Magnetic systems exhibiting spin-canted states have garnered much attention recently for their promising rich exotic properties driven by the real-space spin textures and competing magnetic orders. In this study, we present the structural and magnetic properties of hexagonal 60 nm MnPtGa epitaxial thin films grown by magnetron sputtering on Al2O3(0001) single-crystalline substrates. The MnPtGa film crystallizes in the centrosymmetric P63/mmc (No. 194) space group, showing perpendicular magnetic anisotropy along the c-axis, with a Curie temperature TC = 263 K. In addition, the MnPtGa film undergoes a spin reorientation transition at Tsr = 160 K. We investigated the MnPtGa magnetic ground states using single-crystal neutron diffraction. A structurally forbidden (001) magnetic Bragg reflection emerges below Tsr, indicating the existence of a spin-canted state, where the magnetic moments align ferromagnetically perpendicular to the basal plane, and a non-zero in-plane component exhibits an antiferromagnetic ordering along the c-axis. At 2 K, the refined magnetic moments of Mn are μz = 4.2(4) μB and μx = 1.5(3) μB, projected onto the c-axis and basal plane, respectively. Hence, we determined a 20° Mn spin canting angle off from the c-axis.

Magnetic orderings are classified as collinear, when spins are oriented parallel or antiparallel to each other, or noncollinear, when more complex magnetic structures develop owing to competing magnetic interactions. Heusler compounds belong to a remarkable class of intermetallic ternary materials hosting a variety of ground states, including superconducting and half-metallic compounds, hosting topological Weyl and Dirac points, and exhibiting exotic magnetism with noncollinear ordering and magnetic (anti)skyrmions.1 The experimental observation of a noncollinear magnetic ground state in inverse tetragonal Heusler Mn2RhSn2 has triggered the search for new emergent phenomena in this family of compounds. Thin films and single crystals of the noncentrosymmetric inverse Heusler compounds Mn2RhSn and MnxPtSn (x = 1.4–2) are found to host a variety of nontrivial magnetic structures, ranging from elliptical skyrmions to antiskyrmions and noncoplanar spin textures.3–10 In addition, biskyrmion lattices have been experimentally observed in the centrosymmetric hexagonal Heusler MnNiGa.11 

Another member of the Heusler family with rich noncollinear magnetism is MnPtGa, which crystallizes in two distinct structures. Srivastava et al.12 found that single crystals of MnPtGa have a noncentrosymmetric trigonal (t-) crystal structure (space group P3m1, No. 156) with lattice parameters a = b = 4.35 Å and c = 5.59 Å. This crystal structure breaks the inversion symmetry of t-MnPtGa, allowing the formation of Néel skyrmions. In contrast, Buschow et al.13,14 have previously reported that MnPtGa crystallizes in a centrosymmetric hexagonal (h-) Ni2In-type structure (space group P63/mmc, No. 194) with lattice parameters a = b = 4.336 Å and c = 5.590 Å, where the Mn, Pt, and Ga atoms occupy the 2a, 2c, and 2d Wyckoff positions, respectively. The h-MnPtGa enters a ferromagnetic (FM) state below its Curie temperature (TC) of 263 K. Additionally, powder neutron diffraction identified a rich evolution of magnetic phases in polycrystalline h-MnPtGa.15 As h-MnPtGa is cooled below its Curie temperature, its magnetic order changes from FM to canted antiferromagnetic (AF) and, finally, forms a spin density wave.

In this study, we focus on epitaxial h-MnPtGa thin films and report on their structural and magnetic properties. We measure their magnetization as a function of temperature and magnetic field, thus finding hard magnetic behavior with an easy axis of magnetization along the c-axis (out-of-plane) direction and a temperature-induced spin reorientation transition. Furthermore, single-crystal neutron diffraction sheds light onto the magnetic structure of h-MnPtGa films, where the magnetic order evolves from a collinear FM state to a spin-canted (SC) state below the spin reorientation transition temperature (Tsr = 160 K).

