Magnetic phase diagram of Cu 4−x Zn x (OH) 6 FBr studied by neutron-diffraction and μ SR techniques
Yuan Wei, Xiaoyan Ma, Zili Feng, Devashibhai Adroja, Adrian Hillier, Pabitra Biswas, Anatoliy Senyshyn, Chin-Wei Wang, Andreas Hoser, Jia-Wei Mei, Zi Yang Meng, Huiqian Luo, Youguo Shi, Shiliang Li
MMagnetic phase diagram of Cu − x Zn x (OH) FBr studied by neutron-diffraction and µ SR techniques
Yuan Wei,
1, 2
Xiaoyan Ma,
1, 2
Zili Feng,
1, 3
Devashibhai Adroja,
4, 5
Adrian Hillier, Pabitra Biswas, AnatoliySenyshyn, Chin-WeiWang, Andreas Hoser, Jia-Wei Mei, Zi Yang Meng,
1, 10, 11
Huiqian Luo,
1, 11, ∗ Youguo Shi,
1, 11, † and Shiliang Li
1, 2, 11, ‡ Beijing National Laboratory for Condensed Matter Physics,Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581, Japan ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot Oxon OX11 0QX, United Kingdom Highly Correlated Matter Research Group, Physics Department,University of Johannesburg, PO Box 524, Auckland Park 2006, South Africa Heinz Maier-Leibnitz Zentrum (MLZ), Technische Universit¨at M¨unchen, Garching D-85747, Germany Synchrotron Radiation Research Center, Hsinchu 30076, Taiwan Helmholtz-Zentrum Berlin f¨ur Materialien und Energie, D-14109 Berlin, Germany Shenzhen Institute for Quantum Science and Engineering, and Department of Physics,Southern University of Science and Technology, Shenzhen 518055, China Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics,The University of Hong Kong, Pokfulam Road, Hong Kong, China Songshan Lake Materials Laboratory , Dongguan, Guangdong 523808, China
We have systematically studied the magnetic properties of Cu − x Zn x (OH) FBr by the neutrondiffraction and muon spin rotation and relaxation ( µ SR) techniques. Neutron-diffraction measure-ments suggest that the long-range magnetic order and the orthorhombic nuclear structure in the x = 0 sample can persist up to x = 0.23 and 0.43, respectively. The temperature dependence ofthe zero-field (ZF) µ SR spectra provide two characteristic temperatures, T A and T λ . Comparisonbetween T A and T M from previously reported magnetic-susceptibility measurements suggest thatthe former comes from the short-range interlayer-spin clusters that persist up to x = 0.82. Onthe other hand, the doping level where T λ becomes zero is about 0.66, which is much higher thanthreshold of the long-range order, i.e., ∼ x = 0.66 with the perfect kagome planes. PACS numbers: 75.50.Mm; 75.30.Kz; 76.75.+i
Two-dimensional (2D) kagome antiferromagnetic(AFM) system has attracted great interests since itsstrong geometrical frustration effects can give rise tovarious ground states [1–7]. Especially, it has beensuggested to be one of the best platforms to realizequantum spin liquids (QSLs), which are highly entan-gled quantum magnetism that typically, although notnecessarily, shows no long-range magnetic order down tozero K [8, 9]. Up to now, the most well-studied kagome S = 1/2 magnetic material is the herbertsmithite,ZnCu (OH) Cl , which is believed to host a QSL groundstate [10–13]. However, there is no consensus on whetherits low energy excitations are gapped or gapless [14–19],which is crucial for us to understand the nature of theQSL state. One of the major difficulties lies in the factthat there are always a few percent of Cu ions sittingon Zn sites, which mainly affect the low-energy spinexcitations [17, 20].Recently, there are increasing new materials that alsoconsist of 2D Cu kagome layers [21–27]. While mostof them have magnetic orders, the Zn-doped barlowite(Cu Zn(OH) FBr) provides a promising new platform to study the QSL physics. The structure of barlowiteCu (OH) FBr is composed of 2D Cu kagome layerswith Cu ions in between and shows long-range AFMorder at 15 K[28–30]. Substituting interlayer Cu withZn can completely destroy the order and when thesubstitution is 100%, one expects a QSL ground state[29, 31, 32]. Indeed, the system shows no magnetic order-ing down to 50 mK although its dominate AFM exchangeinteraction is about 200 K [23]. More interestingly, bothNMR and inelastic neutron scattering results suggest ithas a gapped QSL ground state [23, 33]. Compared tothe herbersmithite, it has higher crystal symmetry, whichgives rise to smaller Dzyaloshinskii-Moriya interaction(DMI) [34, 35] and thus makes it further away from thequantum phase transition resulted from the DMI inter-action [36]. Moreover, symmetry lowering has been ob-served in the herbertsmithite