Crystal and magnetic structure of antiferromagnetic Mn₂PtPd

Antiferromagnets (AFMs) are special among magnetic materials as they display magnetic ordering but with zero magnetic moment. Their practical use has been established in many fields especially in spintronics, for instance as pinning layers in giant magnetoresistance (GMR) and tunnel magnetoresistance (TMR) devices [1–13]. Here, the AFM acts as a passive component. The absence of stray fields is a great advantage of AFMs over ferromagnets and thus AFMs may even replace ferromagnets as an active component in spintronic devices. However, it is difficult to manipulate the AFMs due to their vanishing magnetic moment. Recent advances in controlling the antiferromagnetic configurations by electrical switching bear a good prospect for a new era of applications [14]. In addition, high ordering temperatures and large magneto-crystalline anisotropy are desired to enhance the scope for more universal use.

Heusler alloys X₂YZ are a particularly promising class of materials for the search of new AFMs for applications due to their great variability in chemical composition and properties [15–20]. In this regard the recently reported phase Mn₂PtPd is of interest, which was identified in a high throughput computational study by Sanvito et al [21] as a potential new ferromagnetic cubic Heusler alloy. Its subsequent experimental realization, however, rather suggested this material to be a tetragonal antiferromagnetic Heusler compound having space group I4/mmm (TiAl₃-type) with lattice constants a  =  4.03 Å and c  =  7.24 Å [21]. A TiAl₃-type structure would imply ordering of Pt and Pd atoms. A magnetic transition near 320 K was reported [21], but details on the magnetic behaviour are unknown yet. On the other hand, several Mn based binary alloys MnTM with various transition metals TM like Ni, Pt, Pd, Rh, Ir have been reported which are AFMs having high Néel temperatures and the crystal symmetry P4/mmm (L1₀, CuAu-I type) [22–32]. Binary alloys having cubic (B2, CsCl-type) and tetragonal (L1₀, CuAu-I type) structures are the building blocks to design Heusler materials [33]. Combining two binary alloys XY and XZ belonging to the B2 structure results in a regular Heusler (L2₁, Cu₂MnAl-type) structure, given the condition that Y and Z atoms order, whereas a tetragonal Heusler (TiAl₃-type) compound is expected in the case of combining two L1₀ structures. However, ternary alloys X₂YZ adapt the same structure as their binary precursor if there is a complete disorder of Y and Z atoms. Hence, taking into account the chemical similarity between Pd and Pt atoms, Mn₂PtPd could also be considered as a CuAu-I type phase MnPt_0.5Pd_0.5 with a disordered arrangement of Pt and Pd atoms. In this paper we report our powder x-ray and neutron diffraction studies on Mn₂PtPd as well as magnetization and electrical transport measurements. We will show that Mn₂PtPd is a CuAu-I type antiferromagnet with a Néel temperature T_N  =  866(5) K.

A polycrystalline ingot of Mn₂PtPd was prepared by arc melting stoichiometric amounts of constituent elements in the presence of high purity Ar atmosphere. About 2.5 wt % of extra Mn was used to compensate the weight loss due to the evaporation of Mn during the melting. The sample was ground and characterized at room temperature by powder x-ray diffraction (XRD) using a Huber G670 camera (Guinier technique, λ  =  1.540 56 Å (Cu−Kα₁ radiation)). Field and temperature dependent magnetization measurements were performed using a vibrating sample magnetometer (MPMS3, Quantum Design). Temperature dependent magnetization M(T) measurements were carried out from 2 to 400 K in zero field cooled (ZFC) and field cooled (FC) modes. High temperature magnetization measurements were performed during heating and cooling from 300 to 1000 K using the oven option of the MPMS3. The electrical transport properties were investigated using a physical property measurement system (PPMS, Quantum Design). The Hall measurements were performed on a rectangular bar using a five probe geometry at different temperatures from 2 K to 300 K in fields up to 5 T. For the neutron diffraction study, the sample was powdered by grinding followed by annealing at 773 K in an evacuated quartz tube for 24 h. Neutron powder diffraction experiments were carried out on the instrument E6 at the BER II reactor of the Helmholtz-Zentrum Berlin. This instrument uses a pyrolytic graphite (PG) monochromator selecting the neutron wavelength λ  =  2.42 Å. In order to investigate in detail the crystal structure of Mn₂PtPd a powder pattern was collected at 1012 K, well above the magnetic ordering temperature of T_N  =  866 K. The sample was heated up in a quartz ampoule using a high-temperature furnace (AS Scientific Products Ltd., Abingdon, GB). The temperature dependence of the crystal and magnetic structure was investigated between 296 and 1012 K, where 18 and 6 patterns were collected below and above T_N, respectively. Neutron powder patterns were recorded between the diffraction angles (2θ) 5.5 and 136.5°. Rietveld refinements of the powder diffraction data were carried out with the program FullProf [34], using the nuclear scattering lengths b(Mn)  =  −3.73 fm, b(Pd)  =  5.91 fm, and b(Pt)  =  9.63 fm [35]. The magnetic form factor of the Mn atoms was taken from [36].

