Giant gap in the magnon excitations of the quasi-1D chain compound Sr3NiIrO6

1.6 MB·English

by  W. Wu

Giant gap in the magnon excitations of the quasi-1D chain compound
Sr NiIrO
3 6
W. Wu,1 D. T. Adroja,2,3,∗ S. Toth,4,5 S. Rayaprol,6 and E. V. Sampathkumaran7
1Department of Physics and Astronomy and London Centre for Nanotechnology,
University College London, Gower Street, London WC1E 6BT, UK
2ISIS Facility, STFC, Rutherford Appleton Laboratory, Chilton, Oxfordshire OX11 0QX, UK
3Highly Correlated Matter Research Group, Physics Department,
University of Johannesburg, PO Box 524, Auckland Park 2006, South Africa
4Laboratory for Neutron Scattering, Paul Scherrer Institut (PSI), CH-5232 Villigen, Switzerland
5 5Laboratory for Quantum Magnetism, ICMP,
1 Ecole Polytechnique F´ed´erale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
0 6UGC-DAE CSR, Mumbai Center, R-5 Shed, BARC, Trombay, Mumbai 400085, India
2 7Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400005, India
(Dated: January 26, 2015)
n
a
Inelasticneutronscatteringonthespin-chaincompoundSr NiIrO revealsgappedquasi-1Dmag-
J 3 6
netic excitations. The observed one-magnon band between 29.5 and 39 meV consists of two dis-
3 persive modes. The spin wave spectrum could be well fitted with an antiferromagnetic anisotropic
2
exchange model and single ion anisotropy on the Ni site. The extracted dominant anisotropic an-

] tiferromagnetic intra-chain exchange interaction between Ir and Ni ions are Jz = 19.5 meV and
l Jxy =12.1meV.Thesevaluesjustifypreviouselectronicstructurecalculations,showingtheimpor-
e tance of Ir spin orbit coupling on the electron correlations. The magnetic excitations survive up
-
r to 200 K well above the magnetic ordering temperature of TN ∼ 70 K, also indicating a quasi-1D
t nature of the magnetic interactions in Sr NiIrO . Our results not only support the idea of the
s 3 6
. existence of a new temperature scale well above TN, but also emphasize the need to consider new
t
a exchangepathscomplicatedbytheSOC,resultinginadditionalcharacteristictemperaturesinsuch
m spin-chain systems.
-
d PACSnumbers: 75.25.-j,75.30.Cr,75.30.Ds,75.30.Gw,75.40.Gb,75.40.Mg,75.47.Lx
n
o
c Low-dimensional systems, in which quantum me-
[ chanical wave function is confined in one or two

spatial dimensions, exhibit some of the most in-
1
v teresting physical phenomena seen in condensed
5 matter physics [1, 2]. One of these, (quasi-) one-
3 dimensional (1D) spin chain is important for un-
7
derstanding low-dimensional magnetism [1–12] and
5
useful for advancing quantum communications [4,
0
. 5]. The study of quantum spin chains has a long FIG. 1. (Color online) Crystal structure of Sr3NiIrO6
1
history, going back at least to the remarkable exact showing1DNi-Irchainsalongc-axis. Rightside,shows
0
the hexagonal packing of chains viewed along the chain
5 solutionfoundbyBethein1931forthespin-1/2case
direction (i.e. in ab-plane). Dark gray, blue, green and
1 [1]. Spin wave theory, developed by Anderson [13],
red balls show Ir, Ni, Sr and O atoms, respectively.
: Kubo [2] and others in the 1950s [14–17], has given
v
i a clear physical picture of the behavior of three-
X
dimensional (3D) antiferromagnets (AFM) [18, 19].
r However, 1D case remained rather mysterious as spin-chain systems with general formula A3MM’O6
a
(A denotes Sr, Ca, etc and M/M’ denotes transi-
compared to the higher dimensions. Regarding 1D
tionmetals)haveattractedmuchattentioninrecent
case,Haldanefirstsuggestedthatinteger-spinAFM
years, due to their reduced dimensionality [12, 23–
Heisenberg spin chains have a finite gap, and only
38]. This structure consists of 1D chains that are
the half-odd-integer chains are gapless [20, 21].
oriented alongthe c-axis andarrangedin atriangu-
Significant effort has been devoted over the past lar lattice in the ab plane (see Fig. 1). The chains
several decades to understand the behavior of frus- are formed by alternating face-sharing MO trigo-
6
trated quasi-1D spin systems [22], which exhibit a nal prism and M’O octahedra, and intercalated by
6
rich variety of phases due to the enhanced quan- A2+ cation, thus forming a hexagonal arrangement
tum fluctuations in reduced dimensionality. The as shown in Fig. 1.
