1.
Introduction
Heusler compounds have drawn much attention in recent years due to their high Curie temperature (TC)[1, 2] and flexible tunability[3–6], making them complex and diversified, and thus bringing a lot of interesting phenomena[3]. Among these materials, Co–Mn–Al ternary Heusler alloy is an attractive system, especially in the cases of Co2MnAl as a half-metal[7] and Mn2CoAl as a typical spin gapless semiconductor[8–10]. The Fermi levels in both cases lie in the gaps of their minority-spin bands. But in their majority-spin bands, Co2MnAl acts like a metal, while Mn2CoAl is close to a zero-gap semiconductor[11] featuring a semiconducting-like transport behavior[8, 10].
Different from Co2MnAl or Mn2CoAl, we have synthesized Co1.65Mn1.35Al (CMA), an off-stoichiometric alloy Co2MnAl, in which perpendicular magnetic anisotropy (PMA) emerges as a result of residual strain. This material provides a material platform for studying the effect of strain on spin-orbit coupling related phenomena such as anomalous Hall effect (AHE), and could also be a promising candidate for potential applications in spintronic devices due to its PMA characteristic[12]. Therefore, it is meaningful to investigate the physical properties, especially the magneto-transport behavior of the CMA film systematically.
In this work, we report the temperature T dependence of the longitudinal resistivity ρxx and the negative magneto-resistance (MR) at different temperatures of a 20 nm-thick CMA film. The semiconducting-like transport character in the T range between 5 and 300 K implies the existence of an activation energy Ea. It is found that ρxx can be described by a simple activation model with varying Ea in different T regions. The T dependences of the magnetization M are also different correspondingly. The first transition temperature at around 110 K could be ascribed to a transition from localized to itinerant ferromagnetism. We measure the Hall resistivity at several temperatures and obtain the intrinsic anomalous Hall conductivity of ~55 Ω–1cm–1, which is almost twenty times smaller than that of Co2MnAl[13].
2.
Experiments
The single-crystalline film of CMA was epitaxially grown on GaAs (001) substrate by molecular-beam epitaxy (MBE). After the GaAs de-oxidation and buffer layer deposition, a 20 nm-thick CMA film was grown at 200 °C, capped with 2 nm-thick aluminum for protection from oxidation. The sample was patterned to a standard Hall bar, with the channel along the GaAs [110] direction for transport measurements. The magnetic field H was applied perpendicular to the film plane, i.e., parallel with the GaAs [001] direction. The transport data of the film were collected with T between 5 and 300 K and H up to 50 kOe using a physical property measurement system (Quantum Design, PPMS-9). The magnetic properties of CMA film were measured using a superconducting quantum interference device (SQUID) down to 5 K.
3.
Analyses and results
Fig. 1(a) shows the dependence of ρxx on T varying from 5 to 300 K with a zero magnetic field. ρxx increases with decreasing temperature in the whole range of T in our experiment. Different from Co2MnAl[13], ρxx of the CMA film resembles that of Mn2CoAl films following an activation-type dependence[8, 10], which is usually described by a simple activation model[10, 14]: σxx(T) = 1/ρxx(T) = σ0 + σaexp(–Ea/kBT), where σ0 denotes the non-stoichiometric contributions at the low temperature and σa is a coefficient with the same dimension as conductivity, respectively. As shown in Fig. 1(a), an obvious deviation from the fitting curve to ρxx(T > 110 K) is found at temperatures lower than 110 K, which could result from the change of the Ea in the equation. Thus we learn this transition between different T regions divided by the T points at 35 and 110 K. The best fits of the data yield the critical parameters of Ea1 = 34 meV, σ01 = 2.97 × 10–3 μΩ–1cm–1 (110 to 300 K), Ea2 = 15 meV，σ02 = 2.93 × 10–3 μΩ–1cm–1 (35 to 110 K), and Ea3 = 1.4 meV, σ03 = 2.89 × 10–3 μΩ–1cm–1 (5 to 35 K), respectively. To clearly show the change of Ea, we plot the relations of ln(Δσxx) = ln(σxx – σ0) versus 1/T in the inset of Fig. 1(a), which depict good linear dependencies and different slopes in three T regions. According to these results, the CMA film is discovered to have a decreasing Ea when T is lowered, which could be attributed to a band shift with T.
