Room temperature ferromagnetism in the nanolaminated MAX phase (Mn_1−xCr_x)₂GaC Open Access

Layered materials show a richness of properties, brought about by confinement, broken symmetry at interfaces, and interlayer interactions. Artificial multilayer and superlattice structures have been engineered for decades to exploit these effects, and, more recently, layered van der Waals crystals have appeared on the scene. MAX phases are a family of inherently laminated materials on the nanoscale, composed of a transition metal (M), an A-group element (A), and either carbon or nitrogen (X) with the chemical formula M_n+1AX_n (n = 1, 2, 3).¹ The structure is hexagonal, and for n = 1, the elements naturally arrange in distinct atomic layers with the order M–A–M–X–M–A–M–X in the c-axis direction. The M–A bonds are metallic-like, whereas the M–X bonds are covalent, resulting in a highly anisotropic structure with mechanical properties combining many of the salient features of both metals and ceramics.² Furthermore, the A-layers can, in some cases, be selectively etched to produce 2D M–X–M lamellae collectively known as MXenes.^3,4 Theoretical models predict that the laminated structure should result in anisotropic optical, electrical, and magnetic properties, but demonstrating such effects experimentally requires highly oriented single crystal samples and is, therefore, a formidable task. Nonetheless, MAX phases have shown promise in a wide range of contexts, for example as damage tolerant structural materials⁵ and for spintronics.⁶ 

The interest in low-dimensional magnetism^7–9 has fueled the search for new MAX phases exhibiting magnetic order. Only a handful of such phases have been discovered, with magnetic elements in the form of Mn, Cr, or Fe on the M-site^6,10–20 or Mn, Fe, Co, and/or Ni on the A-site.^21–23 In magnetic MAX phases, the anisotropic layered structure gives rise to competing magnetic interactions within the M–X–M trilayers and across the A layers, resulting in complex magnetic ordering. As an example, the most studied of these phases is Mn₂GaC, which exhibits non-collinear magnetic ordering with a sizable remanent magnetization below 210 K, where it undergoes a magnetic phase transition to antiferromagnetic ordering.¹¹ The delicate balance between the two magnetic states means that a metamagnetic transition from the antiferromagnetic to the non-collinear state can be induced above 210 K by applying a magnetic field. In addition, it has recently been shown that Mn₂GaC has a magneto-crystalline anisotropy, with the magnetization preferably lying parallel to the Mn–C–Mn planes.^17,24 In another magnetic MAX phase group, V₂(Sn, A)C with (A = Fe, Co, Ni, and Mn), a small remanent magnetization is observed at 2 K, but no remanence is seen at room temperature.²² Similar results have been obtained for (Cr_0.75Mn_0.25)₂GeC and $(Mo0.5Mn0.5)2$GaC.^10,12 However, no MAX phase has yet been demonstrated to be ferromagnetic with a significant magnetic moment at room temperature. This has prevented their use in practical applications as bulk magnets or in spintronic devices.

Here, we show that a MAX phase in a previously unexplored composition range, $(Mn1−xCrx)2$GaC with x < 0.3, is strongly ferromagnetic up to temperatures far exceeding room temperature. We use first-principles calculations to predict over which range of compositions, ferromagnetism is expected to be the most stable magnetic configuration. We then synthesize these compositions as epitaxial thin films and demonstrate a strong ferromagnetic response. The result is the first MAX phase, which can be used as a magnet in room temperature applications, with great scope for further tuning of its magnetic properties.

