Neutron Diffraction and μSR Studies of Two Polymorphs of Nickel Niobate (NiNb_2O_6)
T.J.S. Munsie, M.N. Wilson, A. Millington, C.M. Thompson, R. Flacau, C. Ding, Z. Gong, S. Guo, A.A. Aczel, H.B. Cao, T.J. Williams, H.A. Dabkowska, F. Ning, J.E. Greedan, G.M. Luke
aa r X i v : . [ c ond - m a t . o t h e r] A p r Neutron Diffraction and µ SR Studies of Two Polymorphs of Nickel Niobate (NiNb O ) T.J.S. Munsie, M.N. Wilson, A. Millington, C.M. Thompson, R. Flacau, C. Ding, S. Guo, Z. Gong, A.A. Aczel, H.B. Cao, T.J. Williams, H.A. Dabkowska, F. Ning, J.E. Greedan,
8, 7 and G.M. Luke
1, 7, 9 Department of Physics and Astronomy, McMaster University, Hamilton, Ontario L8S 4M1, Canada. Department of Chemistry, Purdue University, West Lafayette, Indiana 47907-2084, USA Canadian Neutron Beam Centre, Chalk River, Ontario K0J 1J0, Canada Department of Physics, Zhejiang University, Hangzhou 310027, China. Department of Physics, Columbia University, New York, NY 10027, USA. Quantum Condensed Matter Division, Neutron Sciences Directorate,Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA Brockhouse Institute for Materials Research, McMaster University, Hamilton, Ontario L8S 4M1, Canada. Department of Chemistry, McMaster University, Hamilton, Ontario L8S 4M1, Canada. Canadian Institute for Advanced Research, Toronto, Ontario M5G 1M1, Canada. (Dated: October 6, 2018)Neutron diffraction and muon spin relaxation ( µ SR) studies are presented for the newly charac-terized polymorph of NiNb O ( β -NiNb O ) with space group P4 /n and µ SR data only for thepreviously known columbite structure polymorph with space group Pbcn. The magnetic structureof the P4 /n form was determined from neutron diffraction using both powder and single crystaldata. Powder neutron diffraction determined an ordering wave vector ~k = ( , , ). Single crys-tal data confirmed the same ~k -vector and showed that the correct magnetic structure consists ofantiferromagnetically-coupled chains running along the a or b-axes in adjacent Ni layers perpen-dicular to the c-axis, which is consistent with the expected exchange interaction hierarchy in thissystem. The refined magnetic structure is compared with the known magnetic structures of theclosely related tri-rutile phases, NiSb O and NiTa O . µ SR data finds a transition temperature of T N ∼
15 K for this system, while the columbite polymorph exhibits a lower T N = 5.7(3) K. Our µ SRmeasurements also allowed us to estimate the critical exponent of the order parameter β for eachpolymorph. We found β = 0.25(3) and 0.16(2) for the β and columbite polymorphs respectively.The single crystal neutron scattering data gives a value for the critical exponent β = 0.28(3) for β -NiNb O , in agreement with the µ SR value. While both systems have β values less than 0.3, whichis indicative of reduced dimensionality, this effect appears to be much stronger for the columbitesystem. In other words, although both systems appear to well-described by S = 1 spin chains, theinterchain interactions in the β -polymorph are likely much larger. PACS numbers: 76.75.+i,75.25.-j
I. INTRODUCTION
Most transition metal niobates, ANb O , crystallizein the columbite space group (Pbcn, space group 60) ,seen in Fig. 1a. In columbite, the zigzag edge-sharingchains of AO octahedra are oriented parallel to the c-axis. These are separated by Nb-O edge-sharing chainsin both the bc plane (shown) and by two such chains inthe ac-plane (not shown) leading to dominant one dimen-sional magnetic interactions. The case of cobalt niobate(CoNb O ) has been of strong, recent interest sincethe cobalt ion has an effective spin of and exhibitsa quantum phase transition in a modest applied field,with clear experimental signatures of quantum criticalphenomena previously predicted for the transverse fieldIsing model .Another columbite structure niobate that has beenstudied and is of special interest is NiNb O , where Ni ( S = 1) replaces Co (S eff = ). Short range ferromag-netic spin correlations develop in this material on coolingdue to the dominant intrachain interactions, with longrange antiferromagnetic order ultimately being achievedat T N = 5.7 K due to finite interchain interactions . The magnetic structure of columbite NiNb O was solvedfrom powder neutron diffraction data , but the order pa-rameter has not been reported.Initial attempts to synthesize NiNb O , following pre-viously reported growth techniques , resulted in the for-mation of phases of both the expected columbite struc-ture and a new polymorph crystallizing in P4 /n (spacegroup 86), a space group not previously reported in mem-bers of the AB O family . Structural features of thenew polymorph, β -NiNb O , are shown in Figs. 1b and3a. Of note is the absence of edge-sharing NiO octahe-dra as found in the columbite form, shown in Fig. (1a).Instead, the Ni ions are seen to form a body-centredtetragonal (b.c.t.) lattice, which is identical to thatfound in the closely related phases NiTa O and NiSb O that crystallize in the tri-rutile (TR) structure, P4 /mnm(space group 136). P4 /mnm and P4 /n are related in agroup-subgroup sense via the intermediate P4 /m sym-metry . The principle difference between the structuresin the P4 /n group for nickel niobate and the more sym-metric TR form (P4 /mnm) is the position of the O − ions which results in a highly-distorted NbO octahedronwith six different Nb-O distances in the former. This isFIG. 1: (Colour online)Two polymorphs of NiNb O . The blue (dark) octahedra contain nickel, the green (light)octahedra contain niobium. Images created with VESTA . (a) A bc plane view of the columbite structure showingthe zigzag chains of edge sharing Ni-O octahedra along c. Data from . (b) An ac plane view of the P4 /npolymorph showing the absence of the edge-sharing Ni-O octahedra. B µ eff ( µ B ) θ c ( K ) T ( χ max ) ( K ) T N ( K ) Ref.Ta 4.10 -41 25.5 10.3 Sb 3.00 -50 ∼
30 2.5
Nb 3.35 -37 22.5 14.0 TABLE I: A summary of the bulk magnetic propertiesof NiB O (B = Ta, Sb, Nb) family.attributed to a second order Jahn-Teller distortion . Asa result of these distortions, the P4 /n unit cell has twicethe volume of a TR cell with a = √ T R , c = c
T R .Body-centred tetragonal sublattices are well-known togive rise to low dimensional antiferromagnetism; for ex-ample, K NiF and many related materials exhibit strongtwo-dimensional spin correlations . Spin coupling in thethird dimension is frustrated by the b.c.t. geometry. Thecases of NiTa O and NiSb O are most relevant here.The bulk magnetic properties of these two systems arevery similar to those of NiNb O , as summarized in Ta-ble I.All three materials show a broad χ max above 20K fol-lowed by long range order at significantly lower temper-atures. Recent studies argue that NiTa O and NiSb O are best described as Heisenberg S = 1 linear chain an-tiferromagnets . Thus, the magnetic dimensionalityis a strong function of the positions of the ligands withrespect to the metal ions in the b.c.t. sublattice. This is illustrated in Fig. 2 for the K NiF , TR and the P4 /nstructures. In K NiF the strongest exchange pathwayinvolves nearest-neighbour Ni–O–Ni 180 ◦ linkages result-ing in two-dimensional magnetism. For the TR structurethe dominant exchange is between next nearest neigh-bours involving a M–O–O–M 180 ◦ pathway along [1 1 0],which gives rise to the one-dimensional magnetism. Re-cent Density Functional Theory (DFT) calculations showthat the exchange constant for this pathway is ∼
40 timesstronger than any other in the TR structure . The lig-and positions in P4 /n are very similar to those in TRstructure, with the main difference being that one set ofO ions lies slightly out of the plane of the Ni ions, whereasin the TR structure these ions lie in the same plane. Thisis shown in Fig. 2.The magnetic structures of the two TR phases are sur-prisingly different in spite of similar unit cell constantswhich differ by only 1-2%. For NiTa O , the magneticstructure is quite complex with ~k = [ , − , ]. The mag-netic unit cell is orthorhombic with dimensions a M = √ M = 2 √
2a and c M = 2c, V cellM = 8 V cell . Onthe other hand, for NiSb O the propagation vector is ~k = [ , , ] and the magnetic unit cell dimensions (alsoorthorhombic) are a M = a, b M = 2b, c M = 2c, V cellM = 4V cell . Based on these findings, it is of particular inter-est to determine the magnetic structure for β -NiNb O .We collected neutron diffraction data for β -NiNb O on a powder sample at the Canadian Neutron Bean Cen-FIG. 2: (Colour online) Ni (blue/small) and oxide ion(red and orange/large) positions in the K NiF ,TR(NiTa O and NiSb O ) and NiNb O structuresshown along a (001) square plane defined by the Niions. For K NiF the oxide ions and the Ni ions are inthe same plane. In NiTa O and NiNb O one set of Oions (red) are either exactly in the plane of the Ni ions(Ta) or only slightly out of the plane by 0.096˚A (Nb),while the other set (orange) is either 1.55˚A (Ta) or1.57˚A (Nb) from the plane.tre and on a single crystal sample at Oak Ridge NationalLaboratory at selected temperatures between 4 and 20 K.Using µ SR we studied both polymorphs of nickel niobatein their powder form with zero applied field as a functionof temperature to measure their order parameters and tostudy spin dynamics.