2
Among these spin chain systems, the Ca-based state reactions of NiO, IrO and SrCO [53]. The
2 3
system such as Ca Co O has been extensively in- X-ray powder diffraction (XRD) study at 300 K
3 2 6
vestigated [23, 24, 31–33, 36–38]. The present work shows that the Sr NiIrO sample was single phase
3 6
is primarily motivated by the original report [39] andcrystallizedinthespacegroupR3c(spacegroup
that there exists a characteristic temperature, T∗, No.: 167). The INS measurements were performed
well above long-range magnetic ordering tempera- between5and300Kusingthehighcountratetime-
tureduetoincipientspin-chainorder[40,41]. Such of-flightchopperspectrometer,MERLINattheISIS
investigationsarehoweverrareforSr-basedsystems. facility,UK.Toreducetheneutronabsorptionprob-
The Sr-based spin chain system [26, 42–44] has be- lemfromIr,wefilledthefinepowderofSr NiIrO in
3 6
come a hot topic in condensed matter physics re- athin-Alenvelop. Thesamplewascooleddownto5
centlyowingtoitschemicalflexibility[45]. Astrong KinsidetheHe-exchangegasusingaclosedcyclere-
intra-chain exchange coupling, which may change frigerator. The INS measurements were carried out
sign depending on the metal atom, could exist in with various incident neutrons energies: E = 15,
i
Sr MIrO (M=metal) besides the strong spin-orbit 80, 150 and 500 meV.
3 6
coupling (SOC) of Ir (effective S = 1/2) may lead
to an anisotropic exchange interactions [28, 29] and
spinanisotropyinthehigh-spincarriersuchasNi2+
(3d8, S =1).
Sr MIrO , with M=Co, Cu, Ni, and Zn, have
3 6
been studied previously [26, 28, 29, 46, 47]. In
this connection, magnetic investigations on some of
thesecompoundscanbefoundinourpastliterature
[43,48,49]. InRef.[50],theresonantinelasticX-ray
scattering (RIXS) data revealed gapped spin wave
excitations in Sr CuIrO that could be fitted us-
3 6
ing linear spin wave theory, where a spin-1/2 chain
with an anisotropic exchange interactions induced
bytheSOCwasadopted. WhenM=Zn(completely
filled 3d-shell), AFM spin-1/2 chains are expected
for Sr ZnIrO owing to the super-exchange mecha-
3 6
nism between Ir atoms via oxygen ligands [10, 51].
Incontrast,forM=Ni(S =1forNi2+,followingthe
Hund’s rule), an alternating chain of spin-1/2 and
spin-1 ions are formed along the c-axis [47]. One
would expect a ferromagnetic interaction between
Ni and Ir spins owing to the orthogonality between
3d and 5d orbitals as was first shown by ab initio
FIG. 2. (Color online) Color coded inelastic neutron
calculations[28]. However,recentexperimentaland scatteringintensitymaps,energytransfervsmomentum
theoretical results have shown that the coupling is transfer (Q) of Sr NiIrO measured with an incident
3 6
AFM [29, 52]. This might be due to the strong energy E =80 meV on MERLIN.
i
SOC, which may affect the exchange pathway, thus
changing the sign of exchange interaction [29]. A Thecolor-codedINSintensitymapsofSr NiIrO
3 6
good understanding of the magnetic properties of measured at various temperatures between T = 5
Sr3NiIrO6 may require both high-resolution prob- and300KwithEi =80meVareshowninFig.2(a-
ing technique and spin wave calculations, in which f). At T = 5 K, with the momentum transfer Q
| |
the SOC is presented in the form of anisotropic ex- below4˚A−1,astrongscatteringpeakcanbeclearly
change interaction and spin anisotropies. We have observed between 29.5 meV and 39 meV (Fig. 2),
also carried out the magnetization and heat capac- without any sign of scattering below 30 meV at
ity measurements of Sr3NiIrO6 to characterize the low-Q.Furthermore,wehavenotobservedanyclear
sample quality [53]. magnetic signal above 50 meV in high-energy mea-
In this Letter, we present a combination of surements up to 500 meV. The magnetic origin of
INS measurements and spin-wave calculation for the strong scattering in the 29.5-39 meV band is
Sr NiIrO (the first study of this type). Polycrys- established by the initial reduction in the energy-
3 6
talline sample of Sr NiIrO was prepared by solid- integratedinelasticintensityasafunctionof Q (see
3 6
| |
3
Fig.2in[53])upto4˚A−1 causedbyspin-waveexci- 20 100
(a) SrNiIrO (c) 5 K
tsacatitotner,ianngd. tThhene apnreisnecnrceeasoefwtihtehp|Qho|ndounetsocapthteornionng ) 15 3 6 3700 KK 75
is revealed in the color maps (Fig. 2) by a large en- /f.u. 10 100 K 50
hancement in the intensity between 10 meV and 40 V
e 5 25
meV at high-Q (Q 8 10 ˚A−1). We attribute m
| | ∼ − / Q = 0 - 3.5˚A-1 Q = 8 - 10˚A-1
theobservedmagneticexcitationsbetween29.5and sr 0 0
/
39meVfor|Q|below4˚A−1 tospinwavescattering mb (b) (d) 150 K
fromNi2+ andIr4+ ionsinthemagneticallyordered ( 15 200 K 75
state below 70 K [52], as expected. Amazingly, the ω) 300 K
Q, 10 50
spinwaveexcitationssurviveuptoT =200K(Fig. (
S
2(a-e)). In addtion, the temperature hardly affects 5 25
the magnon lifetime. This type of low-dimensional
magneticanomalycouldbecorrelatedtothecharac- 0 0
-20 0 20 40 -20 0 20 40
teristictemperature,T∗,proposedforthisfamilyof
Energy transfer (meV)
compounds [39], which was subsequently confirmed
by the observation of spin wave excitation in INS
FIG.3. (Coloronline)Q-integratedenergycutsatvari-
study of the single crystal and powder Ca3Co2O6 oustemperaturesfromlow-Q(0to3.5˚A−1)andhigh-Q
[31, 32]. Sr3NiRhO6 (spin-1 and spin-1/2 alternat- (8 to 10 ˚A−1) for Sr3NiIrO6.
