An attractive feature of magnetic adatoms and molecules for nanoscale applications is their superparamagnetism, the preferred alignment of their spin along an easy axis preventing undesired spin reversal. The underlying magnetic anisotropy barrier -a quadrupolar energy splitting -is internally generated by spin-orbit interaction and can nowadays be probed by electronic transport. Here we predict that in a much broader class of quantum-dot systems with spin larger than one-half, superparamagnetism may arise without spin-orbit interaction: by attaching ferromagnets a spintronic exchange field of quadrupolar nature is generated locally. It can be observed in conductance measurements and surprisingly leads to enhanced spin filtering even in a state with zero average spin. Analogously to the spintronic dipolar exchange field, responsible for a local spin torque, the effect is susceptible to electric control and increases with tunnel coupling as well as with spin polarization.The growing interest in nanomagnets, e.g., magnetic adatoms 1 and single-molecule magnets 2 is fueled by prospects of their application in novel spintronic devices whose functionality derives from their unique magnetic features 3 . A key property of such systems is their strong magnetic anisotropy leading to magnetic bistability, required for building blocks for nanoscale memory cells 4,5 and non-trivial quantum dynamics, useful for quantum information processing 6,7 . In either case, operational stability of such devices hinges heavily on the height of the energy barrier opposing the spin reversal. Though recently progress in the control over the magnetic anisotropy by synthesis 8 , mechanical straining 9 , atomic manipulation 10 or electrical gating 11 has been made, achieving of a high spin-reversal barrier still remains a challenge. Incorporating a nanomagnet into an electronic circuit may significantly alter its magnetic properties [12][13][14] , but may also be advantageous. One possible, spintronic route for manipulation of nanomagnets entails ferromagnetic electrodes and uses the spin torque due to spin-polarized scattering 15 or Coulomb interaction 16 , magnetic analogs of the proximity effect in superconducting junctions. In this article, we present another route that combines spintronics with molecular magnetism: high-spin quantum dots can acquire a significant magnetic anisotropy that is purely of spintronic origin, instead of deriving from the spin-orbit interaction, as the tunneling to ferromagnets induces a local, quadrupolar exchange field. Besides providing an alternative approach to electrical manipulation and engineering of superparamagnetic nanomagnets, this new quantity is of key importance for the analysis of experiments that probe atoms or molecules using highly spin-polarized electrodes.
DIPOLAR VS. QUADRUPOLAR EXCHANGE FIELDThe origin of superparamagnetism, usually dominating the magnetic behaviour of a nanomagnet, is a magnetic anisotropy energy barrier. For instance, an adatom with a spin-degenerate ground multiplet (q...