Magnetism of an Fe monolayer on W(110)

We discuss theoretical studies of magnetism in the Fe monolayer adsorbed on the W(110) surface. We first present density-functional studies of the ground state that provide us with basic magnetic parameters, under the assumption the ground state is ferromagnetic. We provide results for the spin and orbital magnetic moments, local density of states, the anisotropy, and measures of the exchange strength as provided by calculations of the energy difference between the ferromagnetic and antiferromagnetic states. We compare these results with those provided by the empirical tight-binding description we have used to describe spin waves in this system, to find good agreement between the two methods where results overlap. Inclusion of spin-orbit coupling within our tight-binding Hamiltonian produces anisotropy close in strength and character to that which emerges from the full density-functional analysis, for example. We then present new calculations of the nature of the spin waves in the monolayer. We point out that the large anisotropy that emerges from our analyses (similar to that found in earlier work), combined with our calculations of the effective exchange, provides a value for the Curie temperature of the film much larger than that found experimentally. An earlier experimental study has suggested that in this system, the effective exchange is much smaller than we find. We conclude that the magnetism in this much studied system is not well understood. We discuss reasons why this may be so.

Figure 1

(Color online) A comparison between the total local density of states in the Fe monolayer provided by the density-functional treatment (black curve) and by the empirical tight-binding description (red curve) of the Fe/W(110) system. The majority spin density of states is above the horizontal line, and the minority spin density of states is below. The zero of energy is chosen to be the Fermi energy.

Figure 2

(Color online) Calculations of the energy change produced by canting spins on one sublattice relative to those on the second sublattice, as one rotates spins from full ferromagnetic alignment to the $c\left(2\times 2\right)$ antiferromagnetic state. The figure shows the change in energy per unit cell of the AFM lattice. This contains two Fe atoms. The results are generated through use of the VASP code, as discussed in the text. The red curves are best fits to a $\text{cos}\theta$ form in the angular regions covered by the plots.

Figure 3

The MCA as a function of direction of the magnetization, as it is swept from the long axis in plane $\left(\left[\overline{1}10\right]\right)$ to the short axis in plane ([001]) and then to the perpendicular to the plane ([110]). The results have been generated with the tight-binding method, as discussed in the text.

Figure 4

(Color online) Spectral density plots, for the case where the wave vector is directed along the $\Gamma L$ direction in the surface Brillouin zone. The wave vector is then directed parallel to the short axis in real space. The wave vector associated with the topmost curve is $0.3{\text{Å}}^{-1}$, and it increases from top to bottom in steps of $0.1{\text{Å}}^{-1}$.

Figure 5

(Color online) Spin-wave dispersion relations along the two principal directions in the surface Brillouin zone, calculated as described in the text.

Figure 6

(Color online) The magnetization as a function of temperature, as calculated from a Heisenberg model which utilizes two different parameter sets. The solid curves are calculations for the case where the spin $S=3/2$, and the dotted curve is for $S=1$. The left-hand panel employs uniaxial anisotropy of 3.5 meV, and exchange parameters taken from Table . The right-hand panel presents calculations which use the very modest exchange strengths proposed in Ref. 5, along with uniaxial anisotropy of 3.5 meV.