Antiferromagnetism in kagome α -Cu 3 Mg(OH) 6 Br 2
Yuan Wei, Zili Feng, Clarina dela Cruz, Wei Yi, Zi Yang Meng, Jia-Wei Mei, Youguo Shi, Shiliang Li
AAntiferromagnetism in kagome α -Cu Mg(OH) Br Yuan Wei,
1, 2
Zili Feng,
1, 2
Clarina dela Cruz, Wei Yi, Zi YangMeng,
1, 5, 6, 7
Jia-Wei Mei, Youguo Shi,
1, 9, 6, ∗ and Shiliang Li
1, 2, 6, † 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 Neutron Scattering Division, Neutron Sciences Directorate,Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA Semiconductor Device Materials Group, National Institute forMaterials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan CAS Center of Excellence in Topological Quantum Computation and School of Physical Sciences,University of Chinese Academy of Sciences, Beijing 100190, China Songshan Lake Materials Laboratory , Dongguan, Guangdong 523808, China Department of Physics, The University of Hong Kong, China Shenzhen Institute for Quantum Science and Engineering, and Department of Physics,Southern University of Science and Technology, Shenzhen 518055, China Center of Materials Science and OptoelectronicsEngineeringUniversity of Chinese Academy of Sciences, Beijing 100049, China
The antiferromagnetism in α -Cu Mg(OH) Br was studied by magnetic-susceptibility, specific-heat and neutron-diffraction measurements. The crystal structure consists of Cu kagome layerswith Mg ions occupying the centers of the hexagons, separated by Br − ions. The magnetic systemorders antiferromagnetically at 5.4 K with the magnetic moments aligned ferromagnetically withinthe kagome planes. The ordered moment is 0.94 µ B , suggesting little quantum and geometricalfluctuations. By comparing the magnetic and specific-heat properties with those of the haydeeite,we suggest that α -Cu Mg(OH) Br may be described by the two-dimensional spin-1 / I. INTRODUCTION
The two-dimensional (2D) spin-1 / . For example, the S = 1/2 Heisenberg an-tiferromagnetic kagome model (AFKM) can give riseto ferromagnetic (FM) order, different types of anti-ferromagnetic (AFM) orders and quantum spin liquids(QSLs) . The AFKM may be realized in many min-erals of the atacamite group with the molecular for-mula as Cu T (OH) X , where T and X are the 3 d non-magnetic transition-metal (Zn, Mg) and the halogen el-ements (F,Cl,Br), respectively. The most well-knownmaterial is the herbertsmithite Cu Zn(OH) Cl , whichshows no magnetic order down to at least 30 mK andis suggested to be a QSL . The structure of γ -Cu Mg(OH) Cl is very similar to that of the herbert-smithite and may also host a QSL state . Recently, newmaterials Cu Zn(OH) FBr and Cu Zn(OH) FCl withsimilar structure have been successfully synthesized andshown to possibly host the gapped Z QSL groundstates .In the above materials, the kagome layers formedby Cu ions are separated with each other by non-magnetic Zn or Mg ions, which may be treated as diamag-netic dilution of the three-dimensional (3D) pyrochlore-like lattice. These non-magnetic ions can also occupythe center of the hexagons in the kagome layers, asfound in kapellasite, α -Cu Zn(OH) Cl and haydeeite, α -Cu Mg(OH) Cl . In this structure, the couplingbetween the kagome layers is through the weak inter- layer O-H-Cl bonding, which should result in highly 2Dmagnetic properties. It had been suggested that thekapellasite may be a gapless spin liquid or noncopla-nar coboc2-type AF order , but later measurementsfound strong Cu/Zn site mixing that makes the AFKMinappropriate . The haydeeite is a rare example of theFM order in the AFKM with T c at 4.2 K . Measure-ments on the single-crystal haydeeite further revealedstrong anisotropic behaviors between the in-plane andout-of-plane magnetic properties . Although the mag-netic structure has not been unambiguously solved, theordered moment is less than 0.2 µ B , suggesting strongquantum fluctuations. Therefore, the haydeeite may bein the proximity to the quantum phase transition be-tween the Heisenberg kagome FM order and the