but not in Cu Zn(OH) FBr[37–40].While the Zn-doped barlowite shows its advantagesin studying the QSL physics on a 2D kagome lattice,it still suffers the same magnetic-impurity issues as theherbertsmithite [23, 33]. To further address the role a r X i v : . [ c ond - m a t . s t r- e l ] J u l xxxxx / C u (a) xxxxx (b)(c) (d) x T = 20 K T = 20 K3.5 K - 20 K FIG. 1. (a) Neutron powder diffraction intensities of the x =0.3 and 0.69 samples at 20 K in the range of large Q ’s. Thelabeled peaks correspond to the orthorhombic peaks in the P nma space group. (b) The (1,0,2) O peaks for x from 0.12 to0.69 samples at 20 K. (c) First three magnetic peaks for the x = 0.12, 0.23 and 0.3 samples obtained by subtracting the20-K data from the 3.5-K data. The solid lines are calculatedresults for the magnetic structure as reported in [29]. All thedata in (a), (b) and (c) have been normalized by major nuclearpeaks after background subtracted. It should be pointed outthat since different instruments have different resolution, thenormalization only provides a rough guide. (d) Temperaturedependence of the magnetic moment for the interlayer Cu ions. of interlayer Cu spins, we systematically study theCu − x Zn x (OH) FBr system by the neutron-diffractionand µ SR techniques. The long-range magnetic order andlow-temperature orthorhombic structure are observed inthe neutron-diffraction experiments for x up to 0.23 and0.43, respectively. The ZF µ SR spectra can be fitted by aphenomenological function, which gives two parameters A and λ , corresponding to the extrapolated zero-timeasymmetry and long-time relaxation rate, respectively.By combining all the results, we provide a phase diagramof the Cu − x Zn x (OH) FBr system by combining previ-ous bulk and µ SR results [29, 32]. Our results are con-sistent with a gapped ground state in Cu Zn(OH) FBr.Polycrystalline Cu − x Zn x (OH) FBr were synthesizedby the hydrothermal method as reported previously [29].The neutron-diffraction data were obtained on SPODIat FRM-II, Germany, WOMBAT at ANSTO, Australia,and the instrument E9 at HZB, Germany. The nuclearand magnetic structures are refined by the FULLPROFprogram [41]. The µ SR experiments were carried out inthe longitudinal field (LF) geometry at MuSR and EMUspectrometers of the ISIS Facility at the Rutherford Ap-pleton Laboratory, Oxfordshire, U.K. The samples weremounted on a 99.995% silver plate, applying dilute GE x xx xx x (a) (b)(c) (d)(e) (f)
FIG. 2. (a) - (f) Time-dependent ZF µ SR spectra at differenttemperatures for the x = 0, 0.12, 0.3, 0.43, 0.52 and 0.61samples, respectively. The solid lines are fitted by Eq. (2). varnish covered with a high-purity silver foil. The µ SRdata were analyzed by the MantidPlot software [42].Figure 1(a) shows the neutron-powder-diffraction in-tensities of the x = 0.3 and 0.69 samples at 20 K. It hasbeen shown that the low-temperature nuclear strucutreof the x = 0 sample is orthorhombic with the space groupof P nma [29]. To see whether the orthorhombic struc-ture exists in these two samples, the panel only plots themagnification of the data at large Q ’s, which shows sev-eral orthorhombic peaks for the x = 0.3 sample but notfor the x = 0.69 sample. Refinements on the data demon-strate that the lattice space group of the x = 0.3 sampleis P nma , the same as that in the x = 0 sample [29]. Thestructure of the x = 0.69 sample is hexagonal with thespace group of P /mmc as that of the x = 0.92 sam-ple [23]. Figure 1(b) gives the (1,0,2) O peak for differentsamples, which shows that the orthorhombic structuremay still present in the x = 0.43 sample. Future stud-ies with large Q ’s data are need to determine at whichdoping level the orthorhombic structure disappears.Figure 1(c) shows the first three magnetic peaks forthe x = 0.12 and 0.23 samples, which can be refined bythe same magnetic structure as in barlowite [29]. In thisstructure, the ordered moment mainly comes from theinterlayer Cu spins, while the magnetic configurationfor the kagome spins is rather hard to be determined dueto their weak ordered moments [29, 30]. The doping de-pendence of the ordered interlayer moment is shown inFig. 