II. EXPERIMENTAL METHODS
A description of the growth of single crystal of bothNiNb O polymorphs has been reported .Some single crystals of β -NiNb O were separated andground into a powder. Approximately 500 mg of samplewas obtained. Powder neutron diffraction data were col-lected at the Canadian Neutron Beam Centre using theC2 diffractometer at 20 K and 3.5 K. Wavelengths of 1.33˚A and 2.37 ˚A were used. The sample was contained ina thin-walled vanadium can and cooled in a closed-cyclerefrigerator.The single crystal diffraction on the β -NiNb O poly-morph was done on a sample that was from the samecrystal as the crushed powder. The crystal was orientedinitially using Laue back-scattering x-ray diffraction andthen realigned with neutrons in situ at the start of theexperiment. The single crystal neutron diffraction ex-periment was performed at the HB3A four-circle diffrac-tometer at the High Flux Isotope Reactor (HFIR) at OakRidge National Laboratory (ORNL) in the USA . Thesample was glued to the top of an aluminum rod andmounted in a closed-cycle helium-4 refrigerator with atemperature range of 4 to 450 K. The measurements useda monochromatic beam of neutrons with a wavelength of1.546 ˚A selected from the (220) Bragg reflection of a bentsilicon monochromator. The scattered intensity was mea-sured using an area detector and the data were analyzedusing the Graffiti software package as well as the Full- Prof suite . More specifically, we generated appropriatedata for the nuclear refinement at 20 K by first fittingthe rocking curves through the measured peak positionsto Gaussians, and then the extracted integrated inten-sities were corrected by the appropriate Lorentz factorsto obtain the experimental F values. A similar pro-cedure was used for the magnetic refinements, althoughthe magnetic signal was first isolated by subtracting thehigh-temperature 20 K dataset from the correspondinglow-temperature 4 K dataset.Muon spin relaxation ( µ SR) is a very sensitivetechnique that probes the internal magnetic field usingthe magnetic moment of the muon. These muons areimplanted in a sample where they penetrate a few hun-dred µ m, rapidly thermalize due to electrostatic interac-tions and finally settle at a Coulomb potential minimumin the material. Appropriate electronic vetoing removesany double counts due to cosmic ray muons or if multiplemuons are generated and become incident on the samplewithin one observation window. A thin muon detectoris placed at the entry to the sample chamber. The thinmuon detector starts a clock registering the entry timeof the muon. The muon will spontaneously decay intoa positron and two neutrinos with a lifetime of 2.2 µ s.In this decay, the positron is emitted preferentially inthe direction of the muon spin at the time of decay. Thepositron will be detected in one of a number of scintilltorssurrounding the sample and this will stop the clock andgive a time from entry to decay. From the large ensembleof these events a histogram of positron counts in opposingdetectors, N A and N B can be generated. Each positroncounter will have an amplitude that fits the decay timeof the muon with a signal representing the local field.By combining two opposing counters we can generate anasymmetry in the signal which is proportional to the spinpolarization function: A = N A − N B N A + N B . The LAMPF time-differential spectrometer with a helium-4 cryostat and aultra low-background copper sample holder were used.This setup is capable of measuring in temperatures inthe range of 2 to 300 K at fields from 0 to 4 kG appliedlongitudinally and allows for small transverse fields (upto ∼
