Giant Linear Magneto-resistance in Nonmagnetic PtBi2
Xiaojun Yang, Hua Bai, Zhen Wang, Yupeng Li, Qian Chen, Jian Chen, Yuke Li, Chunmu Feng, Yi Zheng, Zhu-an Xu
aa r X i v : . [ c ond - m a t . m t r l - s c i ] J un Giant Linear Magneto-resistance in Nonmagnetic PtBi Xiaojun Yang, Hua Bai, Zhen Wang, Yupeng Li, Qian Chen, Jian Chen, Yuke Li, Chunmu Feng, YiZheng,
1, 3, 4 and Zhu-an Xu
1, 3, 4, a) Department of Physics and State Key Laboratory of Silicon Materials, Zhejiang University, Hangzhou 310027,China Department of Physics, Hangzhou Normal University - Hangzhou 310036, China Zhejiang California International NanoSystems Institute, Zhejiang University, Hangzhou 310058,China Collaborative Innovation Centre of Advanced Microstructures, Nanjing 210093,China (Dated: 6 October 2018)
We synthesized nonmagnetic PtBi single crystals and observed a giant linear magneto-resistance (MR) up to684% under a magnetic field µ H = 15 T at T = 2 K. The linear MR decreases with increasing temperature,but it is still as large as 61% under µ H of 15 T at room temperature. Such a giant linear MR is unlikelyto be described by the quantum model as the quantum condition is not satisfied. Instead, we found that theslope of MR scales with the Hall mobility, and it can be well explained by a classical disorder model.PACS numbers: 75.47.Gk; 72.15.Gd; 71.20.Lp; 85.75.BbMaterials exhibiting large magneto-resistance (MR)can not only be utilized to enlarge the sensitivity ofread/write heads of magnetic storage devices, e.g., mag-netic memory and hard drives , but also stimulatemany fundamental studies in material physics at lowtemperatures . Generally speaking, the ordinary MRin non-magnetic compounds and elements is a relativelyweak effect and usually at the level of a few percentfor metals . Moreover, a conventional conductor underan applied magnetic field exhibits a quadratic field de-pendence of MR which saturates at medium fields andshows a relatively small magnitude. Owing to the richphysics and potential applications, the large linear MReffect has drawn renewed interest recently. There aretwo predominant models used to explain the origin ofsuch large linear MR effect, namely, the quantum model and the classical model . The quantum model is pro-posed for materials with zero band gap and linear energydispersion, such as topological insulators , graphene ,Dirac semimetals like SrMnBi , and the parent com-pounds of iron based superconductors . Quantum lin-ear MR occurs in the quantum limit when all of theelectrons fill the lowest Landau level (LL) . In con-trast, the classical linear MR is dominated by disor-der. Materials showing the classical linear MR includehighly disordered systems , and weakly disordered sam-ples with high mobility , thin films, and quantumHall systems . However, it is interesting that the clas-sical linear MR has also frequently been reported in ma-terials with linear dispersions, such as the topologicalinsulator Bi Se , graphene , and the Dirac semimetalCd As , which may be due to their large mobility.Even weak disorder could induce linear MR in high-mobility samples . When the carrier concentration a) Electronic mail: [email protected] is too high for the quantum limit, the linear MR may bedescribed by classical model for disordered systems .In this Letter, we synthesized high quality single crys-tals of nonmagnetic PtBi and investigated the magneto-transport properties. We observed a giant positive linearMR up to 684% under µ H = 15 T at T = 2 K. MR de-creases with increasing temperature, but MR of 61% isstill achieved under a magnetic field of 15 T even at roomtemperature. Regarding the origin of the linear MR, theclose relationship between the MR and the Hall mobilityimplies that the observed linear MR should not be at-tributed to the quantum origin, but may be explained bythe classical model.The PtBi single crystals were synthesized using a self-flux method. Powders of the elements Pt (99.97%) and Bi(99.99%), both from Alfa Aesar, were thoroughly mixedtogether in an atomic ratio of Pt:Bi = 1:8, before beingloaded into a small alumina crucible. The crucible wasthen sealed in a quartz tube in Argon gas atmosphere.During the growth, the quartz tube was slowly heated upto 1273 K and kept at the temperature for 10 h. Finally itwas slowly cooled to 873 K at a rate of -3 K/h, followed bycentrifugation to remove the excessive Bi. The resultingsingle crystals are large plates with a typical dimensionof 3 × × . We cut the single crystal into arectangle of about 1 × × for transport mea-surements. The