Structure and magnetic properties of RAlSi(R=light rare earth)*

Tai Wang(王泰), Yongquan Guo(郭永權(quán)), and Cong Wang(王聰)

School of Energy Power and Mechanical Engineering,North China Electric Power University,Beijing 102206,China

Keywords: RAlSi,crystal structure,magnetic properties

1. Introduction

The topologically electronic and strongly spin-orbit coupling materials have been systematically investigated and their unique characteristics have been revealed so far.[1-14]Weyl semimetals have received great attention due to their unusual characters of space-inversion symmetry breaking for type I or time-reversal symmetry breaking for type II.[1,5,8,10,12]Type-I Weyl semimetals have been realized experimentally in TaAs and its isostructural materials such as TaP, NbAs, and NbP.[5,6,8,9]Though it is difficult to identify the magnetic Weyl semimetals with type II by utilizing the angle resolved photo emission spectroscopic (ARPES) measurement, the unique properties of type-II Weyl semimetals have been experimentally verified by magnetic and electric measurements for some intermetallic compounds such as HgCr2Se4,[14]RAlGe (R=La, Ce, Pr),[11,15-17]SrMnSb2,[10]and Mn3Z(Z= Ga, Sn,Ge).[18,19]The significant coupling of magnetic configurations to semi-metallic electronic structure in magnetic Weyl semimetal may provide technologically useful behavior for sensors and spintronic devices.[20,21]

In recent years,the ternary RAlGe(R=La,Ce and Pr)intermetallics have attracted considerable attention as potential candidates of Weyl semimetals.[11,15-17,21-23]The body tetragonal RAlGe(R=rare earth)with space groupI41mdare firstly predicted to have either type-I or type-II Weyl fermions, depending primarily on the radius of rare earth.[23]The light rare earth based RAlGe (R=La, Ce, Pr) have been experimentally studied.[11,15-17,21-23]LaAlGe and CeAlGe belong to the type-II Weyl semimetals.[22,23]CeAlGe exhibits ferromagnetic characteristics with strong magnetic anisotropy along the crystallographicaaxis and its angular magnetoresistance response exceeds 1000% rad-1along the high symmetry axis within 1°.[11,21]PrAlGe presents the ferromagnetic characteristics along the easycaxis. A large anomalous Hall conductivity of 680 Ω-1·cm-1has been observed,which may be due to the contribution of intrinsic Berry-phase Karplus-Luttinger mechanism.[15]NdAlGe shows the spin-glass-like characteristics at low temperature and van Vleck paramagnetism in high temperature region, respectively.[24]The tetragonal GdAlGe orders ferromagnetically at 21 K,and its magnetic properties are strongly related to its special magnetic structure formed by magnetic Gd3 isosceles triangles. The ferromagnetism may originate from the exchange interaction between two parallel Gd3 isosceles triangles.[25]

Recently, the interest has been extended to the isomorphous RAlSi family. PrAlGe1-xSixis revealed with a transition of the anomalous Hall effect from an intrinsic (xbelow 0.5) to an extrinsic region (xhigher than 0.5).[26]CeAlSi is a new type of ferromagnetic Weyl semimetal,which shows novel anisotropic anomalous Hall responses along the easy and hard axes.[27]The ferromagnetic PrAlSi has a huge anomalous Hall conductivity of～2000 Ω-1·cm-1.[28]The crystal structure of CeAlSi is initially reported as sitedisorderedI41/amd.[29-31]However, the later studies show that the noncentrosymmetrically ordered structure with a space group ofI41mdis preferred,[26]which is an isostructure of CeAlGe.[11,16,21]The same question arises for the preferred structural model in the other RAlSi alloys. According to the international center of diffraction database(ICDD),the crystal structures of RAlSi (R=light rare earth) are the noncentrosymmetric with space group ofI41mdfor R=Ce and Sm; site-disorderedI41/amdfor NdAlSi, respectively.However, no record is available for equiatomic LaAlSi and PrAlSi, which may be considered as RSi2-xAlxsolid solution withx=1. RSi2-xAlxsolid solutions crystallize in body centered tetragonalα-ThSi2type structure with a space group ofI41/amd, where Al and Si occupy randomly the 8ecrystal position.[29,32,33]However,the recent study shows that the equliatomic PrAlSi not only fits the site-disorderedα-ThSi2type structure but also the noncentrosymmetrically orderedI41mdas well. The minor difference between the two models is the temperature factor.[28]Thus, in order to determine the structural models of equiatomic RAlSi(R=light rare earth),the interest has been focused on the crystal structure and magnetic properties of RAlSi in this study.