The phase purity of the sample was examined by powder x-ray diffraction as shown in figure 1. To determine the crystal structure, calculated XRD patterns for both structure models P4/mmm (CuAu-I type with a  =  2.86 Å and c  =  3.61 Å) and I4/mmm (TiAl₃-type with a  =  4.04 Å and c  =  7.23 Å) are shown in addition. The observed diffraction peaks match well with both models. In particular, the lattice parameters compare well with those reported by Sanvito et al [21] using space group I4/mmm (TiAl₃-type, a  =  4.03 Å and c  =  7.24 Å). However, the absence of some additional peaks in the experimental pattern which are present in the calculated I4/mmm pattern suggests that Pt and Pd are atomically disordered and thus Mn₂PtPd rather crystallizes in P4/mmm symmetry. Below we will show the detailed structural analysis using the powder neutron diffraction data.

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To determine the magnetic behaviour and the ordering temperature we have performed magnetization measurements as a function of temperature and field. Figure 2(a) shows the temperature dependence of the magnetization M(T) from 300 to 1000 K and in the inset from 2 to 400 K. For the high temperature M(T) measurements the sample was heated from room temperature to 1000 K and then cooled down to room temperature again in the presence of a magnetic field of 0.1 T. The broad maximum in the M(T) curve indicates that the sample undergoes an antiferromagnetic ordering transition with a Néel temperature (T_N) of about 870 K. The observed T_N for Mn₂PtPd is close to the average of the T_N values of 780 and 970 K which were reported for the binary AFMs MnPd and MnPt, respectively [25, 26, 29–31]. This is further support that Mn₂PtPd rather is a CuAu-I type than a TiAl₃-type AFM material. For obtaining low temperature M(T) data, the sample was cooled down to 2 K and measurements were carried out in the zero field cooled (ZFC) and field cooled (FC) modes from 2 to 400 K at 0.1 T. Both ZFC and FC magnetization curves followed the same path. In contrast to [21] we did not observe any indication for a magnetic transition near 320 K. At temperatures below 100 K an up-turn in the magnetization is apparent. A similar behaviour has been reported for MnPt alloys due to a very small deviation from the equiatomic composition [26]. Therefore, a small amount of off-stoichiometry in the sample could be the reason for this kind of behaviour and also for the irreversibility in the magnetization being observed at 470 K on cooling (figure 2(a)). In figure 2(b) magnetic isotherms M(H) are shown at different temperatures. The linear increase of M with H is in agreement with the anticipated AFM order. There are no indications for a hysteresis or spontaneous magnetization.

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The crystal structure of Mn₂PtPd was refined from a powder neutron diffraction data set collected at 1012 K (figure 3(a)), which is above the magnetic ordering temperature of T_N  =  866 K. The refinements were carried out in the tetragonal space groups P4/mmm (No. 123) and I4/mmm (No. 139), respectively. In the space group P4/mmm the Mn atoms are located at the Wyckoff position 1d(½,½,½), while the Pd and Pt atoms are statistically distributed at the position 1a(0,0,0). The refinement resulted in a satisfactory residual R_F  =  0.0178. In the space group I4/mmm the unit cell is enlarged with the dimensions a  √2  ×  a  √2  ×  2c. In this setting the Mn atoms occupy the position 4d(0,½,¼), while the Pd and Pt occupy different atomic sites located at the positions 2a(0,0,0) and 2b(0,0,½) or vice versa. The refinement resulted exactly in the same residual for both settings, but the obtained residual of R_F  =  0.0357 is considerably enlarged compared to the refinement in P4/mmm. This can be ascribed to the fact that a segregation of the Pt and Pd atoms clearly leads to an emergence of the Bragg reflections 101, 103, and 213 (½ ½ 1½, ½ ½ 1½, and 1½ ½ 1½ in the setting of P4/mmm). Due to the fact that these reflections do not exist the Pd and Pt atoms are statistically distributed at both positions 2a and 2b. Considering the fact that no intensity was detected at these particular reflections we conclude that the crystal structure of Mn₂PtPd can be well described in the space group P4/mmm having the smaller unit cell. The results of the Rietveld refinements are summarized in table 1.

