Transport properties of Heusler compounds Fe_3-xMn_xSi (x = 1.6, 1.7 and 1.8) under magnetic fields

Heusler compounds are intermetallic compounds with the formula X₂YZ, where X and Y are transition elements, and Z is an sp element.¹ It is hoped that they will yield new types of functional materials such as half-metals or magnetic refrigeration materials. Half-metals in particular have attracted significant attention in view of their applications to spintronics.^1–3 Half-metals exhibit 100% spin polarization at the Fermi level, i.e., the density of states for the spin-up electrons is metallic, whereas that for the spin-down electrons is semiconducting. Fe₂MnSi is a Heusler compound and was predicted to be a half-metal on the basis of first-principles band structure calculations.⁴ 

The Fe_3-xMn_xSi compound series shows different magnetic transitions depending on the x value. For x < 0.75, it exhibits a ferromagnetic transition at T_C, whereas for x ≥ 0.75, it was found that there is a drop in spontaneous magnetization as the temperature decreases, indicating a transition from a ferromagnetic (F) phase to one with some antiferromagnetic components.⁵ Here, this phase and the corresponding transition temperature will be referred to as the AF phase and T_A, respectively. Recently, by considering the temperature dependence of magnetization M(T) for x = 1.7, another AF phase was found at temperatures below T_A. This another AF phase and the corresponding transition temperature will be referred to as the AF2 phase and T_A2, respectively.⁶ This transition is characterized by a rapid decrease in M(T) with decreasing temperature. The transition at T_A2 was found to correspond to the meta-magnetic transition observed in previous magnetization measurements.^5,7,8 The transition temperatures at zero field, estimated from M(T), are T_C ∼ 85 K, T_A ∼ 68 K, and T_A2 ∼ 60 K for x = 1.7 ⁶ The transition temperature T_A2 depends on magnetic field, B, whereas T_A does not depend strongly on B.^6,9 Meanwhile, for x = 1.6, T_C and T_A are ∼ 117 K and ∼ 66 K, respectively, whereas T_A2 is not found as for x ≤ 1,5.^10,11 Note that T_C decreases as x increase but T_A is almost constant,⁵ leading to T_C appearing to coincide with T_A at around x = 1.7, although the properties in this x region have been little studied.

Previous studies of electrical resistivity for x ≤ 1.25 have shown that T_C and T_A can be identified from anomalies in the temperature dependence of electrical resistivity, ρ(T).^5,10 The AF2 phase and the AF2-AF transition have yet to be studied by resistivity measurements; hence, this study investigates the properties of the AF and AF2 phases and the AF2-AF transition using measurements of the electrical resistivity, magnetoresistance (MR), and Hall effect for Fe_3-xMn_xSi with x = 1.6, 1.7, and 1.8.

Polycrystalline samples of Fe_3-xMn_xSi with x = 1.6, 1.7, and 1.8 were synthesized by arc-melting, using high-purity elements. The samples were melted and turned over several times to ensure homogeneity. Then, the Fe_1.3Mn_1.7Si and Fe_1.2Mn_1.8Si samples were annealed at 800°C for 2 days and at 600°C for 1 week, respectively. In magnetization measurements we found that annealing improved the sharpness of the transitions but did not influence transition temperatures. The structure was analyzed by powder X-ray diffraction using Cu-Kα radiation, showing that the samples exhibited (111) and (200) superlattice reflections. This indicated that the samples were single-phase, with L2₁ crystal structures. The electrical resistivity, MR, and Hall effect were measured by a four terminal method using a commercial device (Quantum Design PPMS).

Figure 1 shows the ρ(T) results in zero magnetic field for Fe_1.3Mn_1.7Si and Fe_1.2Mn_1.8Si. For Fe_1.3Mn_1.7Si, the slope of the ρ(T) curve changes, as shown by the arrows. These temperatures almost coincide with the T_C and T_A (or T_A2) values obtained by the author’s previous study, and these features of the anomalies at T_C and T_A are consistent with those for smaller x values.^5,10 However, because T_A and T_A2 are so close, it is difficult to identify which transition is causing the anomaly. Although the ρ(T) curve for x = 1.8 also appears to show a slope change at 70 K, it is not very clear. The ferromagnetic transition was not found for x = 1.8 in our magnetization measurement.¹² 

