Dependence of ferromagnetic properties on phosphorus concentration in Ga_1-xMn_xAs_1-yP_y Free

Reliable approaches for manipulating magnetic anisotropy in diluted magnetic semiconductors, especially Ga_1–xMn_xAs, are desirable for achieving device applications of this and related materials.¹ One such promising approach is to alloy Ga_1–xMn_xAs with phosphorous to form the quaternary alloy Ga_1–xMn_xAs_1–yP_y.² It is now well established that GaMnAs films grown epitaxially on GaAs (001) substrate are under compressive strain,³ while GaMnAsP films are under tensile strain.^4,5 Due to these strain conditions, the magnetic easy axis of GaMnAsP films tends to lie perpendicular to the film surface.^4,5 In addition to such tailoring of magnetic anisotropy by changing strain conditions, the bandgap of GaMnAsP is also increased by increasing P concentration, thus tuning the location of the impurity band and leading to a transition from metallic conduction to thermally activated impurity band conduction.⁶ Although several earlier investigations were already carried out on GaMnAsP as a function of phosphorus concentration,^4,5,7 demonstrating the important correlation between magnetic anisotropy and strain, studies of GaMnAsP films are still relatively limited despite the important aspects of its magnetic properties. Recently, a theoretical and experimental study of the magneto-optical properties of thin GaMnAsP films with varying phosphorus fractions shows that the P incorporation has a significant effect on the sensitivity of the Kerr rotation and ellipticity,⁸ thus enabling one to optimize the magneto-optical properties of these films, and to gain insight into both the magnetic domain patterns and domain wall dynamics. Moreover, a newly developed first-principles calculation⁹ has suggested that doping GaMnAs with small amounts of phosphorous results in a reduction of the energy band gap, the exchange constant N_0β, and the exchange interaction J_Mn-Mn, which is contradictory to previous predictions.² These results have encouraged us to further investigate the effect of phosphorous on structural and magnetic properties of this quaternary alloy. To address these issues, we performed a detailed study on a series of molecular beam epitaxy (MBE)-grown Ga_1–xMn_xAs_1–yP_y thin films with different phosphorus mole fractions y, up to 20%. Special attention was given to the effects of annealing on changes of the magnetic properties of this alloy as the phosphorus concentration was varied.¹⁰ 

The Ga_1–xMn_xAs_1–yP_y films used for this study were grown on GaAs (100) semi-insulating substrates by low temperature MBE.¹¹ High-purity Ga and Mn elemental fluxes were obtained from standard effusion cells, and As₂ and P₂ fluxes were generated by cracker cells. The growth was monitored by in situ reflection high energy electron diffraction. Based on the variation of source fluxes and growth time, thicknesses of the films were estimated to range between 50 and 75 nm. During the growth process of GaMnAsP, the substrate temperature was kept at 250 °C. The Mn flux of was well controlled, allowing us to keep the Mn content of the films at a constant value of x = 0.06. The As₂ flux was also kept constant at the beam equivalent pressure ratio of As₂:Ga ∼ 5. The opening of the P source valve was tuned from 0.8% up to 1.6% in steps of 0.4%, aiming at achieving different phosphorous mole fractions y in the films, between 0.1 and 0.2. A reference GaMnAs sample with 6% percent Mn and no phosphorus was also fabricated under the same growth condition.

As shown in Fig. 1, transmission electron microscopy (TEM) provides an insight into the crystalline quality of the quaternary films being grown. The figure reveals a sharp and straight interface between the Ga_1–xMn_xAs_1–yP_y film and the GaAs buffer layer. Moreover, we do not observe any mismatch between the lattices across the interface or any other forms of obvious defects, which suggests that high-quality Ga_1–xMn_xAs_1–yP_y thin epitaxial films had been successfully grown on the GaAs (001) substrate. During TEM measurements, energy-dispersive x-ray (EDX) spectroscopy analysis has also been carried out to estimate the Mn and P concentration in the quaternary alloy. As shown in Fig. 2, the concentrations of P determined by EDX are consistent with the results based on the measured lattice constants, as described later in the paper.