40 Gauss) to be applied using transverse Helmholtzcoils. The time resolution for the data bins was set to 0.2ns and the data collection window was set to 11 µ s plusa 125 ns background measurement for subtraction.The samples used in the µ SR measurements were orig-inally single crystals, but were crushed into a fine powderto remove orientation dependence in the ordered sample;Therefore we expect of the signal to be oscillatory innature, which arises from components of the local mag-netic moment that are perpendicular to the initial muonpolarization. The remaining of the signal, arising fromcomponents of the local magnetic moment that are par-allel to the initial muon spin direction, will cause no pre-cession . With zero applied field, when a sample is in aparamagnetic state with no static magnetism we will seea nearly time independent asymmetry, with deviationscaused by the nuclear magnetic moments. In an orderedFIG. 3: A comparison of the nickel sites in (a) the β polymorph of nickel niobate and (b) the trirutile nickeltantalate. In Fig. 3a the cell of the same dimensions as the tantalate is outlined, demonstrating that for bothmaterials the nickel sublattice has the same body-centred tetragonal symmetry.state, we will see an oscillating asymmetry caused by pre-cession at a frequency that is proportional to the mag-netic field at the stopping site multiplied by the muongyromagnetic ratio, ∼ µ SRfit data package . III. RESULTS AND DISCUSSIONA. Magnetic Structure of the β -NiNb O polymorph We refined the powder data at 20 K, well above T N ∼
15 K, to check the sample quality and for any preferredorientation introduced by the grinding process. Our re-sult shows good agreement with the single crystal model,allowing for a shrinking of the cell dimensions due tocooling. This is shown in Figure 4 and Table II. a = 6.6851(4) ˚A c = 9.0952(6) ˚AAtom x y z B(˚A )Ni 0.5 0.5 0.5 0.3(1)Nb -0.014(1) 0.4739(9) 0.6660(9) 0.5(1)O1 0.005(3) 0.697(1) 0.832(2) 0.26(9)O2 0.008(5) 0.695(1) 0.501(2) 0.26(9)O3 0.292(1) 0.508(3) 0.683(2) 0.26(9)R wp Bragg
TABLE II: Cell constants, atomic positions,displacement factors and agreement indicies for therefinement of powder neutron diffraction data forNiNb O in the P4 /n space group at 20 K. FIG. 4: (Colour online) Rietveld refinement of neutronpowder diffraction data at 20 K for β -NiNb O . Thered circles are the data, the black line is the model, theblue line (below model) is the difference plot and thegreen tick marks locate the Bragg peaks. Thewavelength is 1.33˚A.Data were then collected at 3.5 K to determine themagnetic structure. Three magnetic reflections could beidentified and indexed with ~k = ( , , ) as shown inFig. 5.Attempts to solve the magnetic structure were aidedby representation analysis using the program SARAh .For P4 /n, ~k = (cid:0) , , (cid:1) and Ni at Wyckoff site 4e,there are four irreducible representations (IRs), Γ , Γ ,Γ and Γ , which provide potential basis vectors. Thespin configurations consistent with these refinements areshown in Figure 6 based on the chemical unit cell.Note that the models fall into two sets that are intri-FIG. 5: A difference plot (3.5 K - 20 K) showing threemagnetic reflections indexed on ~k = ( , , ). Theneutron wavelength is 1.33˚A. The fits are to singleGaussians.FIG. 6: Four possible spin configurations for β -NiNb O shown on the chemical unit cell. (Figuremade using VESTA )cately related and cannot be distinguished by unpolar-ized neutron scattering. All the Ni ions are ordered inthe Γ and Γ models, while for Γ and Γ only Ni ionsin every other layer are ordered. The Γ and Γ , takenseparately, seems physically unreasonable as well; thereis no experimental evidence that half of the spins remaineither paramagnetic or in a two-dimensional correlatedstate at 3.5 K. For example, there is no low temperatureCurie-Weiss tail in the measured susceptibility and the I n t en s i t y ( A r b . U n i t s ) Temperature (K) Background Subtracted Intensity Power Law Fit ( = 0.280)NiNb O - [0.5 0.5 0.5] peakSingle Crystal Neutron (HB-3A) FIG. 7: A plot of the T-dependence of the magnetic (cid:0) , , (cid:1) Bragg peak. A power law fit gives a value ofthe critical exponent β = 0.28(3).peak shape of the magnetic reflections, Fig. 5, shows noWarren-like feature. Additionally, since Γ and Γ forma co-representation, they can be combined to form a