ingchain), similartoSr NiIrO , hasalsorevealeda
3 6
clearmagneticexcitationnear20meVupto100K,
which is well above its T =65 K [43]. In addition, independent up to 100 K. In high-Q cuts (Fig. 3(c-
N
the INS study on Sr ZnIrO , which is formed by d)) the absence of this 30-35 meV peak indicates
3 6
spin-1/2 chains, has showed spin wave excitations that it is due to magnetic excitations and its inten-
near4meV(5meV)at5K,buttheexcitationsdis- sitydecreaseswithQasexpectedfromthemagnetic
appear at T = 19 K (16 K). The comparison be- form factor of Ni2+ and Ir4+ ions (see Fig. 2(b) in
N
tweenSr NiIrO andSr ZnIrO suggeststhatthere [53]). Furthermore, at high-Q, a strong peak near
3 6 3 6
existsaone-dimensionalmagneticnatureinthefor- 15 meV (Fig. 3(c-d)) is due to phonon excitations
mer whereas the latter lacks in it. as its intensity is very weak at low-Q. Between 150
This difference can be understood as follows. K and 300 K, at low-Q, the intensity at 30-35 meV
The presence of a giant spin gap and large zone- peakdecreasesandalmostdisappearsat300K,but
boundary energy in Sr NiIrO , can be explained that of 15 meV peak increases. To see magnetic ex-
3 6
only if there exists strong anisotropic magnetic ex- citations clearly, we have subtracted phonon scat-
change interaction and/or single-ion anisotropy ow- tering from the 5 K data using the data of 300 K.
ing to SOC. This is further supported by the small The magnetic scattering at 5 K thus derived in Fig.
spin gap observed in Sr ZnIrO in which the SOC 4(a) reveals a clear magnetic excitation between 30
3 6
would have similar strength compared to that in and 39 meV. To check the Q-dependent intensity
Sr NiIrO . In addition, the intra-chain and inter- of these excitations, we made Q-integrated cuts in
3 6
chain Ir-Ir distances are very similar ( 5.8 ˚A) in threedifferentranges(Fig.4(c)): Q1 =1.5 2˚A−1,
Sr3ZnIrO6, which is much larger than ∼the nearest- Q2 = 2 3 ˚A−1 and Q3 = 3 4 ˚A−1. Th−ese cuts
− −
neighboring Ni-Ir distance ( 2.7 ˚A) in Sr NiIrO . show a double-peak structure with a stronger peak
3 6
∼
Hence it is expected that the intra-chain interac- around 33 meV and a weaker one around 37 meV.
tion is comparable to the inter-chain interaction in Theobservedmagneticinelasticscatteringcanbe
Sr ZnIrO , while the intra-chain coupling is domi- welldescribedusinglinearspinwavetheory[54,55].
3 6
nant in Sr NiIrO . This could result in the disap- The double-peak structure can be approximately
3 6
pearance of 1D magnetism in Sr ZnIrO . attributed to spin waves on the Ir and Ni sites.