2. Material and methods

The nominal composition of RAlSi(R=light rare-earth element)were prepared using arc melting under an argon gas atmosphere and vacuum solid state reaction technology. The purities of raw materials are more than 99.99 wt%. Each sample was remelted four times for its homogeneity. The vacuum annealing process, which could remove the potential metastable phase and residual stress in samples, was carried out at 1023 K for seven days in the vacuum evacuated quartz tube. The crystal structures of RAlSi (R=light rareearth element)were measured using a Rigaku G/max 2500 xray diffractometer with CuKα1radiation (λ=1.54056 ?A).The surface morphologies and element components of RAlSi(R = light rare-earth element) were recorded with the field emission scanning electron microscopy(SEM)equipped with energy dispersive spectra(EDS).The applied field dependence of magnetization(M-H)and temperature dependence of magnetization (M-T) of RAlSi alloys were measured using a superconducting quantum interference device (SQUID).M-Tcurves were measured in the temperature range of 2 to 300 K with an external field of 50 Oe for CeAlSi and PrAlSi,and in the temperature range from 5 to 300 K with an external field of 1 kOe for NdAlSi and SmAlSi, respectively.M-Hcurves of RAlSi alloys were measured in applied fields ranging from 0 to 50 kOe at various temperatures.

3. Results and discussion

In order to determine the crystal structures of equiatomic light rare earth based RAlSi,the three possible structural models, which correspond to the site-disorderedI41/amd, noncentrosymmetrically orderedI41mdand their mixed model,are used for Rietveld structural refinement. The refinement results show that the x-ray diffraction patterns of RAlSi prefer to follow the mixed model, the residual pattern factorRpand residual weight pattern factorRwpare the smallest among the three models. NdAlSi is selected as a typical example,and its x-ray diffraction patterns are refined with the above-mentioned three possible structural models, as shown in Figs. 1(a)-1(c).The difference between site-disorderedI41/amdand noncentrosymmetrically orderedI41mdis small.RpandRwpare corresponding to 12.352%and 16.355%forI41md;12.404%and 16.389%forI41/amd. However,the x-ray patterns of NdAlSi fit the mixed model very well.RpandRwpdecrease to 9.235%and 12.951%, implying that this structural model is acceptable.

Fig. 1. The refined x-ray diffraction patterns of NdAlSi based on the noncetrosymmetrically ordered I41md model (a), the site-disordered I41/amd model(b),and the mixed model(c)of I41md and I41/amd.

The refinement shows that the lattice parameters of the disordered phase is slightly larger than those of the ordered phase. It reveals that the peak separation is necessary for the widened diffraction peaks caused by overlaps of diffraction peaks for the two phases. The refined x-ray diffraction patterns of RAlSi are shown in Figs.2(a)-2(e). The red symbols of+and green lines denote the observed and calculated x-ray diffraction patterns of RAlSi. The intensity differences between the observed and calculated x-ray diffractions are shown in the lowest line. The orange and violet vertical bars represent the peak positions ofI41mdandI41/amdphases, respectively. It is significant that diffraction peak positions ofI41/amdphase shift to the low angle compared to those ofI41mdphase. This phenomenon is ascribed to the increase of lattice parameter for site-disorderedI41/amdphase, induced by the different occupations of Al and Si atoms in two structures. The lattice parameters of RAlSi decrease with increasing the atomic order number of rare earth element due to the lanthanide contraction effect.

The weight proportion of two phases in RAlSi alloys can be estimated by the following equation:[34]

whereSi,Ai,Vi,Ziare the scale factor,molecular weight,cell volume and numbers of molecular in unit cell for theith phase,respectively. The calculations of phase contents reveal that the noncentrosymmetrically ordered phase is the main phase in RAlSi alloy. Table 1 lists the refined structural parameters and phase weight proportions in RAlSi alloys.

Fig.2. The refined and observed XRD patterns of RAlSi.

Table 1. The refined phase structural parameters of RAlSi with structural models of I41md and I41/amd.