stoichiometry and structure of these sin-gle crystals were checked using Energy-dispersive X-rayspectroscopy (EDX) and X-ray diffraction (XRD) mea-surements. All transport measurements were carried outin an Oxford-15 T cryostat with a He4 probe in a Hall-bargeometry, using Keithley 2400 sourcemeters and 2182Ananovoltmeters.As illustrated in Fig. 1(a), PtBi has a layered pyritecrystal structure with the space group of P-3 (No. 147) .Fig. 1(b) shows the X-ray diffraction pattern of the PtBi single crystals. Only multiple reflections of (0 0 l ) planescan be detected, consistent with the layered crystal struc- FIG. 1. (color online) (a), The crystal structure of PtBi . (b),X-ray diffraction patterns of PtBi single-crystal sample. ture depicted in Fig. 1(a). The interplane spacing is de-termined to be 6.16 ˚A, agreeing well with the previousreported value .The temperature dependence of in-plane resistivitycurves under magnetic fields ( || c ) of µ H = 0, 5, 10and 15 T are displayed in Fig. 2(a). In zero field, theroom temperature resistivity is 1.1 µ Ω m and decreasesto 0.13 µ Ω m at 2 K, yielding a residual resistivity ra-tio (RRR) of 8.5. When a field is applied, the resistivityincreases rapidly, corresponding to a large positive mag-netoresistance (MR = ∆ ρ ( H ) /ρ (0) = ρ ( H ) /ρ (0) − µ H = 15 T at T = 2 K [Fig. 2(b)]. To our surprise, the roomtemperature magnetoresistance is still as large as 61% ina field of 15 T.The non-saturating, large linear magnetoresistance inPtBi is quite unusual and contradicts with the semiclas-sical transport theory. For conventional metals, the MRexhibits quadratic field-dependence in the low field rangeand saturates under high field, and the MR is usually of asmall value. For a system with open orbits or Fermi sur-faces, unsaturated MR with quadratic field dependence(or linear field dependence, which critically depends onthe Fermi surface and the relative orientation of mag-netic field) could appear even under high field along theopen orbits while in other directions MR would still showsaturated behavior. As a result, linear field dependenceof MR could be observed in polycrystal sample owing toaveraging effect . Such a giant, non-saturating linearMR in the PtBi single crystal certainly does not fit into H (T) T = 2 K2060100300 (b) ( m ) T (K) H = 15 T 10 T 5 T 0 T (a) FIG. 2. (color online) (a), In-plane resistivity ρ as a functionof temperature T at a series of out-of-plane magnetic fields µ H = 0, 5, 10 and 15 T. (b), The magnetoresistance (MR =∆ ρ ( H ) /ρ (0) = ρ ( H ) /ρ (0) −
1) as a function of magnetic field µ H at a series of temperatures T = 2, 20, 60, 100 and 300K. these two categories.We first consider a quantum explanation for the ob-served linear MR phenomenon in the framework devel-oped by Abrikosov . Following this theory, linear MRwill appear in the quantum limit, when ~ ω c exceeds theFermi energy E F and all the electrons occupy the low-est LL. In such a limit, the quantum magnetoresistivityis calculated as ρ xx = N i B/πn e , where n and N i arethe electron density and the concentration of scatteringcenters, respectively. The equation is valid under thecondition, n ≪ ( eB/ ~ ) / . That is, the quantum linearMR would appear when B ≫ ( ~ /e ) n / . In Fig. 3(a), wehave plotted the temperature dependence of Hall coeffi-cient ( R H ). The Hall resistivity ( ρ yx ) is linearly depen-dent on the magnetic field (not showing here) and thuswe use a single-band model to estimate the charge car-rier density, i.e, n = 1 /eR H and to calculate the criticalmagnetic field of ( ~ /e ) n / . We find that, even at 2K,it needs ∼
271 T to satisfy the quantum condition, whichis far higher than the maximum field of 15 T in our ex-periments. Therefore, the observed linear MR in PtBi dMR/dB d M R / d B ( T - ) (b) d M R / d B () (cm /Vs) T (K) ( c m / V s ) R H ( - m / C ) T (K)(a) FIG. 3. (color online) (a), Hall coefficient versus temperaturefor PtBi . (b), Hall mobility (red hollow circles) and dMR/d B (black solid squares) versus temperature. The inset displaysthe dMR/d B versus Hall mobility.. is unlikely to be explained by the quantum model.Instead, the classical disorder models may provide areasonable explanation for the presence of linear MR inPtBi . In the disorder network model, the linear MR ap-pears when the local current density gains spatial fluctu-ations in both magnitude and direction, as a result of in-homogeneous carrier or mobility distribution . Suchclassical linear MR phenomena have been observed invarious disordered systems, such as Bi Se , n-dopedCd As , and