Structural, thermodynamic, and local probe investigations of a honeycomb material Ag 3 LiMn 2 O 6
R. Kumar, Tusharkanti Dey, P. M. Ette, K. Ramesha, A. Chakraborty, I. Dasgupta, R. Eremina, Sándor Tóth, A. Shahee, S. Kundu, M. Prinz-Zwick, A.A. Gippius, H. A. Krug von Nidda, N. Büttgen, P. Gegenwart, A.V. Mahajan
SStructural, thermodynamic, and local probe investigations of a honeycomb materialAg LiMn O R. Kumar, Tusharkanti Dey, P. M. Ette, K. Ramesha, A. Chakraborty, I.Dasgupta, R. Eremina,
5, 6
Sándor Tóth, A. Shahee, S. Kundu, M. Prinz-Zwick, A.A.Gippius,
9, 10
H. A. Krug von Nidda, N. Büttgen, P. Gegenwart, and A.V. Mahajan ∗ Department of Physics, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India Experimental Physics VI, Center for Electronic Correlations and Magnetism,University of Augsburg, D-86159 Augsburg, Germany Central Electrochemical Research Institute-Madras Unit,CSIR-Madras Complex, Taramani, Chennai 600113, India School of Physical Sciences, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700 032, India Kazan (Volga Region) Federal University, Kremlevskaya st., 18, Kazan, 420008, Russia Kazan E. K. Zavoisky Physical-Technical Institute (KPhTI) of the Kazan ScientificCenter of the Russian Academy of Sciences, Sibirsky tract, 10/7, Kazan, 420029, Russia Laboratory for Neutron Scattering and Imaging,Paul Scherrer Institute (PSI), CH-5232 Villigen, Switzerland Experimental Physics V, Center for Electronic Correlations and Magnetism,University of Augsburg, D-86159 Augsburg, Germany Department of Physics, M.V. Lomonosov Moscow State University, 199991 Moscow, Russia P.N. Lebedev Physics Institute of Russian Academy of Science, 199991 Moscow, Russia (Dated: 16th April 2019)Here we present the structural and magnetic properties of a new honeycomb materialAg LiMn O . The system Ag[Li / Mn / ]O belongs to a quaternary 3R-delafossite family andcrystallizes in a monoclinic symmetry with space group C /m and the magnetic Mn ( S = 3 / ab -plane. An anomaly around 50 K and the presence ofantiferromagnetic (AFM) coupling (Curie-Weiss temperature θ CW ∼ −
51 K) were inferred from ourmagnetic susceptibility data. The magnetic specific heat clearly manifests the onset of magneticordering in the vicinity of 48 K and the recovered magnetic entropy, above the ordering tempera-ture, falls short of the expected value, implying the presence of short-range magnetic correlations.An asymmetric Bragg peak (characteristic of two dimensional order), seen in neutron diffraction,gains intensity even above the ordering temperature, thus showing the existence of short-range spincorrelations. Our electron spin resonance ESR experiments corroborate the bulk magnetic data.Additionally, the (ESR) line broadening on approaching the ordering temperature T N could be de-scribed in terms of a Berezinski-Kosterlitz-Thouless (BKT) scenario with T KT = 40(1) K. Li NMRline-shift probed as a function of temperature tracks the static susceptibility ( K iso ) of magneticallycoupled Mn ions. The Li spin-lattice relaxation rate (1/ T ) exhibits a sharp decrease belowabout 50 K. A critical divergence is absent at the ordering temperature perhaps because of the fil-tering out of the antiferromagnetic fluctuations at the Li site, i.e. , at the centers of the hexagons inthe honeycomb network. Combining our bulk and local probe measurements, we establish the pres-ence of an ordered ground state for the honeycomb system Ag LiMn O . Our ab initio electronicstructure calculations suggest that in the ab -plane, the nearest neighbor (NN) exchange interactionis strong and AFM, while the next NN and the third NN exchange interactions are FM and AFMrespectively. The interplanar exchange interaction is found to be relatively small. In the absenceof any frustration the system is expected to exhibit long-range, AFM order, in agreement withexperiment. I. INTRODUCTION
Materials based on the delafossite structure with thegeneral chemical formula ABO exhibit interesting phys-ical properties [1–5]. In general, A and B -sites in ABO represent monovalent and trivalent cations, respectively,having a linear and octahedral environment of oxygenatoms. In this case, the B -site which is responsiblefor magnetism in delafossite materials forms an edge- ∗ Corresponding author: [email protected] shared triangular lattice or a honeycomb lattice when thesystem crystallizes in hexagonal/rhombohedral or mono-clinic space groups, respectively.There exist a variety of honeycomb materials [6] andin recent years attempts have been made to synthesizedelafossite materials with tetravalent ions at the B -site(honeycomb lattice), which are known as 3 R -delafossites.A few examples of 3 R -delafossites are Ag(Li / Ru / )O [7–9], Ag(Li / Rh / )O [10] and Ag(Li / Ir / )O [10].We would like to mention here that Ag insertion intothe primary structure of Li MO (M = Ru, Rh or Ir)results in its placement between consecutive metal layerswhich essentially reduces the inter-layer connectivity and a r X i v : . [ c ond - m a t . s t r- e l ] A p r thus makes the materials highly two-dimensional (2D) innature.As per some recent theoretical studies [11–13] novelground state properties are expected for 4 d /5 d materi-als depending upon the variation of superexchange en-ergy scale, Hund’s coupling ( J H ) and spin-orbit coupling(SOC). In particular, honeycomb lattice based 5 d ma-terials are at the forefront of current experimental andtheoretical research because of the possibility of stabiliz-ing the Heisenberg-Kitaev Hamiltonian and a rich phasediagram upon variation of the exchange couplings is en-visaged [14]. On the other hand, a different scenariomight emerge while dealing with 3 d transition metal ions,where SOC is much weaker than the other energy scales,namely U (on-site Coulomb repulsion) and J H . For in-stance, it has recently been shown by Wei et al. [15] thatthe 2D honeycomb lattice based Affleck-Kennedy-Lieb-Tasaki (AKLT) state with S = 3 / et al . [16]the multiorbital insulators in the framework of Hubbardmodels with nearest-neighbor hopping on a honeycomblattice could even lead to the S = 3 / S = 3 /