1(d), which suggests that its value does not changewith doping. The decrease of the magnetic-peak inten- (a) (b) x x (c) (d) T A0 T λ xxxxxxx xxxxxxx FIG. 3. (a) & (b) Detailed analysis of the µ SR spectra for the x = 0 and 0.92 samples, respectively. The solid lines are thefitted results according to Eq. (2). The blue and red dashedlines are contributions from the µ -OH and µ -F complexes,respectively. The purple dashed lines show the contributionfrom the exponential decay. (c) & (d) Temperature depen-dence of A /A (30 K ) and λ . The solid lines are guides to theeye. The arrows in (c) and (d) mark the transition tempera-tures of A and λ for the x = 0 sample, respectively. sities is mainly due to the substitution of nonmagneticZn ions. While our neutron-diffraction data cannotdistinguish whether there is magnetic order for the x =0.3 sample because of its very weak signal (Fig. 1(c)),previous µ SR has shown that the magnetically orderedphase can survive up to 0.32 [32].Figure 2 provides the time-dependent ZF µ SR spec-tra for the Cu − x Zn x (OH) FBr system. At high tem-peratures, all of them show oscillation behaviors. Withdecreasing temperature, the oscillation is completely sup-pressed in the time range measured here for the low-doping samples but still presents for the middle dopingsamples. It has been shown that the oscillation is as-sociated with both µ -OH and µ -F complexes [32]. Theactual description of the µ SR spectra needs detailed in-formation of the asymmetry at very low time scale closeto zero, which is not accessible for our data. We thussimply introduce the following equation to account forthe oscillation, D iz ( t ) = [ 13 + 23 cos ( ω i t )] e − σ i t , (1)where i denotes for the µ -OH and µ -F complexes for i = 1 and 2, respectively, and σ i is associated with thedistribution of nuclear fields surrounding the muon spin.The time dependence of the asymmetry can be writtenas follows, ST 0 x T HexagonalOrthorhombic
AFMorder short-range AFM ? QSL
FIG. 4. Phase diagram of Cu − x Zn x (OH) FBr. The AFMorder is the long-range 3D magnetic order involving both theintralayer and interlayer spins. The nuclear structures for thelow-doping and high-doping samples are orthorhombic andhexagonal, respectively, with the crossover happens in thedoping range marked by the shaded area. The short-rangeAFM is from the interlayer Cu ions. The question markindicates the region between about 0.4 and 0.66 with an un-known ground state. The QSL ground state in the x = 1 sam-ple may be extended down to 0.66, as shown by the arrow. T A and T λ are determined by the temperature dependenceof A and λ as shown in Fig. 3(c) and 3(d). T HC and T M are from the heat-capacity and magnetic-susceptibility mea-surements [29]. T ST is from the temperature dependence ofthe frozen fraction from the µ SR measurement reported pre-viously [32]. The dashed lines are guides to the eye. A ( t ) = A [ f D z ( t ) + (1 − f ) D z ( t )] e − λt + A bg (2)where λ describes the weak electronic relaxation of themuons stopping in the sample and A bg is a constanttemperature-independent background for the muon stop-ping on the Ag sample holder. A similar function has alsobeen used in studying the Zn x Cu − x (OH) Cl system[13]. The factor f is introduced to account for differentcontributions from µ -OH and µ -F complexes. For all thesamples measured here, f is found to be 0.88. It shouldbe pointed out that although Eq. (2) cannot preciselydescribe the actual muon relaxation, it provides good ap-proximations of the µ SR spectra for all the samples at alltemperatures as shown in Fig. 2.Figure 3(a) and 3(b) further provide detailed analy-sis of the muon spectra for the x = 0 and 0.92 samples,respectively. The initial fast drop of the asymmetry ismainly due to the µ -OH complex, while the µ -F complexmainly contributes to the oscillation above about 2 µ s[32]. The relaxation term exp( − λt ) is also determinedby the long-time data, which may be related to the µ -F complex. Figure 3(c) and 3(d) show the temperaturedependence of the fitted parameters A normalized byits 30-K value and λ , respectively. For the x = 0 sam-ple, significant changes are found at T N for both A and λ . The temperatures are marked as T A and T lambda ,respectively. With increasing Zn substitution, both T A and T λ decrease but with different rate. While the for-mer is still above 10 K for the x = 0.61 sample, the latterhas already dropped to about 4 K.Figure 4 gives the phase diagram ofCu − x Zn x (OH) FBr by summarizing our resultsand previous studies [29, 32]. It has been previouslysuggested that the magnetic transition temperatures de-tected by the heat capacity and magnetic susceptibility,i.e. T HC and T M , become different in the Zn-substitutedsamples [29]. Here we found that T HC is close to T ST ,which is defined as the temperature where the frozenvolume fraction obtained from the µ SR spectra becomesnon-zero [32]. Since both the heat capacity and frozenvolume fraction are measuring the bulk properties, andour neutron-diffraction data also clearly show magneticpeaks up to x = 0.23, we conclude that the region forthe long-range order AFM order are marked by T HC and T ST .Figure 4 also demonstrates that T M and T A are veryclose to each other, which suggests they have the sameorigin. As shown above, the value of A is not the asym-metry at time zero but rather the extrapolated zero-timevalue after the very-fast initial drop that cannot be de-tected here. For the x = 0 sample, this kind of drop isdue to the local fields from the long-range magnetic or-der [32]. With Zn substitution, the long-range order issuppressed but the magnetic clusters, most likely formedby the interlayer Cu ions, can still survive and pro-vide local magnetic fields to depolarize the muon spins,which will result in the fast initial drop of the asymme-try. This is consistent with previous discussions on theorigin of the T M [29]. Therefore, the area marked by T M and T A is associated with the short-range AFM fromthe interlayer moments. It should be noted that for low-doping samples, the system enters into the short-rangeAFM first and then becomes long-range ordered with de-creasing temperature, which suggests that the long-rangeAFM order should involve kagome spins.Tracing the doping dependence of T λ shows that it endsat about x = 0.66, which is clearly not associated witheither the long-range or the short-range AFM. While itsorigin is unclear, there are a few results that may berelated to it. First, the crossover from the orthorhom-bic to the hexagonal structure may also happen at thesame doping range, as illustrated by the shaded area inFig. 4. The change of the structure should result inthe change of the exchange energies within the kagomeplanes. Second, it has been shown that the µ SR spectrado not change any more for x ≥ ≤ x ≤ < x < T λ , where the ground state of kagome planes is chang-ing from the 3D order to the gapped quantum spin liq-uid though an unknown intermediate state. Third, thevalue of λ is mainly determined by the long-time relax-ation and thus related to the µ -F complex. The positionof the fluorine makes it not sensitive to interlayer spins,as shown by the F NMR measurements [23]. As thelow-energy spin excitations become gapped [23, 33], oneexpect that µ SR spectra from the µ -F complex, whichonly detect very low-energy excitations, will not changewith the temperature any more. These results suggestthat the change of λ at low temperatures for x < x = 1 sample could be extended down to 0.66.It should be noted that the unknown crossover region la-beled by the question mark and the QSL state shouldnot be treated as within the short-range magnetic order,but rather as solely coming from the kagome spin system,which is phase-separated from the interlayer spin system.In conclusions, we establish the magnetic phase dia-gram of the Cu − x Zn x (OH) FBr system by comparingseveral techniques [29, 32]. The short-range spin corre-lations of the interlayer Cu moments can persist up to x ≈ x ≈ µ SR spectra disappears above x = 0.66,which is consistent with a gapped QSL state. Our resultssuggest that the kagome and interlayer spin systems aredecoupled at high-Zn-doping levels and may help us tofurther understand the actual magnetic ground state ofthe 2D kagome antiferromagnet Cu Zn(OH) FBr.This work is supported by the National Key Re-search and Development Program of China (GrantsNo. 2017YFA0302900, No. 2016YFA0300500,No. 2018YFA0704200, No. 2017YFA0303100,No. 2016YFA0300600), the National Natural Sci-ence Foundation of China (Grants No. 11874401, No.11674406, No.11674372, No. 11961160699, No.11774399,No.12061130200, No.11974392, No. 11822411)), theStrategic Priority Research Program(B) of the Chi-nese Academy of Sciences (Grants No. XDB25000000,No. XDB07020000, No. XDB33000000 and No.XDB28000000), Beijing Natural Science Foundation (No.Z180008, No. JQ19002), Guangdong Introducing Inno-vative and Entrepreneurial Teams (No. 2017ZT07C062).H.L. is grateful for support from the Youth InnovationPromotion Association of CAS (Grant No. 2016004). X.M. H. 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