3 6
To see the development of the inelastic magnetic Thestrongerlower-energypeakcorrespondstospin
scattering (at low-Q, 0 to 3.5 ˚A−1) and the phonon waves on the Ni2+ ions since the spin wave inten-
excitations(appearathigh-Q,8to10˚A−1),wehave sity is proportional to the spin quantum number.
extracted Q-integrated energy cuts from the INS Besides, if the large spin gap is attributed to ex-
data as shown in Fig. 3(a-d). At low-Q, between change anisotropy, the upper peak has to be Ir spin
5and100K,wecanseeastronginelasticpeaknear waves,duetothelargerWeissmolecularfieldatthe
30meVwithashouldernear35meV(secondpeak) Ir sites created by the larger spin of the Ni2+ ions.
in Fig. 3(a-b), which remains nearly temperature- The published neutron diffraction data of
4
50 magnetic structure suggests that Jz is AFM and
V) (a) INS (b) SW larger than J . We neglect further neighbor inter-
me40 T = 5 K xy
( actions,basedonsimilar1D-chainmodelsthathave
r
sfe30 been explored for Sr3CuIrO6 [50] and Ca3Co2O6
n
a [31], both has given excellent agreements between
Tr20
y the data and calculation and we could also achieve
g
r10 excellent result with the following simple model
e 0 2 4 6 8 10 12 14
n
E S(Q,ω) (mb/sr/meV/f.u.)
0
0.5 1 2 3 0.5 1 2 3 4
Momentum Transfer ( ˚A -1) =(cid:88)J (cid:0)SxSx +SySy (cid:1)+J SzSz (1)
/meV/f.u.)1118024 (c) QQQSW123 (d) NIri42++ H +ii(cid:88)∈NxiyDzSiizSi+iz1, i i+1 z i i+1
sr 6
/
mb 4 where Si with odd and even i denotes Ir and
) ( 2 Ni spins respectively. Using a two-sublattice single
Q
0
S( 15 20 25 30 35 40 45 50 20 25 30 35 40 45 50 chain unit cell and effective Hamiltonian given by
Energy Transfer (meV) Eq.1thefittingofthespectrumisreducedtoasin-
Simulation scaled down by x0.28 gle parameter fit, D [53]. To fit the observed spin
z
pink Gauss is E resolution
FIG. 4. (Color online) (a) The magnetic scattering at wave spectrum, we have calculated the spin-spin
5 K obtained after subtracting phonon scattering us- correlationfunctionandtheneutronscatteringcross
ing 300 K data, strong scattering below 10 meV is due
section using the simulation package SpinW [56].
to the incoherent background. (b) The simulated spin
Using ω =29.5 meV and ω =39.0 meV, the
wave scattering at 5 K using SpinW program [50] with min max
best fit gives a unique result: D = 7.15(5) meV,
exchange parameters, J = 19.5 meV and J = 12.14 z
z xy −
meVandasingleionanisotropyD=−7.1meV.(c)1D Jz = 19.50(5) meV and Jxy = 12.14(5) meV. The
cuts of the magnetic scattering (symbols show experi- Q-integrated cuts convoluted with the instrumental
mental data) at 5 K for Q1 =1.5−2 ˚A−1 , Q2 =2−3 energy resolution are shown on Fig. 4(c). Fig. 4(d)
˚A−1 and Q3 = 3−4 ˚A−1 and simulated powder aver- shows the spin wave cross section localized on Ni
age spin wave (solid lines) using SpinW program with
and Ir sites separately. The calculated intensity in-
J = 19.5 meV, J y = 12.14 meV and D = −7.1 meV
z x cludes the square of the g-factor of Ni2+ (S = 1,
see (text). (d) shows the separate contributions (or de-
L=3,J =4,g =5/4)andIr4+ (S =1/2,L=2,
composition)oftheNiandIrcalculatedspinwavefrom Ni
(c). The solid Gaussian peak in (c) shows the instru- J = 5/2) ions and the magnetic form factor calcu-
mental energy resolution. lated from tabulated values and the g-factor [57].
The fit shows an excellent agreement with the data
and also the Q-dependence is very well reproduced
Sr NiIrO can be equally well fitted with two dif- (seeFig.4(b)). Theonlysignificantdifferenceisthe
3 6
ferent solutions [52] both with ordering wave vec- Q dependent intensity of the upper Ir mode, where
tor k = (0,0,1). In the first structure, the mo- the measured intensity decreases slower as given by
ments along the chains build up amplitude mod- ourmagneticformfactor. ThissuggestthattheIr4+
ulated AFM order, while in the second one only orbitals are significantly contracted in comparison
two third of the chains are ordered with AFM ar- to the free Ir4+ ion. Ab-initio calculations would
rangement along the chains. In the partially or- be necessary to precisely determine the magnetic
dered chain structure 2/3 of the moments would form factor, however, this is beyond the scope of
contribute to spin wave scattering and 1/3 to the this paper. The calculated spin wave cross section
diffuse scattering. In the spin wave calculations, we agreesverywellwiththemeasureddatainabsolute
assume fully ordered chains of spin-1 and spin-1/2 units assuming fully ordered chains. Thus we can
ions and neglect inter-chain coupling. Owing to the alsoexcludethepartiallyorderedchainstructureas
SOC, we expect strongly anisotropic exchange in- a possible ground state, since it would reduce the
teractionalongthechainandasingle-ionanisotropy spin wave cross section by 1/3.
forthespin-1Nisite. Duetothethreefoldaxisalong In conclusion, we have investigated
the Ni-Ir chains (see Fig.1), the most general ex- Sr NiIrO using inelastic neutron scattering,
3 6
change matrix has two different diagonal elements, along with a spin-wave analysis. Our INS study
J and J and the single-ion anisotropy can have reveals spin wave excitations with with a giant
z xy
only a D component on the Ni-site. The observed energy gap of 30 meV at 5 K. More strikingly,
z
5
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Physics Department, University of Johannesburg,
PhD thesis, MIT (1994).