2, with the intention of exploring some novelground state properties.Herein, we report for the first time the sample prepa-ration, structural, and physical properties of a 3 d tran-sition metal oxide (delafossite) Ag(Li / Mn / )O . Inthis compound, the Mn ions ( S = 3 /
2) form a 2Dhoneycomb lattice with Li-ions positioned at the cen-ter of each honeycomb unit. The material was struc-turally characterized by a combination of x-ray and neu-tron diffraction measurements, along with magnetiza-tion, specific heat, and electron spin resonance (ESR). Inaddition, Li nuclear magnetic resonance (NMR) spec-tra and spin-lattice relaxation rate measurements wereperformed. Structural characterization done with x-rayand neutron diffraction suggest a superstructure (hon-eycomb) formed by magnetic Mn ions in the crystal-lographic ab -plane. Interestingly, the same asymmetricpeak, seen in the paramagnetic region, is found to getmore intense on lowering the temperature, as observed inour neutron diffraction studies. Magnetization data showan anomaly in the vicinity of 50 K and antiferromagneticcoupling is inferred from our susceptibility analysis. An-other thermodynamic measurement, specific heat, alsoconfirms this anomaly and locates the magnetic orderingat 47 K. The integrated intensities of the electron spinresonance ESR absorption lines mimic the bulk magneticsusceptibility. The ESR measurements evidence a criticalbroadening as a function of temperature with a transitiontemperature T N = 45 K. Further, the line broadening onapproaching T N may be alternatively described in termsof a Berezinski-Kosterlitz-Thouless (BKT) scenario with T KT = 40(1) K. The static susceptibility (free from de-fects/impurity) tracked using local probe Li NMR spec- tra measurements also reproduce the anomaly observedin bulk susceptibility measurements, while the Li spin-lattice relaxation rate does not show any sharp anomalyaround the 50 K transition. This is likely due to the sym-metric location of the Li with respect to the magneticMn ions, giving rise to a filtering of antiferromagneticfluctuations. Our experimental results corroborate theestablishment of a magnetically ordered ground state forthe 3 d -based system Ag(Li / Mn / )O which is also sup-ported by first principles electronic structure calculation. II. EXPERIMENTAL AND COMPUTATIONALDETAILS
The polycrystalline samples of the quaternary 3R-delafossite oxide Ag[Li / Mn / ]O were prepared by acombination of sol-gel and ion-exchange methods. First,the starting material Li MnO was prepared by sol-gelroute and then fired at 500°C for 6 hours. After con-firming by x-ray diffraction that Li MnO was singlephase, AgNO was mixed with Li MnO in the ratio 1: 3. The resultant mixture was slowly heated to 300°Cand held for 6 hours following which the desired materialAg[Li / Mn / ]O was obtained by removing the residualbyproduct LiNO by washing the mixture with water.The room temperature powder x-ray diffraction (xrd)measurements were performed using a PANalytical XpertPro x-ray diffractometer with Cu-K α radiation ( λ =1.5418 Å). Neutron diffraction data were taken on theDMC beamline at the Paul Scherrer Institute PSI using awavelength λ = 2 . M measurements in the temperature range 2-400 Kas a function of applied field H were performed on aQuantum Design SQUID VSM with the powder sampleloaded in a capsule and for measurements in the 400-630 K range, the high temperature option of the Quan-tum Design VSM was used. The heat capacity measure-ments were carried out on a Quantum design PPMS us-ing the thermal-relaxation method. ESR was measuredin an ELEXSYS E500 spectrometer (Bruker) at X-bandfrequency of 9.4 GHz in a magnetic field of about H = 18kOe. The spectrometer was equipped with a helium gas-flow cryostat ESR 900 (Oxford Instruments) operating inthe temperature range T = 4 - 300 K. The polycrystallinesamples were immersed in paraffin in suprasil quartz glasstubes and mounted in the cavity. ESR detects the mi-crowave absorption due to magnetic dipolar transitionsinduced between the Zeeman levels of the sample as afunction of the external magnetic field. Due to the lock-in amplification technique by field modulation in ESR,one records the field derivative of the absorption spectra.The Li-NMR measurements (spectra and spin-lattice re-laxation rate 1/ T ) were performed both in the fixed field(93.9543 kOe) and swept field ( ν = 95 MHz) mode to gainfurther insights into the intrinsic static susceptibility ofMn-moments in Ag LiMn O by measuring the line shiftas a function of temperature.All the electronic structure calculations based on DFTpresented in this paper were carried out in the planewavebasis within generalized gradient approximation (GGA)[17] of the Perdew-Burke-Ernzerhof exchange correlationsupplemented with Hubbard U as encoded in the Vienna ab - initio simulation package (VASP) [18, 19] with projec-tor augmented wave potentials [20, 21]. The calculationsare done with usual values of U and Hund’s coupling(J H ) chosen for Mn with U eff ( ≡ U- J H ) = 3.0 eV in theDudarev scheme [22]. In order to achieve convergence ofenergy eigenvalues, the kinetic energy cut off of the planewave basis was chosen to be 600 eV. The Brillouin-Zoneintegrations are performed with 8 × × k -points. The exchange paths were identifiedby calculating hopping parameters by constructing theWannier function using the VASP2WANNIER and theWANNIER90 codes [23]. In addition, to get the mini-mum energy structure, symmetry protected ionic relax-ation was been carried out using the conjugate-gradientalgorithm until Hellman-Feynman forces on each atomwere less than the tolerance value of 0.01 eV/Å. III. RESULTS AND DISCUSSION