SEM morphologies and EDS spectra of RAlSi(R=light rare-earth element) powders are displayed in Figs. 3(a)-3(e).The grain growths exhibit inhomogeneity from large bulks to small pieces with sizes ranging from 0.5 μm to 7 μm, the small grains distribute on the surface of the large ones, and the grains tend to agglomerate with increasing the atomic order number of rare earth element. EDS measurements show that the element compositions of RAlSi alloys are close to the ratio of 1:1:1 as the stoichiometrically equiatomic RAlSi,and the slight deviation from the normal structural formula may be ascribed to the volatilization during the melting process.

Figures 4-7 show that the temperature dependence of magnetizations(M-T)curves of RAlSi alloys measured with field-cooled(FC)and zero-field-cooled(ZFC).CeAlSi is ferromagnetic, as shown in Fig. 4, which ascribes to the interaction between the localf-moments of Ce3+and the noncentrosymmetric lattice.[27]Curie temperature of CeAlSi is 7.7 K,which is close to that of CeAl0.9Si1.1.[35]

Fig.3. SEM morphologies and EDS patterns of RAlSi: (a)for LaAlSi,(b)for CeAlSi,(c)for PrAlSi,(d)for NdAlSi,and(e)for SmAlSi.

Figure 5 shows that PrAlSi orders ferromagnetically at 17.7 K, its Curie temperature is very close to the previously reportedTC= 17.2 K.[26]The cusp-like transitions are observed at 5.2 K for CeAlSi and 16.5 K for PrAlSi. The remarkable difference between ZFC and FC curves suggests that the cusp-like transition may be due to the spin-glass-like phenomenon,which is similar to the thermal irreversibilityχ(T)for RAlX(R=Ce,Pr;X=Ge,Si)in the temperature region ofT ＜TC.[15-17,26,28,36]However, theM-Tcurve of NdAlSi shows only paramagnetic characteristics as shown in Fig. 6.SmAlSi shows complex magnetic properties. According to the FC curve in Fig. 7, SmAlSi shows metamagnetic transition at 10 K and weak ferromagnetic-paramagnetic transition at 143 K. However, the ZFC curve shows an extra magnetic transition at 60 K, which may be due to the disordered arrangement of Sm moment. In addition, the unconventional fluctuations may be due to the heavy-fermion effect in temperature ranges from 50 to 80 K,which is possibly caused by the unconventional magnetic ordering of the involvement of multiple 4f elections of Sm ions in the hybridization process.[37]

Fig. 4. The temperature dependence of magnetization (M-T) for CeAlSi, and the fitted M-T curve based on Curie-Weiss law in paramagnetic region. Inset: the ferromagnetic transition.

Fig. 5. The temperature dependence of magnetization (M-T) for PrAlSi, nd the fitted M-T curve based on Curie-Weiss law in paramagnetic region. Inset: the magnetic transition.

Fig.6. The observed and fitted M-T curves based on Curie-Weiss law of NdAlSi.

Theχ-Tcurves of RAlSi (R=Ce, Pr, Nd) follow the Curie-Weiss law in their paramagnetic region. The fitted curves are shown in Figs.4,5,and 6 for CeAlSi,PrAlSi,and NdAlSi, respectively. The fitted Curie-Weiss temperatureθPis corresponding to-24.33 K for CeAlSi,5.56 K for PrAlSi,and-8.75 K for NdAlSi. The negativeθPimplies the possible antiferromagnetic order in NdAlSi. However, the antiferromagnetism is not experimentally observed in NdAlSi alloy.

Fig.7. The temperature dependence of magnetization for SmAlSi,and the fitting M-T curve based on the van Vleck law in paramagnetic region.

The effective momentμeffis estimated with the equationNμ2eff=3CMKB,whereC,M,KB,Ncorrespond to the Curie-Weiss constant,the molecular weight,the Boltzmann constant and the number of atoms.[38]The calculatedμeff’s are 2.53μBfor CeAlSi, 3.56μBfor PrAlSi and 3.79μBfor NdAlSi.The effective moments of paramagnetic CeAlSi, PrAlSi and NdAlSi are close to the moments of trivalent Ce3+(2.54μB),Pr3+(3.58μB)and Nd3+(3.62μB). This reveals that the contribution to moment originates from rare earth in RAlSi.

