Effect of annealing on the magnetic anisotropy of GaMnAsP layers with graded P concentration

GaAs-based ferromagnetic semiconductors have received much attention during the past decade due to their potential spintronics application.^1–3 A major advantage of this semiconductor alloy is the controllability of its magnetic properties by carriers, which mediate the ferromagnetism in these materials.^4–6 One of the interesting magnetic properties of GaAs-based ferromagnetic semiconductors is their magnetic anisotropy, which determines the direction of magnetization at zero-field. It is known that a GaAs-based ferromagnetic film exhibits complicate magnetic anisotropies including cubic and uniaxial anisotropies, which depend on many parameters, such as Mn interstitial, hole concentration, and strain.^7,8 The investigation further shows that strain is a decisive factor in determining either perpendicular or in-plane magnetic anisotropy of the film. For example, GaAs-based ferromagnetic films favor in-plane magnetization under compressive strain and prefer perpendicular magnetization when the strain is tensile.^8–13 In the case of the quaternary alloy GaMnAs_1−yP_y films grown on GaAs substrates, the train of the film can be tuned between compressive and tensile by varying the concentration of P in the film. This allows one to obtain magnetic films with either in-plane or perpendicular magnetization, depending on the P content of the GaMnAs_1−yP_y film.¹⁴ 

The ability to control concentration P in the quaternary GaMnAs_1−yP_y film offers an interesting structure in which physical properties, such as the bandgap energy and the strain, are continuously varied along the growth direction. Owing to such uniqueness of structure, new magnetic properties are expected in such vertically graded GaMnAs_1−yP_y films. For example, extreme asymmetry of domain walls with respect to the easy axes was observed in earlier studies of such graded structures, indicating the presence of Dzyaloshinskii–Moriya interactions due to symmetry-breaking along the film thickness.¹⁵ In addition, interesting programmable bias effects were also observed in graded GaMnAs_1−yP_y films by transport and magnetization measurements.^16–18 

It is well known that the magnetic properties of GaAs-based ferromagnetic semiconductors, such as Curie temperature and magnetic anisotropy, can be significantly changed by thermal annealing.^13,19–21 This has motivated the present study of the effects of thermal annealing on magnetic properties of graded GaMnAs_1−yP_y films. In this study, we investigate the effect of annealing on the behavior of the magnetic anisotropy in composition-graded GaMnAs_1−yP_y films before and after the specimen is annealed. A detailed investigation of magnetic anisotropy in graded samples was performed using Hall effect measurements, in which an external magnetic field is applied either in-plane or perpendicular to the plane to examine the processes of reversal of in-plane and perpendicular components of magnetization in the film. Interestingly, while the magnetic anisotropy of an as-grown sample changes gradually along the film thickness, as expected from the changing strain, that of an annealed sample separates into two parts, which have either only in-plane easy axes (in the bottom region of the sample) or only a perpendicular easy axis (in the top region). By careful experiments and analysis, we were then able to identify the portions with in-plane and perpendicular magnetizations in the graded films.

GaMnAs_1−yP_y samples were grown on GaAs (100) substrates in a Riber 32 MBE system equipped with elemental sources of Ga, As, Mn, and P. During the growth, the substrate temperature was kept at 250 °C, and the substrate was rotated in order to achieve a homogeneous composition in the film plane. The P concentration y was controlled by P₂ flux, while the As₂/Ga flux ratio was kept constant at ∼10 during the entire growth. The P₂/As₂ flux ratio was increased successively from ∼0 to ∼1/2 in eight steps during the growth of the film, which resulted in a variation of P concentration from 0% to 24% along the growth direction. The step-like concentration of P in the graded sample is shown schematically in Fig. 1(a). The Mn concentration was kept constant at a value of x ≈ 0.06. The thickness of the sample was determined as 103 nm by high-resolution x-ray diffraction measurement, and the Curie temperature of the sample was estimated as 40 K from temperature dependence of resistance.^17,18