The crystal quality of the samples used in this study is additionally confirmed by high-resolution x-ray diffraction (HRXRD) measurements. Figure 3 shows 2θ-ω coupled diffraction scans along the growth direction (which for convenience we will refer to as the c-direction) performed on each thin film specimen using a Bruker D8 Discover high-resolution x-ray diffractometer. The sharpest peaks located around 66.06° represent the (004) Bragg's peak of the GaAs substrate, while the peak positions of each sample at their respective Bragg's condition are displayed as the second highest peak in each spectrum. The intensity of the film peaks, along with clear corresponding Pendellösung fringes, indicates the high crystalline integrity of the epitaxially grown films, without the presence of other phases. A progression of the film peak position is clearly seen with the increasing P concentration, with Bragg angles moving from lower to higher values, indicating a reduction in the lattice constant along the c-direction, in line with the rising in-plane tensile strain of the GaMnAsP films. Note that the lack of asymmetry in the profiles of the film peaks indicates the absence of detectable strain gradients within the entire thickness of the GaMnAsP film.

The mole fractions of Mn and P in the GaMnAsP thin films can be accurately calculated based on this XRD analysis. Taking the XRD spectrum of each GaMnAsP sample with a given P concentration, the location 2θ of the corresponding peak can be used to calculate the vertical lattice constant c using the Bragg law equation. In order to determine the relaxed lattice constant a₀ for the heteroepitaxial layer, one may use¹² 

where a is the lateral lattice constant of the GaMnAs or GaMnAsP epilayer, which is identical with the lateral lattice constant of (001) GaAs substrate (i.e., 5.65353 Å), assuming that GaMnAs and GaMnAsP are coherently strained by the GaAs buffer layer. The parameter $ν$ in Eq. (1) is the Poisson ratio of the heteroepitaxial layer, defined as the negative of the ratio between transverse contraction strain to longitudinal extension strain in the direction of stretching force. The parameter $ν$ for the [001] orientation is related to the elastic stiffness constants C₁₁ and C₁₂ of the material as

For the case of GaMnAsP (where the P content is quite significant) we obtain $ν001$ by interpolating¹³ between the values of elastic constants of GaAs (i.e., C₁₁ = 11.88, C₁₂ = 5.32, and C₄₄ = 5.94 in 10¹¹ dyn/cm²)¹⁴ and GaP (i.e., C₁₁ = 14.05, C₁₂ = 6.20, and C₄₄ = 7.03 in 10¹¹ dyn/cm²).¹⁵ The relaxed bulk lattice constants a₀ for the GaMnAs and GaMnAsP films can then be calculated via Eq. (1).⁵ Using this approach, one can, also determine the out-of-plane state of strain $εzz$ (i.e., longitudinal extension strain) of the heteroepitaxial layer using the relation

where a positive and negative values of $εzz$ indicate compressive and tensile strain, respectively.

The Mn mole fraction x and P mole fraction y can now be determined from the relaxed lattice constants a₀ by using Vegard's law equation for GaMnAsP, derived from the equations of GaMnAs provided by Sadowski et al.,¹⁶ 

where a_LT-GaAs = 5.6533 Å, and a_MnAs = 5.9013 Å, and a_GaP = 5.4505 Å. As shown in Fig. 2, the results obtained by this method are in good agreement with those estimated from EDX measurements (see Fig. 2). Additionally, the precise thickness of a uniform thin epilayer can be calculated from the fringe period $δθP$ of the Pendellösung oscillations¹⁷ using

where $θB$ is the Bragg angle and $λ$ is the x-ray wavelength.

For the purpose of enhancing the ferromagnetic properties of the GaMnAsP films, we annealed a piece of each sample in a furnace tube with protective nitrogen atmosphere at 270 °C for 1 h. The 2θ-ω coupled XRD scans were also carried out on each annealed sample, and the resulting spectra are shown in Fig. 3(b). While there is no significant change in the intensity of the peaks or the period of the fringes, close inspection indicates that the diffraction spectra from the annealed specimens are shifted to the right by about 0.2°, suggesting the elimination of interstitial Mn ions by annealing of the GaMnAsP samples.^18,19 As expected, the degree of tensile strain in the specimens increases with the P content. This tensile strain is now additionally enhanced by the annealing process.

