Zero-field muon-spin relaxation measurements of the frustrated triangular
quantum magnet AgNiO2 are consistent with a model of charge disproportionation
that has been advanced to explain the structural and magnetic properties of
this compound. Below an ordering temperature of T_N=19.9(2) K we observe six
distinct muon precession frequencies, due to the magnetic order, which can be
accounted for with a model describing the probable muon sites. The precession
frequencies show an unusual temperature evolution which is suggestive of the
separate evolution of two opposing magnetic sublattices.Comment: 4 pages, 3 figure

Baker, P. J.

Blundell, S. J.

Brooks, M. L.

Coldea, R.

Hayes, W.

Jansen, M.

Lancaster, T.

Pratt, F. L.

Soergel, T.

English

arXiv

Zero-field muon-spin relaxation measurements of the frustrated triangular quantum magnet AgNiO2 are consistent with a model of charge disproportionation that has been advanced to explain the structural and magnetic properties of this compound. Below an ordering temperature of TN=19.9(2) K we observe six distinct muon precession frequencies, due to the magnetic order, which can be accounted for with a model describing the probable muon sites. The precession frequencies show an unusual temperature evolution which is suggestive of the separate evolution of two opposing magnetic sublattices

Lancaster, T

Blundell, SJ

Baker, PJ

Brooks, ML

Hayes, W

Pratt, FL

Coldea, R

Sörgel, T

Jansen, M

Oxford University Research Archive (ORA)

Physical Review Letters

Anomalous temperature evolution of the internal magnetic field distribution in the charge-ordered triangular antiferromagnet AgNiO2.

Zero-field muon-spin relaxation measurements of the frustrated triangular quantum magnet AgNiO2 are consistent with a model of charge disproportionation that has been advanced to explain the structural and magnetic properties of this compound. Below an ordering temperature of TN = 19.9(2) K we observe six distinct muon precession frequencies, due to the magnetic order, which can be accounted for with a model describing the probable muon sites. The precession frequencies show an unusual temperature evolution which is suggestive of the separate evolution of two opposing magnetic sublattices.Citation: Lancaster, T. et al. (2008). 'Anomalous temperature evolution of the internal magnetic field distribution in the charge-ordered triangular antiferromagnet AgNiO2', Physical Review Letters, 100, 017206. [Available at http://prl.aps.org/]

Blundell, Stephen

Baker, Peter

Hayes, William

Sörgel, T.

Anomalous temperature evolution of the internal magnetic field distribution in the charge-ordered triangular antiferromagnet AgNiO2

Lancaster, Tom

Coldea, Radu

ORA - Oxford University Research Archive

Zero-field muon-spin relaxation measurements of the frustrated triangular quantum magnet AgNiO2 are consistent with a model of charge disproportionation that has been advanced to explain the structural and magnetic properties of this compound. Below an ordering temperature of TN = 19.9(2) K we observe six distinct muon precession frequencies, due to the magnetic order, which can be accounted for with a model describing the probable muon sites. The precession frequencies show an unusual temperature evolution which is suggestive of the separate evolution of two opposing magnetic sublattices

