Magnetism study on a triangular lattice antiferromagnet Cu 2 (OH) 3 Br
aa r X i v : . [ c ond - m a t . s t r- e l ] A p r Magnetism study on a triangular latticeantiferromagnet Cu (OH) Br Z Y Zhao , H L Che , R Chen , J F Wang , X F Sun , , and ZZ He State Key Laboratory of Structural Chemistry, Fujian Institute of Research on theStructure of Matter, Chinese Academy of Sciences, Fuzhou, Fujian 350002, People’sRepublic of China Department of Physics, Hefei National Laboratory for Physical Sciences atMicroscale, and Key Laboratory of Strongly-Coupled Quantum Matter Physics(CAS), University of Science and Technology of China, Hefei, Anhui 230026, People’sRepublic of China Wuhan National High Magnetic Field Center, Huazhong University of Science andTechnology, Wuhan, Hubei 430074, Peoples Republic of China Institute of Physical Science and Information Technology, Anhui University, Hefei,Anhui 230601, People’s Republic of China Collaborative Innovation Center of Advanced Microstructures, Nanjing, Jiangsu210093, People’s Republic of ChinaE-mail: [email protected]
E-mail: [email protected]
Abstract.
Magnetism of Cu (OH) Br single crystals based on a triangular lattice isstudied by means of magnetic susceptibility, pulsed-field magnetization, and specificheat measurements. There are two inequivalent Cu sites in an asymmetric unit.Both Cu sublattices undergo a long-range antiferromagnetic (AFM) order at T N = 9.3 K. Upon cooling, an anisotropy crossover from Heisenberg to XY behavior isobserved below 7.5 K from the anisotropic magnetic susceptibility. The magnetic fieldapplied within the XY plane induces a spin-flop transition of Cu ions between 4.9 Tand 5.3 T. With further increasing fields, the magnetic moment is gradually increasedbut is only about half of the saturation of a Cu ion even in 30 T. The individualreorientation of the inequivalent Cu spins under field is proposed to account for themagnetization behavior. The observed spin-flop transition is likely related to one Cusite, and the AFM coupling among the rest Cu spins is so strong that the 30-T fieldcannot overcome the anisotropy. The temperature dependence of the magnetic specificheat, which is well described by a sum of two gapped AFM contributions, is a furthersupport for the proposed scenario. Keywords : Single-crystal growth, Geometrical frustration, Magnetic transition
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J. Phys.: Condens. Matter agnetism study on a triangular lattice antiferromagnet Cu (OH) Br
1. Introduction
Geometrical frustration embedded in quantum antiferromagnets can introduce numerousunconventional magnetism such as spin ice, spin liquid, and magnetization plateau[1, 2, 3, 4, 5, 6, 7, 8]. Thereinto, spin liquid is the most attractive subjectin modern condensed matter physics [9, 10, 11, 12, 13, 14, 15, 16]. The firstreported candidate is herbersmithite ZnCu (OH) Cl [17], and its parent compoundclinoatacamite Cu (OH) Cl is also a frustrated antiferromagnet [18]. Cu (OH) Clbelongs to M (OH) X ( M = transition metal; X = Cl, Br, I) family, whichhas four frustrated polymorphs named as atacamite, botallackite, clinoatacamite,and paratacamite. When replacing different transition metals or halogens, diversespin fluctuations and exchange interactions can compete with the structure-relatedfrustration effect and result in variously novel ground states. M (OH) X is thereforea good material playground to study the geometrical frustration and the associatedquantum magnetism. In addition, strong magnetic-dielectric-lattice coupling was alsoobserved in M (OH) X signaling the multiferroic behavior and a potential applicationin magnetic storage [19].Investigation of anisotropic magnetism on single crystals is essential to explorephysics of M (OH) X family. However, early studies on M (OH) X were mostlyperformed on polycrystals or microcrystals. Though there exist natural M (OH) X crystals, the purity and size were not sufficient for the exploration of the intrinsicanisotropic magnetism. The lack of large synthetic crystals impedes the deepunderstanding of the physics from two aspects. First, the magnetism is usually differentin powder and crystals. In atacamite Cu (OH) Cl, the synthetic powder showed aspin-glass behavior while the mineral crystal underwent a antiferromagnetic (AFM)transition at T N = 9 K [20, 21]. In paratacamite Co (OH) Cl polycrystalline