Magnetic anisotropies in epitaxial Fe3O4/GaAs(100) patterned structures

Previous studies on epitaxial Fe3O4 rings in the context of spin-transfer torque effect have revealed complicated and undesirable domain structures, attributed to the intrinsic fourfold magnetocrystalline anisotropy in the ferrite. In this Letter, we report a viable solution to this problem, utilizing a 6-nm-thick epitaxial Fe3O4 thin film on GaAs(100), where the fourfold magnetocrystalline anisotropy is negligible. We demonstrate that in the Fe3O4 planar wires patterned from our thin film, such a unique magnetic anisotropy system has been preserved, and relatively simple magnetic domain configurations compared to those previous reports can be obtained.

The well-known spin-transfer torque effect, 1-4 via which the motion of magnetic domain walls can be realized by injection of spin-polarized currents, [5][6][7][8] has become one of the most promising approaches for future information storage with low power consumption. 9,10Before such a spin-based phenomenon could be implemented for practical device applications, a number of fundamental issues have to be tackled.A major current challenge is to reduce the critical current density that is required to trigger the domain wall motion in artificial magnetic micro-or nano-structures.Theoretical calculations have suggested that, in the adiabatic limit and in the absence of extrinsic pinning, the critical current density, j C , has a simple relation with the spin polarization, P, of a given magnetic material, as j C ∝ 1/P. 11,12With this notion, Fe 3 O 4 , a theoretically predicted fully spinpolarized material with high Curie temperature of 858 K 13 and good chemical stability, appears to be especially promising.
Even though previous experiments have indeed verified the above belief, i.e., achieving a spin polarization of ∼80% at best near the Fermi level in the ferrite thin film at room temperature, 14 the utilization of Fe 3 O 4 in domain wall devices remains scarce. 15This is in part attributed to the formation of undesirable domain structures that could result from an interplay between the shape-and the intrinsic cubic magnetocrystalline anisotropies in Fe 3 O 4 . 16For instance, using x-ray photoemission electron microscopy, Fonin et al. observed the appearance of zig-zag shaped domain walls in their 1-µm-wide Fe 3 O 4 rings, 17 as a consequence of the dominant in-plane cubic magnetic anisotropy in the ferrite structures.These zigzag domain walls, with complex wall structure and boundary, could possibly complicate the wall motion, which are certainly setbacks for integrating highly spin-polarized Fe 3 O 4 into the context of spin-transfer torque applications.In this Letter, we report a viable approach to circumvent the above-mentioned complication by taking advantage of a unique in-plane magnetic anisotropy system in high-quality Fe 3 O 4 ultrathin film grown on GaAs(100) by postgrowth oxidation of epitaxial Fe(100).
2][23] On the other hand, from the charge transport measurements in our high-quality epitaxial Fe 3 O 4 film, a resistivity of about 5 × 10 −3 Ω cm has been demonstrated, which is very close to that of bulk single crystal [24][25][26] and much lower than those of the commonly reported Fe 3 O 4 thin.8][29] This largely benefits from our growth method, thereby resulting in the lack of anti-phase boundaries, which has been clearly evidenced by various characterisation techniques. 30,31Considering the comprehensive advantages of our Fe 3 O 4 thin film, our present work should therefore lead to a renewed interest, and offer an unprecedented opportunity to acquire controllable and well-defined domain wall configurations in Fe 3 O 4 patterned structures, without suffering from the intrinsic cubic magnetocrystalline anisotropy of the ferrite.