In order to address annealing effects, the sample was divided into two pieces, one of which was annealed for 90 min at 270 °C in a furnace tube in a protective nitrogen atmosphere. As-grown and annealed samples were then cleaved into sizes of 5 × 5 mm² for Hall device fabrication. For Hall effect measurements, the samples were prepared in the form of a standard Hall bar with 100 μm width and 1500 μm length, as shown in Fig. 1(b). The directions of the applied field and magnetization of the films are indicated by angles $(θH,φH)$ and $(θ,φ)$⁠, where polar angles $θH$ and $θ$ are measured from the [001] crystallographic direction (which is normal to the film plane), and the azimuthal angles $φH$ and $φ$ are measured counterclockwise (CCW) from the [110] direction, which is the direction of the current in the Hall device.

In order to investigate the effects of annealing on magnetic anisotropy in the graded GaMnAs_1−yP_y films, Hall effect measurements were performed on both as-grown and annealed samples. Magnetic field dependences of Hall resistance are shown in Fig. 2, where panels in the first and the second row represent results observed on the as-grown and annealed samples, respectively. Hall resistances plotted in Figs. 2(a) and 2(c) were taken with a magnetic field applied along $φH≈100°$ in the film plane. The observed resistance hysteresis loops show a two-step switching behavior, which is due to the planar Hall effect, with a vertical shift at zero fields between the down-scan (i.e., for magnetic field swept from positive to negative values) and up-scan (i.e., for field sweep from negative to positive values). This vertical separation at zero fields [marked as $RxyIP$ in Figs. 2(a) and 2(c)] is due to the contribution of the anomalous Hall resistance (AHR) caused by the presence of a perpendicular component of magnetization at zero fields. The observation of such staggered Hall resistance hysteresis in an in-plane field scan measurement indicates the coexistence of in-plane and perpendicular magnetization in the graded film at zero fields.

The vertical field scan measurements shown in Figs. 2(b) and 2(d) also show the in-plane and perpendicular magnetization in the graded film. One can clearly see two types of hysteresis: a single hysteresis loop centered at zero-field (marked with $RxyOP$⁠) and two hysteresis appearing at higher negative and positive fields (marked with $RrotIP$⁠). The $RxyOP$ appears due to the abrupt switching of magnetization between vertical easy directions, and the $RrotIP$ is the planar Hall resistance as we observed from the in-plane field scan measurement caused by an in-plane component of magnetization switching within the film plane. Even though the magnetic field is applied perpendicular to the film plane, which gives linear dependence of the Hall resistance on the field strength, a slight misalignment of the field away from the vertical direction results in an in-plane component of an external field. This can initiate the transition of magnetization within the film plane in those sublayers having in-plane anisotropy, and results in slanted shape of double steps marked with $RrotIP$ in Figs. 2(b) and 2(d). The amplitude of the center hysteresis in vertical measurements is directly proportional to the contribution of the perpendicular magnetization originating from those sublayers of the graded film having perpendicular anisotropy.

The fractions of magnetization in the graded samples with in-plane and perpendicular anisotropies can be estimated by considering the magnitudes of the AHR values at zero-field, marked as $RxyIP$ and $RxyOP$ in the figures in the following manner. When the total magnetization of the film is saturated in a vertical direction by a strong perpendicular magnetic field, the amplitude of AHR is $Rxytot$⁠. The ratio of the perpendicular magnetization at zero-field to the total magnetization can then be obtained from the Hall resistance values of $RxyIP,RxyOP$⁠, and $Rxytot$⁠. In the case of the as-grown sample, the ratio of $RxyOP/Rxytot$ is approximately 0.2. This indicates that about 20% of magnetization consists of sublayers with a perpendicular easy axis. The value of $Rxyop/Rxytot$ increases to 0.5 in the annealed specimen, indicating that the amount of magnetization in sublayer with a perpendicular easy axis in the film has increased significantly, up to 50%, as a result of annealing. The vertical magnetization component in the films can also be estimated from in-plane measurement, which show a vertical splitting $RxyIP$ at zero-field. The ratio of $RxyIP/Rxytot$ is about 0.1 in the as-grown sample, indicating that approximately 10% of magnetization in the sample sublayers are preferred to align along the vertical direction at zero-field even when the field is applying in the sample plane. This ratio increases to about 0.5 in the annealed sample, indicating that about 50% of the magnetization in the sample sublayers have preference to align along the vertical direction at zero-field. The results of both in-plane and perpendicular magnetic sweeps clearly show that thermal annealing significantly enhances the magnetization with a perpendicular easy axis in the graded film.

