Exchange interactions and Néel temperature of a Fe monolayer on W(001): A first-principles study

The density-functional study of the magnetic properties of a single Fe monolayer on W(001) is reported. The system possesses, presently unique for Fe layers, antiferromagnetic structure. We demonstrate that the study of the instability of the ferromagnetic state predicts the ground-state antiferromagnetic structure. We use the frozen-magnon technique to evaluate the interatomic exchange parameters for different reference states. The relative role of the Fe-Fe and Fe-W exchange interactions is revealed. The Néel temperature is estimated.

Figure 1

The frozen-magnon energies for Fe ML on W(001) along two lines in the 2D Brillouin zone for three different magnetic reference states: (a) ferromagnetic, (b) antiferromagnetic with $\mathbf{q}=\left(10\right)$ (AFM-I), and (c) antiferromagnetic with $\mathbf{q}=\left(11\right)$ (AFM-II). Here and in the text all reciprocal-space vectors are given in units of $\pi ∕a$. The square inserts in the bottom part of the figures present the reference magnetic structure. Definitions of the points of the Brillouin zone in panels (a) and (b): $\Gamma (0,0),M(1,1),X(1,0),X^{\prime }(0,1)$. In panel (c): $M\left(\frac{1}{2},\frac{1}{2}\right),X(1,0)$. In cases (a) and (c) the points (1,0) and (0,1) are equivalent. In case (b) they are not equivalent. The filled (open) circles show the frozen-magnon energies for the wave vectors parallel to the ferromagnetic (antiferromagnetic) rows of atoms.

Figure 2

The Fe-Fe exchange parameters of a free standing ferromagnetic Fe ML (open square), and for the FM (filled circles) and AFM-II (open circles) reference states of a Fe ML on W(001). The inset compares the nearest-neighbor Fe-Fe exchange parameters of Fe ML on W(001) for three different reference states. The exchange parameters correspond to the Heisenberg Hamiltonian of the form $H_{\mathrm{eff}}=-{\sum }_{i\ne j}{J}_{ij}{\mathbf{s}}_i\bullet {\mathbf{s}}_j$.

Figure 3

(Color online) The spin-resolved Fe $3d$ DOS for Fe ML on W and unsupported Fe ML. The DOS are presented for FM and AFM-II configurations. The dotted lines mark the position of the Fermi level. The energy origin is selected at the Fermi level of the AFM-II structures. Therefore the Fermi energy of the FM structures somewhat deviates from zero. This deviation is $-1.4\mathrm{mRy}$ for $\mathrm{Fe}∕\mathrm{W}\left(001\right)$ and is not noticeable in the figure. For unsupported Fe ML the deviation assumes a larger value of $-7.2\mathrm{mRy}$.

Figure 4

The Néel temperature of the Fe layer on W(001) as a function of the anisotropy parameter $\Delta$. The inset shows a part of the curve with the use of the logarithmic scale on the abscissa.