We will now present the results of our various bulk andlocal probe measurements on Ag LiMn O . A. Structure analysis
Figure 1 depicts the x-ray diffraction pattern forAg LiMn O at 300 K. The x-ray diffraction pattern forAg LiMn O was found to be similar to the isostructuralmaterial Ag LiRu O [7] of the quaternary 3R-delafossitefamily. A peak corresponding to a small amount of Ag isseen in the xrd pattern. An asymmetric reflection (a su-perstructure peak) was also seen around 2 θ ≈
21° (see theinset of Fig. 1). This asymmetric peak (more prominentin neutron diffraction), commonly known as the Warrenpeak [24], arises as a consequence of the irregular stack-ing sequences of layers in a structure. In the presentcase, Mn ions are found to form 2D honeycomb layersin the ab -plane and the irregular stacking pattern resultsfrom the stacking faults which then limit the correla-tion length in the crystallographic c -direction. The x-ray diffraction peaks for Ag LiMn O were found to bebroader than those of Ag LiRu O and the particle sizedetermined from the Scherrer formula is estimated to beabout 20 nm. We then performed microstructure analy-sis from the TEM and selected area electron diffraction(SAED) images depicted in Fig. 1. SAED analysis showsthat the continuous ring patterns (see inset of 1(c)) fromour polycrystalline sample could be well indexed with thehexagonal lattice of Ag LiMn O . Our TEM analysisshowed that the mean size of nanoparticles was between T = 3 0 0 K l = 1.5418 (cid:1) Intensity (arb. units) q o * A g ( a ) ( b )( c )
2 1 /n m
Intensity q o A s y m m e t r i c p e a k
Figure 1. (a) X-ray diffraction pattern for Ag LiMn O with λ = 1 . LiMn O nanoparticles. (c) Selected AreaElectron Diffraction (SAED) of Ag LiMn O nano particleswhere the (hkl) indexing of various rings is shown. MnO (see ex-perimental section) could possibly be the reason for thenano crystallinity of this material.In order to extract information about the unit cellparameters and atomic positions, the x-ray diffractionpattern of Ag LiMn O was refined under the FullProfSuite program [25] using the structural parameters ofAg LiRu O as an initial model. All the Bragg re-flections obtained for Ag LiMn O could be success-fully indexed with a monoclinic space group C /m andthe refined atomic coordinates and lattice constants arelisted in Table I. Because of the particle size being inthe nanometer range, evident from the broadened x-raypeaks and TEM images, microstructure parameters werealso taken into account while refining the crystal struc-ture and a quadratic form of strain formation under Laueclass mmm was considered. The Rietveld refinementquality factors expressed by R wp , R exp , R p and χ havethe values 2.89%, 1.82%, 2.22% and 2.52, respectively.The crystal structure of Ag LiMn O based on x-raydiffraction refinement is shown in Fig. 2. The MnO oc-tahedra form an edge-sharing, 2D, honeycomb networkin the crystallographic ab -plane and the LiO octahderasit at the center of the honeycomb network, see Figs.2(b) and (c). Intercalated Ag atoms go in-between theconsecutive honeycomb layers. Table I. The structural parameters obtained after Rietveld refinement of the x-ray diffraction data collected at a wavelengthof λ = 1.5418 Å for Ag LiMn O under the space group C /m at 300 K. The obtained lattice constants are a = 5 . b = 8 . c = 6 . β = 74 . ◦ .Atoms site x y z B iso OccAg1 2d 0 0.5 0.5 0.52 1Ag2 4h 0.5 0.3271(4) 0.5 0.52 1Li 2a 0 0 0 0.49 1Mn 4g 0 0.6648(11) 0 0.45 1O1 8j 0.4270(23) 0.3471(17) 0.8420(18) 0.36 1O2 4i 0.1459(45) 0.5 0.1393(36) 0.36 1Figure 2. (a) Unit cell of Ag LiMn O in a monoclinic sym-metry with space group C /m . (b) Formation of edge-sharingLiO / MnO octahedra in ab -plane. (c) 2D honeycomb latticeof Mn atoms having Li-atom at its center. In our neutron diffraction data (see the inset of Fig.3), an asymmetric peak is seen to emerge below about 50K while all the other peaks are nearly unchanged. Thismust be from the ordering transition which is evident inother measurements such as magnetic susceptibility, heatcapacity, etc. which are detailed in the following sections.
B. Magnetization
Figure 4 depicts the dc susceptibility ( M / H ) ofAg LiMn O measured in the temperature range 2 −
630 K with an applied field of 30 kOe. The suscepti-bility shows a gradual increase on lowering the tempera-ture before exhibiting a well rounded anomaly at around50 K following which it exhibits an upturn. The anomalyobserved at 50 K might be a signature of magnetic or-der, while the low- T increase of susceptibility could bepartly due to some extrinsic contributions and/or de-fects (see ESR/NMR results later in the paper). TheCurie-Weiss fit ( χ = χ + C/ ( T − θ CW )) to the sus-ceptibility data in the temperature range 240 −
630 Kyields: temperature independent susceptibility χ = − . × − cm /mol Mn, the Curie-Weiss tempera-ture θ CW ∼ -51(1) K, indicative of antiferromagnetic in-teractions among Mn moments, and a Curie constant
20 40 60 80 Ag LiMn O (Bragg)Ag (Bragg) I n t en s i t y ( a r b . un i t s ) q (degree) l = 2.4586 ¯ Ag * Asymmetric peak
DMC
27 30 33 36 39 42 I n t en s i t y ( a r b . un i t s ) q (degree) Figure 3. Neutron diffraction data collected for Ag LiMn O with λ = 2 . LiMn O and the impurity phase Ag, respectively. An enhancementin the intensity of peak at 33° is due to the appearance ofmagnetic order. The impurity peak of Ag is marked with anasterisk. C = 2 . ± .