Figure 2 shows the MR ratio results for x = 1.6, 1.7, and 1.8. Here, the MR ratio is defined as Δρ(Β)/ρ₀ = (ρ_B − ρ₀)/ρ₀, where ρ₀ and ρ_B are the resistivities in zero magnetic field and in a magnetic field B, respectively. For Fe_1.4Mn_1.6Si, a negative MR effect can be observed, i.e., ρ_B decreases with increasing B. This negative MR effect becomes smaller at temperatures above T_C, which is consistent with a previous finding that the MR shows a negative peak at T_C.⁵ The MR becomes very small around room temperature, which is much higher than T_C. On the basis of these results, the negative MR effect is considered to be due to ferromagnetic components. In contrast, Fe_1.3Mn_1.7Si exhibits a positive MR effect in the low-temperature, low-field region, and elsewhere ρ_Β decreases with increasing B, i.e., the MR effect is negative. The slope of Δρ(Β)/ρ₀ can similarly be observed to change from positive to negative for x = 1.8, as indicated by the arrows in Fig. 2. In Figure 3, these points are plotted as solid and open circles in the B-T phase diagram with the results for M(T). Note that for x = 1.8 no transition was recognized above 70 K in the M(T) measurements.¹² The points where MR anomalies were observed for x = 1.7 and 1.8 essentially coincide with the AF2-AF transition lines obtained from M(T) measurements;^6,12 hence, it can be concluded that the MR anomalies indicate AF2-AF transitions. Consequently, the AF2 phase has positive MR, whereas the AF and F phases have negative MR. This can be understood by considering the magnetization results, which show that the AF phase has a large ferromagnetic component, whereas the AF2 phase is believed to be essentially a usual AF state but without ferromagnetic components.⁶ It is assumed that the negative MR effect observed in the AF and F phases is due to the magnetic field aligning the spins, suppressing scattering by spin fluctuations. In the AF2 phase, the spin fluctuations appear to be enhanced by the magnetic field. The AF2-AF transition line shifts toward higher field as x increases, whereas near zero field the transition temperature is left almost unchanged as x varies. This agrees with the magnetization results.

In Fe_1.2Mn_1.8Si, the negative MR effect at high fields decreases above 70 K. This is because the ferromagnetic components disappear above T_A, and the ferromagnetic transition itself disappears.¹² At low fields above 80 K, the AF2-AF transition is difficult to observe in the MR, and the magnetization measurements suggest that there are no transitions above 70 K.¹² Even though there is no evidence of the hysteresis between increasing and decreasing B that was observed in the magnetic field dependence of magnetization at low temperatures, the fact that the AF2-AF transition in MR becomes vague at low temperatures may be related to this hysteresis.^6,12

The Hall resistivity ρ_H was measured for x = 1.6, 1.7, and 1.8 at temperatures between 2 and 300 K. Figure 4(a) shows the results at 70 K, where the arrows show the field cycle. Although ρ_H changes approximately linearly with B, jumps in ρ_H can be observed at zero field for x = 1.6 and 1.7. Defining the size of the jump as 2Δρ_H, Figs. 4(b, c) plot Δρ_H as a function of temperature, comparing this with the M(T) result.⁶ As the changes in Δρ_H with temperature approximately coincide with the M(T) curves, they are considered to be due to the anomalous Hall effect, where the Hall resistivity is proportional to the magnetization. However, in Fe_1.2Mn_1.8Si, a jump at zero field was not recognized, and hence we judged no anomalous Hall effect. These results are consistent with magnetization results; for x = 1.7 spontaneous magnetization appears at temperatures between T_A2 and T_C, whereas for x = 1.8 there is only an AF2-paramagnetic transition at low fields, and no phases with spontaneous magnetization.^6,12

In this study, measurements of the electrical resistivity, MR, and Hall effect were performed on Fe_3-xMn_xSi samples with x = 1.6, 1.7 and 1.8. The MR measurements for x = 1.7 and 1.8 revealed that the slope of the MR effect changes from positive to negative at certain magnetic fields. These transition points almost coincide with the AF2-AF transitions obtained from magnetization measurements. This demonstrates that MR anomalies indicate the AF2-AF transitions. A positive MR effect was observed for the AF2 phase, and negative effects were observed for the AF and F phases, which is consistent with the assumed magnetic orders. As x increases, the AF2-AF transition shifts toward higher fields. The Hall effect measurements showed the anomalous Hall effect for x = 1.6 and 1.7, but not for x = 1.8. This is consistent with the fact that there are phases with spontaneous magnetization for x = 1.6 and 1.7, whereas for x = 1.8 the ferromagnetic transition disappears. Although we consider that for x = 1.8 the transition around 70 K at low fields is the AF2-paramagnetic transition, to elucidate further studies are needed.

We thank G. Adachi for cooperation. This study was carried out as a joint research in the Institute for Solid State Physics, the University of Tokyo (ISSP). We are grateful to T. Yamauchi at the Materials Design and Characterization Laboratory, ISSP, for advice and help. Authors acknowledge support from JSPS KAKENHI Grant Number JP17K06774.