Epitaxial thin films of h-MnPtGa were grown on Al2O3(0001) single-crystal substrates using a BESTEC ultra high vacuum magnetron sputtering system. Before deposition, the chamber was evacuated to a base pressure of less than 8 × 10−9 mbar, while the process gas (Ar 5 N) pressure was set to 3 × 10−3 mbar. For the growth of the films, we used Pt and equiatomic alloy Mn50Ga50 sources in a confocal geometry, applying 18 and 25 W DC power, respectively. The target-to-substrate distance was fixed at 18 cm, and the substrate was rotated during deposition to ensure a homogeneous growth. The films were grown at 500 °C, followed by in situ post-annealing at the same temperature for 30 min to improve the crystallinity of the films. To avoid oxidation of the films, an amorphous Si layer of 3 nm was deposited in situ at room temperature. The composition of the films was estimated as Mn0.31Pt0.35Ga0.34 (which we refer to as MnPtGa henceforth) by energy-dispersive x-ray spectrometry in a FEI Quanta 200 system. The experimental error in determining the stoichiometry of the films was less than 4 at. %. Symmetric and asymmetric x-ray diffraction (XRD) patterns were acquired using a Panalytical X' Pert3 material research diffractometer with Cu Kα1 radiation (λ = 1.5406 Å). The growth rates and film thicknesses were determined from x-ray reflectivity (XRR) measurements, while magnetic characterizations were performed in a Quantum Design MPMS3 SQUID-VSM magnetometer. Single-crystal neutron diffraction was performed using the D10 four-circle diffractometer at the Institut Laue-Langevin (ILL) neutron facility. Thermal neutrons with an incident wavelength of 2.36 Å were selected with a vertically focusing pyrolytic graphite (PG) (002) monochromator combined with a focusing PG analyzer and collected with a point detector. We used a 59.4 nm thick h-MnPtGa film for the structural and magnetic characterizations and a nominally identical 62.2 nm thick film for the single-crystal neutron diffraction measurements. We refer to the samples as 60 nm films henceforth.

Figure 1(a) shows the symmetric radial 2θ–ω scan of the 60 nm h-MnPtGa film on an Al2O3 (0001) single-crystalline substrate. We exclusively observe the (0002) and (0004) Bragg reflections of the film as well as the (0006) peak corresponding to the Al2O3 substrate, which indicates that the film grows in the (0001) orientation with the c-axis crystallographic direction normal to the basal plane of the film. To determine the in-plane crystallographic orientation of the film relative to the substrate, we performed asymmetric azimuthal φ-scans for the {101¯2} and {101¯4} equivalent families of planes of the h-MnPtGa film and Al2O3 substrate, respectively [Fig. 1(b)]. The coincidence in the positions of the reflections indicates that the epitaxial relationship between the film and substrate is MnPtGa(0001)[112¯0] ǁ Al2O3(0001)[112¯0]. Figure 1(c) shows the XRR pattern of the h-MnPtGa film. The well-resolved Kiessig fringes up to (and beyond) θ = 3° highlight the smoothness of the h-MnPtGa films and allow the precise determination of film thicknesses using the GenX software16 to fit the XRR experimental data. Good agreement between the experimental data (circles) and fitted model (continuous line) allows us to determine the thickness and density of the films with sub-nanometer precision.

FIG. 1.

Structural characterization of the h-MnPtGa film. (a) 2θ–ω XRD pattern of the h-MnPtGa film on a (0001)-oriented Al2O3 substrate. The inset depicts the hexagonal primitive unit cell of hexagonal MnPtGa. (b) Asymmetric φ-scans of the hexagonal family of planes {101¯2} and {101¯4} from the film and substrate, respectively. (c) XRR pattern, where the blue circles correspond to the experimental data and the solid red line, represents the least squares fit to the data using the GenX software.

FIG. 1.

Structural characterization of the h-MnPtGa film. (a) 2θ–ω XRD pattern of the h-MnPtGa film on a (0001)-oriented Al2O3 substrate. The inset depicts the hexagonal primitive unit cell of hexagonal MnPtGa. (b) Asymmetric φ-scans of the hexagonal family of planes {101¯2} and {101¯4} from the film and substrate, respectively. (c) XRR pattern, where the blue circles correspond to the experimental data and the solid red line, represents the least squares fit to the data using the GenX software.

