Measurement of the spectral line shapes for orbital excitations in the Mott insulator CoO using high-resolution resonant inelastic x-ray scattering

0.73 MB·

by  L. Andrew Wray

Measurement of the spectral line shapes for orbital excitations in the Mott insulator
CoO using high-resolution resonant inelastic x-ray scattering
L. Andrew Wray,1 J. Li,2 Z. Q. Qiu,2 Jinsheng Wen,2,3 Zhijun Xu,3 Genda Gu,3
Shih-Wen Huang,1 Elke Arenholz,1 Wanli Yang,1 Zahid Hussain,1 and Yi-De Chuang1
1Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
2Physics Department, University of California, Berkeley, CA 94720, USA
3Condensed Matter Physics and Materials Science Department,
Brookhaven National Laboratory, Upton, NY 11973, USA
We establish the spectral line shape of orbital excitations created by resonant inelastic X-ray
scatteringforthemodelMottinsulatorCoO.Improvedexperimentalenergyresolutionrevealsthat
thelineshapesarestrikinglydifferentfromexpectationsinafirstprinciples-basedatomicmultiplet
4
model. Extended theoretical simulations are performed to identify the underlying physical origins,
1
whichincludeapronouncedthermaltailreminiscentofanti-Stokesscatteringontheenergygainside
0
of excitations, and an essential contribution from interatomic many-body dynamics on the energy
2
loss side of excitations.

n
a PACSnumbers: 78.47.je,71.27.+a,78.70.Ck,31.15.-p
J

1
1 INTRODUCTION (a) x (c)
y z CoO RIXS calc 70eV
] 12
l Many types of many-body phases and dynamics de- z-axis
e rive from low energy spin, lattice, phase and orbital 30o
ond-mat.str- m(fidrtohkeebreaursBsgssiotcern×lhbervgpve3eelrsie0a(ninR0rnigongKcIfleiXim=permfxSlrt2aeipeh)t6sneeea-myidbrdns-ioaebmbmraVsooeye)dodpn.tyemtohInsawna.cettetooretrgmlmhRflayueeierpclcesraetoeeibrmvsncxasoheaptuelaunnueletlrtrctlxieieeipmcointlnioneghteeftanielδnbtartsEigmaseiotm>∼ltniattctsu0eloer.lflXc1a[e1ruhet-xe–icVnrosc1taioinuq5yttlsua]euh,testaticaibohtoafnnuoantidssrtt-, Penetration (nm)9(0111b000o)321 C1o0M0OKCo1L000 Intensity (arb. units)48 Incident Photon Energy
c hν(eV) 0 55eV
neglect most many-body dynamics have achieved rea- 1 2 3 1 2 3
[ Energy Loss (eV)
sonably good agreement with experimental direct RIXS

1 spectra [2, 5, 7, 9–11, 14, 15]. For this study, improved
v FIG. 1. Resonant inelastic scattering at the M-edge:
energy resolution of δE 30meV is obtained by usinglow
8 ∼ (a) The scattering geometry is shown. (b) The penetration
7 energy photons at the cobalt M-edge (50eV hν 70eV). length of X-rays in CoO is estimated from Ref. [24]. (c)
≤ ≤
5 With this resolution, clear discrepancies between atomic (left)CoORIXSspectrameasuredat320Kwithincidenten-
2 multipletexcitationsandexperimentalfeaturesinmodel ergies from 55-70eV (0.5eV step) are compared with (right)
1. Mott insulator CoO are revealed. Features on the en- an atomic multiplet model.
0 ergy gain side of excitations are shown to match a ther-
4 mal effect present in multiplet models, referred to here
1 as psuedo-anti-Stokes (pAS) scattering. Features on the persists at a length scale of >100˚A at 310K [21].
