Temperature and crystallographic orientation dependence of the anisotropic magnetoresistance in epitaxial Fe65Co35 thin films

TL;DR

This work investigates how crystal symmetry and temperature affect anisotropic magnetoresistance (AMR) in epitaxial Fe65Co35 thin films on MgO(001). It combines Kerr magnetometry with magnetotransport measurements and a Stoner–Wohlfarth–based energy model incorporating cubic and uniaxial anisotropy to extract $K_c$ and $K_u$, yielding $K_c = -2.36$ kJ/m$^3$ and $K_u = 2.18$ kJ/m$^3$ and demonstrating temperature- and orientation-dependent AMR. The AMR magnitude shows strong crystallographic anisotropy, with $\text{AMR}_{[100]} \approx 0.155\%$ and $\text{AMR}_{[1\bar{1}0]} \approx 0.104\%$ at 300 K, and a ~30% increase along the easy axis as $T$ decreases to 80 K, highlighting the role of spin–orbit coupling and tetragonal distortions. These results establish Fe65Co35 epitaxial films as a platform for tunable, directionally selective magnetic sensing, where crystal orientation and operating temperature tune sensitivity and stability.

Abstract

In this work, we study the anisotropic magnetoresistance (AMR) behavior of [001] epitaxial Fe65Co35 thin films along different crystallographic directions as a function of temperature. The AMR ratio is found to strongly depend on the current orientation relative to the crystal axes, reaching 0.16 % and 0.10 % at room temperature when the current is applied along the magnetic hard and easy axes, respectively. Moreover, the AMR ratio decreases at different rates as the temperature is reduced to 80 K. The longitudinal and transverse magnetoresistance curves were fitted using the Stoner-Wohlfarth formalism to describe the magnetization reversal path and to extract the magnetic anisotropy constants. The fitted cubic and uniaxial anisotropy constants are Kc = -2.36 kJ/m3 and Ku = 2.18 kJ/m3, verifying the change in the cubic anisotropy compared to Fe-richer Fe100-xCox compositions. These results demonstrate that by tailoring the crystalline orientation and temperature dependence of AMR, epitaxial Fe65Co35 thin films can enable the design of magnetic sensors with tunable sensitivity.

Figures (6)

• Figure 1: a) Schematic representation of the atomic arrangement of Fe$_{\mathrm{65}}$Co$_{\mathrm{35}}$ grown epitaxially on MgO. The crystallographic directions of the MgO and of the Fe$_{\mathrm{65}}$Co$_{\mathrm{35}}$ are indicated at the bottom in light blue and in black, respectively. The [100] direction of the Fe$_{\mathrm{65}}$Co$_{\mathrm{35}}$, which corresponds to a hard axis, is rotated by 45$^\circ$ with respect to the [100] of the MgO. Representation of the angles of the magnetization ($\phi_M$) and magnetic field vector ($\phi_H$) measured from the $x$-axis and of the Hall bar setups where the current flows along the b) hard axis [100] and c) easy axis [1$\overline{1}$0], respectively.
• Figure 2: Kerr hysteresis loop of the Fe$_{\mathrm{65}}$Co$_{\mathrm{35}}$/Pt bilayer with the external magnetic field applied along the a) [110] axis and b) [1$\overline{1}$0] axis. The solid lines correspond to the simulated hysteresis loops and the red squares indicate the experimental data.
• Figure 3: Longitudinal $\rho_{l}$ (blue squares) and transverse $\rho_{t}$ (red circles) resistivity as a function of the external magnetic field direction ($\phi_H$) acquired at $T$ = 80 K. The current was applied along the Fe$_{\mathrm{65}}$Co$_{\mathrm{35}}$ a) hard axis ([100]) and b) easy axis ([1$\overline{1}$0]). c) AMR ratio as a function of the temperature acquired with the current applied along the hard axis (purple circles) and easy axis (green triangles). d) $\Delta\rho = \rho_\parallel - \rho_\perp$ as a function of the temperature extracted from the angular dependence of $\rho_{l}$ and $\rho_{t}$ when the current is applied along [110] and [1$\overline{1}$0]. The current density applied was J = 4 $\times$10$^8$ mA/cm$^2$
• Figure 4: Normalized hysteresis loop of the Fe$_{\mathrm{65}}$Co$_{\mathrm{35}}$ layer acquired with the external magnetic field applied along the Fe$_{\mathrm{65}}$Co$_{\mathrm{35}}$ a) [100] (hard) and d) [1$\overline{1}$0] (easy). The red squares and solid line indicate the data acquired when the external magnetic field is decreasing, and the blue circles and solid line correspond to the increasing of the external magnetic field. The simulated hysteresis loops are shown in a black solid line. b), e) $\rho_{l}$ and c), f) $\rho_{t}$ as a function of the external field when the current is applied along the [1$\overline{1}$0] axis and the external field is applied parallel to the hard axis [100] ($\phi_H = 45^\circ$) and along the easy axis ($\phi_H = 0^\circ$). The red squares and blue circles correspond to the data acquired when the external magnetic field is decreasing and increasing, respectively. The insets show the measurements of $\rho_{l}$($H$) and $\rho_{t}$($H$) in the range -150 mT to 150 mT. The data were acquired at 100 K and 120 K.
• Figure 5: Magnetization angle ($\phi_M$) as a function of the magnetic field applied along different directions ($\phi_H$) when the external magnetic field is decreasing from saturation to negative values. Blue squares and red diamonds correspond to the value of $\phi_M$ when the local and the global minima are considered, respectively.