Close modal

To investigate the magnetic properties of the h-MnPtGa films, we performed magnetization measurements over a wide range of temperatures and magnetic fields. Figure 2(a) shows the temperature-dependent magnetization under different protocols, where a magnetic field of 20 mT was applied in the out-of-plane direction (OOP), that is, parallel to the [0001] crystallographic direction. The zero-field-cooled (ZFC) magnetization curve was recorded upon warming in the temperature range of 5–300 K under an external magnetic field μ0H = 20 mT after cooling in a zero magnetic field. The field–cooled (FC) magnetization curve was measured upon cooling from 300 to 5 K under an external magnetic field μ0H = 20 mT. From the FC and ZFC curves, we can observe a paramagnetic (PM) to FM transition below TC = 263 K. The observed disparity in the measured magnetization between ZFC and FC curves, as we reduce the temperature below TC, arises from the sizeable coercivity of the system and therefore finds its origin in the film's magnetic anisotropy. Moreover, the ZFC magnetization curve manifests a kink at Tsr = 160 K, which highlights a thermally induced spin reorientation transition and corresponds to the onset of a SC state, whereby the magnetization gradually decreases as the temperature is reduced.

FIG. 2.

Magnetic properties of the h-MnPtGa film. (a) Temperature-dependent magnetization curves measured under field-cooled (FC) and zero-field-cooled (ZFC) protocols and normalized to the magnetization at 5 K. The vertical dashed lines mark the transition temperatures to the ferromagnetic and spin canted states at 263 and 160 K, respectively. (b) Out-of-plane (OOP) and in-plane (IP) magnetization hysteresis loops at T = 50 K evidencing the PMA of h-MnPtGa films.

FIG. 2.

Magnetic properties of the h-MnPtGa film. (a) Temperature-dependent magnetization curves measured under field-cooled (FC) and zero-field-cooled (ZFC) protocols and normalized to the magnetization at 5 K. The vertical dashed lines mark the transition temperatures to the ferromagnetic and spin canted states at 263 and 160 K, respectively. (b) Out-of-plane (OOP) and in-plane (IP) magnetization hysteresis loops at T = 50 K evidencing the PMA of h-MnPtGa films.

Close modal

Figure 2(b) shows the isothermal magnetization hysteresis loops with the magnetic field applied OOP and in-plane (IP) at 50 K. The comparison of the OOP (blue line) and IP (red line) hysteresis curves indicates that the h-MnPtGa possesses perpendicular magnetic anisotropy (PMA) with an easy axis along the [0001] crystallographic direction. The film exhibits hard magnetic properties with a coercive field of 0.49 T and saturation magnetization Ms = 598 kA/m in the OOP direction. At 5 K, Ms is 629 kA/m (not shown here). For comparison, the reported saturation magnetization value at 4 K of bulk polycrystalline samples by Buschow et al.13 and Cooley et al.15 is 643 and 537 kA/m, respectively. The differences in the magnetization between bulk and thin films can generally be attributed to the slight differences in stoichiometry and antisite disorder.

To further elucidate the magnetic order of the h-MnPtGa thin film, we have performed single-crystal neutron diffraction measurements. The measurements were performed in the temperature range of 300–2 K. A triple-axis configuration in the elastic mode was used to reduce the background and increase the signal-to-background ratio.

The crystal structure of the 60 nm h-MnPtGa in the PM state was analyzed based on a collection of 18 Bragg peaks at 300 K, leading to eight unique independent reflections (see the supplementary material). The refinement of the nuclear structure was performed by the Rietveld method implemented within the FullProf software.17 In a single-crystal neutron diffraction experiment, the integrated intensities Ihkl depend on the nuclear structure factor FN(hkl) as follows:

Ihkl=Aλ3|FN(hkl)|2sin2θ|FN(hkl)|2,
(1)

where (hkl) is the scattering plane, θ is the angle of the incident neutron beam relative to the scattering plane, 2θ is the diffraction angle of the scattered beam, and λ is the monochromatic neutron wavelength. The parameter A includes the overall instrument scaling factor and the absorption and extinction effects. The reliability of the calculated (Fcalc) and observed (Fobs) structure factors of every collected independent Bragg reflection assesses the accuracy of the model employed in the refinement process, as demonstrated by Eq. (1), for the corresponding integrated intensities.

Figure 3(a) shows |Fcalc|2 as a function of |Fobs|2, proportional to the integrated intensities at T = 300 K, in the PM state of the h-MnPtGa film. We find excellent agreement with the P63/mmc space group, leading to a reliability factor (RB) of 6%. Therefore, only the scale and extinction parameters were refined. From the single-crystal neutron diffraction measurements, we determine the lattice parameters of the h-MnPtGa films on Al2O3(0001) at 300 K to be a = (4.3475 ± 0.0007) Å and c = (5.5542 ± 0.0011) Å. The latter value is in excellent agreement with the experimentally estimated c = 5.555 Å, obtained from a room temperature XRD scan.