:
v energy loss side are attributed to intersite interactions For this study, a bulk-like well ordered CoO film with
Xi betweenmultipletexcitationsandlowenergymany-body single-nanometer surface roughness was grown on MgO,
degrees of freedom. and transferred to the RIXS chamber vacuum with min-
r
a imal exposure to the air. The sample was grown by
molecular beam epitaxy (MBE) in an ultrahigh vacuum
MATERIALS AND EXPERIMENTAL METHODS chamber with the base pressure of 2 10−10 torr. Cobalt
×
was evaporated onto a MgO(001) substrate in 2 10−6
×
CoOisalargespinantiferromagnetwithacubicNaCl torr oxygen at room temperature. After evaporation,
crystal structure [16, 17] and predominantly 3d7 cobalt the sample was annealed to 600◦C within a 2 10−6
×
valence [14, 18]. The type 2 Neel transition occurs at torr oxygen atmosphere for 30 minutes, yielding a sur-
roughly 290K [19], however magnetic excitation peaks face roughness under 1nm measured by atomic force mi-
observed by inelastic neutron scattering do not soften croscopy. Samplethicknesswas45nm,muchgreaterthan
significantlyoveratemperaturerangeextendingtoabove the<5nmlayeroverwhichinterfacestrainandexchange
320K [20], and short range antiferromagnetic correlation effec∼ts may be significant [22], and similar to three times
2
the estimated X-ray penetration depth (Fig. 1(b)). M- (a) (c)
C 5
edgemeasurementswereperformedwith 30meVenergy
resolutionatthebeamline4.0.3(MERLIN∼)RIXSendsta- 46 AB nergy
tion(MERIXS)[23]attheAdvancedLightSource(ALS), E E
Lawrence Berkeley National Laboratory. The scattering s) 2 DE 4
geometry is shown in Fig. 1(a). The ratio of resonant nit 0
u 50 60 70
to non-resonant scattering rate (AR/ANR) can be deter- b. Incident Energy (eV) D
minedfromthex-raypenetrationdepthplotinFig. 1(b), ar(b)
where the depth of each resonant dip is proportional to sity ( 5 320KE 3
log(1+A /A ). TheshallowM-edgedipsuggeststhat n
resonantRself-aNbRsorption will have less influence on spec- g Inte 4 CD C
tra at the M-edge relative to higher energy resonances. n 2
eri B
att 3 A
c
S 90K B
TEMPERATURE DEPENDENCE IN MULTIPLET E
RIXS EXCITATIONS 2 D 1
C
The incident energy dependence of RIXS spectra for 1 B A
CoO is presented in Fig. 1(c, left), together with an A 0
atomic multiplet simulation (right panel). The promi- 0
0.5 1 1.50.7 0.8 0.9 1 1.1 1.2
nent feature at 0.8-1.1eV energy loss is associated with
Energy Loss (eV) Energy Loss (eV)
the 4T symmetry multiplet states, which are distin-
2
guished from lower energy states by a larger charge den-
FIG. 2. Thermal changes in experimental line shapes:
sity in eg orbitals. All modeled energy loss features are (a) (red) A fluorescence spectrum of CoO is compared with
convoluted by a 70meV Lorentzian function to represent (black) an atomic multiplet simulation. (b) RIXS data ob-
intrinsic lifetime broadening. tained at energies labeled A-E in panel (a) are overlaid with
black background curves obtained by an automated fitting
The simulation follows the standard Kramers-
functiondescribedinthetext. Reddatapointsaremeasured
Heisenberg method that accurately describes CoO RIXS
at 320K and blue points at 90K, and a dashed vertical line
at the L-edge [14] and NiO at the M-edge [5, 15], with a indicatestheonsetof4T2 excitationintensityat90K.(c)The
renormalized first principles parameter set [25, 26]. The datafrompanel(b)areshownafterbackgroundsubtraction,
crystalfieldperturbationof10Dq=0.98eV(atT=90K)is and normalized so that all 90K measurements have the same
fixedbytheRIXSexcitationenergiesandTanabe-Sugano height. Curvesrepresentmultipletsimulationsfor(darkblue)
diagram for 3d7 cobalt, and reduced by 10% in the in- T=90K, (light red) T=320K, and (green) T=90K electronic
BoltzmannoccupationwiththeT=320Klatticeconstant,and
termediate states due to orbital contraction. The unit
cell volume contracts from V =77.4[1] ˚A3 at 320K arenormalizedtoalignthebluesimulationcurvewiththelow
320K energy lineshape of T=90K data points. An inset at upper
to V =76.5[5] ˚A3 at 90K [27], giving a change of 1-
90K rightillustrateshowthermallypopulatedstates(shadedred)
(V320K/V90K)5/3=-1.9% in the estimated value of 10Dq reduce the excitation energy gap.
