The Growth of High-Crystalline Quality Mn 2 Au (110) Thin Films

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Mn 2 Au is a bimetallic antiferromagnetic with an extraordinarily high Néel temperature of 1600 K. Mn 2 Au has also been found to demonstrate Néel-order spin-orbit torque, allowing for electrical switching of the antiferromagnetic Néel vector. This has led to huge interest in this material for spintronic applications. Here we detail the growth of high quality Mn 2 Au (110) thin films. The films were grown on a high quality Pt (111) buffer layer which was grown on an Al 2 O 3 (0001) substrate. The Mn 2 Au films have excellent crystalline quality as demonstrated by x-ray diffraction, x-ray reflection, and reflection high energy electron diffraction measurements. The Mn 2 Au (110) films are found to grow with three equivalent in-plane rotation domains, caused by the Pt/Al 2 O 3 substrate.

I. INTRODUCTION
Mn 2 Au is an antiferromagnetic (AF) material with an extraordinarily high Néel temperature of approximately 1600 K 1,2 . The first study into the magnetic properties of this material used Mössbauer resonance, and indicated that the material was non-magnetic 3 . Further investigations into its magnetic properties later led to it being classified as possessing Pauli paramagnetism 4 , however, first principle calculations later predicted the material to posses antiferromagnetic order 1 . Recent calculations predicted the easy axis for the Mn magnetic moments to lie along the [110] directions by calculating the magnetocrystalline anisotropy energy constants 5 . The easy axis was experimentally confirmed to lie in the basal plane of Mn 2 Au 2 and subsequently found to lie along the predicted 110 directions 6 . Mn 2 Au has a tetragonal crystal structure (crystallographic space group I4/mmm with magnetic space group Im'mm) with lattice parameters a = 3.328Å and c = 8.539Å 7 . This is shown schematically in Figure 4 (b) 8 . The magnetic structure is most easily understood by noting that each plane of Mn atoms perpendicular to the [001] direction is antiferromagnetically aligned with its neighbouring plane, above and below it. This magnetic structure can also be viewed as the Mn atoms lying on two separate, antiferromagnetically aligned sublattices. These two sublattices are inversion partners -an applied current will induce opposite inverse spin galvanic effects on both of these sublattices (known as the Néel-order spin-orbit torque, or NSOT 9 ), allowing electrical switching of the antiferromagnetic Néel vector. The presence of this effect, its large spin orbit coupling 5 ,and the extremely high Néel temperature of Mn 2 Au has led to it attracting great interest for use in antiferromagnetic spintronic devices.  14 . Here we detail a method for growing Mn 2 Au (110) oriented thin films and their structural characterisation. As the 110 directions have been shown to be the easy directions in Mn 2 Au, each magnetic domain within these (110) out-of-plane oriented films will possess one magnetic easy axis out-of-plane, while in the plane of the material there will be an easy axis and a hard axis separated by 90 degrees. Furthermore, the (110) surface of Mn 2 Au is a pseudo-HCP (Hexagonal Close-Packed) surface, providing growth compatibility with other HCP materials which are commonly used in magnetic tunnel junction (MTJ) devices such as Pt (111) and Co (111) 15 .
While Mn 2 Au has been grown on a variety of substrate and buffer layer combinations (see Table I), each producing a variety of Mn 2 Au film textures, the X-Ray Diffraction (XRD) data of many of the films produced shows the presence of multiple Mn 2 Au phases which do not possess high crystalline quality. One material which is commonly used as a seed layer for the growth of magnetic structures is Pt, as it grows with high crystalline quality on Al 2 O 3 (0001) 16 and can be utilised as an active part of a magnetic device in the form of Co/Pt multilayers, which present perpendicular magnetic anisotropy at specific Co layer thicknesses 17 . Pt has been shown to grow in the (111) orientation on the Al 2 O 3 (0001) surface with 2 in-plane orientations domains 18 . The Pt (111) surface has a hexagonal surface unit cell with a surface lattice parameter of 2.774Å, while the inter-atomic spacing on the Mn 2 Au (110) surface varies from 2.747Å to 2.852Å, matching well with that of the Pt (111) surface. For this reason, we have chosen to use Pt as a seed layer for the growth of Mn 2 Au on Al 2 O 3 .