sample,besides the kagom´e-ice transition at T C = 10.5 K as observed in single crystals, a glasslikefreezing was also found below 3 K which was likely resulted from the micro Co deficiency[22]. Even for powder, paratacamite Fe (OH) Cl synthesized by different groups showedobviously different transition temperatures [23, 24]. Second, the behavior observed inpowder sample is an average of the anisotropic properties which is not able to offeraccurate physical information. For example, two successive field-induced transitionsand a possible magnetization plateau were detected in paratacamite Co (OH) Br [25].A completely flat plateau was suspected to show in the anisotropic magnetizationperformed on a single crystal. For paratacamite Fe (OH) Cl, neutron diffraction gavefour possible magnetic structures, and it was pointed out that only single-crystalexperiment can determine the definite spin configuration [24].In this work, we successfully synthesized large and high-quality botallackiteCu (OH) Br single crystals for the first time. Among all polymorphs, botallackiteis the rarest in nature and little study has been thus carried out. Different from theother three polymorphs in which the magnetic ions constitute a pyrochlore-like network,botallackite has a two dimensional (2D) triangular lattice. Figures 1(a) and 1(b) display agnetism study on a triangular lattice antiferromagnet Cu (OH) Br Figure 1. (a-b) Crystal structures projected in the ab plane and viewed along the a axis, respectively. Hydrogen atoms are omitted for clarity. (c) X-ray diffraction onthe (00 l ) facet. Inset is a photograph of one piece of botallackite Cu (OH) Br singlecrystal. The a and b axes are labeled as arrows. the crystal structure of botallackite Cu (OH) Br. There are two peculiar Cu positionsin an asymmetric unit. Cu1 is octahedrally coordinated by four hydroxyls and two Bratoms whereas Cu2 is surrounded with five hydroxyls and one Br atom, and both copperoctahedra are strongly distorted. The Cu-O bonds constitute a 2D sheet parallel to ab plane, and the Br atoms are located on both sides of each sheet. The 2D sheet canbe considered as a triangular lattice composed of edge-shared Cu1 and Cu2 uniformchains along the b axis which are further connected alternately by sharing two edgesalong the a axis. These sheets are stacked along the c axis through O-H · · · Br bondsso as to develop a three-dimensional network. The resultant weak interlayer interactionaccounts for the good two dimensionality, and botallackite Cu (OH) Br is thus regardedas an S = 1/2 spatial anisotropic triangular lattice compound. As far as we know, onlyone work performed on botallackite Cu (OH) Br polycrystalline sample was reported[26]. A broad peak was observed around 10 K in the magnetic susceptibility, which wasascribed to the long-range AFM transition of Cu ions.In this manuscript, the magnetism of botallackite Cu (OH) Br single crystals isstudied. A slope change of the magnetic susceptibility is observed at T N = 9.3 K whichis associated with the long-range AFM order as confirmed by the λ peak in specificheat, while the broad peak around 10 K is resulted from the development of the short-range AFM correlation. With lowering temperature, a temperature-induced anisotropycrossover from Heisenberg to XY behavior is observed below 7.5 K. When the magneticfield is applied within the XY plane, a spin-flop transition occurs at low fields, andthe magnetic moment is only about half of the saturation of a Cu ion even in 30 T.Considering the distinct local environments of Cu1 and Cu2, individual field-inducedspin reorientation is proposed to account for the magnetization behavior. The low-fieldspin-flop transition is likely related to one Cu site, and the anisotropy energy of the agnetism study on a triangular lattice antiferromagnet Cu (OH) Br