FIG. 3.

Single-crystal neutron diffraction of the h-MnPtGa epitaxial thin film. (a) Rietveld refinement of the nuclear structure in the paramagnetic phase at 300 K. Temperature dependence of (b) the (100) Bragg reflection and (d) the purely magnetic (001) Bragg reflection in the PM (300 K), FM (200 K), and SC (2 K) states. (c) Rietveld refinement of the nuclear and magnetic structures in the FM state at 200 K. (e) Rietveld refinement of the nuclear and magnetic structures in the SC state at 2 K, where both the FM and in-plane AF staggered contributions along the c-axis are included. (f) Noncollinear magnetic groundstate structure at 2 K, where the Mn moments are depicted with a canting angle of 20° away from the c-axis.

FIG. 3.

Single-crystal neutron diffraction of the h-MnPtGa epitaxial thin film. (a) Rietveld refinement of the nuclear structure in the paramagnetic phase at 300 K. Temperature dependence of (b) the (100) Bragg reflection and (d) the purely magnetic (001) Bragg reflection in the PM (300 K), FM (200 K), and SC (2 K) states. (c) Rietveld refinement of the nuclear and magnetic structures in the FM state at 200 K. (e) Rietveld refinement of the nuclear and magnetic structures in the SC state at 2 K, where both the FM and in-plane AF staggered contributions along the c-axis are included. (f) Noncollinear magnetic groundstate structure at 2 K, where the Mn moments are depicted with a canting angle of 20° away from the c-axis.

Close modal

We collected the same set of Bragg reflections below TC in the collinear FM state at T = 200 K. At this temperature, we observe an increase in the intensity of the (100) Bragg reflection [Fig. 3(b)], which signals the appearance of an additional FM contribution to the scattering. Accordingly, the nuclear and magnetic structures were refined, including an FM component that led to a reliability factor RB = 8.5%, as shown in Fig. 3(c). The magnetic moment was found to be 2.8(7) μB per Mn atom along the c-axis.

As we reduce the temperature to 2 K well below Tsr, we observe that the intensity of some nuclear reflections, in particular the (100) Bragg reflection, further increases [Fig. 3(b)] accompanied by the onset of a sizeable (001) Bragg reflection [Fig. 3(d)]. The observation of the structurally forbidden (001) Bragg reflection for the P63/mmc space group of purely magnetic origin signals the existence of a spin reorientation transition toward the SC state. The magnetic reflection intensity depends on the squared modulus of the magnetic structure factor FM(Q), similar to the relation shown in Eq. (1). Neutron scattering senses the components of the magnetic moments projected onto the plane perpendicular to the scattering vector Q = kfki, where ki(f) is the initial (final) neutron wave vector (respectively). Hence, the observation of the (001) reflection signifies the existence of a component of the magnetic moment in the basal plane. The magnetic order is found to be commensurate with the lattice and is characterized by a propagation vector k = (0, 0, 0). This transition to an SC state with an in-plane antiferromagnetic (AF) component, together with a predominantly FM component along the c-axis, is consistent with the canted AF state of bulk polycrystalline h-MnPtGa.15 

Accordingly, the refinement of the nuclear and magnetic structures at 2 K was performed, including both a FM coupling in the basal plane, with the moment along the c-axis, and an AF in-plane component (staggered in the out-of-plane direction). A comparison between the calculated and observed squared structure factors at 2 K is shown in Figure 3(e), corresponding to a reliability factor RB = 9%. The components of the magnetic moment of the Mn atoms were obtained from the refined data at 2 K, with μz = 4.2(4) μB and μx = 1.5(3) μB, leading to a total magnetic moment per Mn atom of 4.5(5) μB at 2 K. The estimated Ms from SQUID magnetometry measurement reaches 3.08 μB per formula unit at 5 K. The limited number of acquired peaks in our single-crystal neutron scattering experiment makes the refinement of both nuclear and magnetic parameters challenging. Furthermore, the antiferromagnetic component is estimated from a unique magnetic diffraction peak. This can account for the observed difference in the estimation of the magnetization between the two techniques. The type of noncollinear magnetic ordering reported here is similar to those observed in Ni2In-type MnXZ intermetallic ternary compounds, where X is a metallic transition element and Z is a main group element,18,19 and appears due to competing AF and FM exchange interactions.20 

Ultimately, from our analysis, we found a Mn spin canting angle of 20° ± 0.9° away from the c-axis at 2 K. The resulting refined magnetic structure of the h-MnPtGa films at 2 K is shown in Fig. 3(f).