PO Box 524, Auckland Park 2006, South Africa
[46] D. Flahaut, S. Hebert, A. Maignan, V. Hardy,
4Laboratory for Neutron Scattering, Paul Scherrer
C.Martin,M.Hervieu,M.Costes,B.Raquet, and
J. M. Broto, Eur. Phys. J. B 35, 317 (2003). Institut (PSI), CH-5232 Villigen, Switzerland
[47] D. Mikhailova, B. Schwarz, A. Senyshyn, A. M. T. 5Laboratory for Quantum Magnetism, ICMP,
Bell, Y. Skourski, H. Ehrenberg, A. A. Tsirlin, Ecole Polytechnique F´ed´erale de Lausanne
S. Agrestini, M. Rotter, P. Reichel, J. M. Chen, (EPFL), CH-1015 Lausanne, Switzerland
Z. Hu, Z. M. Li, Z. F. Li, and L. H. Tjeng, Phys.
6UGC-DAE CSR, Mumbai Center, R-5 Shed,
Rev. B 86, 134409 (2012).
BARC, Trombay, Mumbai 400085, India
[48] A. Niazi, P. L. Paulose, and E. V. Sampathku-
maran, Phys. Rev. Lett. 88, 107202 (2002). 7Tata Institute of Fundamental Research, Homi
[49] A. Niazi, E. V. Sampathkumaran, P. L. Paulose, Bhabha Road, Colaba, Mumbai 400005, India
D. Eckert, A. Handstein, and K. H. Mu¨ller, Solid
State Commun. 120, 11 (2001).
[50] W. G. Yin, X. Liu, A. M. Tsvelik, M. P. M. Dean,
M. H. Upton, J. Kim, D. Casa, A. Said, T. Gog, SYNTHESIS AND SAMPLE
T. F. Qi, G. Cao, and J. P. Hill, Phys. Rev. Lett. CHARACTERIZATION
111, 057202 (2013).
[51] T.NguyenandH.-C.zurLoye,J.SolidStateChem.
The polycrystalline sample of Sr NiIrO ( 6 g)
117, 300 (1995). 3 6
∼
[52] E. Lefranc¸ois, L. C. Chapon, V. Simonet, P. Lejay, waspreparedbysolid-statereactionsinanAratmo-
D.Khalyavin,S.Rayaprol,E.V.Sampathkumaran, sphere at 1200 ◦C. Stoichiometric powder mixtures
R. Ballou, and D. T. Adroja, Phys. Rev. B 90, of NiO (Alfa Aesar, 99.999% purity), IrO (Umi-
2
014408 (2014). core) and SrCO (Alfa Aesar, 99.99% purity) were
3
[53] See Supplementary Materials for technical details.
annealed for 24 hours. The checking of the phase
[54] F. Bloch, Z. Phys. 61, 206 (1930).
purity of the end product and the determination of
[55] J. C. Slater, Phys. Rev. 35, 509 (1930).
unitcellparameterswerecarriedoutusinganx-ray
[56] S. Toth and B. Lake, SpinW library,
www.psi.ch/spinw (2014), arXiv:1402.6069. powder diffractometer (XRD) with Cu-Kα1 radia-
[57] S. W. Lovesey, The Theory of Neutron Scattering tion at room temperature. Furthermore the quality
from Condensed Matter (1986) of the sample was checked using neutron diffraction
, eq. 7.28 measurement at 100 K on the WISH diffractometer
at ISIS facility of the Rutherford Appleton Labo-
ratory (RAL) in the UK. The magnetization and
heat capacity measurements were carried out using
commercial MPMS and PPMS systems (Quantum
Design) respectively in the temperature range of 2
and 300 K.
OurXRDanalysisshowsthattheSr NiIrO sam-
3 6
SUPPLEMENTARY ple was single phase and crystallized in the space
group R3c (space group No.: 167) with Z = 6 for-
MATERIAL
mula units per unit cell. The lattice parameters
7
identity, there are six Ir and six Ni sites in the con-
TABLE I. Refined crystallographic parameters of
ventional hexagonal unit-cell. The aforementioned
Sr NiIrO using the space group R3c at 2 K from neu-
3 6
symmetryleadstoashiftof1/6cbetweenneighbor-
tron diffraction data [1].
ing magnetic atoms along the chains.