014 cm K/mole Mn or an effective param-agnetic moment ∼ . ± . µ B . The electronic config-uration of Mn is 3 d and hence the expected effectivemoment (considering g = 2 as obtained from electronspin resonance discussed later) is 3.87 µ B . Note that thevalue of χ can not be determined very accurately as thesusceptibility has still not leveled off even above 600 K.Consequently, there is some uncertainty in the determi-nation of the Curie constant and θ CW . Further, 10-20nm size grains are present in our sample. Defects on thesurfaces of nanoparticles could also stabilize a momentand contribute to the observed value. A higher than ex-pected effective moment was also observed in CaMnO which increased with oxygen depletion. [26] ( - c m / m o l M n ) T (K)H = 30 kOe 0.00.51.01.52.02.53.0Ag LiMn O ) - ( m o l M n / c m ) Figure 4. Left y -axis: variation of the susceptibility in thetemperature range 2 −
630 K with an applied field of 30 kOeand the Curie-Weiss fit (red line) in the temperature range240 −
630 K. Right y -axis: inverse susceptibility, free fromtemperature independent susceptibility ( χ ), in the tempera-ture range 2 −
630 K. The intercept (dotted black line) on the x -axis gives a Curie-Weiss temperature of about −
51 K.
C. Specific heat
The specific heat of the cold pressed powder sampleof Ag LiMn O was measured and an anomaly was alsonoticed there as was observed in our magnetization data.Figure 5(a) depicts the temperature variation of specificheat C p ( T ) of Ag LiMn O in the temperature range1 . −
200 K in 0 and 90 kOe magnetic field. The C p ( T )data distinctly show the presence of an anomaly around48 K, which is found to be insensitive to the appliedmagnetic field. The magnetic specific heat contribution( C m ) in Ag LiMn O was obtained by subtracting thelattice specific heat C lattice . To estimate the C lattice ofAg LiMn O , an isostructural material Ag LiTi O wasprepared and its specific-heat was measured in zero mag-netic field and prior to subtracting this from the C p ( T )data of Ag LiMn O it was scaled with the C p ( T ) data ofAg LiMn O . Initially, Bouvier scaling [27] was used toscale the lattice specific heat of Ag LiTi O , which givesa correction factor ( θ D ( Mn ) θ D ( T i ) = 0.988) to the temperatureaxis, where θ D ( M n ) and θ D ( T i ) are the Debye tempera-tures for the Mn and Ti compounds, respectively. How-ever, this does not appear to reliably estimate the lat-tice specific heat of Ag LiMn O . In fact, it was foundto exceed the total specific heat of Ag LiMn O . Wethen manually matched the specific-heat of nonmagneticsample, in the high temperature region, by rescaling itstemperature axis by multiplying it by 1.085. The mag-netic specific heat C m is plotted in Fig. 5(b). The C m data clearly show a λ -like anomaly at 47 K. The experi- T (K) LiTi O Ag LiMn O C p ( J / M n m o l K ) T (K) (a)
H = 0 Oe ( b ) C m ( J / M n m o l K )
50 100 150 2000.00.20.40.60.81.0H = 0 OeT (K) (c) D S / ( R l n4 ) Figure 5. (a) Specific heat of Ag LiMn O measured with H = 0 Oe and 90 kOe and nonmagnetic Ag LiTi O (solidline: brown) at H = 0 Oe , used for the estimation of lat-tice contribution. (b) The magnetic specific heat, C m , ofAg LiMn O at H = 0 Oe. (c) Entropy change obtained at H = 0 Oe normalised to Rln(4). mental magnetic entropy change ∆ S , estimated from the C m − T curve, is about 80 ±
5% of the theoretical valueof 11.52 J/Mn mol K for spin S = 3 /
2, as can be seen inFigure 5(c). The transition seen at 47 K approximatelyaccounts for 55% entropy change while nearly the restof the entropy is recovered above 70 K. The recovery ofa significant amount of entropy above the ordering tem-perature is probably suggestive of the presence of short-range magnetic correlations. One should recall that theintensity of asymmetric peak seen in neutron diffractionmeasurements (see inset of Fig. 3) also does not immedi-ately collapse to the peak recorded at 300 K, indicatingagain that magnetic correlations survive at least up to60 K and are in-line with our specific heat analysis.
