Magnetism and Hall effect of the Heusler alloy Co 2 ZrSn synthesized by melt-spinning process

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1 Journal of Magnetism and Magnetic Materials 299 (2006) Magnetism and Hall effect of the Heusler alloy Co 2 ZrSn synthesized by melt-spinning process Wei Zhang a, Zhengnan Qian a,, Yu Sui a, Yuqiang Liu a, Wenhui Su a, Ming Zhang b, Zhuhong Liu b, Guodong Liu b, Guangheng Wu b a Center for the Condensed-Matter Science and Technology, Department of Physics, Harbin Institute of Technology, Harbin , People s Republic of China b State Key Laboratory for Magnetism, Institute of Physics, Chinese Academy of Sciences, Beijing , People s Republic of China Received 18 March 2005; received in revised form 9 April 2005 Available online 11 May 2005 Abstract Magnetization and Hall resistivity have been measured for the Heusler alloy Co 2 ZrSn synthesized by the meltspinning process. The temperature dependence of magnetization follows the spin-wave theory at a low temperature. Abnormal behaviors are observed both in resistance and Hall effect below 8 K. The present Hall resistivity measurement shows that the anomalous Hall effects coexist with normal Hall effects. The negative value of normal Hall coefficient over the whole temperature range reveals that the major charge carriers are electrons. The anomalous Hall coefficient is proportional to the zero-field resistivity, suggesting that magnetic skew scattering is the dominant mechanism in the ferromagnetic regime. The reason for the abnormity below 8 K during transport is discussed. r 2005 Elsevier B.V. All rights reserved. PACS: Cc; Cr; Eb; Lp Keywords: Magnetism; Hall effect; Transport properties; Co 2 ZrSn; Heusler alloy 1. Introduction Heusler alloys [1 3] are ternary intermetallic compounds with the stoichiometric composition X 2 YZ, and attract considerable attention due to Corresponding author. Tel.: ; fax: addresses: zw_2002@126.com (W. Zhang), znqian@hit.edu.cn (Z. Qian). their unique transport, electric, and magnetic properties. For most Heusler alloys, the atoms at Y sites carry a large magnetic moment, and the moments at X sites are usually small, even for transition metals. However, in the case of Heusler alloys such as Co 2 YZ, the situation changed due to the existence of X-site Co atoms [4]. Co atoms mainly carry the magnetic moment in Co-based Heusler alloys Co 2 YZ except for Co 2 MnZ. The Co 2 YZ are of particular interest because the /$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi: /j.jmmm

2 256 W. Zhang et al. / Journal of Magnetism and Magnetic Materials 299 (2006) magnetic moment per Co atom ranges from 0.3 to 1.0 m B in these alloys [5]. It is considered that the magnetic moment on the Co atom depends strongly on the local environment [6]. Up to now, many studies have been carried out on the magnetic properties in Co-based Heusler alloys [7 13]. Nonetheless, great interest remains on the nature of charge transport. Hall effect measurements are very important in this regard in that they can tell us not only the character of carriers but also the nature of magnetic scattering. In ferromagnetic metals, the embedded magnetic moments cause asymmetric scattering of currentcarrying electrons, which in turn produce an additional transverse voltage, called anomalous (or extraordinary) Hall effect. The anomalous Hall field is proportional to the current density and the sample magnetization, so the Hall resistivity r H is generally described as r H ¼ R 0 B þ m 0 R S M, where the first term presents a normal Hall effect, related to the Lorentz force acting on moving charge carriers with R 0 being the normal Hall coefficient and this term is present in nonmagnetic materials as well. The second term, characteristic of a ferromagnet, represents the anomalous Hall effect with M being the macroscopic magnetization and R S the anomalous Hall effect coefficient. A correlation between the Hall signal and magnetization has been well established and used for a variety of applications [14,15]. But the anomalous Hall effect has been poorly understood since its discovery more than a century ago and constituted a challenging problem. In this paper, we report on the results of magnetization and Hall effect measurements of Co 2 ZrSn synthesized by the melt-spinning process and analyze on the origin of an anomalous Hall effect by correlating the anomalous Hall effect and resistance, and finding out that the anomalous Hall coefficient linearly varies with the zero-field resistivity showing the dominance of skewing scattering in Co 2 ZrSn. 2. Experimental The sample was prepared by repeated melting of appropriately composed mixture of high-purity metals in an arc furnace with the weight losses during melting being small and ingots being homogenized by annealing in a vacuum-sealed quartz tube at 800 1C for 3 days and cooled down to room temperature. Also, some of the ingots were subsequently broken up and used for melt spinning and the melt-spun ribbons were prepared by a single wheel technique under argon atmosphere protection with the substrate velocity of the Cu wheel being about 25 m/s. Subsequent X-ray power diffraction measurements at room temperature confirmed the sample Co 2 ZrSn to be of single phase with the Heusler L2 1 structure (space group Fm3m) and lattice parameters of nm. Magnetization, resistance and Hall effect were measured employing the physical property measurement system (Quantum Design PPMS, USA) with accurately controlled field up to 9 T and temperature between 1.9 and 350 K. Resistance and Hall effect measurements were carried out by the four terminal AC techniques. 3. Results and discussion Fig. 1 shows the magnetization M as a function of magnetic field H for Co 2 ZrSn at temperatures of 5, 15, 50, 100, 200 and 300 K, respectively. The sample is ferromagnetic in the whole temperature range and the magnetization approaches saturation at the magnetic field of 1200 Oe. The spontaneous magnetizations M S (0,T) were obtained from an extrapolation of the M vs. 1/H plots to 1/H-0, and then M S (0,0) of emu/g corresponding to 1.56 m B per formula unit is determined by fitting M S vs. T plot, namely each Co atom carries 0.78 m B since the magnetic moment of Co 2 ZrSn is mainly confined to the Co atoms. This value is slightly smaller than the value obtained by Ziebeck [5], which may be due to the result of the impurity that was introduced during the melt-spinning process. Saturation magnetization vs. temperature plot is shown in Fig. 2, which exhibits the characteristics of a ferromagnet. The curve should follow the functional form MðTÞ ¼Mð0Þð1 AT 3=2 Þ according to the spin-wave theory, and the value of A is K 3/2 by fitting the data for Co 2 ZrSn to