2. Methods Cu (OH) Br single crystals were grown using a conventional hydrothermal method.Stoichiometric CuBr and Cu(NO ) · O were dissolved in 2 mL deionized water,and then sealed in an autoclave equipped with a 28 mL Teflon liner. The autoclaveswere heated at 230 ◦ C for 4 days under autogenous pressure and then cooled to roomtemperature at a rate of 1.5 ◦ C/h for 6 days. The as-grown single crystals are darkgreen with elongated hexagon shape, as shown in the inset to Fig. 1(c). The typicalsize of the crystals is 5 mm × × α radiation ( λ = 0.71 ˚A)at room temperature. The refined lattice parameters a = 5.6613(11) ˚A, b = 6.1596(7) ˚A, c = 6.0829(9) ˚A, and β = 93.569(15) ◦ are consistent with previously reported [26]. Thelargest facet of the as-grown single crystal was checked to be parallel to the ab plane asseen from the x-ray diffraction on the (00 l ) facet in Fig. 1(c), and the length directionwas further confirmed to be along the b axis. In this work, the direction perpendicularto the ab plane is defined as c ∗ axis.Magnetic susceptibility and magnetization were measured using a SQUID-VSM(Quantum Design) between 2 and 300 K up to 7 T. Specific heat was measured bythe relaxation method between 2-150 K using a PPMS (Quantum Design). Pulsed-fieldmagnetization was performed at 2 K up to 30 T on a self-built platform in WuhanNational High Magnetic Field Center (China).
3. Results and Discussion
Temperature dependencies of the magnetic susceptibility χ ( T ) measured along the threedirections in B = 0.1 T are shown in Fig. 2. No difference is observed in the field-cooling(FC) and zero-field-cooling (ZFC) measurements. Above 100 K, χ ( T ) follows well theCurie-Weiss law χ = χ + C/ ( T − θ CW ), where χ is a temperature-independent term.The Curie-Weiss temperatures for three directions are θ CW ,a = -21.7(7) K, θ CW ,b = -15.5(4) K, θ CW ,c ∗ = -19(1) K, and the effective moments are deduced to be µ eff ,a =1.80 µ B /Cu , µ eff ,b = 1.73 µ B /Cu , µ eff ,c ∗ = 1.89 µ B /Cu , respectively. The negative θ CW suggests a dominant AFM interaction among Cu spins. Upon cooling, χ ( T ) isgradually increased and exhibits a broad peak around 10 K. This is a common featurein the low-dimensional antiferromagnets and indicates the development of short-rangeAFM correlation. With further lowering temperature, χ a and χ c ∗ show a sudden dropat about 9 K, which is associated with the AFM order of Cu spins on account of agnetism study on a triangular lattice antiferromagnet Cu (OH) Br ( - e m u / m o l ) T (K) = 0.1 T d / d T ( a r b . un it ) T N Figure 2.
Temperature dependencies of the magnetic susceptibility measured in 0.1T along the three directions. The differentials of the magnetic susceptibility along the a and c ∗ axes are also plotted. the inevitable interlayer interaction. The transition temperature is defined as the peakposition of the differentials in Fig. 2. Apparently, the broad peak observed around 10K in the previous polycrystalline study is related to the short-range AFM correlationrather than the AFM order [26]. The absence of the anomaly across T N in χ ( T ) in thatwork might be due to a different sample quality in different growth condition, whichfurther highlights the importance of single crystals in understanding the physics of thequantum antiferromagnets.At lower temperatures, a minimum is observed in χ b at 7.5 K. The presence of theminimum is a remarkable feature for the exchange-anisotropy crossover from Heisenbergto XY behavior in two-dimensional antiferromagnets [6, 27, 28, 29, 30, 31]. When thetemperature is decreased, the XY anisotropy becomes significant and a large amountof spins are confined in the plane. As a result, the in-plane χ ( T ) decreases faster, whilethe perpendicular component is reduced with canted ferromagnetic moment along thefield direction. Consequently, a minimum finally occurs in the out-of-plane component,and the minimum position is usually defined to be the crossover temperature belowwhich the AFM correlation becomes irrelevant in the out-of-plane component. Sincethe minimum appears in χ b , the magnetic XY plane is therefore the ac ∗ plane whichis not identical to the triangular layer from the crystal structure determined at roomtemperature. X-ray diffraction performed below 7.5 K is demanded to investigate thecrystal structure and explore the origin of the exotic XY anisotropy.Figure 3 shows the magnetization M ( B ) measured in static fields up to 7 T alongthe three directions. At 2 K, both M a and M c ∗ exhibit a step-like enhancement withincreasing magnetic field. Upon warming, the critical field for M a is almost unchanged( ∼ M c ∗ .Since the applied field is within the XY plane, the step-like enhancements observed in M a and M c ∗ are likely resulted from the spin flop of Cu spins. However, the different agnetism study on a triangular lattice antiferromagnet Cu (OH) Br ( B / C u + ) B // a ( B / C u + ) B (T) (c) ( B / C u + ) B // b
Figure 3.