D. ESR Results
To investigate the correlated magnetism originating asa result of interacting Mn-moments, arranged in a hon-eycomb geometry, ESR measurements were performed asa function of temperature. In order to study the spin dy-namics of Ag LiMn O and to get the evolution of thecorresponding ESR parameters with temperature, theESR line shape was analyzed. Typical ESR spectra of apowder sample of Ag LiMn O are shown in Fig. 6. Allspectra consist of a single exchange-narrowed resonanceline — i.e., any line splitting or inhomogeneous broad-ening is averaged out by the isotropic exchange interac-tion. The resonance line is well described by a Lorentzshape at resonance field H res with half width at half max-imum ∆ H including the counter resonance at − H res and -0.2-0.10.0 -202-0.4-0.20.00.2 -200200 2 4 6 8-0.20.00.2 0 2 4 6 8-20020 T = 10 K Ag LiMn O T = 52 K n = 9.36 GHz ES R s i gna l ( a r b . un i t s ) T = 25 K
T = 75 K
H (kOe)
T = 40 K
H (kOe)
T = 120 K
Figure 6. ESR spectra of Ag LiMn O obtained at X-band frequency for different temperatures. Solid lines indicateLorentz curves as described in the text. n = 9.36 GHz H r e s ( k O e ) g = 1.99 (a)(b) ~(T-T N ) -1.37 ~T - ~ BKT:T KT = 40 K D H ( k O e ) T (K) (d)(c) C /C = 0.04 Q = -33 K C /T I ES R ( a r b . un i t s ) C /(T- Q ) Ag LiMn O /I ES R ( a r b . un i t s ) T (K)
Figure 7. The temperature dependence of the ESR parame-ters of Ag LiMn O (a) resonance field (dashed line indicates g = 1 . a small contribution of dispersion (D) to the absorption(A) given by the (D/A) ratio in case of large line widthas described in Ref. [28]. The results of ESR line shapefitting for some representative spectra are shown by solidlines in Fig. 6.The ESR line is related to the manganese exchangecoupled system. The temperature dependencies of theresonance field, the linewidth, the intensity, and the in-verse intensity are summarized in Fig. 7. Starting withthe resonance field (see Fig. 7 (a))in the upper left frame,we obtain a g value of g = hν/µ B H res = 1 .
99 at high tem-perature which is typical for Mn ions (spin S = 3 /
2) inan octahedral ligand field with its half-filled t g triplet.On decreasing temperature, the g -factor remains approx-imately constant down to a weak anomaly at T N = 48 Kand then decreases on further cooling followed by a di-vergence on approaching zero temperature. Focusing on the integrated intensity and its inverserepresentation shown in the frames on the right hand sidein Fig. 7, the data above T N are perfectly described by aCurie-Weiss law I = C / ( T − θ ) with a Weiss tempera-ture θ = −
33 K. Below T N the temperature dependenceof the intensity is well approximated by a pure Curie law I = C /T (dashed line). As the integrated intensity cor-responds to the spin susceptibility, it turns out from thecomparison of the prefactors C and C that below T N only 4% of the spins contribute to the ESR signal, i.e.weakly interacting spins, which are not involved in theantiferromagnetic order e.g. at the surface of the powdergrains or at defect sites.Turning finally to Fig. 7 (b), the linewidth is found todepend strongly on temperature, indicating two differ-ent spin-dynamic regimes above and below T N . Startingfrom a value of about 200 Oe at high temperature, thelinewidth is found to increase with decreasing tempera-ture, diverging close to the antiferromagnetic phase tran-sition with values larger than 1 kOe. On further cooling,the linewidth recovers to about 800 Oe but diverges againwith values above 3 kOe below 4 K.The broadening of the ESR line on approaching T N may be treated in terms of critical behavior due to slow-ing down of spin fluctuations in the vicinity of an order-disorder transition. This causes the divergence of the spincorrelation length, which in turn affects the spin-spin re-laxation time of exchange narrowed ESR lines resultingin the critical broadening, given by∆ H ( T ) = ∆ H + A (cid:18) T N T − T N (cid:19) β (1)where the first term ∆ H describes the limitingtemperature-independent linewidth for the exchange nar-rowed regime, while the second term reflects the criticalbehavior with the critical exponent β . The dashed andthe solid lines on the left lower panel in Fig. 7 representa least-squares-fit of the linewidth data. The best fittingwas obtained with the parameters ∆ H = 221(2) Oe, A = 13(2) kOe, T N = 45(1) K and β = 1 . T N obtained here is close to that from our heatcapacity data. Below T N , the residual ESR signal di-verges approximately with a power law T − . .Given the fact that the critical exponent of the di-vergence above T N is significantly smaller than the ex-pected value of 2.6 for the 2D Heisenberg antiferromag-netic model[29], the line broadening on approaching T N may be alternatively described in terms of a Berezinski-Kosterlitz-Thouless (BKT) scenario like in the case ofthe honeycomb system BaNi V O [Ref. [30]] with spin S = 1 Ni . Indeed the temperature dependence of thelinewidth is very well approximated by the expression∆ H = A exp(3 b/ ( T /T KT − . ) + ∆ H (2)with the Kosterlitz-Thouless temperature T KT =40(1) K, the parameter b = 0 . A =11(2) Oe and the residual linewidth ∆ H = 196(5) Oe,as shown in the lower left frame of Fig. 7 The BKT sce-nario indicates the spin-spin relaxation via magnetic vor-tices, governed by the vortex correlation length whichdiverges at T KT due to vortex-antivortex pairing. Orig-inally this topological phase transition was derived forthe XY model by Berezinskii [31] and by Kosterlitz andThouless [32]. But later on it was shown [33] that al-ready a weak anisotropy is enough to provide a BKTscenario. Concerning 2D spin S = 3 / A CrO with A = H, Li, Na,Cu Ag, Pd [34, 35]. In those Heisenberg antiferromag-nets the frustration of the antiferromagnetic couplingsgives rise to so called Z vortices [36]. Returning to thepresent Mn system, the obtained fit parameters are com-parable to those found in BaNi V O . The parameter b < π/ . T N istypical for quasi-2D-antiferromagnets, where the 3D anti-ferromagnetic order masks the Kosterlitz-Thouless tran-sition. Using the relation[37] T N − T KT T KT = 4 b [ln( J/J )] (3)derived for quasi 2D antiferromagnets (exchange constant J ) with weak planar anisotropy and inter-plane coupling J we obtain a ratio J/J ≈
40, if we use the experimentalvalue of b , (or ≈ b = π/ θ CW in spite of the 2D nature might resultfrom a renormalisation of T N due to a large in-plane AFcorrelation length. [38] E. NMR Results
In order to develop a microscopic understanding of themagnetic properties, Li ( I = 3 / γ π = 16 .