[28]. An external exchange field of J∗ = 0.0126eV is
takenfromneutronscatteringmeasurements[20,21],and
calculated spectra are summed over all 3 [100] magnetic
domain configurations. more clearly, background curves for the elastic tail (Fig.
Core hole lifetimes are calculated using the SCLC 2(b,black)) are obtained with an automated fitting func-
method [15, 29], with a 3d-3p transition rate C re- tion. The function approximates the background by fit-
V
duced by 10% relative to that estimated for the M-edge ting the local tangents and radius of curvature of a cir-
of NiO [15], and a slow rate factor for non-multiplet de- cular contour from data points at energies above and
cays C =0.15eV. These lifetime estimates accurately below the excitation. Examining the background sub-
CC
reproduce detailed incident energy dependence of RIXS tracted curves in Fig. 2(c) reveals that the prominent
spectra such as the sudden appearance of an inelastic 1eV 4T feature shifts to lower energy at high temper-
2
∼
peak from 57.5-58eV in Fig. 1(c), and the narrow fluo- ature, the slope of the energy gain intensity onset be-
rescencepeaksaround57-60eVinFig. 2(a). Themethod comes much shallower, and RIXS peak heights drop by
describedinRef. [15]hasbeenusedtosimulatecoherent 10-20%. At both high and low temperature, the energy
resonantelasticemissionseeninFig. 2(a)andthestrong gainsideofthepeakhasasharperslopethantheenergy
elastic tails in Fig. 1(c, right). loss side. At 90K, the leading edge closely resembles a
A pronounced softening occurs on the leading edge of 70meV Lorentzian, while full peak width at half maxi-
RIXS intensity when temperature is raised from 90K mum is 160meV. The irregular shape near 1eV energy
∼
to 320K (Fig. 2(b)). To observe the 4T feature loss is suggestive of multiple closely spaced features with
2
3
(a) anti-Stokes scattering (b) “pseudo-anti-Stokes” the onset energy shift (Fig. 2(c), green curve). Simul-
m m
taneouslyweightingmultipletstateoccupancieswiththe
E=E(4T2)-Es 320K Boltzmann distribution reproduces the high tem-
nergy E=-Es 4T2 panerdatduarteaopnoseinttlsi)n,easshawpeelsl calsostehlye (dFroigp. i2n(co)v,erreadllcpueravke
E
height [17].
E0s 4T1 4T1 Thermal population of low energy modes softens the
leading edge slope by allowing in-gap excitations. The
Time Time
(c) first three excited states of the simulation are primar-
s)5 ily associated with excitations of spin (20meV), spin or-
nit AS pAS bit (38meV) and mixed (47meV) degrees of freedom re-
u4
b. spectively, as also discussed from perturbation theory in
y (ar3 pAS Ref. [18]. These states have 22%, 11% and 8% occupa-
sit2 tion respectively at 320K, and the ground state has only
n
nte1 45% occupation. When cooled to 90K, the system is al-
I most fully in the ground state (93%). Taken collectively,
0
-0.1 0 0.1 0.70.80.9 1 1.71.81.9 2 2.12.22.32.4 correlations with the resonance profile, excitation ener-
Energy Loss (eV)
gies and temperature dependence strongly suggest that
the atomic multiplet model is accurately describing elec-
FIG. 3. Pseudo-anti-Stokes features from thermally
populated modes: (a) A schematic shows a typical anti- tronic symmetries and energetics on the scattering site.