First-principles calculations based on density functional theory were carried out to determine the stability of $(Mn1−xCrx)2$GaC with 0 ≤ x ≤ 1. Different magnetic configurations were taken into account in the stability calculations to determine the most likely magnetic ordering. The configurations considered were paramagnetic (PM), ferromagnetic (FM), and several antiferromagnetic (AFM) arrangements, i.e., multilayered AFM ordering of α consecutive M layers (where α = 2, 4) with the same spin direction before changing sign upon crossing an A layer (AFM$[0001]2A$ and AFM$[0001]4A$⁠) and antiparallel spins within one M layer (in-AFM1). These magnetic configurations are schematically shown in Fig. 1. Since we are interested in the stability upon substituting Mn by Cr in $(Mn1−xCrx)2$GaC, the identified set of most competing phases for 0 < x < 1 is a linear combination of Mn₂GaC and Cr₂GaC. The corresponding isostructural formation enthalpies ΔH_iso are calculated with Eq. (1) (see Sec. V). Figure 1 shows ΔH_iso (at 0 K) and isostructural Gibbs free energy of formation, ΔG_iso (estimated at 1000 K with the addition of configuration entropy), for the entire composition range. Since the focus is on the quaternary system with a disorder of Mn and Cr on the M site and the synthesis of MAX phases is performed at elevated temperature, ΔG_iso is the more relevant parameter in terms of stability.

$(Mn1−xCrx)2$GaC is found to be stable for all x, but with different spin configurations giving the lowest energy for different values of x. The in-AFM1 configuration is of lowest energy in the Cr-rich region, i.e., for x > 0.6. For Mn-rich conditions, FM is favored but with AFM$[0001]4A$ close in energy. For pure Mn₂GaC, AFM$[0001]4A$ is the lowest energy spin configuration. Both Mn₂GaC and Cr₂GaC have been synthesized before and found to be thermodynamically stable.^16,25–27 Mn₂GaC has experimentally been shown to be in an AFM$[0001]4A$-like magnetic configuration at room temperature,^11,17 whereas Cr₂GaC is thought to be paramagnetic.²⁸ Some compositions of the $(Mn1−xCrx)2$GaC solid solution have also been previously synthesized both as thin films^11,13,16,27 (x = 0.5) and in bulk (x ≥ 0.7),^15,25,29,30 as shown by the orange diamonds in Fig. 1(a). These compositions have been found to be weakly ferro- or ferrimagnetic at well below room temperature. However, the composition range of 0 < x < 0.5, where our calculations show that the FM configuration is lowest in energy, has hitherto not been studied.

$(Mn1−xCrx)2$GaC films were synthesized by DC magnetron sputtering as described in Sec. V and found to have x in the range 0.00–0.29 by energy dispersive x-ray spectroscopy (EDX) measurements. Figure 2(a) shows the XRD overview scans of the sample series. The characteristic MAX phase (000l) basal plane peaks are seen in all the samples, and there are no detectable competing phases present. In addition to the (000l) peaks, we observe peaks corresponding to the $(101̄3)$ and $(202̄6)$ planes, showing that the films have two distinct growth orientations. The $(101̄3)$ plane has a tilt of 59° with respect to the (0006) plane, and this is, therefore, referred to as the tilted phase. From the known difference in the relative intensity of the $(101̄3)$ and (0006) peaks in Mn₂GaC (100% and 18%, respectively), we estimate that the films have between 49% and 71% of $(101̄3)$ oriented grains parallel to the substrate plane (see the supplementary material for details). This tilted growth has previously been seen in pure Mn₂GaC grown on MgO(111) substrates,¹⁷ as well as in other epitaxial MAX phase films.³¹ 

The inset of Fig. 2(a) highlights the $(101̄3)$ and (0006) peaks, showing the progression as the Cr content is increased. The peaks broaden with increasing Cr content, indicating a reduction in crystallite size. From these XRD scans, the a and c lattice parameters were extracted from the $(101̄3)$ and (0006) peak positions (see the supplementary material), which allows us to quantify the changes in unit cell volume upon substituting Mn by Cr.

Figure 2(b) shows a pole figure of the $(101̄3)$ peak in the x = 0.12 film. This figure is representative of all the films in the sample series, as all of them show the same features. There is a large peak in the center from the grains with the $(101̄3)$ planes parallel to the film plane and a set of sixfold symmetric discrete peaks at χ = 59°. This shows the epitaxial nature of the film, albeit with mixed crystal orientations. The additional satellite peaks are due to twinning and have previously been seen in the pure Mn₂GaC phase.¹⁷ This behavior is observed when two growth orientations coexist, with both (000l) and $(101̄3)$ oriented grains in the plane of the film.