II. EXPERIMENTAL DETAILS
Pt layers were deposited by e-beam evaporation in a DCA M600 MBE system with a base pressure of 2 × 10 −10 Torr. Single crystal Al 2 O 3 (0001) substrates were sonicated in isopropyl alcohol for 15 minutes before being inserted into the MBE for film growth. The Al 2 O 3 substrates were annealed at 600 • C for one hour prior to deposition of the Pt. The Pt films were deposited at a rate of 0.05Å s −1 as determined by a calibrated quartz crystal monitor and the substrate was held at a temperature of 550 • C during growth. Details on the characterisation of the Pt films are given in the supplementary material ? .
The Mn 2 Au thin films were grown in the same growth chamber as was used to grow the Pt layers. For film growth, Mn and Au source material were evaporated simultaneously from separate Knudsen cells. The Au Knudsen cell was held at a temperature of 1282 • C, while the temperature of the Mn Knudsen cell was found to provide stoichiometric Mn 2 Au at a temperature of 937 • C. These cell temperatures were found to provide Mn and Au atomic fluxes in a 2:1 ratio by growing separate Mn and Au films and measuring their thickness and density with X-Ray Reflectivity (XRR) and cross checking with a beam flux monitor located at the sample growth position. This resulted in an overall Mn 2 Au growth rate of approximately 0.25Å s −1 . For all samples, the substrate temperature was reduced to 250 • C from the Pt growth temperature of 550 • C upon completion of growth of the Pt seed layer. Simultaneously, the Knudsen cells were brought to their operating temperatures.
The stoichiometry of the Mn 2 Au films was qualitatively assessed by analysing the XRD patterns of samples post-growth. When the Mn flux was too low MnAu phases could be seen in the XRD, while when the Mn flux was too high α-Mn would appear. This off-stoichiometric growth would be accompanied by a concomitant change in the RHEED, becoming a transmission-like pattern, indicative of island growth. Quantitative stoichiometric determination via X-ray Photoelectron Spectroscopy (XPS) was found to be unreliable; this is discussed in the supplementary material. A typical XRD pattern of a thick, stoichiometric Mn 2 Au/Pt/Al 2 O 3 film is shown in Figure  S2 in the Supplementary material. Only the (110) phase of Mn 2 Au is seen to be present. Figure 1 shows archetypal RHEED images after completion of each layer taken along the two Al 2 O 3 high symmetry directions which are separated by 30 • . An electron beam energy of 20 keV was used to produce all of the RHEED images shown here. The RHEED images of the Al 2 O 3 substrate were taken at the annealing temperature of 600 • C, the images of the Pt layer were taken at the growth temperature of 550 • C, and those of the Mn 2 Au layer were taken at room temperature. The measured streak spacings in the Al 2 O 3 and Pt images were corrected for thermal expansion to their room temperature values 20,21 . This was found to only alter the measured spacings by an amount on the order of one pixel. The sharp diffraction spots seen along both directions of the Al 2 O 3 substrate are indicative of a high quality single crystal surface, while the streaky nature of the RHEED patterns for the Pt and Mn 2 Au layers indicate that they have flat surfaces consisting of grains or crystalline domains smaller than the coherence length of the electron beam 22 .

