### Equipment and techniques

The analysed samples were grown by solid source MBE. The samples comprise a 500-nm GaAs buffer grown at 580°C, followed by either a 25-nm (sample S25) or a 100-nm (sample S100) GaAsBi layer grown at approximately 380°C ± 10°C. The GaAsBi layers were capped with a 100-nm GaAs layer grown at the GaAsBi growth temperature. An As_{4}/Ga/Bi beam equivalent pressure ratio of 40:2:1 and a growth rate of 1.0 μm/h determined from reflection high energy electron diffraction (RHEED) oscillations were used for both samples.

For room-temperature photoluminescence (RT-PL) measurements, the excitation source was a 532-nm diode pumped solid-state laser operating with an excitation power density of 114 Wcm^{−2}. The emitted PL was collected by a Cassegrain lens and then focused onto the entrance slit of the monochromator before being detected by a liquid nitrogen cooled germanium detector. A phase-sensitive lock-in detection technique was also used to eliminate the contribution from the background light to the measured PL. Structural and analytical analyses were performed in cross-sectional samples prepared using conventional techniques by transmission electron microscopy. Diffraction contrast imaging and selected area electron diffraction (SAED) patterns were obtained in a JEOL 1200EX (JEOL Ltd, Akishima-shi, Tokyo, Japan) at 120 kV. HRTEM images for fast Fourier transform (FFT) reconstruction were obtained with a JEOL-2100 at 200 kV. Z-contrast high-angle annular dark field (HAADF) in scanning TEM mode and energy-dispersive X-ray (EDX) spectroscopy with an Oxford Inca Energy-200 detector (Oxford Instruments, Abingdon, UK) were performed in a JEOL 2010 at 200 kV. HRTEM images were post-processed for FFT reconstruction and geometrical phase analysis (GPA) by using the GPA software running in a MATLAB routine and Digital Micrograph software (GATAN Inc., Pleasanton, CA, USA).

### Order parameter estimation

The Bragg-Williams LRO parameter (

S) is used to quantify the degree of ordering across two types of site occupied by atom A and B,

*α* − and

*β* − sites, respectively. It can be defined as follows [

13]:

$S=\frac{{r}_{\alpha}-{x}_{\mathrm{A}}}{{y}_{\beta}}=\frac{{r}_{\beta}-{x}_{\mathrm{B}}}{{y}_{\alpha}},$

where *r*_{
α
} (*r*_{
β
}) is the fraction of α-sites (*β*-sites) occupied by the right atom A (B), *x*_{A} (*x*_{B}) is the atom fraction of A (B) and *y*_{
β
} (*y*_{
α
}) denote the fraction of *β* − sites (*α* − sites). For a completely random crystal, *r*_{
α
} = *x*_{A} and *S* = 0, while for a perfectly ordered structure, *S* = 1. Numerous studies have been conducted to determine the degree of ordering through different techniques, such as nuclear magnetic resonance [14], PL [15] and X-ray diffraction [16]. In X-ray and electron diffraction methods, LRO parameters have been determined from the ratio of superlattice and fundamental reflection intensities weighted by their structure factors by applying kinematical diffraction theory [17].

In general, the electron diffraction method to determine structure factors of alloys does not always allow determination of the LRO parameters because superlattice reflections of ordering alloys are not amenable to critical voltage techniques [

18]. Conventional TEM has also been used in this way; however, the weak intensity of extra reflections makes it impossible to carry out a study of image intensity similar to that described by Baxter et al. [

19]. To circumvent this, an estimation of the order parameter from the HRTEM images taken at different zones inside the GaAsBi layer was carried out. It is well known that HRTEM images are a two-dimensional intensity pattern produced from a complex interference of the electron beams exiting from the analysed sample. These images carry quantitative information of the sample, namely atomic structure, lattice parameters/strain and chemical information [

20]. Furthermore, FFT reconstruction of HRTEM images provides information about the periodicity of the atomic structure which can be correlated to the electron diffraction patterns registered at the back focal plane of the objective lens [

21]. In the following, we interpret the bright spots in the FFT images as diffraction spots (reflections) from crystallographic planes of the crystalline phases in the structures. CuPt

_{B} ordering in zinc-blende GaAsBi occurs in the alternating {111} planes of group V atoms resulting in a diffraction spot at ½ (111). The intensity of the extra reflections depends on the level of said ordering; hence, the higher the grade of ordering the more intense in the extra reflection in the FFT. Thus, an estimation of

S is given by [

22]:

$S={\left(\frac{{I}_{S}}{{I}_{111}}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\frac{\left|{\mathit{F}}_{111}\right|}{\left|{\mathit{F}}_{S}\right|},$

where *I*_{
s
} and *I*_{111} are the intensity of the ½(111) and (111) spots, respectively; *F*_{s}, is the structure factor for a fully ordered alloy and is given by *F*_{
s
} = 2(*f*_{As} − *f*_{Bi}) and *F*_{111} = 4(*f*_{III} − *if*_{V}) is the structure factor for the {111} reflections.

The absolute diffracted intensity is subject to errors due to several experimental parameters. In order to reduce the error in the measurements, the integrated intensity around the ½(111) and (111) spots is normalized by subtracting the background around the signal obtained close to each diffraction spot, respectively. The FFT method from HREM images, on the other hand, provides LRO parameters in a small selected microscopic area, and therefore, it enables microscopic fluctuations of LRO parameters to be examined.

### Ordering maps from geometric phase algorithm

HRTEM images allow us to extract information on compositional variations and/or the state of deformation of the nanostructures by comparing the actual positions of the unit cells in the image with a reference lattice using such techniques as the peak pairs algorithm or geometric phase analysis [23, 24]. Even though these programs are mainly applied to the analysis of the deformation present in the nanostructures, they can be used to perform other types of studies such as the spatial location of different phases and grains [25]. We follow a similar procedure here in order to obtain a spatial map of the distribution of the ordering.

The procedure used for calculating the phase image, the Bragg filtered image and numerical moiré image using the GPA are as described by Hÿtch and co-workers [

24,

26]. Briefly, the method consists of constructing a differential phase map for a given Bragg region with respect to a reference lattice. In our case, we build numerical moiré images at position

*r*,

*M*(

*r*), by superimposing the real lattice with a reciprocal lattice vector smaller than the average lattice where

*M* is a magnification constant as [

25,

27]:

$M\left(\mathbf{r}\right)=\frac{2\pi {\mathbf{g}}_{\mathbf{r}}\cdot \mathbf{r}}{M}-2\pi {\mathbf{g}}_{\mathbf{r}}\cdot \mathbf{u}\left(\mathbf{r}\right),$

where **g**_{
r
} is the reference lattice in reciprocal space and **u**(**r**) is the displacement of the atomic column position from its nominal position. Following this procedure, two translational moiré images (we used *M* = 1) are obtained using **g**_{
r
} as the reference position of each (111) spot in the FFT pattern and a Bragg mask that includes the collinear ½(111) spot associated with the ordering arrangement. The final RGB multilayer reconstructed image is formed from the two inverse FFT (iFFT) images of these selected masks. The spatial localization of ordering in each of the {111} planes is represented in the sets of red and green fringes. In order to improve visualization, a null matrix blue layer is used as background. The red and green fringes in this resultant image are consistent with the presence of ordering where the moiré spacing is proportional to 1/(g − g_{r}).