To investigate the local film structure and elemental composition, the film with x = 0.22 was characterized using transmission electron microscopy (TEM). Figures 3(a)–3(e) show a high-angular annular dark field scanning TEM (HAADF-STEM) image with the corresponding elemental maps obtained by energy-dispersive x-ray spectroscopy (EDX). The maps show a uniform distribution of Mn and Cr and no phase segregation. This, together with the shift in the x-ray diffraction peaks, strongly indicates that the Cr is substituting the Mn uniformly throughout the film and is not forming a secondary phase. High-resolution HAADF-STEM images with increasing magnification are shown in Figs. 3(f)–3(h). The lowest magnification shows the presence of multiple grains, and the two distinct $(101̄3)$ and (0006) orientations of the grains are clearly visible at intermediate magnification. At high magnification, the laminated MAX phase structure within the crystal grains is apparent.

Figure 4(a) shows the magnetic hysteresis measurements performed at 300 K, with the MgO background subtracted (for details of this procedure, see Sec. V and Ref. 17). The diamagnetic and paramagnetic signals have also been removed. All the Cr containing films exhibit a strong ferromagnetic (FM) response at room temperature, as evidenced by the clear remanent magnetization, a coercivity, and S-shaped hysteresis loops. This behavior is qualitatively the same in the temperature range studied (see below). This is in stark contrast to the pure Mn₂GaC film, which undergoes a transition from a non-collinear magnetic state to an antiferromagnetic state at around 210 K. In the AFM state, it exhibits a metamagnetic transition that moves to higher fields as the temperature is increased. This can be seen in the 300 K data in Fig. 4(a) at 2.5 T (blue curve).

The remanent magnetization of the films, M_r, is shown in Fig. 4(b) as a function of temperature. The samples with x = 0.00 and x = 0.06 have an unusual temperature dependence, with the non-collinear to AFM transition being evident in the pure Mn₂GaC sample starting at 210 K. For samples with 0.12 ≤ x ≤ 0.29, a typical FM temperature dependence is seen, with a gradual decrease in the remanent magnetization with increasing temperature. Interestingly, the remanent magnetization peaks for x = 0.12 and then decreases as the Cr content is increased further. This is also the case for the saturation magnetization M_5 T (at 5 T), which can be seen in the supplementary material. There is a sharp increase in remanence between x = 0.06 and 0.12 before it slowly decreases as more Cr is added. The magnetization of $(Mn1−xCrx)2$GaC with x = 0.12 is the strongest of the series, reaching a saturation magnetization of 1.25 μ_B/M-atom at 3 K and maintaining 0.90 μ_B/M-atom at 300 K. Similarly, it has the largest remanent magnetization of 0.67 μ_B/M-atom at 3 K and 0.44 μ_B/M-atom at 300 K. Here, M in μ_B/M-atom refers to the sum of Mn and Cr located at the M sites of the MAX phase (M₂AX).

Figure 5 shows the critical temperature T_c, the magnetization at 5 T and remanence together with the measured change in lattice parameters and unit cell volume, all as a function of Cr content. The critical temperature is defined as the temperature where the remanent magnetization is reduced to zero (also known as the Curie temperature in a ferromagnetic material) and can be considered a measure of the (mean) magnetic interaction strength J. The critical temperature peaks for x = 0.12 at 489 K (216 °C), which is also the composition having the largest magnetization. The resistivity follows a similar but opposite trend, as shown in the supplementary material, with a minimum of ∼360 μΩ cm in the range 0.06 ≤ x ≤ 0.12. There is a clear correlation between T_c, the magnetization, and the change in unit cell volume. As x is increased, the volume reaches a minimum at x = 0.12 due to a contraction in both a and c. With further increasing x, the c lattice parameter expands. The resulting minimum in volume is accompanied by a maximum in T_c and magnetization.