Unit cell dimensions: a=b=9.6089(4) ˚A
c=11.1678(4) ˚A
Angles: α=β =90◦,γ =120◦ MAGNETIZATION AND HEAT CAPACITY
Atom Site x y z
Sr 18e 0.3636(3) 0 1/4 0.15 H = 0.1 T ZFC
Ni 6a 0 0 1/4 ) 200 FC
u
Ir 6b 0 0 0 em 150
/
O 36f 0.1828(3) 0.0247(4) 0.1140(2) mol) 0.10 mol 100
mu/ -1χ ( 50
TABLE II. Selected distances between atoms in (e 0.05 0
Sr NiIrO . χ 0 100 200 300
3 6
Bond Bond length (˚A)
0.00
Intra-chain Inter-chain
0 50 100 150 200 250 300
Ir-Ir 5.584 5.852
Temperature (K)
Ni-Ni 5.584 5.852
Ni-Ir 2.792 5.625
FIG.5. (Coloronline)Magneticsusceptibilitymeasured
Sr-O 2.477 inzero-fieldcooled(redtriangles)andfield-cooled(black
Ir-O 2.014 circles)conditionsusing0.1Tfield. Theinsetshowsthe
inversesusceptibilityversustemperature. Thesolidline
Ni-O 2.183
denotes the linear Curie-Weiss fit between 150 and 300
O-O 2.710
K.
Sr-Sr 3.206
Sr-Ni 3.494
Figure 5 shows the magnetic susceptibility (χ)
of Sr NiIrO as a function of temperature in zero-
3 6
field-cooled (ZFC) and field-cooled (FC) conditions
TABLEIII.BondanglesonselectedatomsinSr3NiIrO6. measured in an applied magnetic field of 0.1 T. Al-
though both the ZFC and FC susceptibilities arise
Atoms Angles (◦)
sharply below T =70 K, these exhibit considerably
Ir-O-Ni 80.59◦
different behavior below T = 20 K. While the ZFC
Ir-O-Ir 106.90◦
signalsharplydropsbelow20K,theFCsusceptibil-
Ni-O-Ni 110.80◦
ity is almost constant below 20 K. Similar behavior
was previously reported [7, 9] and also observed in
single crystals of Sr NiIrO in external field paral-
3 6
at T = 100 K were determined from the neutron lel to the c-axis [1]. Furthermore, the spin-chain
diffraction experiment [2], values are shown in Ta- compound Sr NiRhO (T = 65 K) also exhibits
3 6 N
bleI,whichareconsistentwithpreviousreports[3– very similar behavior in the ZFC and FC suscepti-
6]. The different bond lengths and inter atomic dis- bility [10–12]. On the other hand, the susceptibil-
tances are shown in Tab. II and selected bond an- ities of Sr ZnIrO (T = 19 K) [13][4, 14, 15] and
3 6 N
glesaregiveninTab.III.Thecrystalstructurecon- Sr ZnRhO (T = 16 K) [8, 11, 12] do not show
3 6 N
sists of chains aligned along the c-axis, formed by any difference between ZFC and FC susceptibility
alternating face-sharing NiO trigonal prisms and below T . It is a general trend for the spin-chain
6 N
IrO octahedra. The chains are arranged on a tri- systemsofthisfamilyhavingtwodifferentmagnetic
6
angular lattice in the ab-plane. There are two Ir atomsalternatingalongthechaintoexhibitconsid-
ions in the primitive unit at (0,0,0) and (0,0,1/2), erable different behavior in the temperature depen-
and two Ni atom at (0,0,1/4) and (0,0,3/4). Tak- dentsusceptibilityforZFCandFC.Theinversesus-
ing into account the rhombohedral-lattice transla- ceptibilityofSr NiIrO exhibitsaCurie-Weiss(CW)
3 6
tions t = (2/3,1/3,1/3), t = (1/3,2/3,2/3), and behavior between 200 and 300 K with an effective
1 2
8
total moment of 3.54(5)µ per formula-unit and Sr NiIrO at300Kis254Jmol−1K−1,whichisina
B 3 6
·
paramagnetic CW temperature of 22.1(3) K for goodagreementwiththatexpectedfromthelattice
−
ZFCdata(seeinsetofFig.5). Howeverthesevalues contributionbasedonDulongandPetitlaw[17](for
should be taken as rough estimates, due to the dif- n-atom molecules Cp 3nR=274.4 Jmol−1K−1),
∼ ·
ferenttemperaturedependenceoftheparamagnetic showing that magnetic correlations are completely
susceptibility of Ir and Ni ions. The negative sign lost at room temperature.
of the CW temperature indicates dominant antifer-
romagnetic interactions. Furthermore, χ exhibits a 20
broad maximum below 100 K, indicating the low- (a) T = 5 K, E = 30-38 meV
dimensional nature (or due to frustration) of the u.)
magnetic interactions in Sr3NiIrO6. The measured /f. 15
ac-susceptibility has a peak in the real part (χ(cid:48)) at sr
/
20 K [1], which shows strong frequency dependence mb 10
(i.e. peak position increases with frequency) and (
t.
the time dependent magnetization follows logarith- n
I
mic decay at 20 K. These results show the impor- c. 5
S
tance of magnetic frustration due to the triangular
nature of the crystal structure.