Stokes scattering process. Thermal fluctuations cause the The multiplet scattering processes that lead to the
scatteringsitetostartinaspinflipexcitedstate[2,5,9]with thermalbuild-upofintensityontheenergygainsideofa
energyES,withinthe4T1groundstatemanifold. Anincident chargeexcitedfinalstatehavestrikingsimilaritytoanti-
photon excites the system into intermediate resonance states
StokesRamanemission. Anti-Stokesscatteringprocesses
(m), and a scattered photon is emitted as the system decays
annihilatethermallyexcitedlowenergymodesandresult
into the lowest energy state of the ground state manifold.
The resulting RIXS feature appears at negative energy loss in energy gain features in scattering spectra. A repre-
(E = ES). (b) In a pseudo-anti-Stokes scattering process, sentative anti-Stokes process in multiplet calculations is
−
thesystemevolvesthroughthesameinitialandintermediate drawn in Fig. 3(a), in which the system evolves from a
statesasanti-Stokesscattering,butthefinalstateisthelow- spinexcitedinitialstatetothelowestenergystateofthe
est energy state of a higher energy multiplet manifold (e.g. 4T groundstatemanifold. Inamany-bodycontext,this
4T2). (c) Spectral line shapes of low energy multiplet exci- is 1similar to the annihilation of a thermal magnon. In
tations are compared at (blue) T=90K and (red) T=320K
what we are calling pseudo-anti-Stokes (pAS) emission,
using the same 10Dq value. Anti-Stokes and pseudo-anti-
Stokestailsappearontheenergygainsideofallmultipletfea- the system evolves from a thermally excited initial state
tures. Thespectraareaveragedoverincidentenergy,andthe to the lowest energy state of a different multiplet state
T=90Kcurveintensityhasbeenenhancedby13%toroughly manifold (e.g. 4T ), resulting in intensity on the energy
2
align peak heights. gain side of a multiplet excitation. In a many-body con-
text, the pAS scattering process drawn in Fig. 3(b) can
be thought of as simultaneously annihilating a thermal
a continuum-like tail towards higher energy. magnon and creating an in-gap charge excitation (exci-
In lower resolution studies, it is common practice to ton).
tune atomic multiplet models so that excitation features The matrix elements and momentum dependence of
are centered on experimental peaks, and to account for pASscatteringarenotidenticaltotrueanti-Stokesemis-
much of the peak width using lifetime (Lorentzian) and sion,buttheclosemetaphorbetweenthetwoprovidesan
experimental resolution (Gaussian) broadening. How- intuitive way to understand thermal changes through-
ever, the high resolution measurements in Fig. 2(c) are out the simultated RIXS spectrum. To isolate electronic
not compatible with this approach. A broadened atomic Boltzmann effects from the energy shift brought on by
multiplet calculation (Fig. 2(c), blue curve) cannot si- lattice relaxation, high and low temperature Boltzmann
multaneously match the sharp leading edge and higher weighted simulations in Fig. 3(c) are performed with
energy structure on the energy loss side of the excita- the same 10Dq crystal field parameter optimized for
tion. T=320K. Thermal broadening of all excitations is asym-
Themultipletmodelisthereforeusedonlytosimulate metrical, with greater intensity on the energy gain side,
theenergeticallysharpstatesattheleadingedgeofinten- as seen from the high and low temperature calculations
sity,tobetterunderstandwhytheslopeandleadingedge in Fig. 3(c). The energy scale and fractional intensity of
energy change with temperature. Changing the crystal pAS intensity on the energy gain side of multiplet exci-
field parameter 10Dq by 1.9% as expected for thermal tations are quite similar to true anti-Stokes emission for
lattice expansion accounts for just approximately half of most of the CoO multiplet excitations.