It is known that the lattice of GaMnAs epilayer under compressive strain does not relax even with thickness up to several micrometers due to the their low growth temperature,²⁰ so it is natural to assume that the lattice of GaMnAsP thin films is also fully strained when grown by this method. To confirm this assumption, reciprocal space mapping (RSM) measurements were carried out on the as-grown GaMnAsP specimen using Bruker D8 Discover HRXRD equipment. As shown in Fig. 4, the RSMs of the as-grown GaMnAsP sample with about 14.9% P were measured in the vicinity of the symmetric (004) and asymmetric (⁠$2¯2¯4$⁠) Bragg peaks. The very narrow Q_x-direction peaks corresponding to the GaMnAsP layers, along with the presence of interference fringes due to multiple reflections within the GaMnAsP layer, indicate a sharp interface between the GaMnAsP layer and the GaAs substrate. This, together with the relative sharpness of the GaMnAsP peak, suggests that the contents of Mn and P are uniform (i.e., the gradients of Mn and P concentrations are negligible) throughout the epilayer. Since Q_z represents the inverse of vertical lattice constant, and Q_x represents the inverse of lateral lattice constant of the crystal (assuming the lattice is in-plane isotropic), the data in Fig. 4 (the results are similar for all as-grown and annealed GaMnAsP samples) confirm that the lattices of GaMnAsP film are fully constrained by the GaAs substrate layer up to y = ∼0.20 (i.e., fully pseudomorphic, with no detectable relaxation throughout the thickness of the film). This can be seen from the fact that the value of Q_x of GaMnAsP lies directly above the Q_x of the substrate, indicating the same lateral lattice parameter in both layers. The vertical lattice constant of GaMnAsP is smaller than GaAs due to its larger Q_z, in accordance with the results we obtained from the 2θ-ω coupled scans.

The magnetic properties of both as-grown and annealed GaMnAsP films in the sample series, as well as the corresponding reference GaMnAs samples, were investigated using a Quantum Design MPMS XL superconducting quantum interference device (SQUID) magnetometer. Temperature-dependent measurements were performed with the magnetic field applied perpendicular to the film plane (along the [001] axis) and parallel to the film plane along the [100] axis. The corresponding hysteresis loops for both orientations were measured at T = 5 K.

The preferential orientation of the magnetic moments in the GaMnAs film is in-plane, as indicated by the blue (dark gray) line in the inset in Fig. 5(a), which remains above the red (light gray) line up to the Curie temperature. This preference for the in-plane orientation is also evident in the hysteresis loops in Fig. 5(a): the loop, measured with the field applied along the in-plane [100] direction, has a normal rectangular shape, while almost no loop can be observed when the field applied normal to the film plane. In the case of GaMnAsP samples, on the other hand, there are two noteworthy effects of the increasing phosphorus mole fraction. First, the projection of the total magnetization on the vertical axis is generally increasing as the mole fraction of P increases, which can be seen from the elevating red line and the submerging blue line in the insets of Fig. 5, and from the developing out-of-plane red hysteresis loops that gradually change from hard-axis-like elongated loops to easy-axis-like rectangular shapes as one progresses from Figs. 5(b) to 5(d). Second, the Curie temperature T_C is seen to decrease monotonically from 77 K observed in the sample with no P to 40 K for the specimen with y = 0.2, a decline of approximately 1.6 K per 1.0 percentage point increase in phosphorus concentration. We note parenthetically that the hysteresis loop characteristics in Fig. 5(b) (i.e., magnetization switches at ±400 Oe for red loop) and Fig. 5(d) (i.e., two-step hysteresis loops for blue curve) suggest the existence of a large cubic anisotropy fields in these films.²¹ 

