Strong current-direction dependence of anisotropic magnetoresistance in single crystalline Fe/GaAs(1 1 0) films
Introduction
Magnetoresistance (MR), the effect of magnetism on charge transport, brings about many novel phenomena and fascinating applications in spintronics [1]. The giant magnetoresistance (GMR) [2], [3] and the tunneling magnetoresistance (TMR) [4], [5], [6], [7], which exhibit large magnitudes of MR, have been extensively explored because of intriguing physics as well as their current and future applications in industries. The conventional anisotropic magnetoresistance (AMR) [8], [9], [10], [11], [12], [13] along with many newly discovered related MR effects such as spin-Hall MR [14], [15], Rashba MR [16], spin-orbit MR [17], [18], Hanle MR [19], and unidirectional MR [20], [21] are also essential to the spintronics technology. The interplay between these effects in single or multilayered structures offers new physics and potential applications in spin-dependent transport [22], [23]. At the same time, new challenges arise in the accurate understanding of these complex MR effects. Many MR effects are related to spin-orbit coupling (SOC), and therefore they strongly depend on the electronic structure of the materials. Thus, it is crucial to explore the relationship between MR effects and the electronic structure in the materials. In this regard, crystalline systems offer an ideal platform for elucidating the physical origins of various MR effects, as well as providing tailored MR properties for the relevant applications.
Out of the many MR effects, AMR is one of the most fundamental magneto-transport properties in ferromagnetic (FM) materials, which describes the dependence of the longitudinal resistivity on the magnetization orientation relative to the current direction [9]. The mechanism of AMR is usually attributed to the s-d scattering influenced by the SOC [9], [10], [11], [12], [13]. Phenomenologically, the AMR in polycrystalline FM films can be expressed as , where is the angle between and , and and are the resistivity for and , respectively. Therefore, AMR in polycrystalline materials has a clear two-fold symmetry with respect to the magnetization orientation. Moreover, the transverse resistivity also depends on the magnetization orientation, which is usually called the planar Hall effect (PHE). The PHE in polycrystalline FM film can be expressed as , so the PHE also has a two-fold symmetry with the same -dependent amplitude as its AMR counterpart.
Unlike polycrystalline FM materials, single-crystalline FM materials have much more complex transport properties due to the crystallographic orientations, and therefore are better systems for exploring the intrinsic mechanism of AMR. In single-crystalline FM systems, the AMR is related not only to the direction of the magnetization, but also to the orientation of the current with respect to the crystal axes [8], [9]. As a result, the AMR in single crystalline films deviates from the regular dependence, particularly an additional four-fold symmetry could be observed in some FM systems [8], [24], [25], [26], [27], [28], [29]. The additional terms emerge as a result of the SOC, which reflects the effect of the crystalline axes. The AMR effect in single-crystalline FM systems has been theoretically proposed [8], [9] and experimentally studied in manganite [28], diluted magnetic semiconductor [30], [31], magnetite Fe3O4 [24], [25], [26], [27], [32], and transition metals such as Co [33] or Ni [29] films. In the past, most studies on the current-direction dependent AMR effect were performed on the (0 0 1) film of a cubic bulk FM material, thus the AMR effect as a function of magnetization direction angle shows a clear in-plane four-fold symmetry due to the lattice structure [8], [24], [25], [26], [27], [28], [29]. In a recent work [34], the current-direction dependent AMR effect in a Fe/GaAs(0 0 1) system displayed a symmetry transition from two-fold to four-fold upon increasing Fe thickness, which was attributed to the emerging interfacial spin-orbit field with the symmetry at the Fe/GaAs(0 0 1) interface. However, it should be noted that the Fe(1 1 0) system also has a crystalline symmetry, but arising from the bulk. It is still not clear how such bulk symmetry influences the AMR properties, despite a few earlier studies showing the deviation of AMR properties in Fe(1 1 0) films away from the conventional relation [35], [36]. In addition, the PHE is expected to strongly depend on the current orientation as well, but has not been experimentally explored.
Here, we systematically investigated the current-direction dependence of both AMR and PHE in single crystalline Fe films grown on GaAs(1 1 0) substrates. Both longitudinal and transverse AMR curves show clear deviations from the conventional and dependence, respectively. The current-direction dependence contains both two-fold and four-fold symmetries for AMR, however, only four-fold symmetry can be observed for PHE. We further show that the current-direction dependence of both AMR and PHE can be well explained by the phenomenological model with a series expansion of the resistivity tensor with respect to the direction cosines of the magnetization. The resistivity coefficients are found to increase with the temperature, which can be attributed to the increase of electron-phonon scattering. Moreover, the measured AMR ratios could show a difference more than one order of magnitude for different current directions. Such a strongly current-direction dependent AMR effect provides a plausible way to tailor on-demand MR properties in single crystalline FM materials.
Section snippets
Experiment
Fe/GaAs(1 1 0) films are prepared by molecular beam epitaxy in an ultrahigh vacuum (UHV) chamber with a base pressure of [37], [38], [39]. To perform transport measurement, un-doped GaAs(1 1 0) substrates with high resistivity are used. In the UHV chamber, the GaAs(1 1 0) substrates are cleaned by bombardment with 1 keV Ar+ ions for 1 h, and the sample is rotated during the Ar+ bombardment. Then the GaAs(1 1 0) substrates are annealed at 600 °C for 45 min before thin
Results and discussion
The magnetic properties of the Fe film are firstly characterized by the longitudinal magneto-optic Kerr effect (MOKE) at room temperature. Fig. 1(b) displays the typical magnetic hysteresis loops of the Fe(1 1 0) film with the field along Fe, and directions. The easy axis of the system is clearly identified along the Fe[0 0 1] direction by the square-shape loop. It should be noted that the saturation Kerr signals are different in the hysteresis loops because of the crystalline
Conclusion
In summary, we systematically studied the current-direction dependence of anisotropic magnetoresistance and planar Hall effect in single crystalline Fe(1 1 0) films. The longitudinal and transverse resistivities with the current away from the crystal axis clearly deviate from conventional and dependences. The AMR amplitude shows both two-fold and four-fold symmetries with respect to the current direction, but only exhibits a four-fold symmetry. Our studies show that
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The authors thank C. Won and Y. Ji for valuable discussions. This project was supported by the National Key Basic Research Program of China (Grant No. 2015CB921401), National Key Research and Development Program of China (Grant No. 2016YFA0300703), National Natural Science Foundation of China (Grants No. 11474066, No. 11734006, No. 11974079 and No. 11434003), and the Program of Shanghai Academic Research Leader (No. 17XD1400400).
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