4
INTERATOMIC SHAKE-UP AND THE sites and 2 for next nearest neighbors, consistent with
EXCITATION LINE SHAPE the vectors labeled in Fig. 4(a). The prefactor of 1.5
represents the 3/2 spin moment. The operator n has
X
TheresultspresentedinFig. 2showthatatomicmulti- a value of 1 if a 1eV orbital excitation is present on
∼
pletsimulationsaccuratelypredictchangesattheleading the scattering site and 0 otherwise. Non-magnetic crys-
edge of the 4T excitation. However, most of the asym- tal field interactions are considered by adding a charge
2
metric line shape of the 4T excitation is unexplained, correlation Hamiltonian term V˜:
2
andmustinvolveexciteddynamicsthathavenotyetbeen
touched on. Because the line shape is not explained in (cid:88)
V˜ =n n V (3)
a single atomic multiplet picture, it is necessary to con- X z2 ζ
i
sider many-body interactions with electronic degrees of i
freedom on the 12 nearest neighbor and 6 next neigh- wheren isanelectronnumberoperatoractingonthe
z2
bor cobalt atoms surrounding the scattering site. In- 3d syimmetry orbital of the i indexed site. Spatial
3z2−r2
teractions between the 4T2 excitation and local many symmi etry of the interaction is set by the zi coordinate
body degrees of freedom occur because the 4T2 excita- axis, which is parallelto a vector connecting the indexed
tioninvolvesaredistributionofelectrondensityfromt2g site to the scattering site. Linking the intersite interac-
orbitals that point towards nearest neighbor Co atoms, tion to n is equivalent to treating the 4T excitation as
z2 2
into eg orbitals that overlap strongly with oxygen pσ or- a point-soiurce perturbation located along the axis con-
bitals. For Co atoms that neighbor the scattering site, necting the Co scattering site to a neighboring Co site,
thiswilllowertheenergyofd-orbitalsthatpointtowards whichperturbsd-orbitalsextendingfromtheneighboring
the scattering site and enable magnetic exchange inter- site.
actions through the vacated t2g state. A shift in the 4T2 excitation onset energy is avoided
A fully interacting quantum model is not practical to by setting the lowest energy atomic eigenstate on each
implement with such a large cluster basis in a 3D crys- neighbor of the scattering site to 0eV for both values of
tal. We therefore neglect the entanglement of electronic n through an additional factor C˜ . This is necessary
X X
states on neighboring Co atoms. In this approximation, because an average effect of the B˜ and V˜ interactions is
all many-body eigenstates Ψσ that incorporate multi- implicitlyincludedwithinthecrystalfield10Dqparame-
| (cid:105)
ple Co atoms are obtained by matrix multiplying over ter. TheresultingHamiltonianH˜ =H˜ +V˜+B˜+C˜
mult X
the single atom multiplet states: buildsonthemultipletHamiltonianusedforsimulations
in the previous section (H˜ ), and acts on an effective
mult
Co O cluster. The Hamiltonian is constructed such
(cid:89) 19 44
Ψσ = Ψ0σ Ψiσ (1) that all RIXS spectral features are unchanged except for
| (cid:105) | (cid:105) | (cid:105)
i the 1eV4T excitation. EachCositehas12lowenergy
2
∼
states, extending up to 140meV above the single-site
where |Ψ0σ(cid:105) is an atomic multiplet eigenstate of the ground state. Nonzero va∼lues of J and V allow the 4T
scattering site, and Ψ represents an atomic multiplet ζ ζ 2
iσ
| (cid:105) excitationtoperturblowenergystatesymmetriesonsur-
eigenstate of a neighboring site, with i indexing the 18
rounding Co sites, giving a small probability that charge
nearest or next-nearest neighbor Co sites. The wave-
excitations will trigger low energy 0-140meV excitations
function of each Co site, Ψ , is determined by an in-
iσ
| (cid:105) on neighboring sites.