To enhance the saturation magnetization and to increase the Curie temperature^11,12 in the GaMnAsP films, low temperature annealing was carried out, as mentioned earlier. After annealing, due to the out-diffusion of Mn interstitials, the total magnetization measured by SQUID can be treated as nearly the total sum of all the magnetic moments of substitutional Mn ions in the thin film. As shown in Fig. 6, the total magnetization is around 40 emu/cm³ at T = 5 K and does not change with the variation of the P mole fraction. The Curie temperature T_C of each sample is enhanced by about 40 K after annealing relative to the value in as-grown films and also follows the nearly-linear declining trend with increasing P concentration observed in the as-grown specimens. A second consequence of annealing is to strengthen the perpendicular magnetic anisotropy of the GaMnAsP films by eliminating the effects of interstitial Mn through increasing not only the hole concentration but also the tensile strain. A clear preference of magnetization for the out-of-plane orientation can be seen in all annealed GaMnAsP samples with P mole fraction above 10%, and this preferential M orientation holds for all temperatures up to T_C. As seen in Fig. 5, nearly rectangular hysteresis loops are obtained along the out-of-plane easy axis. One should also note that there is a clear positive monotonic correlation between the P concentration and the coercivity, which suggests that a stronger perpendicular magnetic anisotropy is achieved by incorporating phosphorus into GaMnAsP film, resulting in increasing the barrier for switching the magnetization M between its two vertical easy axes.

To sum up the results in Figs. 5 and 6, Curie temperature T_C and saturation magnetization M_s at T = 5 K are plotted in Fig. 7 as a function of P concentration for the as-grown and annealed GaMnAsP films. As shown in Fig. 7, after low temperature annealing, saturation magnetization is increased by 20%–60%, and the Curie temperature increases by around 40 K for both GaMnAs and GaMnAsP films, indicating that the incorporation of P in GaMnAs films (either through the presence of P per se or through the reduction of the lattice constant) does not have a significant effect on the incorporation of Mn in the interstitial sites or on the out-diffusion of Mn interstitials. It should be mentioned that an increase in the Mn-hole exchange integral J_pd, and consequently in the Curie temperature, has been predicted based on the decrease in the lattice constant in the quaternary alloy.² However, our experimental results, which are consistent with previous reports²² and with recent theoretical calculations,⁹ show that the Curie temperature decreases systematically with the incorporation of P. These results may be attributed to a decrease in the ability of the charge carriers to mediate ferromagnetic ordering,⁹ i.e., to an increase of the localization of holes in the GaMnAsP alloy. This, however, will require a further detailed investigation.

In this paper, we investigated a series of quaternary ferromagnetic semiconductor Ga_1–xMn_xAs_1–yP_y films grown by MBE on GaAs (100) substrates, with thicknesses ranging between 50 and 75 nm. The films were grown with different phosphorous concentration y ranging from 0.10 to 0.20, and with a constant Mn content of x = 0.06. Detailed structural and magnetic characterizations of both as-grown and annealed samples were carried out by HRXRD and SQUID. A clear relationship between Mn and P concentrations and the lattice constants of the resulting materials is observed and analyzed. Well-defined pendellösung fringes observed in the films obtained in this study indicate high growth quality of the obtained quaternary alloys. Transition from compressive strain in GaMnAs epilayer to tensile strain in GaMnAsP epilayers grown on GaAs can be observed in the form of a monotonic shift of the observed Bragg peaks toward larger angles in 2θ-ω XRD spectra. Reciprocal space map scans investigated in the vicinity of the asymmetric (⁠$2¯2¯4$⁠) crystal plane indicate that the lattice is fully strained in the GaMnAsP film even when P concentration approaches 0.20. Magnetization measurements show a clear trend of a decreasing Curie temperature with increasing P concentration. Additionally, by adding phosphorous into the GaMnAsP alloy, one observed a gradual reorientation of the magnetic easy axis from an in-plane direction to out-of-plane. Finally, the low temperature annealing of the GaMnAsP quaternaries results in a dramatic improvement of the ferromagnetic properties of these quaternary alloys, showing an increase of T_C of each sample by more than 40 K. Finally, the very rectangular shape of the hysteresis loops measured in magnetic fields applied perpendicular to the film plane indicates that the tensile strain in the GaMnAsP under investigation are characterized by a strong perpendicular magnetic anisotropy and thus have significant potential for increasing the density of spintronic devices.²³ 

This work was supported by the NSF Grant No. DMR14-00432, Basic Science Research Program through the NRF of Korea funded by the Ministry of Education (No. 2015R1D1A1A01056614), and a grant from Korea University.