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In the neutron powder patterns collected at 296 K (figure 3(b)) two strong magnetic reflections were observed at the 2θ positions 34.8 and 53.4°. This can be ascribed to a long-range magnetic ordering of the Mn moments. These reflections could be indexed as (½ ½ 0)_M and (½ ½ 1)_M using the smaller unit cell (crystal structure type with space group P4/mmm) as described above. These two reflections can be generated by the rule (hkl)_M  =  (hkl)_N  ±  k, where the propagation vector is k  =  (½,½,0). This suggests that the magnetic unit cell parameters are doubled along the a and b axes. In this type of magnetic ordering the magnetic moments of the Mn atoms are antiferromagnetically coupled along the a and b axes with the spin sequence  +− +−.... From a symmetry analysis using the program BASIREP of the FullProf suite [34] one obtains two irreducible representations, which describe a spin structure, where the moments are either aligned parallel to the tetragonal c axis or aligned within the ab plane, respectively. Our Rietveld refinements clearly show that the Mn moments are aligned within the tetragonal ab plane, resulting in a residual R_M  =  0.0214, where the intensity ratio of the first two magnetic reflections is I(½ ½ 0)_M/I(½ ½ 1)_M  =  1.0. Assuming a spin alignment parallel to the c axis one obtains a considerably enlarged ratio of 3.3. In our refinements we further assumed the magnetic moments to be aligned parallel to the directions [1 1 0] or [1 0 0]. For these two models we practically obtained the same residuals, which shows that we are not able to determine the moment direction within the tetragonal ab plane. It has been reported that MnPt exhibits two different magnetic structures [30]. At high temperatures above 750 K, the Mn moment lies in the basal plane whereas it undergoes a spin-flip transition in a broad temperature region ranging from 750 to 570 K, leading to a magnetic structure with Mn moments aligned parallel to the tetragonal c axis. By contrast, MnPd exhibits only the magnetic structure with the moments lying in the ab plane.

The same spin structure is also adopted by Mn₂PtPd throughout the whole temperature range. There are no indications for a spin-flip transition. It is noted that we did not observe any significant change in the magnetic configuration below 470 K which indicates that the irreversibility in the M(T) curve (figure 2(a)) is rather related to off-stoichiometry or defects than being an intrinsic bulk property.

The determined moment value at 296 K is µ_exp(Mn)  =  4.09(10) µ_B, which is similar as for many other magnetic intermetallic alloys containing Mn [24–26, 29, 31, 37]. The temperature dependence of the magnetic moment of the Mn atom was investigated in the temperature range from 296 to 1012 K. In figure 4(a) it is seen that the saturation of the magnetic moments is almost reached at 296 K. The magnetic order disappears at the Néel temperature T_N  =  866(5) K. The lattice parameters, the c/a ratio, and the volume of the unit cell are displayed in figures 4(b) and (c) respectively. The lattice parameters at 296 K are a  =  2.86 Å and c  =  3.62 Å. Interestingly, the Rietveld refinements of the powder patterns revealed a strong change of the lattice parameters near the Néel temperature, which results in a pronounced increase of the tetragonal distortion as reflected in the c/a ratio. This is ascribed to the fact that the apical bond length d_a(Mn–Mn) is strongly elongated below T_N, whereas the equatorial bond length d_e(Mn–Mn) is shortened (see table 1). A similar strong magneto-elastic coupling on going from the paramagnetic to the AFM phase was observed for MnPd and the lattice anomaly was attributed to deformation sensitive nearest neighbour Mn–Mn interactions [29]. On the other hand, the cell volume is continuously decreasing to lower temperatures without pronounced anomalies near the Néel temperature.

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Figure 5(a) shows the electrical resistivity as a function of temperature from 2 K to room temperature. The sample exhibits metallic behaviour and has resistivity values of the same order of magnitude (10⁻⁵ Ω cm) as those of MnPt [26] and MnPd alloys [25]. We measured the Hall resistivity ρ_H at different temperatures between 2 and 300 K as shown in figure 5(b). The straight line behaviour of the Hall resistivity with the applied field is expected for the collinear AFM structure which shows a normal Hall effect. Anomalous Hall effects scaling with the magnetization are only found for ferromagnets or peculiar types of non-collinear antiferromagnets [38]. The calculated carrier concentration from Hall measurements is shown in the inset of figure 5(b). The carrier concentration is given by the equation $n={{\mu }_{0}}H/e{{\rho }_{H}}$, where µ₀ is the vacuum permeability, H is the applied field and e is the elementary charge. The carrier concentration is of the order of 10²¹ cm⁻³. The Hall resistivity decreases and carrier concentration increases with increase in temperature.

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We found that Mn₂PtPd adopts the L1₀ (CuAu-I)-type crystal structure similar to MnPt and MnPd binary alloys. As for MnPd the magnetic moments of the Mn atoms (~4 µ_B) are antiferromagnetically coupled in the ab-plane without evidence for a spin-flip transition. Mn₂PtPd has an ordering temperature T_N  =  866 K which is the average of the ordering temperatures of MnPd and MnPt. A pronounced change in the lattice parameters near T_N shows strong magneto-elastic coupling. We observe that Mn₂PtPd has metallic characteristics analogous to MnPt and MnPd.

This work was financially supported by the ERC Advanced Grant 'TOPMAT' (No. 742068). We thank Walter Schnelle and Ralf Koban for the high temperature magnetization measurements and Horst Borrmann for XRD measurements.