Heisen-berg cuboc2 AF order .The idea for the compound of Cu Mg(OH) Br comesfrom the substitution of interlayer Cu in the bar-lowite Cu (OH) FBr, which has perfect Cu kagomelayers with Cu ions between them and is antifer-romagnetically ordered at about 15 K . It hasbeen theoretically suggested that Zn or Mg ionscan replace the interlayer Cu in barlowite and thusdilute the AF order to give rise to a QSL state asin herbertsmithite . While this proposal has beenshown to succeed in Cu Zn(OH) FBr , no Mg-substituted barlowite has been reported. In this pa-per, we follow the same route in synthesizing the Zn-substituted barlowite to grow Mg-substituted barlowite.However, the final product is Cu Mg(OH) Br becauseMgF cannot be dissolved in water. Since it has the a r X i v : . [ c ond - m a t . s t r- e l ] A p r a bc a b MgCuODBr (a)(b) 2 ( degree ) θ FIG. 1. (a) Neutron powder diffraction intensities of α -Cu Mg(OD) Br (red dots) at 10 K. The calculated inten-sities are shown by the black lines. Short vertical greenlines represents Bragg peak positions, vertical red lines rep-resents Al peaks. The blue line shows the difference be-tween measured and calculated intensities. The weightedprofile R-factor ( R wp ) is 14.6%. (b) Nuclear structure of α -Cu Mg(OD) Br (3D and top views).Site x y z B (˚A )Mg 0.00000 0.00000 0.00000 0.281(406)Cu 0.50000 0.00000 0.00000 0.131(131)Br 0.33333 0.66667 0.63819(90) 0.117(155)O 0.82592(32) 0.17418(32) -0.14100(64) 0.511(120)D 0.19300(41) 0.80700(41) 0.28666(98) 0.398(140)TABLE I. Nuclear structure parameters of α -Cu Mg(OD) Br at 10 K. P /mmc (No. 194): a = b = 6 . c = 6 . α = β = 90 ◦ , γ = 120 ◦ . same crystal structure as kapellasite and haydeeite, welabel it as α -Cu Mg(OH) Br . The system orders anti-ferromagnetically at about 5.4 K but the configurationof the moments within the kagome plane is FM with theordered moment of 0.94 µ B . Our results suggest that α -Cu Mg(OH) Br is in the FM region of the phase di-agram in the AFKM. II. EXPERIMENTS α -Cu Mg(OH) Br was synthesized by the hydrother-mal method as described previously . The mixture of1.5-mmol Cu (OH) CO and 6-mmol MgBr · O wassealed in a 50-ml reaction vessel with 25-ml water, whichwas slowly heated to 200 ◦ C and kept for 12 hours. Thepolycrystalline samples were obtained by washing theproduction with the deionized water. To produce deuter-ated samples, Cu (OD) CO and heavy water were used in the above process. The Mg content is determined bythe inductively coupled plasma mass spectrometer. Themagnetic susceptibility and heat capacity were measuredby the MPMS and PPMS (Quantum Design), respec-tively. The magnetic and nuclear structures were deter-mined by neutron diffraction experiments performed onthe HB-2A diffractometer at HFIR, USA, with the wave-lengths of both 2.4103 and 1.5395 ˚A. III. RESULTS AND DISCUSSIONS
Figure 1(a) shows the neutron powder diffraction re-sults at 10 K. There is no structural transition observedsince the pattern at 300 K is similar to that at 10 K.Accordingly, the material has a hexagonal structure withthe space group of P /mmc . Detailed refinement re-sults are shown in Table I. The large R wp is mainly dueto the use of aluminum can and the presence of impuri-ties. These chemical impurities only exist in the deuter-ated samples as shown by the room-temperature x-raymeasurements. Figure 1(b) gives the nuclear structure.The Cu ions form kagome planes, which are separatedby Br − ions. The Mg ions sit at the centers of thehexagons within the Cu kagome planes.At 1.6 K, the system becomes magnetically orderedas shown by the new peak in Fig. 2(a). The subtractionbetween 1.6 and 10 K data provides more magnetic peaksas shown in Fig. 2(b). The k-search method is based onthe first 5 possible magnetic peaks. The best result givesout a propagation vector k = (0, 0, 0.5). Sarah wasused to check the possible structures from the resultsof representational analysis based on the nuclear spacegroup and magnetic k vector (0, 0, 0.5). There were3 irreducible representations (IR or Γ 1,3 and 5 ) as aresult of the analysis. All the basis vectors were tried.The Γ 1 and 3 can not fit the data at all. The bestresult comes from Γ5 BV 2. The other basis vectors forΓ5 other than Basis Vector 2 can not give good fits tothe data. The inset of Fig. 2(b) shows the magneticstructure. The moments at Cu positions are confinedwithin the kagome planes and ferromagnetically alignedalong b-axis. Along the c-axis, the moments are alignedantiferromagnetically.Figure 2(c) shows the temperature dependence of themagnetic peak at (0, 0, 0.5) in the nuclear structuralnotation. Figure 2(d) shows the temperature dependenceof the refined moment, which can be fitted by M (1 − T /T N ) β . The values of M and β are 0.94 ± µ B and 0.29 ± M at 0 K is consistent with the ordered moment gS for a S = 1/2 system with g = 2. The value of β is close tothat in a classical 3D Ising (0.326) or Heisenberg (0.367)system.Figure 3(a) gives the temperature dependence of themagnetic susceptibility χ , which clearly shows an AFphase transition at T N = 5.54 K. No significant dif-ference is found between the field-cooled and zero-field- (a) (d)(b)(c) 1.6 K - 10 K FIG. 2. (a) Neutron powder diffraction intensities of α -Cu Mg(OD) Br (red dots) at 1.6 K. The lines represent thesame meanings as those in Fig. 1(a). The vertical blue linesrepresent magnetic peaks. The arrow shows the new peakappeared at this temperature. The weighted profile R-factor( R wp ) is 14.1%. (b) The difference (blue lines) between theintensities at 1.6 K and 10 K for α -Cu Mg(OD) Br . Thered lines represent the calculated intensities for the magneticpeaks. The vertical green lines represent magnetic peaks. Theinset shows the magnetic structure. (c) The temperature de-pendence of the magnetic peak at (0, 0, 0.5). (d) The tem-perature dependence of the the moment. The error bars arefrom the refinements. The solid line is the fitted result asdescribed in the main text with T N fixed at 5 K. cooled processes. Above T N , χ still strongly depends onthe magnetic field, which suggests the presence of two-dimensional spin fluctuations. The inset shows the tem-perature dependence of χ − at 50 kOe. The fitting athigh temperatures gives a Curie temperature θ of about34 K and an effective moment of 1.77 µ B , which is closeto the value for S = 1/2 with g = 2. Figure 3(b) showsthe field dependence of the magnetization M . At 2 K, M becomes saturate above 20 kOe with the saturated mo-ment of 0.95 µ B , which also suggests that the system is S = 1/2. By taking the first derivative, two features can beseen at H ≈ H ≈ H is similar to the saturated field for
50 Oe 100 Oe 1 kOe χ ( e m u / m o l ) T ( K ) T N -40 -20 0 20 40-20-15-10-505101520 M ( x e m u / m o l ) H ( kOe ) (a) (b)(c) (d) -40 -20 0 20 40050100 H ∆ M ( e m u / m o l ) H ( kOe ) H -40 -20 0 20 400.00.51.01.5 H d M / d H ( x e m u / m o l ) H ( kOe ) H H = 50 kOe χ - ( m o l / e m u ) T ( K )
FIG. 3. (a) Temperature dependence of the magnetic suscep-tibility χ at 50 Oe, 100 Oe and 1 kOe. The arrow indicatesthe AF phase transition temperature. The inset shows thetemperature dependence of χ − at 50 kOe. The dashed lineis the linear fit to the high-temperature data. (b) M - H loopsat 2 and 20 K. (c) dM/dH at 2 and 20 K. (d) The differenceof M between increasing and decreasing fields at 2 and 20 K. field parallel to the kagome planes in haydeeite , whichsuggests that the coupling between the kagome planes isweak. These two characteristic fields can also be seen bythe hysteresis behavior as shown in Fig. 3(d).Figure 4(a) shows the specific heat of α -Cu Mg(OH) Br at several magnetic fields. TheAF transition results in a large peak, which becomes abroad hump above 3 T due to the suppression of thetransition. The background of the specific heat canbe estimated by fitting the data from 15 to 30 K with C = αT + βT as shown by the dashed line in Fig.4(a). The fitted values for α