Oxford University Research Archive

Anomalous Temperature Evolution of the Internal Magnetic Field Distributionin the Charge-Ordered Triangular Antiferromagnet AgNiO2T. Lancaster,1,* S. J. Blundell,1 P. J. Baker,1 M. L. Brooks,1 W. Hayes,1 F. L. Pratt,2 R. Coldea,3 T. Sörgel,4 and M. Jansen41Clarendon Laboratory, Oxford University Department of Physics, Parks Road, Oxford OX1 3PU, United Kingdom2ISIS Facility, Rutherford Appleton Laboratory, Chilton, Oxfordshire OX11 0QX, United Kingdom3H.H. Wills Physics Laboratory, University of Bristol, Tyndall Avenue, Bristol BS8 1TL, United Kingdom4Max-Planck Institut für Festkörperforschung, Heisenbergstrasse 1, D-70569 Stuttgart, Germany(Received 2 August 2007; published 10 January 2008)Zero-field muon-spin relaxation measurements of the frustrated triangular quantum magnet AgNiO2 areconsistent with a model of charge disproportionation that has been advanced to explain the structural andmagnetic properties of this compound. Below an ordering temperature of TN  19:92 K we observe sixdistinct muon precession frequencies, due to the magnetic order, which can be accounted for with a modeldescribing the probable muon sites. The precession frequencies show an unusual temperature evolutionwhich is suggestive of the separate evolution of two opposing magnetic sublattices.DOI: 10.1103/PhysRevLett.100.017206 PACS numbers: 75.50.Ee, 75.40.s, 75.50.y, 76.75.+iMagnetic frustration of spins in triangular-lattice anti-ferromagnets has been studied in a variety of experimentalsystems [1,2]. The series XNiO2, in which planes of Ni3(t62ge1g) ions are arranged at the vertices of a triangularlattice, provides the possibility that not only the magneticbut also the charge and orbital degrees of freedom may befrustrated. Although it is expected that the fourfold ground-state degeneracy of an isolated Ni3 ion would be lifted viaa cooperative Jahn-Teller (JT) distortion (implying orbitalordering [3]) followed by magnetic ordering at a lowertemperature [4], the triangular geometry of the XNiO2(X  Na, Li, Ag) system may frustrate both of thesetransitions and the ground state of such a system continuesto be a matter of debate [4–6].Three energy scales determine the physics of theseorbitally degenerate systems [7]: the on-site Coulombenergy U, the electronic bandwidth W, and the intra-atomic Hund rule coupling JH. In insulating systems(such as NaNiO2), for which U W, the degeneracy ofpartially occupied orbital states is usually lifted by a co-operative JT distortion as described above. This contrastswith an itinerant system for which W  U (such asLaNiO2) where the kinetic energy term dominates andthe JT distortion is suppressed. It has recently been pro-posed [7] that in an intermediate regime where U and Ware comparable, JH may overcome the on-site repulsionleading to charge ordering (CO). This provides anothermethod for the system to lift its orbital degeneracy, thistime by removing degenerate electrons at some sites, lead-ing to double occupation at others.Such a CO scheme has been advanced [8] to explain thecrystal structure and magnetic properties of recently syn-thesized hexagonal AgNiO2, a polymorph [9,10] of thebetter known rhombohedral polytype [11]. This materialis a moderately delocalized metal [9] whose orbital degen-eracy may be lifted [8] by a3p3pCO transition,achieved via 3e1g ! e2g  2e0:5g . This transition is indicatedby a structural distortion to a tripled unit cell with ex-panded and contracted NiO6 octahedra. The e2g ions, whichcorrespond to S  1, Ni2, are located at 13 ;23 ;14, and theseso-called Ni1 sites form the tripled triangular lattice asshown in Fig. 1(a). The Ni1 spins order magnetically belowT  20 K in a collinear structure of spins aligned along thec direction, organized in ferromagnetic rows of stripesrunning parallel to b and alternating in direction along a[Fig. 1(a)]. The e0:5g sites [Ni2 located at 0; 0;14 and Ni3 at13 ;23 ;34] form a honeycomb network around the Ni1 sitesand appear to have a much reduced ordered moment(  0:1B) due to hybridization [8]. It should be notedthat complete disproportionation is not required in order tofoster the complete spin polarization on a particular sitethat is proposed in the model. The delocalized nature of thesystem makes it possible for the band of states correspond-ing to a class of sites to be completely polarized, despitebeing composed of a mixture of e2g and e0:5g states [7].Muon-spin relaxation (SR) measurements have beenemployed to explore the properties of the XNiO2 systemfor X  Na [12] and Li [13] from a local perspective. Inthis Letter we report SR measurements made onAgNiO2. Our results may be explained in terms of theCO model described above providing further evidencefor the existence of this newly proposed phase. We showthat the magnetically ordered phase shows very little dis-order, with six muon precession frequencies observed withvery little