III. RESULTS AND DISCUSSION
The RHEED pattern shown here for the Mn 2 Au layer is typically present after the growth of <5 nm of Mn 2 Au and persists throughout growth, even in the thickest films grown (∼120 nm). Along the Al 2 O 3 [1010] direction the Mn 2 Au is seen to possess the same streak spacing as both the underlying Pt seed layer and the Al 2 O 3 substrate, corresponding to the Al 2 O 3 a lattice parameter; 4.758Å.
While the oxygen sublattice of the Al 2 O 3 surface appears to be in an HCP arrangement, it is only approximately so 23 . The slight deviations in the O atomic positions from those of the ideal HCP lattice results in the periodicity viewed along the Al 2 O 3 [1120] direction being three atomic spacings, leading to the smaller RHEED streak spacing seen.
The Mn 2 Au layer does appear to reproduce the same streak spacing as Al 2 O 3 , however, rather than being caused by a surface lattice which has distortions from the ideal HCP lattice positions, this reduced streak spacing is due to the presence of both Mn and Au on the Mn 2 Au (110) surface. When viewed along the Al 2 O 3 [1120] direction, the rows of atoms perpendicular to this direction, which are responsible for producing the symmetry in the RHEED pattern, contains both Mn and Au atoms. This is demonstrated in Figure 4 (a). This produces a periodicity equal to three times that of the inter-atomic spacing of the Mn 2 Au surface, giving rise to a RHEED pattern which has the same streak spacing as Al 2 O 3 . However, When viewed along the Al 2 O 3 [1010] direction, the perpendicular rows of atoms responsible for producing the RHEED pattern consist of only a single element and so the RHEED pattern appears identical to that of a monatomic HCP lattice, such as the Pt (111) surface. A schematic of the growth relations of Al 2 O 3 , Pt, and Mn 2 Au is shown in Figure 4 (a). As the Pt layer does not show this reduced streak spacing along the [1120] direction it can be concluded that the Pt atoms form the expected HCP surface lattice rather than continuing the lateral symmetry of the underlying Al 2 O 3 oxygen lattice. Post-annealing of the films in the growth chamber in UHV conditions at the Mn 2 Au growth temperature of 250 • C was not found to have any impact on the surface quality of the films, as measured by RHEED. For this reason, the samples were cooled to room temperature upon completion of the growth of the Mn 2 Au layer. The close agreement between these two values implies that both layers are a single crystalline domain throughout their thickness. While the Pendellösung fringes of both the Mn 2 Au and Pt layers show that the films are crystalline in the growth direction of the layers, it can not distinguish between the situation where the deposited films consist of a single inplane rotation domain or multiple rotation domains. To find the in-plane epitaxial relation between the layers in Al 2 O 3 /Pt/Mn 2 Au and to seek the presence of any rotation domains, azimuthal (φ) XRD scans were carried out. The scans were performed on a sample with a thick 120 nm Mn 2 Au layer so as to enhance the signal from the weakly diffracting asymmetric peaks.
These φ-scans are shown in Figure 3. The Al 2 O 3 substrate shows the expected three-fold symmetry. While the φ-scan of the Pt {100} planes would be expected to produce 3 peaks separated by 120 • as the sample is rotated through 360 • , 6 peaks are instead observed, implying that two domains, rotated by 60 • with respect to each other, are present in the Pt buffer layers grown on Al 2 O 3 (0001). The equal intensity of all six of the peaks suggests that these two domains are present in equal amounts across the sample. As the surface lattice of Pt (111) is hexagonal and thus possesses 6-fold symmetry, having both domains present will not affect the symmetry seen in RHEED measurements as they will appear equivalent; explaining their absence in both the RHEED images shown previously and in the previous work of Farrow et al. 18 . Similarly, the Mn 2 Au φ-scan would be expected to only show 2 diffraction peaks due to the {310} planes, separated by 180 • . As six peaks can be seen, this indicates that there are three equivalent domains present in the films, rotated by 60 • with respect to each other.
To confirm this, a φ scan was performed on a second Mn 2 Au diffraction peak. The Mn 2 Au (222) diffraction peak is expected to show the same two-fold symmetry as the (310)   For use in future magnetic devices, Mn 2 Au will be most useful as ultra thin films (≤10 nm) in order to be able to reach the extremely high current densities needed for electrical switching of the magnetic order 24 . Reduction of the Mn 2 Au thickness to this regime will also push the finite size Néel temperature towards room temperature from the extremely high bulk value of 1500 K, which is necessary for the thermal setting of exchange bias devices. To this end, the high quality MBE-grown Mn 2 Au films demonstrated here show high promise for such size reduction, as they were found to grow with low roughness, minimal strain, and were found to consist of a single crystalline domain in the out of plane direction. We have compiled a table of all the various Mn 2 Au thin film/substrate combinations as known to us in Table I. Our films are one of three works which were able to obtain Mn 2 Au with only a single crystal phase present, and the first demonstration of single phase, (110) oriented films. While it is difficult to quantitatively estimate the effect that parastic crystalline phases in antiferromagnetic materials will have on devices constructed from these materials, previous work has demonstrated an increase in Mn 2 Au (110) films, in contrast to (001) oriented films are expected to have one out-of-plane easy axis (along [110]) and one in-plane easy axis (along [1][2][3][4][5][6][7][8][9][10]). This would need to be confirmed via X-ray Magnetic Linear Dichroism-Photoemission Electron Microscopy (XMLD-PEEM) or neutron diffraction measurements, as has been previously done for Mn 2 Au (001) thin films 26 . This makes our (110) films unsuitable for NSOT measurements in the in-plane geometry previously used for (001) Mn 2 Au films 27 . Additionally, the magnetic sublattices in Mn 2 Au should be compensated for textured Mn 2 Au (110). The compensated moments at the interface may make this orientation unfavourable for exchange bias and spin-orbitronic effects such as the Tunnelling Anisotropic Magnetoresistance (TAMR) effect. Further study needs to be done on our films to understand which model for exchange bias will apply to our compensated films (i.e., the models of Mieklejohn 28 or Malozemoff 29 ). The HCP surface of the (110) films is highly compatible with other HCP and pseudo-HCP surface materials that are used in MTJ devices such as the Pt (111) shown here, and Fe (110) and Co (111) that we will show in future work (in preparation).

IV. CONCLUSION
To conclude, we have presented here the growth of high-crystalline quality, MBE-grown Mn 2 Au (110) films which was made possible by the use of a Pt (111) Au [111] respectively. The Mn 2 Au layers show minimal strain compared to bulk lattice parameters, and grow with a low roughness and high crystalline quality, as evidenced by the Pendellösung fringes present in the XRD data.

V. SUPPLEMENTAL MATERIAL
See Supplemental Material for a discussion of the characterisation of Pt thin films, a large-range XRD scan of a Mn 2 Au thin film, and a discussion on the stoichiometry of our Mn 2 Au films.