and β are 0.0265 J/molK and 2.86 × − , respectively, similar tothose in barlowite . Figure 4(b) shows the temperaturedependence of the entropy released associated with themagnetic transition, which is obtained by the integrationof C/T after subtracting the background as describedabove. The value of ∆ S AF at high temperature is about3 J/mol Cu K, which is just about half of Rln2. Thissuggests that spin correlations are formed well above T N ,consistent with the results in the magnetic susceptibilitymeasurements.Interestingly, there is an upturn of C below 0.2 K asshown in the inset of Fig. 4(a), which can be fitted as C ∝ T − / . This kind of temperature dependence sug-gests that the upturn is not from the nuclear schottkyanomaly or magnetic impurities. Moreover, the specificheat should move to higher temperatures under fields ifit comes from the nuclear schottky anomaly or magneticimpurities. Instead, it is suppressed at 30 kOe and thusshould be related to the intrinsic kagome system before (a)(b)
0 kOe90 kOe S ( J / m o l C u K ) T ( K )Rln2
0 kOe 10 kOe30 kOe 90 kOe C / T ( J / m o l K ) T ( K ) C ( J / m o l K ) T ( K ) T -3/2 FIG. 4. (a) Temperature dependence of
C/T at several fields.The black dashed line is the fitted result for the phonon con-tribution as discussed in the main text. The inset shows thespecific heat C below 1 K. (b) Magnetic entropy associatedwith the magnetic transition at 0 and 90 kOe. the spins are fully polarized by the field. The entropybetween 0.07 K to 0.2 K is about 0.12 J/mol K. It is notclear what is the origin of this upturn, but it is rathersurprising since the system shows no exotic propertiesfrom other measurements.The above results suggest that α -Cu Mg(OH) Br ex- hibits 2D kagome ferromagnetism similar to haydeeite α -Cu Mg(OH) Cl , although the system orders anti-ferromagnetically along the c-axis. The ordered mo-ment in haydeeite is just 0.2 µ B due to strong quan-tum fluctuations, and it is suggested to sit near theboundary between the FM and cuboc2 type noncopla-nar AFM parts in the phase diagram of the kagome lat-tice for a FM nearest-neighbour interaction . The α -Cu Mg(OH) Br is mostly likely in deep region of theFM part as its ordered moment is 0.94 µ B . Whilethis makes α -Cu Mg(OH) Br less interesting due tothe lack of frustration effects, it is worth noting thatit may be another platform to study the topologicalbands in the kagome ferromagnet as observed in Cu[1,3-benzenedicarboxylate(bdc)] . IV. CONCLUSIONS
Our systematically studies on the magnetism in α -Cu Mg(OH) Br demonstrate that it orders antiferro-magnetically below 5.54 K but the spins ordered ferro-magnetically within the kagome planes. The FM stateof the kagome planes can be achieved easily by applyinga weak magnetic field and its fluctuations survive above T N . Our results suggest that α -Cu Mg(OH) Br is inthe deep region of the FM part in the phase diagram of2D AFKM. ACKNOWLEDGMENTS
This work is supported by the Ministry of Scienceand Technology of China (Grants No. 2017YFA0302900,No. 2016YFA0300502, No. 2016YFA0300604), the Na-tional Natural Science Foundation of China (Grants No.11874401, No. 11674406, No. 11574359, No. 11674370,No. 11774399, No. 11474330), the Strategic Priority Re-search Program(B) of the Chinese Academy of Sciences(Grants No. XDB25000000 and No. XDB07020000, No.XDB28000000), and the National Thousand-Young Tal-ents Program of China. Research conducted at ORNL’sHigh Flux Isotope Reactor was sponsored by the Scien-tific User Facilities Division, Office of Basic Energy Sci-ences, US Department of Energy.Y.W. and Z.F. contributed equally to this work. ∗ [email protected] † [email protected] S. Sachdev, Phys. Rev. B , 12377 (1992). H. C. Jiang, Z. Y. Weng, and D. N. Sheng, Phys. Rev.Lett. , 117203 (2008). O. Janson, J. Richter, and H. Rosner, Phys. Rev. Lett. , 106403 (2008). S. Yan, D. A. Huse, and S. R. White, Science , 1173(2011). H.-C. 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