The spin-dependent stability calculations are in remarkably good agreement with the experimental results. The calculations predict phase stability over the entire range of 0 ≤ x ≤ 1, which is confirmed by the thin film synthesis (presented here and elsewhere). Furthermore, theory suggests that ferromagnetic ordering of the M-site moments is the most stable configuration in the range 0.06 < x ≤ 0.50. Our magnetic characterization shows that films with 0.06 < x ≤ 0.29 are, indeed, strongly ferromagnetic. However, it should be noted that we cannot rule out that the ferromagnetic response observed experimentally is non-collinear in nature. At x = 0.06, there are clear signs of competing interactions, which result in a magnetic response that is neither clearly ferromagnetic nor antiferromagnetic. This is consistent with the calculations that show that the FM and AFM$[0001]4A$ configurations are close to degenerate for this composition. For Cr content below 6 at. % or above 50 at. %, the AFM configurations are the lowest in energy. However, the closeness of the different configurations can explain why metamagnetic transitions and non-collinear magnetic order and/or very low critical temperatures are observed in these cases.

It has previously been shown for Mn₂GaC that the magnetization is sensitive to a change in the lattice parameters^6,24 and that the magnetic transition from AFM- to FM-like ordering coincides with a contraction in the c lattice parameter. The calculations show that in the $(Mn1−xCrx)2$GaC system, the FM configuration has the smallest c lattice parameter (see the supplementary material). The experimental data are in partial agreement with these results although we observe a maximum in the critical temperature and magnetization where there is a minimum in the film volume rather than in the c lattice parameter. In the case of epitaxial thin films, the a lattice parameter is constrained due to the bonding with the substrate, as shown in Fig. 5. This results in anisotropic strain, which counteracts the contraction of the c lattice parameter, and this may explain the discrepancy between theory and experiments. However, the general trends observed in the lattice parameters are qualitatively consistent with theory. This implies that strain engineering may be a feasible way to control the strength of the FM interaction, thus allowing us to tune the critical temperature and magnetization, as previously suggested by Dahlqvist and Rosen.²⁴ The large number of isostructural MAX phases with similar lattice parameters, which could be combined in epitaxial heterostructures, makes this a highly appealing prospect.

Phase pure thin films of $(Mn1−xCrx)2$GaC were synthesized in the range from x = 0.00 to x = 0.29 on MgO(111) substrates, and their structural and magnetic properties were characterized. Partial substitution of Mn with Cr on the M-site results in a MAX phase, which is strongly ferromagnetic at room temperature. Its saturation magnetization of 1.25 μ_B/M-atom at 3 K is almost 35 times larger than the previously reported magnetization of the (V, Mn)₃GaC₂ MAX phase (0.036 μ_B/M-atom at 100 K and 0.026 μ_B/M-atom at 300 K).³² To put this into context, the magnetic moment of Fe and Ni at 0 K is 2.22 and 0.61 μ_B/atom, respectively, giving a magnetization of 1745 kA/m for Fe and 521 kA/m for Ni at 0 K. The magnetization of (Mn_0.88Cr_0.12)₂GaC is 516 kA/m at 3 K, making it comparable to Ni at low temperatures, but the magnetization falls off faster as the temperature is increased due to a lower critical temperature of 489 K vs 627 K for Ni. The ferromagnetic response is associated with a contraction in the unit cell volume, suggesting that the magnetization might be even further enhanced with strain engineering using different substrates and/or MAX-phase heterostructures. In addition, (Mn_0.88Cr_0.12)₂GaC is significantly lighter than Fe and Ni, which means that its mass magnetization values compare even more favorably with those of typical magnetic metal alloys, such as transformer steel. Furthermore, the inherently laminated structure results in high resistivity values of ∼360 μΩ cm, which is, for example, important for reducing eddy currents in transformer core applications. These magnetic properties, combined with the mechanical advantages of the MAX phase structure, make this material a serious contender for bulk magnets in power electronics.