dephasing. However, the temperature evolutionof the frequencies is unusual and points to the separateevolution of the Ni1 sublattice (described above) and anadditional sublattice that may be formed from small mo-ments on the Ni2 and Ni3 sites.Powder samples of hexagonal AgNiO2 (with<1% of therhombohedral polytype) were prepared as described inRef. [9]. Zero-field (ZF) SR measurements werePRL 100, 017206 (2008) P H Y S I C A L R E V I E W L E T T E R Sweek ending11 JANUARY 20080031-9007=08=100(1)=017206(4) 017206-1 © 2008 The American Physical Societymade on the sample using the DOLLY instrument at theSwiss Muon Source (SS). The sample was wrapped in25 m Ag foil and mounted on a Ag backing plate. In aSR experiment [14], spin-polarized positive muons arestopped in a target sample, where the muon usually occu-pies an interstitial position in the crystal. The observedproperty in the experiment is the time evolution of themuon-spin polarization, the behavior of which dependson the local magnetic field B at the muon site, and whichis proportional to the positron asymmetry function At.Typical ZFSR spectra measured above and below TNare shown in Fig. 2(a). Above the magnetic transition thespectra are well described by an exponential relaxationfunction as expected for a paramagnet with dynamicallyfluctuating magnetic moments [15]. Below TN we observeoscillations in the time dependence of the muon polariza-tion (the ‘‘asymmetry’’ [14]) which are characteristic of aquasistatic local magnetic field at the muon stopping site.This local field causes a coherent precession of the spins ofthose muons for which a component of their spin polariza-tion lies perpendicular to this local field (expected to be 23 ofthe total spin polarization). The frequency of the oscilla-tions is given by i  jBij=2, where  is the muongyromagnetic ratio (  2 135:5 MHz T1) and Bi isthe average magnitude of the local magnetic field at the ithmuon site. Any fluctuation in magnitude of these localfields will result in a relaxation of the oscillating signal,described by relaxation rates i [see Eq. (1)].The measured spectra for AgNiO2 are unusual in thatthey are composed of oscillations at several frequencieswith very low depolarization rates. This suggests the ex-istence of several, well-defined, magnetically inequivalentmuon sites in the material. In order to account for allfrequencies in the spectra measured below TN , maximumentropy analysis was used to decompose the signal. Theresults are shown in Figs. 2(b) and 2(c), where six well-defined frequencies are seen, corresponding to six mag-netically inequivalent muon sites in the material. We labelthese 1–6 in order of decreasing magnitude at T 1:6 K. SR spectra are recorded in the time domain,and a knowledge of the number of frequencies allows usto use time-domain fitting for more detailed analysis. In amagnetically ordered powder with N magnetically inequi-valent muon sites, we would expect the spectra to be of theform At XNi1Ai1323eit cos2iti Abg; (1)where Abg represents a constant background contributionfrom those muons that stop in the sample holder or cryostattail and the 13 term accounts for that fraction of muon-spincomponents that lie parallel to the local magnetic field. Themeasured spectra were fitted to Eq. (1), with N  6.Constant nonzero phases i were also required to fit thedata due to the difficulty in determining t  0 in thespectra and the high oscillation frequencies involved. All0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0t ( s)0510152025A(t)(%)28 30 32 34 36 38 40 42 44 46 48(MHz)Spectralweight(arb.)0 5 10 15 20T (K)1020304050(MHz)(a)(b) (c)1.6 K1.6 K20.1 KFIG. 2 (color online). (a) Time-domain SR spectrum mea-sured above and below the antiferromagnetic transition withtime-domain fits as described in the main text. (b) Maximumentropy analysis of the spectrum measured at T  1:6 K show-ing six distinct frequencies. (c) Temperature evolution of thefrequency spectrum extracted from maximum entropy analysis.Ni1Ni3Ni2O+Ni3 Ni2Ni1O+d(a))c()b(FIG. 1 (color online). (a) Structure of AgNiO2 viewed alongthe c direction with proposed muon stopping sites shown. Themagnetic structure involves ordered Ni1 sites with momentsaligned parallel ( sign) or antiparallel ( sign) to the cdirection, surrounded by a honeycomb of Ni2 and Ni3 sites.The  and  signs on the Ni3 sites give the orientation of theNi1 spins in the neighboring layer directly above and below. Thethick lines show the chemical unit cell, while the dashed lineindicates the mirror plane for the magnetic structure (see text).