dependent calculation, with σ indicating the magnetic
Calculations in Fig. 4 isolate the effect of B˜ and V˜
exchange field orientation on the scattering site, and the
intersite interactions on the charge excitation line shape
magnetic orientation on other sites fixed by the antifer-
bytreatingthescatteringsitecomponentofthe4T exci-
romagnetic order [30]. The local Hamiltonian on neigh- 2
tation as a 0eV delta function. Several important trends
boring sites is modified to account for different intersite
are evident when the V and J terms are explored inde-
energetics following the transfer of charge from t to e ζ ζ
2g g
pendently. First, V has a far greater effect on the line
symmetries in the 1eV 4T excited states. Changes in 1
2
∼ shape than V , which may be understood because the V
magneticexchangearedescribedbyaddinganexcitation- 2 1
triggered exchange field B˜ oriented parallel to the mag- perturbationdirectlydisruptsthe[100]groundstateaxis
of rotation for orbital angular momentum. Second, the
netic orientation on the scattering site:
largest likely value of J , -1.4meV, is also insufficient to
2
influence the excitation line shape. The J parameter
2
B˜ =1.5 n (cid:88)J , (2) represents the suppression of oxygen mediated superex-
X ζ
× change, which has a mean field interaction strength of
i
1.4meV seen from the antiferromagnetic exchange field
HereJ istheamplitudeofthe4T excitation-induced (1.4meV=12.6meV/(6 1.5)). Thus only the V and J
ζ 2 1 1
×
change in local magnetic interactions. The index ζ takes haveimmediateimportanceindeterminingtheexcitation
a value of 1 for the interaction with nearest neighbor Co line shape.
5
(a) V1,J1 (c) 5
5
- - -
V1=-30meV E: hν=65eV
1 V2,J2 4 J1=10meV
+ + 2 +
3 4
- - -
(b) 2 ) D: 64eV
s
10 t
V1=V2=0eV 1 uni3
V2=0.1eV .
b
5 V1=-0.06eV 0 ar C: 61.5eV
s) V1=-0.1eV 5 dE=35meV y (
unit 4 dk sit2
b. 0 λ=2 en
y (ar10 J1=J2=0eV 3 Int B: 58.6eV
ensit 5 JJ21==-11.04mmeeVV 2 1
nt
I 1
J1= A: 57.9eV
20meV
0 0
-0.2 0 0.2 0.4-0.2 -0.1 0 0.1 0.2 0.3 0
Energy Loss (eV) Energy Loss (eV) 0.7 0.8 0.9 1.0 1.1 1.2
Energy Loss (eV)
FIG. 4. Intersite electronic shake-up interactions: (a)
Thescatteringsiteishighlightedinredina[001]planeofthe
FIG.5. Mergingshake-upandmultipletmodels: Asim-
CoOlattice,withrelativeantiferromagneticspinorientations
ulation of the scattering site and its 12 nearest Co neighbors
indicatedby’+’and’-’signs. Parametersdescribingintersite
is thermalized to (dark blue curves) T=90K and (light red
interactions are labeled for (vector 1, [110] direction) nearest
curves) T=320K to match experimental data. Data curves
and (vector 2, [100] direction) next-nearest cobalt neighbors
are reproduced from Fig. 2(c), and are measured at the inci-
ofthescatteringsite. (b)Theeffectof(top)Vand(bottom)J
dent energies labeled.
shake-up parameters is simulated. Green curves representing
nearestneighborinteractions(V2=0.1eVandJ2=2.1meV)are
nearlyidenticalto(black)thetrivialcurveswithnoshake-up
parameters applied. (c) Data points obtained by averaging
the five T=90K curves in Fig. 2(c) are compared with (top) Ameaningfulanalogycanbedrawnbetweentheprob-
a shake-up simulation and (bottom) a Poisson distribution. abilistic triggering of low energy excitations on atoms
that neighbor a localized charge excitation and the Pois-
son distribution of high-repetition stochastic processes.
