Temperature-dependent magnetic properties of ultrathin Fe films: Interplay between local environment and itinerant ferromagnetism

The magnetic properties of ultrathin Fe films are determined as a function of temperature in the framework of a functional-integral itinerant-electron theory. The environment-dependent electronic structure is derived from a realistic $d$-band model and a real-space recursive expansion of the local Green’s functions. The statistical average of spin fluctuations is performed within the static approximation and a layer-resolved alloy analogy by treating disorder in the virtual crystal approximation and in the coherent potential approximation. Results are given for the temperature dependence of the local moments, layer magnetizations $M_l\left(T\right)$, and spin fluctuation energies of ultrathin bcc (001) films. These are compared with the corresponding bulk results in order to quantify the role of dimensionality. Strain and local environment effects are quantified by varying the interatomic bond length $d$. A strong nonmonotonous dependence of $M_l\left(T\right)$ as a function of $d$ is revealed, which can be correlated with the environment dependence of the electronic structure and with the resulting changes in the ground-state magnetic moments and spin fluctuation energies. Finally, goals, limitations, and possible extensions are briefly discussed.

Figure 1

Temperature dependence of the magnetization $M$ for bulk bcc Fe (dots) as obtained by using (a) the VCA and (b) the CPA. The open circles are the corresponding local magnetic moment as given by Eq. (21).

Figure 2

Local spin-fluctuation energy $\Delta F\left(\xi \right)=F\left(\xi \right)-F\left({\xi }^{0+}\right)$ in bulk bcc Fe, where $F\left({\xi }^{0+}\right)$ refers to the minimum of the free energy for $\xi >0$. The average of spin fluctuations in the surrounding medium is performed using (a) the VCA and (b) the CPA. The considered reduced temperatures $t=T∕T_C$ are indicated in the inset.

Figure 3

Temperature dependence of the magnetization of a (001) Fe monolayer calculated by using the VCA. Results are given for several values of the nearest-neighbor bond length $d$ $(r=d∕d_{\text{bulk}})$.

Figure 4

Temperature dependence of the magnetization of a (001) Fe monolayer calculated by using CPA. Results are given for several values of the nearest-neighbor bond length $d(r=d∕d_{\text{bulk}})$.

Figure 5

Local spin-fluctuation energy $\Delta F\left({\xi }_l\right)=F\left({\xi }_l\right)-F\left({\xi }_l^{0+}\right)$ in a bcc (001) Fe monolayer with different NN distances $d$: (a) $r=d∕d_{\mathrm{b}}=1$, (b) $r=0.91$, (c) $r=0.88$, and (d) $r=0.87$. $F\left({\xi }_l^{0+}\right)$ refers to the minimum of the free energy $\xi >0$. The considered reduced temperatures $t=T∕T_C$ are indicated in the inset. The VCA is used for the average of spin fluctuations in the surrounding medium.

Figure 6

(a) Ground-state magnetization $M_l\left(0\right)$ and (b) Curie temperature $T_C$ of a bcc (001) Fe monolayer as a function of the nearest-neighbor distance $d$. Dots (crosses) refer to VCA (CPA) results.

Figure 7

Layer magnetization $M_l\left(T\right)$ of a five-layer bcc (001) Fe film in the VCA. $l=1$ (dots) refers to the surface layers, $l=2$ (open circles) to the layers below the surface, and $l=3$ (crosses) to the central layer. The dashed curve shows the corresponding bulk results.