The temperature dependence of susceptibility for SmAlSi does not fit the Curie-Weiss law in the paramagnetic region.The surplus molar magnetic susceptibility most likely comes from a typical behavior of Sm3+ions,which ascribe to the different multiplets betweenJ=5/2(ground state)andJ=7/2(first excited state).[39-43]In the paramagnetic region,the susceptibility of SmAlSi follows the modified van Vleck paramagnetic mode with an equation ofχ=χ0+C/(T-θP).[44,45]The effective magnetic moment is 0.329μB,which is smaller than the moment of Sm3+(0.85μB). Such a reduction reveals a pronounced crystal field effect in SmAlSi.[39,44,45]The small positive value ofθPindicates dominant ferromagnetic interactions for the magnetism of SmAlSi.[39]

Fig. 8. The observed and fitted field dependences of magnetizations for RAlSi: (a) for CeAlSi, (b) for PrAlSi, (c) for NdAlSi and (d) for SmAlSi.

Figure 8 shows that RAlSi(R=Ce,Pr,Sm)exhibit mixture of ferromagnetism and paramagnetism,however,NdAlSi presents only the paramagnetic character. In paramagnetic region, the magnetizing curves for RAlSi follow a linear equation as follows:

whereHandχare the external field and susceptibility,respectively.

The field dependence of magnetization curves for the RAlSi alloys follows the mixture magnetism model as follows:[46,47]

The first term originates from the contribution of ferromagnetic phase, which is based on the Langevin model,[48]and the second term contributes to magnetization originating from the paramagnetic phase, whereMsandχare the saturation moment and susceptibility,respectively.

The fitted and observed magnetization curves for RAlSi are marked with circles and solid lines as shown in Fig.8,respectively. Table 2 lists the fitted parameters of PrAlSi and NdAlSi in the paramagnetic region. The paramagnetic susceptibilityχof RAlSi is enhanced with increasing the atomic order number of rare earth elements from Ce to Nd, which may be due to the increasing moment of trivalent rare earth ions. Table 3 lists the fitted parameters of RAlSi (R=Ce,Pr,Sm)alloys based on the mixture model of ferromagnetism and paramagnetism. For ferromagnetic RAlSi (R=Ce, Pr),the saturation moment of PrAlSi is larger than that of CeAlSi,which is due to the large moment of trivalent Nd compared to that of Ce3+. Thus, it implies that the saturation momentMSdepends on the moment of trivalent rare earth. With increasing temperature, the fittedMSof CeAlSi shows an opposite tendency with its susceptibilityχ.Msis going down,whereas the susceptibilityχis going up. The susceptibility of SmAlSi shows a decreasing tendency with increasing temperature,which may be due to its various magnetic transitions.

Table 2. The fitted parameters of RAlSi(R=Ce,Pr,Nd)in their paramagnetic regions.

Table 3. The fitting parameters of RAlSi(R=Ce,Pr,Sm)with the mixed model of ferromagnetism and paramagnetism at various temperatures.

4. Conclusion

RAlSi (R=light rare earth) alloys consist of two phases according to x-ray diffraction,which are corresponding to the site-disordered phase with group space ofI41/amdand the noncentrosymmetrically ordered phase with space group ofI41md. The ordered phase is the main phase in RAlSi alloy. RAlSi alloys show nonmagnetic character for R=La,low temperature ferromagnetic order for R=Ce,Pr,and paramagnetic character for R=Nd, respectively. SmAlSi shows metamagnetic transition at 10 K and weak ferromagnetic order at 143 K,respectively. RAlSi(R=Ce,Pr,Nd)follow the normal Curie-Weiss law in their paramagnetic regions, however, SmAlSi follows the van Vleck paramagnetic model. In the paramagnetic region, the susceptibilities of RAlSi are enhanced with increasing the atomic order number of rare earth element. The magnetization curves of RAlSi (R = Ce, Pr,Sm) follow the mixed model of ferromagnetism and paramagnetism. The fittedMSdepends on the moment of trivalent rare earth. For ferromagnetic RAlSi (R=Ce, Pr), theMSof PrAlSi is larger than that of CeAlSi. With increasing temperature,the fittedMSof CeAlSi shows an opposite tendency with its susceptibilityχ.Msis going down, whereas the susceptibilityχis going up. The susceptibility of SmAlSi shows a decreasing tendency with increasing temperature.This may be due to its various magnetic transitions. The studies reveal that the magnetic property of RAlSi originates from the rare earth.