546 MHz/T)nuclear magnetic resonance (NMR) measurements werecarried out on polycrystalline Ag LiMn O .The obtained Li-NMR spectra in the entire measuredtemperature range display a shoulder along with themain line, see Fig. 8. The main line is found to be broad-ened and shifted to the lower field side as a function oftemperature with respect to the Li-NMR line measuredfor the isostructural diamagnetic sample Ag LiTi O ,while the shoulder remained almost unshifted on loweringthe temperature. The asymmetry (shoulder) in spectracould result from the anisotropy of hyperfine coupling.It must be noticed that, this asymmetry is most likelynot from any chemical disorder between Li/Ru as our x-ray diffraction refinement results discard this possibility.Surprisingly, the asymmetry in spectra was also seen inthe isostructural material Ag LiRu O [Ref. [9]]. Inter-estingly, the hydrogenated analogue of Ag LiIr O , i.e.H LiIr O does not show significant asymmetry in HNMR line shape [39].We analyzed the powder averaged Li NMR spectra ofAg LiMn O , similar to the previously studied material ref N o r m a li z ed I n t en s i t y ( a r b . un i t s ) H (kOe)
Figure 8. Li NMR spectra measured at different temper-atures with fixed field 93.54 kOe ( T -range 300-80 K) and bysweeping the field at the transmitter frequency 95 MHz ( T -range 2 . −
93 K). The swept field spectra were corrected foran average offset field of about 14 Oe because of a small offsetin the field of the field sweep magnet compared to the fixedfield magnet. The fixed field data were scaled to the sweepfield data using an appropriate multiplier. The vertical dot-ted line indicates the Li-NMR reference field measured foran isostructural diamagnetic sample Ag LiTi O . Ag LiRu O , by fitting the spectra to a combination ofthe anisotropic shift parameters K iso and K aniso . A fewrepresentative simulated patterns are shown in Fig. 9.The extracted K iso from Li NMR spectra in the tem-perature range 300 − K iso data follow the bulk suscep-tibility data down to about 50 K and show an anomalyaround the ordering temperature. The low- T deviationof the bulk susceptibility from the NMR shift could bethe result of some extrinsic impurity contribution or in-trinsic defects. The hyperfine coupling constant ( A hf )and the chemical shift obtained from the K - χ plot (in-set of Fig. 10) yield 1.45 ± µ B and 0.009(6)%,respectively.The Li NMR spin-lattice relaxation rate (1 /T ) mea-surements were performed with the intention to studythe low-energy spin dynamics or to probe the q -averageddynamical susceptibility of Ag LiMn O in the tempera-ture range 2 −
300 K at the transmitter frequency 95 MHz.The saturation recovery method was employed to mea-sure the 1 /T data. In order to deduce the spin-latticerelaxation time from the measured data, the data werefitted to a combination of two exponential decays givenby the equation:(1 − m ( t ) /m (0)) = Aexp ( − x/T L ) + Bexp ( − x/T S )where T L and T S are the long and short componentsof spin-lattice relaxation time with A and B being con-stants. (c) N o r m a li z ed I n t en s i t y H (kOe) = 95 MHz MHzMHz
Experimental Simulation N o r m a li z ed I n t en s i t y (a) H = 93.954 kOe H = 93.954 kOe 100K (b) (d) = 95 MHz 2.4K
H (kOe)
Figure 9. Simulated Li NMR spectra and experimentallycollected Li NMR spectra (for Ag LiMn O ) at differenttemperatures are shown by green solid lines and red opencircles, respectively for fixed field data ((a) and (b)) and fieldsweep data ((c) and (d)). Figure 11(a) depicts a plot for Li nuclear magneti-zation saturation recoveries at selected temperatures forAg LiMn O . A two-component spin-lattice relaxationwas also observed in Ag LiRu O . This could resultfrom an incomplete saturation of the NMR line leadingto spectral diffusion and an initial fast recovery. The longcomponent of the spin-lattice relaxation rate (1 /T L ) forAg LiMn O is illustrated in Fig. 11(b). The 1 /T L datain the temperature range 300 −
60 K do not show any vari-ation as a function of temperature, however, below about60 K 1 /T L starts to deviate from this behavior. At theantiferromagnetic ordering temperature, the 1 /T L datashould have also exhibited a distinct anomaly, but nopeak was seen and a smooth decrease was noticed in1 /T L data in the temperature range 2 −
50 K. The ab-sence of the signature of any AFM order in the 1 /T L data most likely results from a cancellation of the anti-ferromagnetic fluctuations at the Li position because ofits symmetric position in a honeycomb network of Mnatoms. So, because of the 2D symmetric arrangementof Mn atoms around Li atom, which sits in the middleof honeycomb lattice, the 1 /T L data measured for Linuclei will not sense fluctuations in the hyperfine fieldperpendicular to the applied field. Thus one, in princi-ple, does not expect to see any sharp kink or any crit-ical divergence in the 1 /T L data. This finding furtherstrengthens the idea of a symmetric crystallographic po-sition of Li atom, 2a (0, 0, 0), with respect to its sur-rounding Mn atoms in a unit cell and also an absenceof Li/Mn site disorder. The 1 /T L becomes very longwith decrease in temperature as static order develops andthere is absence of any fluctuations. LiMn O ( - c m / m o l M n ) K iso K i s o ( % ) T (K) 0.51.01.52.02.5 (T)
Kiso K i s o ( % ) (10 -2 cm /mol Mn) Figure 10. The left y -axis shows the K iso (blue open circles)as a function of temperature and the right y -axis depicts thebulk susceptibility (solid line) data for Ag LiMn O . Theinset shows a plot of K iso versus χ with temperature as animplicit parameter.