In summary, we have studied the structural and magnetic properties of (0001)-oriented high-quality 60 nm epitaxial h-MnPtGa films. Magnetic measurements reveal that centrosymmetric h-MnPtGa films exhibit PMA with a TC (263 K) close to room temperature and a thermally induced spin reorientation transition at Tsr = 160 K. We further examine the onset of the noncollinear magnetic order using single-crystal neutron diffraction and demonstrate the remarkable applicability of the latter technique to epitaxial thin films. We find a transition from the FM state to a canted AF state below Tsr, with the Mn moments tilting away from the c-axis upon cooling. The spin-canted state in h-MnPtGa opens up the possibility of realizing the recently predicted chiral Hall effect in canted FM and AF systems,21 allowing for further investigations of chiral magnetism, with the prospect of electrical detection and manipulation of noncollinear magnetic structures in epitaxial thin films. In addition, this noncollinear magnetic order in h-MnPtGa can be a forerunner of field-induced skyrmion lattices, similar to other centrosymmetric magnets.11,22,23

See the supplementary material for further details.

This work was supported by the Deutsche Forschungsgemeinschaft (DFG) under SPP 2137 (Project No. 403502666) and the European Union's Horizon 2020 research and innovation programme under FET-Proactive Grant Agreement No. 824123—“Skyrmion-Topological Insulator and Weyl Semimetal Technology” (SKYTOP). C.F. and D.S.I. also acknowledge the support from the DFG via Projects B05 and C03 of the Collaborative Research Center SFB 1143 (Project No. 247310070) at the TU Dresden and from the Würzburg-Dresden Cluster of Excellence on Complexity and Topology in Quantum Matter—ct.qmat (EXC 2147, Project No. 390858490). The neutron diffraction experiment at D10 was conducted under Proposal No. 5-54-366.24 

The authors have no conflict to disclose.

The data supporting the findings of this study are available from the corresponding authors upon reasonable request.

