Ballistic Anisotropic Magnetoresistance (BAMR)

 

J. Velev, R. Sabirianov,¹ S. S. Jaswal, and E. Y. Tsymbal 

¹ Department of Physics, University of Nabraska, Omaha, Nebraska 

 

Electronic transport in ferromagnetic ballistic conductors is predicted to exhibit ballistic anisotropic magnetoresistance (BAMR) – a change in the ballistic conductance with the direction of magnetization. This phenomenon originates from the effect of the spin-orbit interaction on the electronic band structure, resulting in a change of the number of bands crossing the Fermi energy with the magnetization direction. The significance of this phenomenon is illustrated by first-principles calculations of the ballistic conductance in ferromagnetic Ni and Fe nanowires. Funded by NSF-MRSEC, NSF, and NRI.

 
The mechanism of electronic transport changes dramatically in constrained geometries of the nanometer scale when the dimensions are reduced to less than the mean free path of electrons. In this case electronic transport becomes ballistic rather than diffusive. When the constriction width is comparable to the Fermi wavelength the conductance becomes quantized.  If the constriction is formed by a slowly changing width of the wire, the ballistic conductance is given by  G = Ne²/h, where N is the number of open conducting channels, i.e. the number of transverse modes at the Fermi energy. This quantity is affected by the spin-orbit interaction. The effect is anisotropic because the orbital momentum is coupled to the spin causing the projection of the former to be different depending on the magnetization direction. By changing the magnetization direction one can, therefore, change the number of bands crossing the Fermi energy and thereby affect the ballistic conductance. We designate this phenomenon as the Ballistic Anisotropic Magnetoresistance (BAMR) effect.

The significance of the BAMR effect is illustrated by ab-initio calculations of the ballistic conductance of very thin ferromagnetic wires for magnetization parallel and perpendicular to the axis of the wire. There is a sizable difference in the conductance for the two orientations of the magnetization giving rise to an appreciable BAMR. The BAMR effect stems from the spin-orbit interaction which lifts the degeneracy of the d bands for the magnetization parallel but not perpendicular to the wire axis. This changes the number of conducting channels if the degenerate levels lie close to the Fermi energy:

Band structure of a monoatomic Ni wire.

The BAMR is different from AMR observed in bulk materials because no electron scattering is responsible for it. BAMR can be either positive or negative and has a very different angular dependence compared to AMR:

 

Paper:

J. Velev, R. Sabirianov, S. S. Jaswal, and E. Y. Tsymbal, "Ballistic Anisotropic Magnetoresistance",  Physical Review Letters   94, 127203 (2005).

 

 

The predicted BAMR effect has recently been observed in electrodeposited Co nanocontacts - see BAMR - experimental confirmation

 

 

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