0
)
u.
300 r/f. (b) Ni2+ (cid:31)j0+C2 · j2(cid:28)2
s
/
b Ir4+ j+C j 2
) m 8 (cid:31)0 2 · 2(cid:28)
K 200 (
C (J/mol/p 100 /mol/K)1057005 c Sc. Int. 4
C (Jp 2500 25 50 75 gneti
0 T (K) Ma
0
0 T 100 200 300
N 0 2 4 6 8
Temperature (K)
Q (˚A-1)
FIG.6. (Coloronline)Heatcapacityversustemperature
FIG.7. (a)Scatteringintensityasafunctionofmomen-
of Sr NiIrO . The inset shows the heat capacity vs
3 6 tumtransferofSr NiIrO integratedinenergybetween
temperature plot in an expanded scale. 3 6
30 and 38meV measured at 5 K. (b) Magnetic scatter-
ingintensityonly,obtainedbysubtractingphononback-
We have also measured the heat capacity of ground. The solid lines show the magnetic form factor
for Ni2+ (blue line) and Ir4+ (green line) scaled to the
Sr NiIrO between 2 K and 300 K (see Figure
3 6
data.
6) and haven’t found any clear signature of mag-
netic phase transition down to 2 K, even though
the neutron diffraction study clearly reveals the
present of magnetic Bragg peaks below 70 K [1],
confirming AFM magnetic order below 70 K. On SPIN WAVE CALCULATIONS
the other hand, the neutron diffraction data did
not show any clear change in the magnetic struc- We propose a simple magnetic Hamiltonian,
turebetween2Kand70K.Itshouldbenotedthat where we take into account only interactions be-
theheatcapacityofSr NiRhO [11,16], didnotre- tween nearest neighbor magnetic atoms along the
3 6
vealanymagneticphasetransitioneither,butthose c-axis and single ion anisotropy of the Ni2+ ions.
of Sr ZnIrO [14, 15] and Sr ZnRhO [8] exhibit a Thismodelgivesaperfectfittotheinelasticneutron
3 6 3 6
clearλ-typeanomalyatthemagneticorderingtem- scattering(INS)powderdata,thisalsojustifiesthat
perature. This might indicate that the absence of the interchain interactions can be neglected. Due
theλ-typeanomalyinSr NiIrO isstronglyrelated to the rhombohedral-translations every Ni-Ir chain
3 6
to the low-dimensional nature in magnetic struc- are equivalent to a single chain with two atoms.
ture. The observed value of the heat capacity for We denote the Ir and Ni atoms with sublattice a
9
denotedbyD . Theallowedmatrixelementsofthe
z
Ni-Ir bond is determined by the point group sym-
Ir4+
metry of the center of the bond that is C . This
3
allows anisotropic exchange, with different J and
z
J values,alsoDzyaloshinskii-Moriyainteractionis
xy
Ni2+ allowed parallel to the c-axis that we neglect here.
With the above assumptions we propose the follow-
ing effective spin Hamiltonian:
(cid:88) (cid:16) (cid:17)
= J sˆz sˆz +J sˆx sˆx +sˆy sˆy +
H z a,i b,i xy a,i b,i a,i b,i
i
(cid:88) (cid:16) (cid:17)
+ J sˆz sˆz +J sˆx sˆx +sˆy sˆy +
z a,i b,i+1 xy a,i b,i+1 a,i b,i+1
c
i
+(cid:88)D (cid:0)sˆz (cid:1)2. (2)
z b,i
i
a b The first two sums describe the anisotropic ex-
changeinteractiononboththeNiandIrsites,while
FIG. 8. One of the possible magnetic structure of the last term describes the single-ion anisotropy of
Sr3NiIrO6stabilizedatlowtemperatureinacommensu- the Ni sites. In the observed magnetic structure
rate phase with propagation vector k =(0,0,1). Green the spins point along the z-axis AF order along the
and orange lines denote intrachain and interchain cou-
chain. The classical ground state of Eq. 2 is identi-
plings respectively. Structure of symmetry P3c(cid:48)1 cor-
cal to this if J is positive and J > J for zero
responding to global phase ϕ = 0. For global phase z | z| | xy|
anisotropy. Assuming the AF ground state, we cal-
ϕ = π/6 there is a possibility to have zero moment on
Ni and Ir for the Ni-Ir chain at (x,y,z) [1]. culatedthespinwavedispersionusingtheHolstein-
Primakoff transformation [18] to reduce the Hamil-
toniantonon-interactingbosons(magnons)andap-
and b respectively. We restrict our spin Hamilto- plied the Bogoliubov transformation to diagonalize
nian using the crystallographic space group. The the quadratic form [19]. Since there are two sub-
point group symmetry D of the Ni atom allows lattices, we obtained two ω (Q) spin wave modes
3 1,2
only a single anisotropy parameter along the c-axis dispersing along the chain direction:
(cid:12) (cid:113) (cid:12)
ω (Q)=(cid:12) D2s2+2D J s (s +s )+Jz2(s +s )2 2J2 s s (1+cos(Q c/2))+D s +J (s s )(cid:12).