Following the growth recipe developed in our previous work, epitaxial Fe thin film with a thickness of 3 nm was first deposited on GaAs(100) substrate at room temperature and at a rate of 2 Å/min, using electron-beam evaporation in a molecular beam epitaxy system with a base pressure of 6 × 10 −9 mbar.Afterwards the Fe film was oxidized in situ in an O 2 partial pressure of 5 × 10 −5 mbar for 180 s at 500 K, 32,33 thereby forming a stoichiometric Fe 3 O 4 film with its thickness twice that of the original Fe film, i.e., 6 nm. 34,35The oxidized film was further patterned by focused ion beam lithography (30 keV Ga + , 10 pA ion beam current) into several sets of planar wires, as shown in Fig. 1.These wires are 10 µm long with the width ranging from 0.5 µm to 1 µm.The long axes of the wires are either parallel or perpendicular to the easy axis of the uniaxial anisotropy in the film.Specifically, patterns 1 and 2 contain a series of 1-µm-wide wires, with their long axes along the [0-11] and [011] directions of the GaAs substrate, respectively; the wires in pattern 3, with a width of around 0.5 µm, have their long axes along the [0-11] direction.][38] We first illustrate, in Fig. 2, the magnetic hysteresis loops of the planar wires in patterns 1-3, in order to examine the evolution of the magnetic anisotropies originally existing in the continuous film.The hysteresis loops were acquired by a home-built focused magneto-optical Kerr effect (f-MOKE) magnetometer, with a 1 µm laser spot on the samples, and the magnetic fields were applied along the two major crystallographic axes, [0-11] and [011], of the GaAs(100) substrate.From Figs. 2(a)-(b) one can see that the Fe 3 O 4 continuous film exhibits a strong uniaxial anisotropy, K U , having its easy and hard axes along the [0-11] and [011] directions, respectively, as expected.Simultaneously a negligible cubic magnetocrystalline anisotropy, K 1 , is superimposed, as shown in Table I. 18 Therein K U and K 1 of the continuous film were obtained from our previous work on numerical fitting of the angular dependences of the ferromagnetic resonance field of the film. 18igure 2 is expected to reorient the easy axis into the [011] direction due to the large demagnetizing field along the [0-11] direction, they still follow the easy-and hard magnetization axes of the thin film, as shown in Fig. 2(e)-(f).This observation suggests that the uniaxial anisotropy has been well preserved after the lithographic process, and plays a decisive role over the cubic-and the shape anisotropy in determining the overall switching behavior of the 1-µm-wide wires.One more interesting observation is the smaller coercivity in pattern 3 than that in pattern 1 along the [0-11] direction, when comparing Fig. 2(g) to Fig. 2(c).This seems to contradict to one's intuition that larger demagnetizing field in narrower wires should be able to provide larger coercivity.The only plausible TABLE I. Magnetic anisotropy constants, K U and K 1 , used for LLG simulations of pattern 1-3.The experimental values for continuous film are also listed in the first column for ease of comparison.W is the wire width, x denotes the direction of the wire long-axis relative to the GaAs(100) substrate.reason for this reduction should, therefore, be the strong relaxation of the original uniaxial anisotropy in the 0.5-µm-wide wires.

Film
We have attempted to reproduce the hysteresis loops by means of the LLG Micromagnetics Simulator, 39 as shown in Fig. 2(i)-(j).The material parameters used for the simulations are as below: saturation magnetization M S = 480 emu/cm 3 , exchange stiffness constant A = 1.3 × 10 −11 erg/cm, and damping coefficient α = 0.3; the cell size was 10 × 10 × 6 nm 3 .The two most important parameters, K U and K 1 , for best-fitting are shown in Table I, where we can see that the K U of the continuous film has been largely retained in patterns 1 and 2, while has a strong relaxation in pattern 3.Although an in-depth analysis of such a decrease in the K U is out of the scope of this work, we would like to point out that the relaxation of the uniaxial anisotropy in this case might be closely related to the chemical bonding at the Fe 3 O 4 /GaAs(100) interface, which has been discussed by some of us elsewhere. 18Equally important is the negligible K 1 values observed in both of our film and patterned wires, which are significantly lower than those in bulk Fe 3 O 4 and in other reported Fe 3 O 4 thin films. 17,40nother aspect one may notice in the second column of Fig. 2 is that the experimental magnetization curves along the hard axis look more difficult to be saturated than the calculated ones do.This is primarily attributed to the existence of localized nonuniform magnetization caused by or close to the interfacial defects, 41 which requires much higher field for saturation.We attempted to model this by treating the film as two layers, namely, a thick layer with only domain-rotation considered and a thin one at the interface with interfacial defects involved, and modified the simulation accordingly.One such calculated result by the modified simulation for pattern 1 is illustrated in the inset of Fig. 2(j), which indeed seems to better match the experimental curve.
