Yong Nie(聶勇), Zheng Chen(陳正), Wensen Wei(韋文森), Huijie Li(李慧杰), Yong Zhang(張勇),Ming Mei(梅明), Yuanyuan Wang(王園園), Wenhai Song(宋文海), Dongsheng Song(宋東升),Zhaosheng Wang(王釗勝),?, Xiangde Zhu(朱相德),?, Wei Ning(寧偉),§, and Mingliang Tian(田明亮),5

1Anhui Key Laboratory of Low-energy Quantum Materials and Devices,High Magnetic Field Laboratory,HFIPS,Chinese Academy of Sciences,Hefei 230031,China

2Department of Physics,University of Science and Technology of China,Hefei 230026,China

3Key Laboratory of Materials Physics,Institute of Solid State Physics,HFIPS,Chinese Academy of Sciences,Hefei 230031,China

4Information Materials and Intelligent Sensing Laboratory of Anhui Province,Key Laboratory of Structure and Functional Regulation of Hybrid Materials of Ministry of Education,Institutes of Physical Science and Information Technology,Anhui University,Hefei 230601,China

5School of Physics,Anhui University,Hefei 230601,China

Keywords: linear magnetoresistance,thermal expansion,specific heat,structural distortion

In the past, a number of materials with rhombohedral CaCu4P2-type structures[1]have been synthesized, including the arsenidesACu4As2(A= Na, K, Ca, Sr, Ba, Eu)[2–5]andAAg4As2(A= Sr, Eu),[6–9]the antimonidesACu4Sb2(A=Na, K),[10]and the phosphidesACu4?xP2(A=Ca, Sr,Ba,Y,La–Nd,Eu–Yb).[11–13]These compounds exhibit complex interplay between different orders, such as the coexistence, competition, and/or correlation of magnetism,[6,7,14]charge density waves,[15]and structural phase transitions.[16]For example,in the layered magnetic compound EuAg4As2,a phase transition was observed at 120 K,and incommensurate noncollinear long-range antiferromagnetism developed below 9 K.[6]In CaCu4As2, multilayer quantum Hall effects and phase transition below 51 K were observed.[15]Meanwhile,in recently reported EuCu4As2, both a large negative magnetoresistance(?55%,at 35 K,9 T)near the magnetic transition temperature and a large positive magnetoresistance (60% at 2 K,9 T)at lower temperatures were observed.[4]As a result of these observations, the investigation of other members of the CaCu4P2family may help to explore more exotic phenomena that contribute to this area.

In this work, we focus on the phosphides SrCu4?xP2,which adopt the space group ofin the rhombohedral CaCu4P2structure.[13]We synthesized high-quality SrCu4?xP2single crystals and performed detailed physical property measurements and structural characterization,together with electrical transport, magnetization, specific heat,thermal expansion and transmission electron microscope(TEM) analysis.Linear magnetoresistance (LMR) was observed,with no signature of saturation up to 12 T.As a result of detailed data analysis,we consider that this LMR originates from mobility fluctuation, and the PL model can be applicable here.Meanwhile,we observed a phase transition at 140 K,where both the resistivity and heat capacity showed significant anomalies.Thermal expansion revealed a subtle lattice parameter variation nearTp,while the structural characterization showed that there is no structure transition below and aboveTp.Our experimental data suggested that this transition is a nonmagnetic transition and likely in relation to the structural distortion.

Single crystals SrCu4?xP2were grown via the Bi–Cu flux method.The stoichiometry of the starting raw materials of Sr shots (3N purity), Cu plates (4N purity), red phosphorus pieces (3N purity) and Bi shots (5N purity) was 1:8:2:35 in molar ratio.The oxide layers of the Sr shots were scraped off from the surface.The mixture was placed inside an alumina crucible and sealed in a quartz tube, slowly heated to 1050°C, then kept at this temperature for 20 h, and finally cooled to 850°C at a cooling rate of 3°C/h before separating the flux in a centrifuge.Phase purity was checked via x-ray diffraction using a Rigaku-TTR3 with Cu-Kαradiation.The chemical stoichiometry of both samples was determined from an energy dispersive spectrum (EDS) equipped upon a Helios nanolab600i.Resistivity and specific heat measurements were performed using a physical properties measurement system (PPMS-14T, QD Inc.).Magnetization measurement was performed using a magnetic properties measurement system(MPMS3-7T,QD Inc.).TEM analysis and selected area electron diffraction(SAED)were performed using a Talos F200X equipped with a liquid-nitrogen-cooled holder.Thermal expansions were measured using a homemade strain gauge[17]and capacitance dilatometer,[18]respectively.