3 W. Zhang et al. / Journal of Magnetism and Magnetic Materials 299 (2006) Fig. 1. Magnetization dependence of the magnetic field for Co 2 ZrSn at various temperatures, the inset is the part of the curve at lower magnetic field. In this way, the Curie temperature is determined to be 448 K, which is consistent with the earlier magnetic measurements [8]. Fig. 3 shows the variation of the Hall resistivity r H as a function of magnetic field H at a selected temperature for Co 2 ZnSn. The curves significantly deviate from linear dependence and show profiles similar to those of the field dependence of the magnetization. r H almost saturates beyond a certain B and varies linearly with a slope and an intercept m 0 R S M S. It is evident that the appearance of a nonlinear field dependence of Hall resistivity is due to the anomalous Hall effect and indicates the existence of some kind of magnetic scattering. Moreover, the curve of 5 K is different from the others. Subsequently, we performed measurements of the Hall resistivity between 2 and 8 K with 1 K interval to obtain detailed information on the variation of Hall resistivity at a low temperature (see Fig. 4). The results show that both temperature and magnetic field have a direct effect on the abnormity that occurred at low temperature. The abnormity disappears entirely in zero field around 7 K. It should be noted that a similar situation also appears in the resistance vs. temperature plot. Fig. 5 presents the results of the resistance measurement. The resistance of Co 2 ZrSn exhibits a typical behavior of metals and a striking abnormity occurring at low temperature. The steep decrease of resistance with decreasing Fig. 2. Temperature dependence of magnetization for Co 2 ZrSn under a field of 50 koe Inset (a) shows the data as a function of T 3/2 at low temperature and inset (b) shows the square of magnetization versus the temperature. this functional form. The spin-wave stiffness coefficient D in the spin-wave dispersion _o ¼ Dq 2 can be calculated using the relation [16] A ¼ 2:612ðV=SÞðk B =4pDÞ 3=2, where V is the volume per magnetic atom, S the spin and k B the Boltzmann constant. Calculation for Co 2 ZrSn gives the value of D as mev A 2. In order to determine the Curie temperature of Co 2 ZrSn, we also present the square of magnetization vs. the temperature plot, as shown in inset (b) of Fig. 2, and then extrapolate the linear portion to M 2 ¼ 0. Fig. 3. Hall resistivity as a function of field for Co 2 ZnSn at indicated temperature.