(b) Proposed muon stopping sites occur 1 Å from each oxygenion. Taking the oxygen position as the origin of coordinates,muons are found at   65	 and   38	, separated by 1.4 Åfrom the Ni planes along c. (c) As (b) but viewed along c.PRL 100, 017206 (2008) P H Y S I C A L R E V I E W L E T T E R Sweek ending11 JANUARY 2008017206-2components occurred with the same amplitude Ai A0=6 across the temperature range T < TN , from whichwe conclude that each of the muon sites occurs with thesame probability and that the material is magneticallyordered throughout its bulk.The temperature evolution of the fitted frequencies isshown in Fig. 3(a), which is seen to be identical to thatextracted from the maximum entropy analysis [Fig. 2(c)].The magnitude of the frequencies i are expected to act asan order parameter for a magnetic system. The variation ofthese frequencies is therefore unusual, with some frequen-cies decreasing and some increasing with increasing T.However, the average frequency av behaves as expected,decreasing smoothly as T is increased towards TN . Fits ofthe average frequency to the phenomenological formavT  av01 T=TN	 yield   2:4, 	  0:3,and TN  19:92 K. This estimate for TN is consistentwith the results of previous studies of AgNiO2 [9].The relaxation rates i are shown in Fig. 3(d). For T <17 K we note that the magnitudes of all relaxation rates iare very low. This implies [15] that the distribution of localfields is exceptionally narrow at all muon sites and that thespin disorder in AgNiO2 is remarkably low. All i havevery similar temperature dependence except 5 and 6,which are larger than 1–4 across the entire temperatureregime and show a rough decrease with increasing tem-perature for T < 17 K. As TN is approached from below,all i increase sharply as would be expected for the onsetof critical fluctuations near a magnetic transition.A knowledge of iT  0 allows a determination of themuon sites in AgNiO2. Dipole fields were calculated in asphere containing 105 Ni ions, using the magnetic struc-ture described above [8]. A positive muon’s stopping po-sition is usually 1 Å from the electronegative O2 ion [16]and calculated local magnetic fields corresponding to theobserved frequencies are found at several positions around1 Å from each oxygen ion. In order to narrow the choice ofmuon sites, the electrostatic potential was also calculatedat positions on the 1 Å sphere surrounding an oxygen,assuming the proposed [8]3p3pCO on the Ni sites.Two distinct regions of negative electrostatic potential arefound, separated from the Ni planes along c by 1.4 Å andoccurring closer to the Ni1 ions (which have e2g) than theNi2 and Ni3 ions (with e0:5g ). These regions are found tocontain the positions where the local magnetic fields giverise to the observed precession frequencies. For each oxy-gen ion we may therefore identify two muon sites. We takean oxygen as the origin of a polar coordinate system[shown in Fig. 1(b)] with the z direction parallel to the caxis and the x direction defined by the projection onto thea-b plane of the vector joining the O2 and the Ni1 ions.The muon sites are found 1 Å from the origin at   65	(plus sign for oxygens above the Ni planes, minus for thosebelow) and   38	 and   38	. These proposedmuon sites are shown in Fig. 1. For the 12 muon sitessurrounding a Ni1 ion [Fig. 1(a)], the proposed magneticstructure involving alternating ferromagnetic rows of or-dered moments gives rise to six magnetically distinct sites.This is because the magnetic structure has a mirror planethat runs transverse to the magnetic stripe direction[Fig. 1(a)] and which causes sites linked by this symmetryto be equivalent. This approach accounts successfully forthe six observed magnetic frequencies. Unfortunately,however, the large field gradients in these positions, alongwith the possibility of small moments on the Ni2 and Ni3sites, make it difficult to assign precise positions for eachof the observed frequencies.We now turn to the unusual temperature dependence ofthe frequency spectrum. The exceptionally small relaxa-tion rates permit the extraction of the detailed temperaturedependence of the local magnetic field at each muon site.Normalizing the frequencies i by the average valuei=2av [Fig. 3(b)] gives three pairs with approximatelyequal and opposite gradients. These pairs (1  6, 2 4, and 3  5) are shown in Fig. 3(c) to yield approxi-mately flat lines when added together, demonstrating thatthey vary in equal and opposite senses about the average.01020304050i(MHz)1234560.81.01.2i/av0.00.51.0( 1+ 6)/2 av( 2+ 4)/2 av( 3+ 5)/2 av0 5 10 15 20T (K)01234i(MHz)123456(a)(b)(c)(d)FIG. 3 (color online). (a) Temperature evolution of the fre-quencies i, extracted from the spectra measured below TN ,fitted to Eq. (1). (b) The normalized frequencies i=2av formthree pairs with roughly equal and opposite gradients. (c) Addingthe pairs of normalized frequencies as indicated results inapproximately flat lines. (d) Relaxation rates i showing a steepincrease as TN is approached from below.PRL 100, 017206 (2008) P H Y S I C A L R E V I E W L E T T E R Sweek ending11 JANUARY 2008017206-3This suggests that within a pair, one muon site sees anincrease in local magnetic field at the expense of its part-ner, which