying a temperature difference or a voltage bias across the junction. For unequal spin polarizations in ferromagnetic metals, it is shown that the character of the anisotropy is essentially determined by the properties of the weaker ferromagnet. By increasing the temperature in this metal or introducing a voltage bias, its influence can be suppressed such that the dominant contribution to the anisotropy is interchanged to the stronger ferromagnet. With increasing coupling strength between the molecular vibrations and the electrons, the nature of the anisotropy is locked into favoring easy-plane magnetism.