The layered compound SrCu4?xP2crystallizes in the rhombohedral CaCu4P2structure.The structure can be regarded as the insertion of an additional itinerant Cu2layer within the Cu2P2layer of the trigonal CaAl2Si2-type stacking of –A–Cu2P2–A–, as illustrated in Fig.1(a).[13]Sr ions are located between the Cu2P layers.The single-crystal chemical composition in this work, obtained by EDS, is Sr:Cu:P=15.17:55.61:29.21, i.e., SrCu3.67P1.93.Figure 1(b)shows the XRD patterns of the single crystals of SrCu4?xP2.The diffraction peaks of the crystal face are well indexed with the (00l) plane, which is the same as those reported in EuAg4As2.[6,7]As shown in the inset of Fig.1(b), the full width at half maximum(FWHM)of the rocking curve of the(003)peak reaches as low as 0.24°,indicating the high quality of the as-grown single crystals.

Fig.1.(a) An illustration of the crystal structure of SrCu4?xP2 in one unit cell.(b) The XRD patterns of the as-grown single crystals of SrCu4?xP2.The inset is the rocking curve at the(003)peak.(c)The temperature dependence of resistivity at zero field.(d)The temperaturedependent magnetization of SrCu4?xP2 in the low-temperature region.

We firstly measured the temperature-dependent resistivity (ρ–T) of SrCu4?xP2at zero magnetic field, as shown in Fig.1(c), which exhibits metallic behavior with a kink at 140 K; the possible origin of this kink could be related to structure distortion and will be discussed briefly later.The magnetization curve suggests a paramagnetic background in SrCu4?xP2at low temperatures,as shown in Fig.1(d).The observed negative susceptibility could be due to the diamagnetic background of the sample holder during the measurement.

Figure 2(a)shows the field-dependent magnetoresistance(MR), defined as[ρ(B)?ρ(0)]/ρ(0)×100%, with theH||caxis.TheMRreaches 130%up to 12 T at 2 K with no sign of saturation.It exhibits semiclassical quadratic dependence in the low field.[19]and linear behavior in the high field.As the temperature increases, theMRgradually decreases to 13% at 120 K.We also carried outMRmeasurement with a magnetic field up to 30 T,as shown in Fig.2(c).TheMRreaches 370%at 32 T at 1.6 K and continues to increase with the magnetic field.Similar linearMRhas been observed in many materials,such as Cd3As2,TlBiSSe,and BaMnBi2.[20–22]

Fig.2.(a) The MR as function of the magnetic field at various temperatures with H||c.Inset: quadratic fitting using the relationship MR=A2·B2 in the low-field region,and linear fitting using MR=A1·B at T =2 K.(b)The MR curve at 1.6 K with a magnetic field up to 32 T.

The origin of linearMRcan arise from distinct mechanisms, including Abriskosov’s theory for materials with gapless linear energy–momentum dispersions for electrons and the classical Parish–Littlewood model (PL model) for strongly inhomogeneous systems.According to Abriskosov’s theory,[23,24]in the quantum limit, linearMRarises when all the electrons fill the lowest Landau level.However,linearMRcould be observed in a low magnetic-field range,which is not the case in our SrCu4?xP2; thus, Abriskosov’s theory should not be applicable here.

Fig.3.(a)The magnetic-field-dependent dMR/dB at various temperatures.A crossover field Bc is defined as the intersection between the two fitting lines.(b)The temperature dependence of MR at H =12 T and the crossover field Bc.The inset is the temperature dependence of the mobilityμ.(c)Linear behavior of MR at H=12 T and mobilityμ.(d)Linear behavior of the crossover field with inverse mobility 1/μ.

We now turn to the classic PL model,[25]which has been used widely to understand the linearMRbehavior in disordered Ag2±δSe/Ag2±δTe, n-doped Cd3As2,[20,26–28]and narrow-band semiconductors.[29]In these materials,linear MR could be observed due to the existence of large mobility fluctuation.Based on this model,theMRshould be proportional to the mobility(MR∝μ)and the crossover fieldBc,and the mobility obeys the relation withBc∝1/μ.Figure 3(a) presents the field derivative of theMR, dMR/dB, at various temperatures.The crossover fieldBccan be determined from the intersection of the quadratic and linear regimes.According to Kohler’s rule,R(B)/R(0)≈1+(μB)2, the mobility can be estimated from the low-field slope of dMR/dBcurves.As the temperature increases,theMRand mobility monotonically decrease, while the crossover fieldBcincreases, as shown in Fig.3(b).TheMRvs.μandBcvs.1/μrelations are demonstrated in Figs.3(c)and 3(d); both display linear relations,in good agreement with the PL model.We noticed that the linearMRofn-Cd3As2.[20]and Ag2?δSe[30]originated from the disorder caused by Cd-rich and Ag defects, respectively.Therefore,we propose that the LMR of SrCu4?xP2originates from disorder caused by a Cu deficiency.