From the fitting of the magnetization curves in Fig. 2, we found that no matter what dimension the wire has, the cubic magnetic anisotropy is always much smaller than the uniaxial-and the shape anisotropy.In the following, we will address the main issue on whether this negligible K 1 would indeed lead to a more desirable domain configurations for spin-transfer torque applications.To answer so, micromagnetic simulations have been performed by the LLG simulator for Fe 3 O 4 rings, with the width of 1 µm and 0.5 µm, respectively.The ring shape was chosen for its high geometry symmetry, guaranteeing the ease of trapping magnetic domain walls by applying an external magnetic field, [42][43][44] and also for ease of comparison to the previous reports. 16,17The simulation results, by taking the parameters used for Fig. 2, are shown in Fig. 3, where we find that the zig-zag domain walls, as a consequence of the strong fourfold in-plane magnetocrystalline anisotropy of the film in the previous studies, 17 can be avoided in both rings and far more simplified domain structures 16,17 are revealed.Specifically, when being saturated along the hard axis ([011]), followed by relaxation at zero field, our 1-µm-wide Fe 3 O 4 ring exhibits four 180 • walls with a narrow boundary in the equilibrium state at remanence, as shown in Fig. 3(a).While in Fig. 3(b), only two domain walls have been observed in the 0.5-µm-wide Fe 3 O 4 ring, i.e., one head-to-head and one tail-to-tail walls, dividing the ring into two magnetic domains, with the in-plane magnetization following the perimeter of the ring.Most importantly, the reported additional 90 • reorientations arising from the influence of magnetocrystalline anisotropy 17 have not been observed.The 0.5-µm-wide Fe 3 O 4 ring, therefore, exhibits an onion-state magnetic configuration as found in 3d metal rings, 43,45 which have been widely used as unit cells for domain wall devices, profiting from ease of the shape tailoring with negligible intrinsic magnetic anisotropies in those materials.
It is noteworthy that the simulations with K 1 = 0 have also been carried out, which essentially show identical domain configurations to Fig. 3(a) and (b), further suggesting that the marginal K 1 in our epitaxial thin film has nearly no influence in the domain formation and is therefore negligible.These above findings form the key results of the present work, which provide a possibility of avoiding the complex domain structures caused by K 1 via utilization of our Fe 3 O 4 thin film.In particular, when the width of the ring is reduced to 0.5 µm, simple domain configuration as found in 3d metal rings can be obtained, due to relaxation of both the uniaxial and cubic anisotropies.For the strong uniaxial anisotropy preserved in the 1-µm-wide ring, its influence on the domain wall structures during the motion requires further current-driven experiment to evaluate.
The present study demonstrates a remarkable approach to generate simple domain configurations in half-metallic Fe 3 O 4 patterned structures, based on the unique magnetic anisotropy system in epitaxial Fe 3 O 4 /GaAs(100).Combined with the high spin polarization and Curie temperature, and good chemical stability of Fe 3 O 4 , the patterned structures from our high-quality magnetite thin film are promising candidates for future current-driven applications in the domain wall devices, where small threshold currents as well as simple wall structures are strongly preferred.
FIG. 1. SEM images of (a) pattern 1, (b) pattern 2, and (c) pattern 3. The white arrows indicate the directions of the easy ([0-11]) and hard ([011]) axes of the uniaxial magnetic anisotropy in the Fe 3 O 4 thin film, prior to focused ion beam lithography.