56K 79K 112K 131K
5K 10K 15K 20K 39K - m ( t ) / m ( ) t (msec) (a) (b) / T ( s e c - ) T (K) = 95MHz
Figure 11. (a) Recovery of the Li longitudinal nuclear mag-netisation as a function of delay time at a few representativetemperatures. (b) Spin-lattice relaxation rate as a functionof temperature for the long component T L (smaller rate). F. Electronic structure calculation
In order to identify the dominant exchange paths andthe relevant spin Hamiltonian of the system we have per-formed first principles electronic structure calculation us-ing VASP. The MnO octahedral units that host mag-netism form an edge shared honeycomb geometry in the a − b plane with Li ions at the center of the honeycomb.Upon relaxation, the distances of three nearest neighbor(NN) Mn atoms become 2.926 Å and 2.932 Å with co-ordination two and one respectively. The Mn-O-Mn an-gles in the respective NN paths are 102.33 ◦ and 102.61 ◦ .The MnO octahedra have a monoclinic distortion andhence the Mn-O bond-lengths are unequal (1.876 Å to1.878 Å) as also the Mn-O-Mn bond angles (77.68 ◦ to95.05 ◦ ).In order to understand the basic electronic structure,we have first carried out non-spin polarized calculationsenforcing the spin degeneracy. The octahedral crystalfield breaks the degeneracy of 5 d states of Mn atomsinto triply degenerate t g and doubly degenerate e g stateswhich get further split due to monoclinic distortion main-taining crystal field splitting between t g and e g states tobe 2.5 eV. The calculations reveal that the Mn t g statesare half filled consistent with the Mn ( d ) configurationresulting in a metallic solution.Next we have performed spin polarized calculationswith FM arrangement of Mn spins within the GGAapproximation. A plot of the spin polarized densityof states (DOS) for the FM configuration shown inFig.12(a) reveals that in the majority spin channel theMn-d t g states are completely filled and the minorityt g states are complete empty with an exchange splittingof about 0.62 eV. The e g states in both the spin channelsare completely empty. In the FM calculation, the totalmoment per formula unit, containing 2 Mn atoms, iscalculated to be 6.0 µ B which further supports the 4+charge state of Mn and also consistent with experimen-tally calculated value of µ eff (4.46 ± µ B ). FMcalculation gives magnetic moment per Mn site to be2.68 µ B as the rest of the moment lies in the ligandsites (0.04 µ B / O) due to substantial hybridization.Inclusion of Coulomb correlation (U) further increasesthe exchange splitting (0.99 eV) and localizes the d orbitals which essentially increase the moment of Mn(2.95 µ B / Mn). NN NNN
AFM FM
Exchange mechanism(b)e g t -2 0 2 4 E-E F in eV -202 D O S ( s t a t e s / e V ce ll ) t t e g e g Mn-dO-p (a)
Figure 12. (a) The orbital decomposed spin polarized DOS.The cyan shaded region and the red dotted lines, respectively,show the contribution of Mn- d and O- p states per atom. (b)The schematic diagram for the NN AFM and NNN FM ex-change interaction mechanism. In order to identify the nature of the ground state wehave calculated the energies of different possible collinearmagnetic configurations namely FM, AFM-1, AFM-2and AFM-3. The results are shown in Table-II. In theAFM-1 configuration, all nearest neighbor interactions(J and J ) are antiferromagnetic similar to the groundstate AFM solution of a bipartite lattice. In the AFM-2configuration, among the two types of NN interactions,J is AFM while J is ferromagnetic. On the contrary the AFM-3 configuration has FM J and AFM J inter-actions. From Table II it is evident that AFM-1 is thelowest energy configuration with NN interactions antifer-romagnetic. Table II. Variation of the magnetic moments (in the GGA+ U calculation) on the various ions for different orderingarrangements and their corresponding energies are tabulatedhere.
Magnetic Total Moment Moment/Mn Moment/O Gap ∆E/f.u.Configuration /f.u. in µ B in µ B in µ B in eV in meVAFM-1 0.0 2.88 0.0 1.54 0.0AFM-2 0.0 2.91 0, ± ± Now for a quantitative estimate of Mn inter-site ex-change strengths, we have calculated symmetric ex-change interactions with "Four State" method based onthe total energy of the system with few collinear spinalignments. If the magnetism in the system is fully de-scribed by the Heisenberg Hamiltonian, the energy forsuch a spin pair can be written as follows [40]: E = − J S · S + S · h + S · h + E all + E (4)where J ij is the symmetric exchange coupling alongbond which connects spin pair i and j . h = − P i =1 , J i S i and h = − P i =1 , J i S i and E all = − P i,j =1 , J ij S i · S i and E contains all other non-magnetic energy contributions.The second (third) term in Eqn. 4 corresponds to thecoupling of the spin 1 (2) with all other spins in the unitcell except spin 2 (1), E all characterizes the exchangecouplings between all spins in the unit cell apart fromspins 1 and 2. The exchange interaction strengthbetween site 1 and 2 obtained with total energy offour collinear spin alignments (such as (1 ↑ ↑ ), (1 ↑ ↓ ),(1 ↓ ↑ ), (1 ↓ ↓ )) has the expression [40] J = − E ↑↑ + E ↓↓ − E ↑↓ − E ↓↑ S (5)The first (second) suffix of energy ( E ) tells the spin stateof site 1 (2). The obtained symmetric exchange interac-tions are J = -2.59 meV (AFM), J = -2.28 meV (AFM),J = 0.54 meV (FM), J = 0.69 meV (FM), J = -0.16 meV(AFM) and J = -0.15 meV (AFM) and the respectiveexchange paths are shown in 13(c). The possible mech-anism of spin conserved exchange couplings for the NNAFM exchange interactions (J and J ) and FM secondneighbors (J and J ) are shown in Fig.12(b). For NNAFM alignments, exchange splitting and inter-site hop-pings are the key parameters while for the FM arrange-ment, spins have to overcome the crystal field splittingwith nearest neighbor superexchange hopping to obey theHund’s coupling. The strongest nearest neighbor (NN)0interactions along with the finite (though small) furtherneighbor interactions results in the long ranged AFM or-dering in the system. The Wannier function plots in Fig. J J J J J J J J (a) (c) J (b) J J Figure 13. (a) and (b) are two different Wannier orbitalsconnecting NN Mn atoms. (c) Different symmetric exchangeinteractions corresponding to neighbor distances. NN J andJ interactions are marked with black and cyan solid lines.NNN interactions J and J , 3rd neighbors J and J andinterplane interaction are denoted with orange, red, brown,blue and grey dotted lines respectively. ∼ ◦ ) from π along paths J favor an antiferromagnetic alignment inaccordance with Goodenough-Kanamori-Anderson rules[41–44], which is consistent with our results. To checkthe strength of inter-layer coupling along c direction wehave fixed the static intra-plane magnetic arrangementto AFM-1 and applied the above mentioned "Four state"method to calculate the interlayer exchange J . The in-terplanar coupling strength is estimated to be FM innature with magnitude 0.14 meV. Theoretically calcu-lated θ CW from these exchange strengths turns out to be − .