The J parameter is assigned larger amplitudes than When several excitations are likely to occur simultane-
1
J , because electron mobility and interactions between ously, the simulated line shape tends to evolve into a
2
near neighbor Co atoms are thought to be much greater Poisson-like (Gaussian-like) distribution as seen for the
than oxygen mediated mobility between next neighbor J =20meV simulation in Fig. 4(b, bottom). However,
1
Co sites [31]. Either J or V can potentially explain when there is unlikely to be more than one simultaneous
1 1
the full width of the experimental line shape, however excitation on neighbors of the RIXS scattering site, the
J appears to give a better line shape correspondence spectrum can easily become irregular, with prominent
1
with data and does not require strong interactions - just bumps at the energies of specific low energy atomic mul-
J 10meV is sufficient. The V parameter is assigned a tiplet excitations (Fig. 4(b, top)). When the calculation
1 1
∼
negative sign because it comes from a reduction in t is fitted to our data in the Fig. 4(c, top), the average
2g
charge density on the scattering site, but the qualitative chance of triggering an excitation of any energy is only
effect of the V perturbation is sign independent. The 6% per atom (Poisson λ 2/3), suggesting that both
1
∼
effect of the J parameter does not depend at all on its thestochasticphysicsofthePoissondistributionandthe
1
sign, because the scattering site has an equal number of intrinsic 140meV distribution of low energy states are
∼
spin aligned and antialigned nearest neigbor Co sites. A contributing factors to the 160meV experimental peak
∼
comparison with T=90K RIXS data is presented in Fig. width. Fitting RIXS data with the Poisson distribution
4(c, top), using a balance of V and J intersite interac- gives parameters of λ=2 (17% excitation chance/atom)
1 1
tion parameters, and Boltzmann weighting the model to and dE/dk=35meV, likely overstating the probability of
T=90K. lowenergyexcitationsoccurringonthenearneighborCo
6
atoms. Energy Loss (eV)
Full simulations that include the atomic multiplet 2.0 2.2 2.4
states of the scattering site allow a comparison with s)1
t
the temperature and incident energy dependence of ni
u
RIXS measurements (Fig. 5). Overall line shapes are . Nd RIXS
b Co RIXS
matched well by the simulation, including the broader ar (NSNO)
andsmoothercharacteristicshapeofT=320Kdata. Cor- ( (CoO)
y
respondence with temperature dependence at the lead- sit
ingedgeofscatteringintensity(0.8-0.9eV)remainsquite n
e
good when the thermalized states of neighboring sites nt0
I
are considered, strongly supporting the analysis of Fig. 0.8 1.0 1.2
2(c). Theseresultshavegreatconceptualimportancefor Energy Loss (eV)
timeresolvedpump-probeRIXSsystemscurrentlyinde-
velopment, because they show that RIXS can effectively FIG. 6. RIXS on a spectator atom: (black, dia-
reveal the thermal (or pumped/athermal) occupancy of monds)TheCoO4T2 excitationmeasuredathν=61.5eVand
low energy electronic degrees of freedom. T=320K is overlaid with (gray, circles) a room temperature
ff RIXS excitation spectrum from Nd spectator atoms in
Nd1.67Sr0.33NiO4+δ (NSNO). Energy loss for NSNO is dis-
playedonthetopaxis,andisshiftedby1.2eVrelativetothe
DISCUSSION
CoO incident energy axis.