newsymmetry-allowed model. Refinements on the powderusing each of these models gave equally probable valuesfor every model due to the small number of magneticpeaks obtained from the powder neutron scattering. Wetherefore collected single crystal neutron diffraction datato determine the magnetic structure.Two series of single crystal measurements were made.First, the intensity of the strongest magnetic peak, (cid:0) , , (cid:1) as determined from the powder neutron diffrac-tion data, was measured from just above T N to 4 K andthe results are shown in Fig. 7. The data below the crit-ical temperature were then fit to a power law given bythe expression: II = A (cid:12)(cid:12)(cid:12)(cid:12) T − T C T C (cid:12)(cid:12)(cid:12)(cid:12) β (1)where II is the normalized intensity, T is the temper-ature, T C is the transition (critical) temperature and β is the magnetic critical exponent. The fitted values are T N = 13.6(2) K and β = 0.28(3). Note that β is at 1 σ of the expected value for the 3D Ising model (0.31), at2 σ of the 3D XY model (0.345) and within 3 σ of the3D Heisenberg model (0.36) . Nonetheless, the rangeof data available is too narrow and of insufficient pointdensity near T C to determine an accurate value for β andthis must be left to further study.The second set of scans performed was a survey of bothmagnetic and structural peaks at a temperature below (4K) and above (20 K) the transition temperature. We firstperformed a single crystal nuclear refinement with the 20K data, and the resulting parameters agreed well withthose from our powder diffraction measurement. Mag-netic refinements were then performed with a (4 K - 20K) temperature difference dataset, which ensured that Moment Γ moments Γ moments Γ + Γ moments µ a µ b µ c TABLE III: The values of the refined moments fromsingle crystal neutron diffraction data for variousmodels.the magnetic scattering was isolated appropriately. Weconsidered all candidate models discussed previously inthe neutron powder diffraction section.The values of the Ni ordered moments are given inTable III for the Γ and Γ models, and the refinementquality is presented for these two cases in Fig. 8a and8b. Neither of these models fit the data well and theΓ model yielded a Ni moment that is too large to beconsistent with a simple spin-only S = 1 picture. Wealso tried to fit the data with Γ + Γ model discussedpreviously. This model clearly provides the best fit tothe data as indicated by the lowest χ and R-factor ofthe three refinements attempted; the refinement resultfor the Γ + Γ model is displayed in Fig. 8c. The Ni mo-ments were originally unconstrained in this refinement,resulting in nearly collinear moments pointing along thea-axis in adjacent ab-layers. The moments were then con-strained to be collinear in adjacent layers and point ex-actly along the a-axis, which changed the goodness of fitnegligibly. For this reason, the magnetic structure of theconstrained refinement is considered to be the final solu-tion; the ordered Ni moment obtained in this case isshown in Table III and a schematic of the structure is pre-sented in Fig. 9. The determined magnetic structure for β -NiNb O is consistent with the exchange interactionhierarchy expected from crystal structure considerations.As explained previously, the strongest exchange inter-action likely corresponds to the in-plane 180 ◦ Ni–O–O–Ni pathway, which should be strongly antiferromagnetic.We note that this strong exchange pathway alternatesalong the a- and b-axes in adjacent ab-plane layers ofNi . Furthermore, all other superexchange interactionsare mediated by two or three ions with less favourablegeometries for strong orbital overlap, and therefore oneexpects β -NiNb O to be best described by a series ofcoupled antiferromagnetic Ni chains that ultimatelyachieve long-range order due to weak interchain interac-tions.When comparing the magnetic structure for NiNb O with those for NiSb O and NiTa O in Fig. 10, thereare interesting similarities and differences. The