Note further that, while in the annealed sample, the fraction of magnetization with perpendicular easy axis obtained above in both in-plane and vertical measurements are nearly the same, the magnetization fractions measured in the two configurations in the as-grown sample are different (i.e., 0.2 obtained in the vertical measurements and 0.1 in the in-plane measurements). This difference indicates the presence of an intermediate region in the as-grown sample that has both in-plane and perpendicular magnetic easy axes.^17,18 Such a region containing two orthogonal easy axes can form in films with graded composition, in which strain changes continuously from compressive to tensile. Due to such grading, the strain can be close to zero in the middle region of the film, allowing both in-plane and perpendicular easy axes to coexist simultaneously. In such an intermediate region, the magnetization will then align along the in-plane easy axes during an in-plane field scan, and it will align along the perpendicular easy axis during a vertical field scan. This field-direction-dependent response of the intermediate sublayer will then cause a difference of 0.1 in calculating the portion of the vertical magnetization component in the film using the in-plane and vertical measurement data. This means that the as-grown sample consists of three regions: one having only in-plane easy axes, one having only perpendicular easy axis, and a region between them that has both in-plane and perpendicular easy axes.^17,18

Having identified the variation of magnetic anisotropy along the growth direction of the graded GaMnAs_1−yP_y film, we can now discuss the details of magnetization reversal. A representative case is shown in Fig. 3, where magnetization alignments in the annealed graded film are schematically drawn at positions corresponding to the Hall resistance data obtained during in-plane field scans. The upper and lower arrows in the schematic diagrams indicate directions of magnetization for sublayers of the graded sample with perpendicular and in-plane easy axes, respectively, as shown in right side inset of Fig. 3.

In the down-sweep case, magnetizations of both regions are aligned with the external magnetic field along $φH≈100°$ at the beginning of the sweep (position 1). As the field strength decreases, magnetizations in the two regions are relaxed toward their own easy-axis direction. In this process, a small tilt of the in-plane field away from the film plane determines the relaxation of magnetization with the perpendicular easy axis (i.e., the upper sublayers of the graded film) toward either the up- or the down-direction. In our present experimental setup, the field tilt for a positive field is in the up-direction. This results in the alignment up (i.e., along [001]) for the upper region of the film, while for the lower region remains in the field direction (i.e., along $[1¯00]$⁠), as shown in position 2 of Fig. 3. When the field direction is reversed, and the strength is increased, the lower region first rotates its magnetization by $90°$ within the film plane, while vertical magnetization in the upper sublayers remains in the up-direction (position 3). As the negative field continues to increase, a second $90°$ rotation occurs in the lower region of the film (position 4). With further increase of the negative field, the vertical component of the field caused by the tilting also increases, becoming strong enough to cause a transition of the perpendicular magnetization to the down-direction in the upper film region (position 5). Finally, as the strength of the negative field keeps increasing, the magnetizations of both regions saturate toward the negative in-plane field direction, resulting in a parallel alignment of magnetization in the entire sample, as shown in position 6. In the case of up-sweep, a similar rotation of magnetization occurs, as shown by the series of schematic diagrams at the bottom of Fig. 3.