sees a decrease, as temperature is increased. In apolycrystalline material the muon-spin polarization de-pends only on the magnitude of the local magnetic fieldat the muon site. Our picture of the six muon sites inAgNiO2 therefore comprises three pairs of sites, wherethe pairs see opposing variation with temperature in themagnitude of the local dipole fields. Figure 3(b) shows thatthis effect is quite small (but clearly detectable) and thatthe variation in local field at a particular muon site is &15% about the average.A possible explanation for this anomalous behavior in-volves a continuous temperature evolution of the directionof the ordered moment, so that the field magnitude in-creases at one muon site while correspondingly beingreduced at another. Such a reorientation would not changethe amplitudes associated with each frequency componentdue to the effects of angular averaging necessary for ourpolycrystalline sample, so would be consistent with ourmeasurements. However, it is difficult to see how a reor-ientation would be energetically favored as it would in-volve the interactions between spin components in the cdirection (i.e., along the local threefold easy axis) driving areorientation to directions in the a-b plane along a furtherthreefold symmetric easy axis. If these components were toorder with the same wave vector as the components alignedalong c, two of the three in-plane spins could not pointalong their local easy axis direction. We note further that itis unlikely that this effect is caused by a temperature-dependent reordering of charges. The structural distortionthat indicates the CO transition occurs above room tem-perature and involves the expansion and contraction ofNiO6 octahedra. Any charge reordering should be observ-able as a change in Ni—O bond lengths, which is not seenin neutron diffraction studies [17].A more probable scenario involves the separate tempera-ture evolution of two magnetic sublattices. A second mag-netic sublattice could arise from Ni2 and Ni3 sites, whichband-structure calculations suggest [8] may carry a mag-netic moment of 0:1B. An ordered moment on this secondsublattice may be induced by the large ordered moment onthe Ni1 sites and would, therefore, presumably lie along c.Although the temperature dependence of the Ni1 momentwill be determined by Ni1 intrasublattice exchange, the Tdependence of the Ni2,3 sublattice would most likelydepend not only on its intrasublattice exchange but alsoon its interaction with the large Ni1 moment, possiblycausing the two sublattices to evolve differently in tem-perature. This scenario would require that the pairs ofmuon sites be arranged such that a decrease at one sitewould also lead to an increase at another. For example, ifthe Ni3 sites become spin-polarized by interaction with theNi1 sites in the planes immediately above and below, theNi3 sublattice will give rise to a small additional dipolarfield which augments that produced by the Ni1 sublatticefor half the muon sites, but diminishes the field for theother half. Thus a temperature-dependent interplanar cou-pling between Ni1 and Ni3 sites could give rise to theanomalous temperature evolution that we have observed.This work was carried out at SS, Paul ScherrerInstitute, Villigen, Switzerland. We are grateful to RobertScheuermann for experimental assistance. This work issupported by the EPSRC. T. L. acknowledges supportfrom the Royal Commission for the Exhibition of 1851.*t.lancaster1@physics.ox.ac.uk[1] M. F. Collins and O. A. Petrenko, Can. J. Phys. 75, 605(1997).[2] A. Harrison, J. Phys. Condens. Matter 16, S553 (2004).[3] D. I. Khomskii, Phys. Scr. 72, CC8 (2005).[4] F. Vernay et al., Phys. Rev. B 70, 014428 (2004).[5] M. V. Mostovoy and D. I. Khomskii, Phys. Rev. Lett. 89,227203 (2002).[6] J.-H. Chung et al., Phys. Rev. B 71, 064410 (2005).[7] I. I. Mazin et al., Phys. Rev. Lett. 98, 176406 (2007).[8] E. Wawrzyńska et al., Phys. Rev. Lett. 99, 157204 (2007).[9] T. Sörgel and M. Jansen, Z. Anorg. Allg. Chem. 631, 2970(2005).[10] T. Sörgel and M. Jansen, J. Solid State Chem. 180, 8(2007).[11] Y. J. Shin et al., J. Solid State Chem. 107, 303 (1993).[12] P. J. Baker et al., Phys. Rev. B 72, 104414 (2005).[13] T. Chatterji, W. Henggeler, and C. Delmas, J. Phys.Condens. Matter 17, 1341 (2005).[14] S. J. Blundell, Contemp. Phys. 40, 175 (1999).[15] R. S. Hayano et al., Phys. Rev. B 20, 850 (1979).[16] E. Holzschuh et al., Phys. Rev. B 27, 5294 (1983).[17] E. Wawrzyńska et al. (unpublished).PRL 100, 017206 (2008) P H Y S I C A L R E V I E W L E T T E R Sweek ending11 JANUARY 2008017206-4

Anomalous temperature evolution of the internal magnetic field
  distribution in the charge-ordered triangular antiferromagnet AgNiO2

Anomalous temperature evolution of the internal magnetic field distribution in the charge-ordered triangular antiferromagnet AgNiO2

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