magneticstructure of all three systems satisfies the dominant AFexchange interaction described above. More specifically,all three materials consist of moments oriented along the[110] direction in the TR or TR-like cell that form AF-coupled chains running along the same direction, consis-tent with Fig. 2 and DFT calculations for NiTa O .Differences arise in the coupling of these AF chains to F ( A r b i t r a r y ) Q (¯ -1 ) F ObservedF Calculated Residual = 11.8 R factor = 12.4 FitNiNb O (a) (b) FitNiNb O F ( A r b i t r a r y ) Q (¯ -1 ) F Observed F Calculated Residual = 7.98 R factor = 10.4 (c) + FitNiNb O F Observed F Calculated Residual = 6.91 R factor = 9.41 F ( A r b i t r a r y ) Q (¯ -1 ) FIG. 8: A comparison of fits of the actual data fromsingle crystal neutron scattering on NiNb O to theexpected scattering given a different magnetic basisvectors. The calculated and observed values of F , theresiduals, χ and R-factor for (a) the Γ , (b) Γ , and (c)Γ + Γ models are shown.FIG. 9: The full magnetic structure of NiNb O in theΓ + Γ basis. (Figure made using VESTA )adjacent chains both within and between layers, whichemphasizes the importance of the interchain interactionson determining the precise magnetic structure. In fact,the magnetic structures and the magnetic unit cells ex-pressed in terms of the parent TR chemical cell are dif-ferent for all three phases. For NiSb O a M = 2a T R ,b M = b T R and c M = 2c T R giving V M = 4V T R . ForNiTa O a M = 2 a T R , bM = 2(2 )b T R and c M = 2c T R ,giving V M = 8V T R while for NiNb O a M = 2a T R , b M = 2b T R and c M = 2c T R also yielding V M = 8V T R . Thisis a remarkable result, given the close structural similar-ities among the three materials. The exact position ofthe ligands relative to the metal ions seems to serve as avery sensitive tuning parameter for the weak interchaininteractions, which leads to the diverse magnetic groundstates observed for this family of materials.
B. Zero Field µ SR on the β -NiNb O polymorph Zero field µ SR measurements of β -NiNb O are pre-sented in Fig. 11a. Asymmetry spectra at several tem-peratures with superimposed fits are shown. Each of thespectra are offset by a value of 0.05 per temperature stepfor clarity. At 2 K, it is evident that in the first 0.2 µ sthere is strong oscillation in the asymmetry, indicative oflong range order in the material. A fast Fourier transformshowed that there are likely two oscillating components,so the data was fit to the 3-component form given by thefollowing expression: A ( t ) = A cos ( γ µ Bt + φ ) e − λ t + A cos ( γ µ δBt + φ ) e − ( σ t )22 + A e − λ t (2)Fitting this form, the value of α , the phase φ and thetotal asymmetry (A + A + A ) were set to a constantdetermined by fitting a weak transverse field run. Thescaling factor between the two fields (B) was fit globallyand found to be 0.540(3). γ µ is the muon gyromagneticratio. λ n are the relaxation rates in µ s − of the n th term.The first two terms are relaxing, oscillating components FIG. 10: A comparison of the magnetic structures for(a) NiSb O , (b) NiTa O and (c) β -NiNb O projected along the c-axis and with two adjacent layersshown. In (c) the larger chemical cell is indicated by thedarker solid lines and the smaller TR-like chemical cellby the lighter solid lines. In all three diagrams thedashed lines indicate the magnetic unit cell. a a Images (a) and (b) reprinted from Journal of Magnetism andMagnetic Materials, 184, Ehrenberg, H; Wltschek, G;Rodriguez-Carvajal, J; and Vogt, T, Magnetic Structures of theTri-Rutiles NiTa O and NiSb O , 111–115, 1998, withpermission from Elsevier with an exponential (first term) and Gaussian (secondterm) envelope. The final term is a non-precessing com-ponent, which is fitting the long time tail of the signal,typical of relaxation due to fluctuations of the local field.Each individual asymmetry was fit as a free parameter.The values of the local fields at the two muon stoppingsites, as determined by fits to the data, are