Magnetic-field dependencies of the magnetization along three directions atdifferent temperatures. tendencies of the critical fields deserve further investigations to explore the differencebetween M a and M c ∗ . In contrast, M b shows a linear increase with the magnetic field.The anisotropic magnetic susceptibilities measured up to 7 T are displayed in Fig.4. At low fields, both χ a and χ c ∗ are quickly decreased at low temperatures due tothe XY anisotropy. When the field is higher than the spin-flop transition field, thelow-temperature magnetic susceptibility is increased resulting in a minimum whichcorresponds to the transition from paramagnetic state to the spin-flop state. On theother hand, the behavior of χ b is almost unchanged in the magnetic fields suggesting arobust XY anisotropy.From Fig. 3 it is clearly seen that M c ∗ is largest as compared with the other twocomponents, while it is only about 0.33 µ B /Cu in 7 T and much smaller than thesaturated moment of a Cu ion. To explore the possible magnetic phase transitionsin higher fields, pulsed-field magnetization is performed up to 30 T at 2 K. As shownin Fig. 5, except for the spin-flop transition at lower fields, there is no extra transitionfound in higher fields when the magnetic field is applied in the XY plane. In spite of theslow increase above 10 T, there should not be magnetization plateau in Cu (OH) Br.In triangular lattices, the 1/3 magnetization plateau is stabilized by the quantum agnetism study on a triangular lattice antiferromagnet Cu (OH) Br T (K)
B // b ( - e m u / m o l ) B // c* (a) (b) (d)(c)
B // a B // aB // c*B // b
T (K) (f)(e)
Figure 4.
Anisotropic magnetic susceptibilities measured in various magnetic fieldsbelow 1 T (a-c) and above 3 T (d-f) along the three directions.
B // aB // c* ( B / C u + ) (T) Figure 5.
Magnetization measured in pulsed fields up to 30 T at 2 K with field appliedin the XY plane. fluctuations, and an upward concave curvature is usually appeared before entering intothe plateau phase. The rounding of the magnetization in Cu (OH) Br seems more likethe spin polarization process. It should be mentioned that the magnetization is a bitsample dependent, that is, the enhancement of the magnetization across the spin-floptransition for the crystals grown from different batches is somewhat different, but themagnitude at high fields is always close or smaller than 0.5 µ B . Such difference has nosignificant influence on discussing the ground state in the following section. agnetism study on a triangular lattice antiferromagnet Cu (OH) Br (c)(b) C p ( J / K m o l ) (a) C m a g / T ( J / K m o l ) S ( J / K m o l ) B c C mag aT exp(- /T) + bT exp(- /T) T T (K) C m a g ( J / K m o l ) B = 0
Figure 6.