1.
K.
Manna
,
Y.
Sun
,
L.
Muechler
,
J.
Kübler
, and
C.
Felser
,
Nat. Rev. Mater.
3
,
244
(
2018
).
2.
O.
Meshcheriakova
,
S.
Chadov
,
A. K.
Nayak
,
U. K.
Rößler
,
J.
Kübler
,
G.
André
,
A. A.
Tsirlin
,
J.
Kiss
,
S.
Hausdorf
,
A.
Kalache
,
W.
Schnelle
,
M.
Nicklas
, and
C.
Felser
,
Phys. Rev. Lett.
113
,
087203
(
2014
).
3.
J.
Jena
,
R.
Stinshoff
,
R.
Saha
,
A. K.
Srivastava
,
T.
Ma
,
H.
Deniz
,
P.
Werner
,
C.
Felser
, and
S. S. P.
Parkin
,
Nano Lett.
20
,
59
(
2020
).
4.
P. K.
Sivakumar
,
B.
Göbel
,
E.
Lesne
,
A.
Markou
,
J.
Gidugu
,
J. M.
Taylor
,
H.
Deniz
,
J.
Jena
,
C.
Felser
,
I.
Mertig
, and
S. S. P.
Parkin
,
ACS Nano
14
,
13463
(
2020
).
5.
A. K.
Sharma
,
J.
Jena
,
K. G.
Rana
,
A.
Markou
,
H. L.
Meyerheim
,
K.
Mohseni
,
A. K.
Srivastava
,
I.
Kostanoskiy
,
C.
Felser
, and
S. S. P.
Parkin
,
Adv. Mater.
33
,
e2101323
(
2021
).
6.
A. K.
Nayak
,
V.
Kumar
,
T.
Ma
,
P.
Werner
,
E.
Pippel
,
R.
Sahoo
,
F.
Damay
,
U. K.
Rößler
,
C.
Felser
, and
S. S. P.
Parkin
,
Nature
548
,
561
(
2017
).
7.
J.
Jena
,
B.
Göbel
,
T.
Ma
,
V.
Kumar
,
R.
Saha
,
I.
Mertig
,
C.
Felser
, and
S. S. P.
Parkin
,
Nat. Commun.
11
,
1115
(
2020
).
8.
P.
Swekis
,
A.
Markou
,
D.
Kriegner
,
J.
Gayles
,
R.
Schlitz
,
W.
Schnelle
,
S. T. B.
Goennenwein
, and
C.
Felser
,
Phys. Rev. Mater.
3
,
013001
(
2019
).
9.
P.
Swekis
,
J.
Gayles
,
D.
Kriegner
,
G. H.
Fecher
,
Y.
Sun
,
S. T. B.
Goennenwein
,
C.
Felser
, and
A.
Markou
,
ACS Appl. Electron. Mater.
3
,
1323
(
2021
).
10.
Y.
Li
,
B.
Ding
,
X.
Wang
,
H.
Zhang
,
W.
Wang
, and
Z.
Liu
,
Appl. Phys. Lett.
113
,
062406
(
2018
).
11.
W.
Wang
,
Y.
Zhang
,
G.
Xu
,
L.
Peng
,
B.
Ding
,
Y.
Wang
,
Z.
Hou
,
X.
Zhang
,
X.
Li
,
E.
Liu
,
S.
Wang
,
J.
Cai
,
F.
Wang
,
J.
Li
,
F.
Hu
,
G.
Wu
,
B.
Shen
, and
X. X.
Zhang
,
Adv. Mater.
28
,
6887
(
2016
).
12.
A. K.
Srivastava
,
P.
Devi
,
A. K.
Sharma
,
T.
Ma
,
H.
Deniz
,
H. L.
Meyerheim
,
C.
Felser
, and
S. S. P.
Parkin
,
Adv. Mater.
32
,
e1904327
(
2020
).
13.
K. H. J.
Buschow
and
P. G.
van Engen
,
Phys. Stat. Sol. A
76
,
615
(
1983
).
14.
K. H. J.
Buschow
and
D. B.
De Mooij
,
J. Less Common Met.
99
,
125
(
1984
).
15.
J. A.
Cooley
,
J. D.
Bocarsly
,
E. C.
Schueller
,
E. E.
Levin
,
E. E.
Rodriguez
,
A.
Huq
,
S. H.
Lapidus
,
S. D.
Wilson
, and
R.
Seshadri
,
Phys. Rev. Mater.
4
,
044405
(
2020
).
16.
M.
Björck
and
G.
Andersson
,
J. Appl. Crystallogr.
40
,
1174
(
2007
).
17.
J.
Rodríguez-Carvajal
,
Physica B
192
,
55
(
1993
).
18.
W.
Bażela
,
A.
Szytuła
, and
W.
Zając
,
Solid State Commun.
38
,
875
(
1981
).
19.
H.
Shiraishi
,
T.
Hori
,
N.
Ohkubo
,
K.
Ohoyama
, and
Y.
Yamaguchi
,
J. Appl. Phys.
93
,
6996
(
2003
).
20.
Y.
Youa
,
G.
Xua
,
J.
Tanga
,
Y.
Gonga
, and
F.
Xu
,
Intermetallics
106
,
88
(
2019
).
21.
J.
Kipp
,
K.
Samanta
,
F. R.
Lux
,
M.
Merte
,
D.
Go
,
J.
Hanke
,
M.
Redies
,
F.
Freimuth
,
S.
Blügel
,
M.
Ležaić
, and
Y.
Mokrousov
,
Commun. Phys.
4
,
99
(
2021
).
22.
N. D.
Khanh
,
T.
Nakajima
,
X.
Yu
,
S.
Gao
,
K.
Shibata
,
M.
Hirschberger
,
Y.
Yamasaki
,
H.
Sagayama
,
H.
Nakao
,
L.
Peng
,
K.
Nakajima
,
R.
Takagi
,
T. H.
Arima
,
Y.
Tokura
, and
S.
Seki
,
Nat. Nanotechnol.
15
,
444
(
2020
).
23.
S.
Hayami
and
Y.
Motome
,
Phys. Rev. B
103
,
024439
(
2021
).
24.
R.
Ibarra
,
D.
Inosov
,
B.
Ouladdiaf
, and
A.
Sukhanov
, “
Noncollinear magnetic structure in metallic PtMnGa
,”
Institut Laue-Langevin (ILL) Data
(
2021
).

Supplementary Material