We now return to the kink of the SrCu4?xP2on theρ–Tcurve.As shown in Fig.4(a), the temperature-dependent resistivityρxxpresents a small hysteresis between the cooling and heating cycles.Such a kink onρxx–Tcurves has been observed in EuAg4As2[6]and CaCu4As2,[15]which has been attributed to the structural distortion or charge density wave(CDW).In the following,we will focus on this transition,together with specific heat, thermal expansion and TEM analysis.

We firstly compare the temperature-dependent resistivityρxxwith the heat capacity.Figure 4(b)shows the temperaturedependent heat capacity (Cp) measurements.It is found that the heat capacityCpshows a remarkable hump anomaly aroundTp, with independence from the applied magnetic fields.These results demonstrate that the anomaly nearTporiginates from a thermodynamic phase transition with a nonmagnetic nature.By subtracting the background from the data and integrating(Cp?Cfit)/T,we obtain ΔSto be 0.72 J/mol·K.Temperature dependences of thermal expansion(ΔL/L)in theabplane and along thec-axis.As shown in Fig.4(c),a slight drop of thec-axis about ΔLc/Lc～0.062%andabplane about ΔLab/Lab～0.075% were probed when the temperature decreased from 145 K to 130 K.We note that this lattice distortion is significantly smaller than a typical crystal structural transition with a lattice change of the order of～0.5%–1%.[31,32]

To check whether the anomaly nearTpis related to the structure transition, we carried out structural characterization via SAED studies using the TEM technique.Figures 5(a)and 5(b) show, respectively, the SAED patterns with the electron incidence parallel to the[0001]direction at 300 K and 100 K for SrCu4?xP2.It is clear that the patterns are the same above and belowTp, except for the variations of the spot brightness intensity.No noticeable change in the crystal structures in the space group occurs.In previous work on EuAg4As2,a similar phase transition has also been observed,[6]where a superlattice structure emerges belowTpin the x-ray diffraction precession study.Here,this transition in SrCu4?xP2should not arise from structural phase transition or CDW,but is due to the subtle lattice changes, as shown in Fig.4(c).A similar transition was also observed in EuCu4As2[4]and SrAg4As2.[33]Convergent beam electron diffraction (CBED) or scanning tunneling microscope(STM)measurements are helpful in determining the underlying physics of the uniqueTptransition in SrCu4?xP2.

Fig.4.(a)The temperature-dependent resistivity under cooling(blue line)and heating (red line) processes for SrCu4?xP2.(b) The temperature-dependent specific heat capacity(Cp)curves at H =0 T,3 T near Tp in SrCu4?xP2.The inset shows the heat capacity by subtracting the background and transition entropy in the transition region.(c)Thermal expansion of lattice parameters along the c-axis and in the ab plane in SrCu4?xP2.

Fig.5.(a) and (b) The SAED patterns of SrCu4?xP2 taken along the zone axis[0001]at 300 K and 100 K,respectively.

In conclusion,we performed systematical investigation of SrCu4?xP2single crystals.Large non-saturating LMR was observed,which should originate from the disorder caused by Cu deficiency.A phase transition was observed atTp～140 K,with anomalies in resistivity and heat capacity.The thermal expansion measurements and structural characterization proved that there are only subtle lattice parameter changes nearTp.Our measurements demonstrate that the transition of SrCu4?xP2does not endure any type of magnetic or crystal structural changes,but is likely associated with structural distortion.

Acknowledgements

Project supported by the National Key Research and Development Program of China(Grant Nos.2023YFA1607403,2021YFA1600201, and 2022YFA1602603), the Natural Science Foundation of China(Grant Nos.U19A2093,U2032214,and U2032163), the Collaborative Innovation Program of Hefei Science Center, CAS (Grant No.2019HSC-CIP 001),the Youth Innovation Promotion Association of CAS (Grant No.2021117), the Natural Science Foundation of Anhui Province (No.1908085QA15), the HFIPS Director’s Fund(Grant No.YZJJQY202304), and the CASHIPS Director’s Fund (Grant No.YZJJ2022QN36).A portion of this work was supported by the High Magnetic Field Laboratory of Anhui Province.