Our model treats the multiplet state as a rapidly im-
posedclassicalperturbationonitssurroundings,whichis
outstrongelectroniclocalization,long-livedorbitonscan
equivalent to regarding it as a quantum quench: a sud-
have cleanly resolved momentum dispersion [13], which
den change in the parameters of a system Hamiltonian,
would be be obscured if the expected number of phonon
whichcreatesnewdynamics[32]. Quantumquenchesare
scattering events were large (Poisson λ > 1). Coupling
theoretical abstractions that can only be approximated
to electronic degrees of freedom can als∼o be minimized
in experiments, and resolving the absolute accuracy of
by measuring RIXS from spectator atoms in a largely
this picture will require future high resolution and mo-
d8 system, as high spin d8 sites have fairly classical
mentum resolved studies. The idea that localized core
spin with only 3 low energy multiplet degrees of free-
electron excitations can cause a simple quantum quench
dom that have weak excitation matrix elements with re-
that acts on neighboring atoms has been widely applied
spect to the V- and J- type perturbtations considered
inmodelsof“shake-up”or“indirect”resonantscattering
in our model. The room temperature RIXS spectrum
processes[4,6,8,10,12]. Thepresentsituationisunusual
fromNdspectatorsitesinthelargelyd8 nickelatesystem
however in that the origin of the intersite perturbations
Nd Sr NiO iscomparedwithCoORIXSdatain
is the atomic 4T valence excitation, rather than a core 1.67 0.33 4+δ
2 Fig. 6. The electronically simple Nd f-orbital excitation
hole resonance state. The Poisson-resembling line shape
is energetically sharp and does not reveal clear signs of
isthusintrinsictowell-resolvedlowenergyorbitalexcita-
energy loss features from phonon shake-up.
tions in CoO, and not an artefact of the RIXS resonance
process. Shake-up effects from intermediate core hole states
The model shows that quite weak electronic shake-up cannot be responsible for the effect in our data, be-
interactions can account for the observed line shape and cause RIXS curves excited via intermediate states with
temperature dependence, and provides approximate up- a Γm 0.5eV inverse lifetime, such as curve A, would
∼
perlimitsofJ =10meVandV =100meVforthestrength lead to very different excitation line shapes than the
1 1
of those interactions. However, it is also possible that a intermediate states of curves D-E which have lifetimes
measurablecomponentoftheshake-upintensityisdueto of Γm > 2eV (from SCLC). Moreover, the intermediate
coupling between the multiplet excitations and phonons. state inverse lifetimes are much larger than the inverse
We have not specifically modeled the phonon shake-up dephasing times for low energy states (∆E<140meV),
component because high resolution RIXS studies have greatly limiting any intermediate state shak∼e-up effect
notyetresolvedevidenceforlargecouplingconstantsbe- on the neighboring Co quantum states.
tween phonons and charge neutral multiplet final states. In summary, the model large spin Mott insulator CoO
Charge-bearing particles (e.g. electrons and holes) and has been studied with high resolution RIXS, revealing a
transitions that change the principle quantum number Poisson-likelineshapethatisunliketheLorentzian(life-
of an electron (e.g. L- or K-edge resonance) cause all time broadened) excitation contours in atomic multiplet
d-orbitals to expand or contract significantly in Hartree- models. Temperature dependence of an anti-Stokes-like
Fock calculations, and are more natural candidates for tail on the energy gain side of the prominent 4T feature
2
strongphononshake-upprocesses. In1Dmaterialswith- is found to be consistent with the thermal population of
7
low energy states, suggesting that high resolution RIXS (2011).
can be used to ‘take the temperature’ of a generic elec- [12] C. J. Jia C.-C. Chen, A. P. Sorini, B. Moritz, and T. P.
tron system. The energy loss contour of the excitation is Devereaux, New J. Phys. 14, 113038 (2012).
[13] J. Schlappa, K. Wohlfeld, K. J. Zhou, M. Mourigal,
explainedbyapoly-atomicmodelinwhichtheexcitation
M. W. Haverkort, V. N. Strocov, L. Hozoi, C. