Clear evidence of interfacial anomalous Hall effect in epitaxial $L{1}_0$ FePt and FePd films

Anomalous Hall effect in epitaxially grown $L{1}_0$-ordered FePd and FePt films on MgO(001) has been investigated as a function of the film thickness ($d$). It is found that the anomalous Hall resistivity can be described by conventional scaling law, i.e., ${\rho }_{\mathrm{AH}}=a{\rho }_{xx}+b{\rho }_{xx}^2$ with longitudinal resistivity ${\rho }_{xx}$. It is interesting to find that both $a$ and $b$ parameters approximately change as a linear function of the inverse film thickness. The linear $1/d$ dependencies can be attributed to the symmetry breaking at the surface. Moreover, the bulk and in particular the surface contributions to the parameters $a$ and $b$ in $L{1}_0$ FePt films are enhanced, compared with those of $L{1}_0$ FePd films, due to larger spin orbit interaction of heavier Pt atoms. It is indicated that not only the bulk but also the interface components of $a$ and $b$ are tuned by the spin-orbit interaction. The present results might stimulate further theoretical investigation of the mechanism of the anomalous Hall effect.

Figure 1

XRR (a) and XRD patterns (b) of epitaxial FePt films with different thickness, atomic force microscope pattern of 17.6-nm-thick FePt film (c), and pole figures of 17.6-nm-thick FePt film ($2\theta =41.{05}^{\circ }$) and the corresponding MgO substrates ($2\theta =36.{94}^{\circ }$) (d). For clarification, the curves in (a) and (b) are vertically shifted. The small red arrows in (b) mark the Laue oscillations of the 14.9-nm-thick sample.

Figure 2

Measured Hall loops of $L{1}_0$ FePt (left column) and FePd (right column) films. The inset numbers refer to film thickness. The measurements were performed at 275 K. For FePt films, the curves are offset by 1030, 760, 490, 240, and 0 $\mu \mathrm{\Omega }\mathrm{cm}$ for $d=5.0$, 9.4, 12.7, 14.9, and 20.4 nm, respectively. The curves of FePd are shifted by 400, 300, 200, 100, and 0 $\mu \mathrm{\Omega }\mathrm{cm}$ for $d=7.0$-, 9.0-, 10.8-, 22.0-, and 25.2-nm films, respectively.

Figure 3

[(a) and (d)] ${\rho }_{xx}$, [(b) and (e)] ${\rho }_{\mathrm{AH}}$, and [(c) and (f)] normalized spontaneous magnetization $M_S$ for $L{1}_0$ FePt [(a)–(c)] and FePd [(d)–(f)]. The inset numbers in (a), (b), (d), and (e) refer to film thickness in the unit of nanometers. In (c) and (f), the film thickness is 17.6 and 22.0 nm, respectively. Solid lines in (c) and (f) refer to the $T^2$ fitting results.

Figure 4

${\rho }_{\mathrm{AH}}/\left[{\rho }_{xx}f\left(T\right)\right]$ versus ${\rho }_{xx}$ for $L{1}_0$ FePt (a) and FePd (b). Solid lines in (a) and (b) refer to a linear fit of ${\rho }_{\mathrm{AH}}/\left[{\rho }_{xx}f\left(T\right)\right]=a_0+b_0{\rho }_{xx}$. The inset numbers refer to film thickness in the unit of nanometers.

Figure 5

$a_0$ (a), $b_0$ (b), and ${\rho }_{xx}$ (c) versus $1/d$ for $L{1}_0$ FePt (solid squares) and FePd (solid circles) films. For comparison, $b_0$ for $L{1}_0$ FePt (open squares) and FePd (open circles), and $b$ for epitaxial Fe (solid upward triangles) [13] and ${\mathrm{Co}}_2\mathrm{MnAl}$ (solid downward triangles) films [45], fitted with a new scaling law proposed by Tian et al. [13], are also given in (b). In (c), the measurements were performed at 275 K. The inset in (c) shows the electronic scattering at the surface and the interface. In (a), (b), and (c), solid lines refer to the linear fitting results.