We also performed Hall resistance measurements at several temperatures in order to investigate changes in magnetic anisotropy with temperature in our graded films. Using the analysis described above, we estimated the portion of magnetization with a perpendicular easy axis in the film for each temperature. The results are plotted in Fig. 4(a), where the solid and open symbols represent data obtained with in-plane and vertical field scan measurements, respectively. In the case of the annealed sample (plotted with squares), the ratio of the vertical component remains approximately at 50%, indicating no significant change of magnetic anisotropy up to 40 K. Additionally, the ratio of in-plane to perpendicular magnetizations in the annealed sample is nearly the same in all temperatures, indicating that the two well-defined magnetic regions with either in-plane or perpendicular magnetic anisotropies are not affected by the increasing temperature. In the case of the as-grown sample, vertical measurements give the fraction of magnetization with a perpendicular easy axis to be around 20% of total magnetization. The fraction with a perpendicular easy axis obtained from in-plane measurements, however, is consistently smaller than that obtained from vertical measurements, indicating the presence of an intermediate region that has both in-plane and perpendicular easy axes simultaneously, up to 30 K in the as-grown film.

In order to demonstrate the effect of annealing on the magnetic anisotropy of the graded GaMnAs_1−yP_y film, in Figs. 4(b) and 4(c), we schematically draw the fractions of the magnetizations with different anisotropies for the as-grown and the annealed samples, showing the dramatic increase of portion with perpendicular anisotropy in the annealed film. Note that Figs. 4(b) and 4(c) are visualization to get the fraction of magnetization in the film, which does not represent the volume fraction. Such increase of perpendicular anisotropy may due to the out-diffusion of interstitial Mn in the film caused by annealing, which reduces the lattice parameter of GaMnAs_1−yP_y in addition to the changes of hole concentration, magnetization, and Curie temperature,^17,18,22 thus increasing the sample volume with tensile strain. Such a change of strain then increases the perpendicular magnetization component of the annealed film. In addition, the intermediate portion of the sample with both in-plane and perpendicular easy axes disappears in the annealed film, leading to only two types of magnetic anisotropies, either with only in-plane or only perpendicular easy axes in the sample. As a result, two orthogonal magnetizations form in the annealed film, with in-plane orientation in the region near the bottom of the film and with vertical orientation in the top sample region, as illustrated in Fig. 4(c). This suggests that films with graded compositions, together with annealing, can be strategically used to realize magnetic systems with orthogonal magnetic configurations.^23,24

We investigated the effects of annealing on the magnetic anisotropy of phosphorus-graded GaMnAs_1−yP_y samples, in which P concentration changes along the growth directions. In the case of as-grown film, we have observed three types of magnetic regions: one with in-plane easy axes, one with perpendicular easy axis, and an intermediate region with both in-plane and perpendicular easy axes. This observation is consistent with continuously increasing P concentration in the graded film, leading to a gradual transition of strain from compressive to tensile as the P concentration increases. However, the magnetic anisotropy profile in the graded film significantly changes when the graded film is thermally annealed: annealing increases the portion of magnetization with a perpendicular easy axis and nearly eliminates the intermediate layer that has both in-plane and perpendicular easy axes. This study thus demonstrates that annealing a graded GaMnAs_1−yP_y film can be used to form a bilayer with well-defined orthogonal (in-plane and perpendicular) magnetic anisotropies.

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) of Korea (No. 2021R1A2C1003338); the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MSIT) (No. 2022M3F3A2A03014536); the NRF under the BK21 FOUR program at Korea University, Initiative for Science Frontiers on Upcoming Challenges by Korea University Grant; and National Science Foundation (Grant No. DMR 1905277).

The authors have no conflicts to disclose.

Seul-Ki Bac: Data curation (equal); Formal analysis (equal); Investigation (equal). Sanghoon Lee: Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Supervision (equal); Writing – original draft (equal). Xinyu Liu: Investigation (equal). Margaret Dobrowolska: Funding acquisition (equal). Jacek K. Furdyna: Formal analysis (equal); Funding acquisition (equal); Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.