8K which is very close to experimentally obtainedvalue, − J NN J inter ) is nearly 19.0 which suggeststhat the magnetic network in primarily of 2D in nature. IV. CONCLUSIONS
In summary, a new honeycomb material Ag LiMn O has been studied using x-ray diffraction, neutron diffrac-tion, magnetization, specific heat, ESR and NMR mea-surements and first principles calculations. An asym-metric peak, signature of superstructure, is seen in boththe x-ray and neutron diffraction and it is found togrow in intensity below about 50 K before saturatingat lower temperatures. This suggests magnetic order-ing of the honeycomb lattice. The susceptibility mea- surements carried out for Ag LiMn O show an anomalyaround 50 K and the presence of antiferromagnetic inter-actions ( θ CW ∼ −
51 K) among Mn moments. The neu-tron diffraction data measured down to 2 K clearly showthe onset of magnetic ordering below 50 K, in agreementwith the anomaly observed in the susceptibility data ofAg LiMn O . The heat capacity measurements furthersupport long-range magnetic order in Ag LiMn O byexhibiting a sharp peak in the measured specific heataround 47 K. The entropy change inferred from the heatcapacity data suggests that the system needs to be heatedto nearly 1.6 times the ordering temperature to recoverthe full entropy. This suggests that 2D magnetic correla-tions start building up at high temperature; on cooling,a fraction of the entropy is already lost when the sam-ple locks into LRO around 50 K. Our local probe LiNMR spectra measurements done on the powder sam-ples, which basically measure the static susceptibilityalso support thermodynamic measurements by exhibit-ing a clear anomaly in the measured Li NMR shift. The Li spin-lattice relaxation rate, which is a measure ofthe q -averaged dynamical susceptibility, does not showa peak as observed in other measurements presumablybecause of the cancellation of antiferromagnetic fluctua-tions at the center (Li-site) of the hexagon also implyingthat the structure remains that of a regular honeycombwith Li sitting at the centers of the honeycomb network.However, Li 1 /T too shows a sharp decrease of nearlyfour orders of magnitude below about 50 K indicatingthe quenching of magnetic fluctuations due to the onsetof magnetic order. Taken together, our thermodynamicand Li NMR shift measurements evidence the emer-gence of an ordered ground in the 3 d honeycomb mate-rial Ag LiMn O . Our experimental results are corrobo-rated by first principles electronic structure calculations.Our ab initio calculations find that the NN interactionsJ are antiferromagnetic. The further neighbor inter-actions also do not give rise to any frustration. Thus,in the case of a dominant Heisenberg term (as might beexpected in this case), and even a small inter-planar cou-pling (as per our calculations) the honeycomb system dis-plays long-range order as seen here. The manifestationof 2D effects in Ag LiMn O is seen from the analysis ofthe T -dependence of the ESR linewidth above the tran-sition temperature. We obtained a Kosterlitz-Thoulesstemperature of about 0 . T N which is typical for quasi-2D-antiferromagnets. The weak interplanar coupling issufficient to lock the system into 3D order which thenmasks the Kosterlitz-Thouless transition. V. ACKNOWLEDGMENTS
This work is partially based on experiments performedat the Swiss spallation neutron source SINQ, Paul Scher-rer Institute, Villigen, Switzerland. We thank Depart-ment of Science and Technology (DST), Govt. of Indiafor financial support through the BRICS project Heli-1magnets. ID thanks DST, Govt. of India and TRCfor financial support. R. Kumar acknowledges CSIR,India and IRCC, IIT Bombay for awarding him fellow-ships for the completion of this work. P. M. Ette ac-knowledges CSIR, INDIA for providing financial supportunder CSIR-SRF Fellowship (grant no. 31/52(14)2k17).AVM would like to thank the Alexander von Humboldt Foundation for financial support during the stay at theUniversity of Augsburg. The work of RE were donewithin the framework of fundamental research AAAA-A18-118030690040-8 of FRC Kazan Scientific Center ofRAS. A.A.Gippius acknowledges the financial supportfrom the RFBR Grant No. 17-52-80036. 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