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Figure1.
(Color online) (a) T dependence of the zero-field ρxx varying from 5 to 300 K. The fitting curves using activation model in different T regions are plotted in red, blue and green lines, respectively. The inset gives a linear relation between ln(Δσxx) and 1/T in the corresponding T ranges. (b) The MR at several selected temperatures. The inset shows the temperature dependence of MR at specific applied field.
The relations of MR with H are selectively presented in Fig. 1(b). The MR is defined as (ρxx – ρxx0)/ρxx0 × 100%, where ρxx0 = ρxx(H = 0). The negative MR is observed over the whole T range, which is usually ascribed to the spin-dependent scattering in similar systems[10, 15]. And it means that this scattering, which is inevitably affected by magnetism, dominates MR compared to the contributions of the cyclotron effect in our measurement with H lower than 50 kOe[16]. There are two major changes of MR with T and H, respectively. One is that MR (T > 200 K) clearly changes much more slowly than those at low temperatures when H is not larger than 30 kOe. This variation could be an evidence for different activation modes in different T regions, consistent with the implications from ρxx(T). Another difference is that the MR approaches a linear trend when it reaches about 30 kOe and higher. This linear dependency between MR and H has been reported in the Mn2CoAl and some other spin gapless systems[8, 17]. Moreover, the MR of the CMA film shows a maximum in the temperatures between 50 and 100 K as shown in the inset of Fig. 1(b). The maximum value of MR here could possibly result from the change of the band structure rather than the combined influence of the impurity and the spin-dependent scattering reported in Mn2-CoAl[8, 9].
In order to learn whether a similar transition happens for the ferromagnetism of this sample, we carried out the magnetic measurements using a SQUID magnetometer. The sample was cooled down to 5 K with H = 0 and then saturated by a magnetic field as high as 50 kOe. After H was set at 20 Oe, the T dependence of M along the [001] direction was measured by heating the sample from 5 to 280 K. The results are shown in Fig. 2(a). For our CMA film, a linear dependence of M2 on T2 is observed with T ranging from about 110 to 280 K, which is ordinary in itinerant ferromagnetic materials such as MnSi[18] and ZrZn2[19]. Therefore, M(T) can be fitted by the formula of M(T) = M(0)×[1 – (T/TC)2]1/2. The best fit yields the parameters of M1(0) = 292 emu/cm3 and TC = 640 K, close to 693 K of Co2MnAl[2] and 720 K of bulk Mn2CoAl[8]. However, an obvious deviation from this T2 behavior is observed when T is lower than 110 K. In the T range between 43 and 110 K, the more rapid variation of M versus T can be described by the classical Bloch T3/2 law: M(T) = M(0)(1 – ηT3/2), where η is related to the spin-wave stiffness constant and exchange coupling energy. It means that the variation of M(T) in this T range could be attributed to collective spin wave excitations[17]. The best fit of the curve yields the M2(0) and η values of 294 emu/cm3 and 1.8 × 10–5 K–3/2, respectively. Furthermore, an enhanced changing rate of the M(T) curve occurs in the lowest T range between 5 and 35 K. Although the picture of this anomalous behavior is still unclear in our system, the M(T) curve may be described by an exponential dependence: M(T) = M(0)(1 – αexp(–Δ/T)), where the coefficients α = 1.64 × 10–2 and Δ = 3.74 × 10–2 K are obtained. To show the change of M(T) near 110 K more clearly, the dependences of ln(1 – M(T)2/M(0)2) (T ~ 110–280 K) and ln(1 – M(T)/M(0)) (T ~ 43–110 K) on T are plotted in Fig. 2(b), showing good linearity in both regions. Combining the above results of transport and magnetic measurements, the transition of ρxx and M could be originated from the same contributions because similar changes take place near 35 and 110 K.