plotted infigure 11b. The extracted temperature dependence ofthe two local fields were fit simultaneously to a powerlaw model, giving a value for the critical exponent β =0 . F = A (cid:12)(cid:12)(cid:12)(cid:12) T − T C T C (cid:12)(cid:12)(cid:12)(cid:12) β (3)where F is the internal field, T is the temperature, T C is the transition (critical) temperature and β is thecritical exponent for the order parameter. A value of T N = 14.5(3) K was determined from the fit, which agreeswell with previous measurements . The fit also yieldeda value for the critical exponent β = 0 . σ away from the fitvalue. This implies that reduced dimensionality is impor-tant in this material and is consistent with both previousDFT work and the magnetic structure determined byneutron diffraction above. (a)
20K 15.5 K 15 K 14.5 K 14 K 12 K 2K O ff s e t A sy mm e t r y Time ( s)-NiNb O ZF Fit Data (b) -NiNb O ZF Site Magnetism
Site 1 Site 2 Power law fit ( = 0.25 – 0.03) I n t e r na l F i e l d ( G ) Temperature (K)
FIG. 11: Selected data and internal field fits from zero field µ SR measurements performed on the β -NiNb O polymorph. Panel (a) (Colour online) shows fits of µ SR data from 2 to 20 K for β -NiNb O . Each asymmetry plotis offset by +0.05 for clarity. There is a distinct reduction in the local field with increasing temperature, followed bya transition to the paramagnetic state above 15 K. In panel (b), we plot the internal magnetic field strength at twodifferent muon sites in β -NiNb O . (a) Columbite NiNb O ZF Fit Data O ff s e t A sy mm e t r y Time ( s) (b)
Columbite-NiNb O ZF Site Magnetism
Site 1 Site 2 Power Law Fit( = 0.16 – 0.02) I n t e r na l F i e l d ( G ) Temperature (K)
FIG. 12: Selected data and internal field fits from zero field µ SR measurements performed on the columbitepolymorph of NiNb O . In panel (a) (Colour online) we show fits of µ SR data from 2 to 20 K for the columbitepolymorph of NiNb O . Each asymmetry plot is offset by +0.05 for clarity. There is a distinct decrease in the localfield with increasing temperature, followed by a transition to the paramagnetic state above 5.7 K. In panel (b) weplot the internal magnetic field strength at two different muon sites in the columbite polymorph of nickel niobate. C. Zero Field µ SR on the columbite polymorph
Similar µ SR measurements were performed on thecrushed single crystal powder sample of the columbitepolymorph of nickel niobate. The results from the tem-perature sweep with zero field applied are shown in figure 12. From a fast Fourier transform, it was again evidentthat there were two primary components. As in the casefor the β -NiNb O polymorph, there was also a relaxingtail. The function used to fit this data was: A ( t ) = A cos ( γ µ Bt + φ ) e − λ t + A cos ( γ µ δBt + φ ) e − λ t + A e − λ t (4)The difference between this function and Eqn. 2 is thatboth oscillating components have exponential front ends.Here we found the ratio, δ to be 0.493(4).In Fig. 12a, it is evident that there is a very slow de-crease in the oscillation frequency with increasing tem-perature between 2 and 5 K. This trend is followed bya very large drop in frequency above 5 K, and the os-cillations disappear completely between 5.25 and 6 K.Finally, by 10 K (not shown) there is only a very weakrelaxation of the signal remaining.Figure 12b plots the internal field strength against tem-perature. A power law fit was performed using Eqn. 3.A transition temperature of T N = 5.7(3) K was foundfrom the fit, which is in good agreement with previ-ous work . The fit also revealed a critical exponent β = 0.16(2), which is even lower than the value found forthe β -polymorph and therefore further away from typical3D universality class exponents. This result emphasizesthat columbite NiNb O is a low-dimensional magneticsystem and likely can be described by weakly-coupled S = 1 spin chains; therefore it is the true S = 1 cousin tothe interesting S eff = ferromagnetic Ising chain systemCoNb O . IV. CONCLUSION
