Magnetic phenomena, spin-orbit effects, and Landauer conductance in Pt nanowire contacts: Density-functional theory calculations

Platinum monatomic nanowires were predicted to spontaneously develop magnetism, involving a sizable orbital moment via spin-orbit coupling, and a colossal magnetic anisotropy. We present here a fully-relativistic (spin-orbit coupling included) pseudopotential density functional calculation of electronic and magnetic properties, and of Landauer ballistic conductance of Pt model nanocontacts consisting of short nanowire segments suspended between Pt leads or tips, represented by bulk planes. Even if short, and despite the nonmagnetic Pt leads, the nanocontact is found to be locally magnetic with magnetization strictly parallel to its axis. Especially under strain, the energy barrier to flip the overall spin direction is predicted to be tens of meV high, and thus the corresponding blocking temperatures large, suggesting the validity of static Landauer ballistic electrical conductance calculations. We carry out such calculations to find that inclusion of spin-orbit coupling and of magnetism lowers the ballistic conductance by about $15÷20\%$ relative to the nonmagnetic case, yielding $G\sim 2G_0$ $\left(G_0=2e^2/h\right)$, in good agreement with break junction results. The spin filtering properties of this highly unusual spontaneously magnetic nanocontact are also analyzed.

Figure 1

Electron band structure of the infinite monatomic Pt wire with interatomic distance of $2.66\text{Å}$ calculated with SR (upper panel) and FR (lower panels) pseudopotentials. For the FR, more realistic case, the bands for nonmagnetic as well as for both magnetic polarizations (magnetic moment parallel or perpendicular to the wire axis) are shown. The bands are labeled according to their symmetry (see text). The number of bands crossing the Fermi level (number of conductance channels) is provided on each panel. The spin magnetic moment per atom is also given for magnetic states.

Figure 2

(Color online) Planar average (in the $xy$ plane) of the spin magnetization as a function of $z$ for three-, four-, and five-atom Pt nanowire contacts calculated with FR pseudopotentials. The magnetic states with parallel and perpendicular polarization in the four- and five-atom case are shown by solid and dashed lines, respectively. The magnetic moments (in Bohr magnetons) within a sphere with radius of $2.5\text{Å}$ are shown for all nanowire atoms. The vertical dashed lines show the positions of the bulk lead surfaces; the positions of nanowire atoms, with a mutual spacing of $d=2.66\text{Å}$, are indicated by arrows.

Figure 3

Transmission coefficient (per spin) versus energy for the three-atom nanowire Pt contact at $d=2.66\text{Å}$ (upper panel) in the SR approximation, where spin-orbit coupling is not included, and the contact is nonmagnetic. Note the anticipated value of ballistic conductance of $2.7G_0$, considerably higher than typical experimental values in the range $1.5–2.0G_0$. The lower panels show the LDOS projected on different atomic orbitals of the middle nanowire atom.

Figure 4

Ballistic conductance of three-, four-, and five-atom nanowire Pt contacts. Here SR and FR calculations are compared including in the latter case, the conductances for both parallel and transverse magnetic states as well as for the nonmagnetic state. The FR state with parallel magnetization corresponds to the nanocontact ground state, with a ballistic conductance of about $2G_0$. The ideal contactless maximal conductance of a perfect infinite nanowire (deduced from the channel number in the band structure of Fig. 1) is also provided for each case.

Figure 5

Eigenchannel decomposition of the FR total transmission at the Fermi energy calculated at the $\overline{M}$ 2D $\mathbf{k}$ point (see the inset). Here (as well as at the $\overline{\Gamma }$ point), due to the symmetry, the half-integer $m_j$ can be assigned to each transmission eigenchannel (see text).