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Figure2.
(Color online) T dependence of M varying from 5 to 280 K. (a) The fitting curves using T2, T3/2 and exponential dependences in different T regions are plotted in red, blue and green lines, respectively. The formulas describing M(T) in corresponding T regions are shown. (b) The linear relations of ln(1–M(T)2/M(0)2) (red line) and ln(1–M(T)/M(0)) (blue line) versus T.
Fig. 3(a) shows the measured Hall resistivity ρxy varying with H and T after the subtraction of the background signals coming from ρxx. ρxy is dominated by the anomalous Hall signal, which reflects the ferromagnetism corresponding to the hysteresis loop shown in the inset. The Hall resistivity is generally described by the formula: ρxy(H) = RoH + RAM(H), where Ro and RA are the ordinary and anomalous Hall coefficient, respectively. When H is large enough to saturate a ferromagnetic material, the slope of ρxy(H) is mainly determined by Ro = 1/(nq) based on the one band model, where n is the carrier concentration and q equals the charge of an electron. However, in the CMA film, we notice that the slope of ρxy(H) gradually becomes larger when H is increased, which seems to be contradicted with the saturation state shown in the hysteresis loop. Considering the different behaviors of MR when H is lower and higher than 30 kOe, M could also change gradually with H which is not evident compared to the remanent magnetization. We then obtain ρAH as the value of ρxy(H = 0) for estimating the anomalous Hall conductivity (AHC). In general, the anomalous Hall resistivity ρAH can be described in terms of ρxx in the form of ρAH = βρxx + γρxx2, where β characterizes the extrinsic skew scattering and γ denotes the intrinsic origin or the extrinsic side-jump scattering[20]. The ρxx and ρxy are measured simultaneously in our experiment and ρAH shows a linear dependence on ρxx2 as shown in Fig. 3(b). The γ can be described by the slope value of ρAH versus ρxx2, which is estimated to be ~55 Ω–1cm–1 in favor of a topological origin from Berry phase effect in the case of ρxx ~ 300–350 μΩ·cm[9, 20, 21]. Therefore, the intrinsic AHC of the CMA film is almost twenty times smaller than that of Co2MnAl film[14] but relatively larger than that of bulk Mn2CoAl[8].
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Figure3.
(Color online) (a) ρxy(H) varying with H and T after the subtraction of the background signals originated from ρxx. The inset shows the hysteresis loop at 5 K perpendicular and parallel to the film plane. (b) The relation between ρAH and ρxx2. The slope value is estimated to be about 55 Ω–1cm–1.
4.
Conclusion
In conclusion, we have systematically investigated the magneto-transport properties of a 20 nm-thick CMA film. The film exhibits semiconducting-like transport behavior below 300 K. Its longitudinal resistivity ρxx(T) is properly described by a simple activation model with different activation energies in three T regions separated by 110 and 35 K. The activation energies are 34, 15 and 1.4 meV in the temperature range of 110–300, 35–110, and 5–35 K, respectively. Similar transitions at nearly the same temperature in M(T) have also been discovered, implying a same origin of the transitions of ρxx(T) and M(T), which might probably be related to the bands’ shift. The Curie temperature is estimated to be ~640 K, which is a typical value among full-Heusler alloys. An intrinsic AHC of about 55 Ω–1cm–1 is obtained from the linear dependence of ρAH versus ρxx2. Further experiments and calculations are needed to understand the relations between the transitions and the band structures of the film.
Acknowledgements
This work was supported by the Ministry of Science and Technology under Grant Nos. 2015CB921500, 2017YFB0405701 and the National Natural Science Foundation of China under Grant Nos. U1632264 and 11704374.