We have presented both neutron diffraction and µ SRdata on the β -polymorph of NiNb O as well as µ SRdata on the columbite polymorph. Combined powderand single crystal neutron diffraction data allowed usto solve the magnetic structure unambiguously for β -NiNb O . We find a collinear arrangement of Ni moments, which is consistent with a dominant in-planeAF exchange path that alternates along the a andb axes in adjacent Ni layers. β -NiNb O is bestdescribed as an S = 1 chain system with significantinterchain interactions, ultimately leading to long-rangemagnetic order at T N = 15 K. This picture is supportedby µ SR measurements, which find a critical exponentfor the order parameter β = 0.25(3). µ SR was alsoused to determine β = 0.16(2) in the case of columbitepolymorph. This exceptionally small value indicatesthat low dimensionality is an intrinsic property of thecolumbite polymorph, which is consistent with expecta-tions for a weakly-coupled S = 1 chain system. Inelasticneutron scattering measurements will be indispensablefor determining the coupling strength between the Ni chains in these two polymorphs, and it will be extremelyinteresting to compare the inelastic neutron scatteringspectrum of columbite NiNb O to the cobalt analogue. V. ACKNOWLEDGEMENTS
Partial funding for this research came from an OntarioGraduate Scholarship (OGS) award and National Scienceand Engineering Research Council (NSERC) Grants. Re-search at the High Flux Isotope Reactor at the Oak RidgeNational Laboratory was sponsored by the Scientific UserFacilities Division, Office of Basic Energy Sciences, USDepartment of Energy. Research at the Canadian Neu-tron Beam Centre was supported by the Canadian Nu-clear Laboratories, Chalk River, Canada.We would like to thank A.M. Hallas for assistancewith the preliminary work as well as useful discussionsthroughout the data collection and writing process.We would like to thank the staff at TRIUMF NationalLaboratory, specifically Dr. G. Morris and Dr. B. Hittifor their assistance, guidance and support throughoutthe µ SR measurements. H. Weitzel, Zeitschrift f¨ur Kristallographie-Crystalline Ma-terials , 238 (1976). P. W. C. Sarvezuk E. J. Kinast, C. V. Colin,M. A. Gusm˜ao, J. B. M. da Cunha, and O. Isnard., Journalof Applied Physics (2011). R. Wichmann and H. M¨uller-Buschbaum, Zeitschrift f¨uranorganische und allgemeine Chemie , 101 (1983). S. Kobayashi, S. Mitsuda, M. Ishikawa, K. Miyatani, andK. Kohn, Phys. Rev. B , 3331 (1999). T. Kunimoto, K. Nagasaka, H. Nojiri, S. Luther, M. Mo-tokawa, H. Ohta, T. Goto, S. Okubo, and K. Kohn, Journalof the Physical Society of Japan , 1703 (1999). R. Coldea, D. A. Tennant, E. M. Wheeler, E. Wawrzynska,D. Prabhakaran, M. Telling, K. Habicht, P. Smeibidl, andK. Kiefer, Science , 177 (2010). C. M. Morris, R. Vald´es Aguilar, A. Ghosh, S. M. Kooh-payeh, J. Krizan, R. J. Cava, O. Tchernyshyov, T. M. Mc- Queen, and N. P. Armitage, Physical Review Letters ,137403 (2014). A. W. Kinross, M. Fu, T. J. Munsie, H. A. Dabkowska,G. M. Luke, S. Sachdev, and T. Imai, Physical Review X , 031008 (2014). I. Cabrera, J. D. Thompson, R. Coldea, D. Prabhakaran,R. I. Bewley, T. Guidi, J. A. Rodriguez-Rivera, andC. Stock, Physical Review B , 014418 (2014). T. Liang, S. M. Koohpayeh, J. W. Krizan, T. M. McQueen,R. J. Cava, and N. P. Ong, Nature Communications (2015). K. Momma and F. Izumi, Journal of Applied Crystallog-raphy , 1272 (2011). C. Heid, H. Weitzel, F. Bourdarot, R. Calemczuk, T. Vogt,and H. Fuess, Journal of Physics: Condensed Matter ,10609 (1996). I. Yaeger, A. Morrish, and B. Wanklyn, Physical Review B , 1465 (1977). D. Prabhakaran, F. R. Wondre, and A. T. Boothroyd,Journal of Crystal Growth , 72 (2003). H. P. Beck, Zeitschrift f¨ur Kristallographie-Crystalline Ma-terials , 843 (2012). T. Hahn, The International Union of Crystallography, DReidel Publ Co, Dordrecht (1983). P. S. Halasyamani and K. R. Poeppelmeier, Chemistry ofMaterials , 2753 (1998). L. L. J. de Jongh.
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