1,2 (cid:12)± z b z z b a b a b − xy a b · z b z a− b (cid:12)
(3)
where Q is the momentum of the magnon in ˚A−1 If we determine the bottom and the top of the
units, c is the lattice parameter. In order to fit the spin wave band from the INS data, there is only a
measured spectrum, we calculated the bottom and singlefreeparameterD tobefitted. Bycalculating
z
top energies of the spin wave band (ω and ω ). If the powder spin wave spectrum by averaging out
b t
D <ω /4 we got: sufficiently enough random sample orientations for
z t
a series of D values, we could determine D by a
z z
J =ω /2 (4) direct comparison of the simulation and data.
z t
J2 =D (ω +ω )+1/4ω2 1/2ω2 1/4ω ω , An alternative fitting of the data is possible if
xy z t b t − b − b t weassumethatweonlyobservethelowerspinwave
band. Thusthereisanupperbranchthatwemissed
while if D >ω /4 we got:
z t
either due to its small INS cross section within our
measuredmomentumtransferandenergyrangeorit
J =ω 2D (5)
z t z
− wasaboveourmaximummeasuredincidentneutron
J2 = 2D (ω +ω )+ω2 1/2ω2+1/2ω ω .
xy − z t b t − b b t energy (Ei =500 meV). Detection of spin waves at
10
highenergiesismuchharderduetothecutoffofthe [6] D. Mikhailova, B. Schwarz, A. Senyshyn, a. M. T.
INSintensityathigherQvaluesbecauseofthemag- Bell, Y. Skourski, H. Ehrenberg, a. a. Tsirlin,
neticformfactor. Wesimulatedthisscenariowithin S. Agrestini, M. Rotter, P. Reichel, J. M. Chen,
Z. Hu, Z. M. Li, Z. F. Li, and L. H. Tjeng, Phys.
our spin wave model. The highest possible energy
Rev. B 86, 134409 (2012).
oftheupperbandis75meVassumingnegativeD ,
z [7] D. Flahaut, S. Hebert, A. Maignan, V. Hardy,
this belongs to D = 0 meV, J = 37.5 meV and
z z C.Martin,M.Hervieu,M.Costes,B.Raquet, and
Jxy =20 meV. In this case the gap is induced only J. M. Broto, Eur. Phys. J. B 35, 317 (2003).
by the difference between J and J . However in [8] A. D. Hillier, D. T. Adroja, W. Kockelmann, L. C.
z xy
this case the lower band in the Q-integrated cuts Chapon, S. Rayaprol, P. Manuel, H. Michor, and
would be symmetric as a function of energy, which E. V. Sampathkumaran, Phys. Rev. B 83, 024414
(2011).
is not consistent with the data, where the inelastic
[9] D. Mikhailova, B. Schwarz, A. Senyshyn, A. M. T.
peak shows a shoulder higher energies. In addition,
Bell, Y. Skourski, H. Ehrenberg, A. A. Tsirlin,
the Q-dependence of the lower magnon band would
S. Agrestini, M. Rotter, P. Reichel, J. M. Chen,
showtheNiformfactormainly,whichdoesn’tfitthe Z. Hu, Z. M. Li, Z. F. Li, and L. H. Tjeng, Phys.
data either, where the upper shoulder has clearly Rev. B 86, 134409 (2012).
different Q-dependence than the peak intensity at [10] K. Stitzer, W. Henley, J. Claridge, H.-C. zur Loye,
35meV,seeFig.4(c-d)inthemanuscript. Thuswe and R. Layland, J. Solid State Chem. 164, 220
can exclude that there is an upper undetected spin (2002).
[11] S.Rayaprol,K.Sengupta,E.V.Sampathkumaran,
wave branch with great confidence.
andY.Matsushita,J.SolidStateChem.177,3270
(2004).
[12] N. Mohapatra, K. K. Iyer, S. Rayaprol, and E. V.
Sampathkumaran,Phys.Rev.B75,214422(2007).
[13] T.NguyenandH.-C.zurLoye,J.SolidStateChem.
∗ [email protected] 117, 300 (1995).
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