4 258 W. Zhang et al. / Journal of Magnetism and Magnetic Materials 299 (2006) Fig. 4. Hall resistivity as a function of field for Co 2 ZrSn between 2 and 8 K. Fig. 5. Variation of the resistance with temperature measured during heating between 5 and 350 K for Co 2 ZrSn, the inset is the part of the curve at lower temperature. both R 0 and R S is negative over the whole temperature range, and a negative R 0 can be regarded as a characteristic of electron-like charge carriers. In addition, it is customary in ferromagnetic metals to compare the anomalous Hall coefficient R S with the zero-field resistivity r xx to determine the origin of anomalous Hall effect. R S depends on two different mechanisms, that is, skew-scattering and side-jump. The former can be accounted for with a classical Boltzmann equation. It is related to the spin orbit coupling and characterized by a constant spontaneous Hall angle: y H ¼ r H =r by which angle the scattered carriers deviate from their original trajectories. The latter, a constant lateral displacement Dy (side-jump) of the charge carrier s trajectories at every scattering event, is nonclassical and is also related to the spin orbit interaction. Generally speaking, R S follows the expression R S ¼ ar xx þ br 2 xx, where the first term stands for the skew component, and the second term gives the side-jump contribution to the anomalous Hall coefficient. To understand the origin of the anomalous Hall effect, we plot the zero-field resistance R dependence of the anomalous Hall coefficient R S which is taken from low-field slope of curve in Fig. 3. As shown in insert (b) of Fig. 6, R S is proportional to R and also to r xx since R can be described as R ¼ Ar xx (A is a constant). The linear relation is in agreement with the classical skew scattering temperature starts from the temperature of around 7 K. The abnormal behavior at low temperature can be tentatively attributed to the impurity associated with superconductivity since the microstructure defect and phase impurity were possibly introduced during the melt-spinning process. The value of R 0 and R S can be estimated from the Hall resistivity vs. magnetic field plots on the condition that R 0 is negligible compared to R S.As indicated by Hurd [17], the slope of the curves below technical saturation is ðqr H =qhþ H!0 ffi R S and at high field is ðqr H =qhþ H!1 ffi R 0. The analysis of our data indicates that the value of Fig. 6. The linear relation between the anomalous Hall coefficient R S and the zero-field resistance R.

5 W. Zhang et al. / Journal of Magnetism and Magnetic Materials 299 (2006) theory, where moving carriers experience a force due to the magnetic field produced by a localized magnetic moment and are scattered asymmetrically [18] ) and the Scientific Research Foundation of Harbin Institute of Technology (Grant no. HIT ). 4. Conclusions The result of the magnetization measurement can be interpreted by the spin-wave theory. Transport properties of Heusler alloy Co 2 ZrSn as presented here indicate the presence of an abnormal behavior at low temperature which is affected obviously by the magnetic field and temperature. This behavior can be ascribed to the impurity associated with superconductivity. The Hall effect measurement shows the presence of an anomalous Hall effect. The anomalous Hall coefficient linearly varied with the zero-field resistivity, indicating that an anomalous Hall effect is caused by skew scattering. Acknowledgements This work is supported by the National Natural Science Foundation of China (Grant no. References [1] F. Heusler, et al., Phys. Ges. 5 (1903) 219. [2] P.J. Webster, et al., Contemp. Phys. 10 (1969) 559. [3] J. Tobola, et al., J. Alloys Compd. 296 (2000) 243. [4] P.J. Webster, et al., J. Phys. Chem. Solid 32 (1971) [5] K.R.A. Ziebeck, et al., J. Phys. Chem. Solid 35 (1974) 1. [6] A. Jezierski, Phys. Stat. Sol. B 196 (1996) 357. [7] M. Terada, et al., J. Phys. Soc. Japan 36 (1974) 620. [8] P.G. van Engen, et al., J. Magn. Magn. Mater. 30 (1983) 374. [9] E. DiMasi, et al., Phys. Rev. B 47 (1993) [10] P. Mohn, et al., J. Magn. Magn. Mater (1995) 183. [11] K.U. Neumann, et al., J. Phys. Condens. Matter. 14 (2002) [12] A. Yamasaki, et al., Phys. Rev. B 65 (2002) [13] A.U.B. Wolter, et al., Phys. Rev. B 66 (2002) [14] G. Bergman, Phys. Today 32 (8) (1979) 25. [15] A. Gerber, et al., J. Magn. Magn. Mater (2002) 90. [16] Y. Noda, et al., J. Phys. Soc. Japan 40 (1976) 699. [17] C.M. Hurd, Plenum Press, New York, [18] S.H. Chun, et al., J. Appl. Phys. 85 (1999) 5573.