The $(Mn1−xCrx)2$GaC films were grown by direct current magnetron sputtering (dcMS) on 1 × 1 cm² MgO(111) substrates from a 7.5 cm diameter 99.9% pure Mn target, a 7.5 cm 99.99% C target, a 5.0 cm 99.95% Cr target, and a liquid Ga target made from 99.9999% Ga pellets in a specially made 5.0 cm crucible. During sputtering, the Ga target was maintained in liquid form. The working gas was 99.999% purity argon at a flow rate of 20 sccm, and a throttle valve was used to adjust the growth pressure to 0.40 Pa. The vacuum chamber used has a base pressure of $<5×10−7$ Pa; however, at the growth temperature of 550 °C, the base pressure rose to 2 × 10⁻⁶ Pa after preheating the substrate for 60 min. For the duration of the growth, the sample holder was rotated by ±360° at a rate of 12 revolutions per minute. These growth conditions are the same as in a previous study of Mn₂GaC films;¹⁷ except here, Mn is partially substituted by Cr. This includes the growth temperature, pressure, and a slight excess of Ga, which diffuses to the surface of the films.

The Mn, Cr, and C targets were rate-calibrated to get the composition in the correct range prior to the growth of a series of $(Mn1−xCrx)2$GaC samples. The chemical composition was then determined by energy dispersive x-ray spectroscopy (EDX) in a Zeiss Supra 25 electron microscope as x = 0.00, 0.06, 0.12, 0.22, and 0.29. It should be noted that the C and Ga content cannot be measured with any certainty because C content is not reliably determined by EDX and the samples contain an excess of Ga on the surface. The thickness of the films was found to be 140 ± 4 nm from x-ray reflectivity (XRR) measurements.

The structural properties of the films were investigated by x-ray diffraction (XRD) and x-ray reflectivity (XRR) using a Panalytical Empyrean diffractometer in line focus mode. For diffraction, the incident side had a two-bounce hybrid monochromator with 1/8° divergence slit; on the diffracted side was a PIXcel^3D detector operating in 1D mode.

Scanning transmission electron microscopy (STEM) imaging and energy dispersive x-ray spectroscopy (EDX) were performed in the Linköping double-corrected, monochromated, high-brightness, FEI Titan³, equipped with a Super-X EDX detector and operated at 300 kV. The specimen for TEM examination was prepared by mechanical grinding followed by Ar⁺-ion milling using a Gatan Precision Ion Polishing System.

The magnetic properties were measured using vibrating sample magnetometry (VSM) in the temperature range from 3 to 300 K in a 5 T cryogen free magnet system from Cryogenic and in the range from 300 to 750 K in a Lake Shore 8600 system with a single stage variable temperature option and a 2 T electromagnet. The magnetization was calculated by dividing the measured moment by the film volume, and to convert to units of Bohr magnetons, we used the measured unit cell volume, which contains four M atoms. The temperature dependence of the magnetization and the remanent magnetization were determined by performing full hysteresis loops at each temperature. The MgO background signal was removed by measuring full hysteresis loops on a bare substrate for temperatures $≤300$ K. To join together measurements from both systems, a linear fit of data above ±4.5 T for the cryogenic system and ±1.5 T for the Lake Shore system was performed to remove dia- and paramagnetic effects. This mainly affects x = 0.00, which might not be fully saturated at 5 T, as well as x = 0.06, which has some paramagnetic behavior.

The resistivity of the films was measured using a Jandel four-probe system with equally spaced probes arranged in a straight line geometry. Full current–voltage curves were recorded to ensure that good ohmic contacts were obtained and the resistivity calculated from the sheet resistance using the film thickness.