epitaxial graphene on SiC . In the clas-sical model, the slope dMR/d B is predicted to be pro-portional to the Hall mobility: dMR/d B ∝ µ . Indeed,the dMR/d B , which is defined as the slop of the linearlyfitting line of the linear region of MR at higher fields, ex-hibits the same temperature dependence (see the blacksolid squares in Fig. 3(b)) as the Hall mobility (red hol-low circles). The curve of dMR/d B versus µ can be fittedlinearly very well, as shown in the inset of Fig. 3(b). Thisstrongly suggests that the origin of the observed linearMR in our sample could be classical.This classical origin can be further verified by scal-ing the inverse Hall mobility with the crossover magneticfield ( B ∗ ) . We define the B ∗ , marked by the arrow, asthe crossing point of linear fits at the low and high fieldregimes, which are shown as blue dashed lines in the in- () (Vs/m ) () H (T) T = 2 KB*
FIG. 4. (color online) B ∗ versus inverse Hall mobility. Inset:Field dependence of MR (black hollow squares) at T = 2 K.The two dashed blue lines are the linear fits at the low andhigh field regimes. The point B ∗ , marked by the arrow, isdefined as the crossing point of these two lines.. set of Fig. 4. In the classical model, the crossover field ispredicted to be linearly proportional to the inverse Hallmobility: B ∗ ∝ /µ . Fig. 4 shows B ∗ versus inverse Hallmobility, which displays good linear dependence, consis-tent with the classical model well. This further confirmsthat the origin of the observed linear MR could be classi-cal. The disorder in the single-crystalline samples couldcome from the Bi-site vacancies. The occupation of Bisites obtained by EDX is around 94%, which confirmsthe existence of Bi-site vacancies.In summary, we performed detailed magnetotrans-port property measurements in the PtBi single crystals.PtBi exhibits very large linear magnetoresistance (684%in 15 T field at 2 K). The giant linear MR can scale wellwith the mobility. Our work indicates that the giant lin-ear MR could arise from the classical origin, which makesPtBi an appealing system for both practical use and fur-ther investigation on its physic properties.This work is supported by the National Basic ResearchProgram of China (Grant Nos. 2014CB921203 and2012CB927404), NSF of China (Contract Nos. U1332209and 11190023), the Ministry of Education of China (Con-tract No. 2015KF07), and the Fundamental ResearchFunds for the Central Universities of China. Y. Moritomo, A. Asamitsu, H. Kuwahara, and Y. Tokura, Nature , 141 (1996). J. Daughton, J. Magn. Magn. Mater. , 334 (1999). A. Urushibara, Y. Moritomo, T. Arima, A. Asamitsu, G. Kido,and Y. Tokura, Phys. Rev. B , 14103 (1995). M. N. Ali, J. Xiong, S. Flynn, J. Tao, Q. D. Gibson, L. M.Schoop, T. Liang, N. Haldolaarachchige, M. Hirschberger, N. P.Ong, and R. J. Cava, Nature , 205 (2014). F. Y. Yang, K. Liu, K. Hong, D. H. Reich, P. C. Searson, and C.L. Chien, Science , 1335 (1999). A. Husmann, J. B. Betts, G. S. Boebinger, A. Migliori, T. F.Rosenbaum, and M. L. Saboungi, Nature , 421 (2002). W. J. Wang, K. H. Gao, Z. Q. Li, T. Lin, J. Li, C. Yu, and Z.H. Feng, Appl. Phys. Lett. , 182102 (2014). N. V. Kozlova, N. Mori, O. Makarovsky, L. Eaves, Q. D. Zhuang,A. Krier, and A. Patan`e, Nat. Commun. , 1097 (2012). A. A. Abrikosov, Sov. Phys. JETP , 746 (1969); A. A.Abrikosov, Phys. Rev. B , 2788 (1998); A. A. Abrikosov, EPL , 789 (2000). M. M. Parish and P. B. Littlewood, Nature , 162 (2003). X. Wang, Y. Du, S. Dou, and C. Zhang, Phys. Rev. Lett. ,266806 (2012). A. L. Friedman, J. L. Tedesco, P. M. Campbell, J. C. Culbertson,E. Aifer, F. K. Perkins, R. L. Myers-Ward, J. K. Hite, C. R.EddyJr., G. G. Jernigan, and D. K. Gaskill, Nano Lett. , 3962(2010). J. Park, G. Lee, F. Wolff-Fabris, Y. Y. Koh, M. J. Eom, Y. K.Kim, M. A. Farhan, Y. J. Jo, C. Kim, J. H. Shim, and J. S. Kim,Phys. Rev. Lett. , 126402 (2011). K. K. Huynh, Y. Tanabe, and K. Tanigaki, Phys. Rev. Lett. , 217004 (2011). J. Hu, M. M. Parish, and T. F. Rosenbaum, Phys. Rev. B ,214203 (2007). C. Herring, J. Appl. Phys. , 1939 (1960). A. Narayanan, M. D. Watson, S. F. Blake, N. Bruyant, L. Drigo,Y. L. Chen, D. Prabhakaran, B. Yan, C. Felser, T. Kong, P. C.Canfield, and A. I. Coldea, Phys. Rev. Lett. , 117201 (2015). J. Hu and T. F. Rosenbaum, Nat. Mater. , 697 (2008). S. H. Simon and B. I. Halperin, Phys. Rev. Lett. , 3278 (1994). Y. Yan, L. Wang, D. Yu, and Z. Liao, Appl. Phys. Lett. ,033106 (2013). T. Biswas, and K. Schubert, Journal of the Less Common Metals , 223 (1969). A. B. Pippard,
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