Temperature dependence of the specific heat. (a) Total specific heat in zerofield. Inset: specific heat in different magnetic fields parallel to the c ∗ direction. (b)Magnetic specific heat divided by temperature and the entropy change in zero field.(c) Magnetic specific heat in a log-log plot. The solid line is a fit including two gappedAFM contributions. The dashed line is the T dependence. Figure 6(a) displays the specific heat C p measured in zero field. A λ peak is observedat T N = 9.3 K, which is consistent with the magnetic susceptibility and associated withthe AFM order. When the field is applied within the XY plane ( B k c ∗ for example),the transition temperature is gradually decreased with reduced magnitude, as shown inthe inset to Fig. 6(a). The lattice contribution C L can be described according to theThirring approximation [32] C L = 3 sR (1 + X n =1 Bnu-n ) , (1)where u = [( T /T b ) + 1] and T b = θ D /2 π , θ D is the Debye temperature, s is the numberof atoms per molecule, R is the gas constant, and B n are free parameters. As seen inFig. 6(a), the experimental curve is well reproduced between 16 and 120 K with thefitting parameters θ D = 565(3) K, B = -2.43(1), B = 3.12(2), B = -1.70(1). Themagnetic contribution C mag can then be extracted from C p by subtracting C L . The agnetism study on a triangular lattice antiferromagnet Cu (OH) Br C mag / T and the entropy change as a function of temperature are present in Fig. 6(b).The entropy recovery at 20 K is about 3.2 J/Kmol, a little smaller than the expected R ln2 for S = 1/2 systems.In view of the AFM ground state and no detectable FC/ZFC splitting in χ ( T ),Cu1 and Cu2 spins should order antiferromagnetically in different manners. Since thelocal environments of Cu1 and Cu2 are distinct, the magnetic field may induce thespin-flop transition step by step due to the different anisotropic energies. The step-likeenhancement observed in M ( B ) at low fields is likely related to one Cu site, which isgradually polarized in high fields. The fact that the in-plane magnetic moment is abouthalf of the saturation moment of a Cu ion even if the magnetic field is applied ashigh as 30 T indicates that the anisotropy energy of the other Cu site is too strong toovercome and the rest Cu ions are still in a AFM arrangement.The conjecture of the separate spin-flop transitions for Cu1 and Cu2 are alsosupported by the magnetic specific heat. As plotted in Fig. 6(c), C mag deviatesfrom the gapless T dependence below T N . Also a single gapped AFM model C mag ∼ T exp( − ∆ /T ) gives a meaningless energy gap (not shown). Based on the abovediscussion, C mag is found to be best reproduced by the sum of two gapped AFMcontributions with different energy gaps as below [33] C mag = aT exp( − ∆ /T ) + bT exp( − ∆ /T ) . (2)As the solid line shown, the fit yields ∆ = 4.7(2) K and ∆ = 38(4) K. The yielded ∆ is much larger than ∆ , which means a stronger anisotropy energy and a much highercritical field to rotate the rest Cu spins.
4. Conclusions
Single crystals of the triangular lattice antiferromagnet Cu (OH) Br are successfullysynthesized and the magnetic properties are characterized by means of magneticsusceptibility, pulsed-field magnetization, and specific heat. Inequivalent Cu ions areordered antiferromagnetically at T N = 9.3 K concurrently. When lowering temperature,an anisotropy crossover from Heisenberg to XY type is observed at 7.5 K, demonstratingthat the spins are antialigned in the ac ∗ plane. When the field is applied within the XY plane, a spin-flop transition occurs at lower fields. The magnetic moment in 30T is about half of the saturation of a Cu ion. A scenario that the inequivalentCu spins individually reorient under magnetic field is proposed to account for themagnetization behavior. A model including two gapped AFM contributions describeswell the temperature dependence of the magnetic specific heat. The exotic magnetismin Cu (OH) Br is possibly resulted from the delicate balance between the geometricalfrustration, spin fluctuations, and complicated exchange interactions. agnetism study on a triangular lattice antiferromagnet Cu (OH) Br Acknowledgements
This work was supported by the National Natural Science Foundation of China (NSFC)(Grant Nos. U1832166, 51702320, 21573235, and U1632159), the Chinese Academyof Sciences (CAS) under Grant No. KJZD-EW-M05, and the Opening Project ofWuhan National High Magnetic Field Center (Grant No. 2015KF08). XFS acknowledgesupport from NSFC (Grant Nos. U1832209 and 11874336) and the National BasicResearch Program of China (Grant Nos. 2015CB921201 and 2016YFA0300103). JFWacknowledge support from NSFC (Grant No. 11574098).
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