All first-principles calculations were performed by means of density functional theory (DFT) and the projector augmented wave method,^33,34 as implemented within the Vienna Ab initio Simulation Package (VASP) version 5.4.1.^35–37 We used the spin polarized generalized gradient approximation (GGA) as parameterized by Perdew–Burke–Ernzerhof (PBE) for treating the electron exchange and correlation effects.³⁸ We considered selected spin configurations based on results for Cr₂GaC and Mn₂GaC,^11,39 namely ferromagnetic (FM) and several antiferromagnetic (AFM) configurations; multilayered AFM ordering of α consecutive M layers (where α = 2, 4) with the same spin direction before changing sign upon crossing an A layer (AFM$[0001]2A$ and AFM$[0001]4A$⁠) and antiparallel spins within one M layer (in-AFM1). In addition, paramagnetism (PM) has been modeled using the disorder local moment (DLM)⁴⁰ approach where the spin-correlation functions are equal to zero for at least the first 10M-coordination shells. For Mn₂GaC, this corresponds to disordered magnetic moments in (Mn↑_0.5Mn$↓0.52$GaC being simulated by means of the special quasi-random structure (SQS) method⁴¹ using a supercell with 64 Mn, 32 Ga, and 32 C atoms, i.e., 4 × 4 × 1 or 16 M₂AX unit cells. For $(Mn1−xCrx)2$GaC, DLM was modeled using 4 × 4 × 2 unit cells with initial disordered Mn moments. The plane wave energy cutoff was set at 400 eV, with k-point grids with a spacing of 0.05 $Å−1$ according to the Monkhorst–Pack method.⁴² The total energy is minimized through the relaxation of the unit-cell shape and volume and internal atomic positions.

To model chemical disorder of Mn and Cr on the M sublattice for $(Cr1−xMnx)2$GaC, we used the SQS method⁴¹ with supercell sizes consisting of 2 × 2 × 2, 4 × 2 × 1, 4 × 3 × 1, 4 × 4 × 1, and 4 × 4 × 2 unit cells, i.e., 72–256 atoms per supercell. Convergence tests show that these supercells give a qualitatively accurate representation and a quantitative convergence in terms of calculated formation enthalpies and lattice parameters.

The supplementary material contains additional results from first-principles calculations, including lattice parameters (Fig. S1, Table S1) and magnetic moments (Fig. S2). It also includes measured lattice parameters and critical temperatures for the film series (Table S2), a wider area TEM elemental EDX map examining the chemical uniformity over larger length scales (Fig. S3), further magnetic measurements showing the saturation magnetization (Fig. S4) and coercive field (Fig. S5) as a function of temperature, and the measured resistivity of the films (Fig. S6).

This work was funded by the University of Iceland Research Fund and the Icelandic Research Fund (Grant Nos. 174271 and 217843). The authors acknowledge ARTEMI, the Swedish National Infrastructure in Advanced Electron Microscopy, supported by the Swedish Research Council and the Swedish Foundation for Strategic Research (Grant Nos. 2021-00171 and RIF21-0026). The calculations were carried out using supercomputer resources provided by the Swedish National Infrastructure for Computing (SNIC) at the National Supercomputer Center (NSC), partially funded by the Swedish Research Council through Grant Agreement No. 2018-05973. J.R. acknowledges the support from the Swedish Research Council (Grant No. 2019-04233) and the Göran Gustafsson Foundation for Research in Natural Sciences and Medicine.

The authors have no conflicts to disclose.

E. B. Thorsteinsson: Conceptualization (equal); Formal analysis (lead); Investigation (lead); Software (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (lead). M. Dahlqvist: Conceptualization (equal); Formal analysis (lead); Methodology (lead); Software (equal); Visualization (equal); Writing – review & editing (equal). A. Elsukova: Formal analysis (equal); Investigation (equal); Visualization (equal). A. Petruhins: Investigation (supporting). P. O. Å. Persson: Funding acquisition (equal); Writing – review & editing (equal). J. Rosen: Conceptualization (equal); Funding acquisition (equal); Writing – review & editing (equal). A. S. Ingason: Conceptualization (equal); Writing – review & editing (equal). F. Magnus: Conceptualization (equal); Funding acquisition (equal); Project administration (lead); Supervision (lead); Writing – original draft (equal); Writing – review & editing (lead).

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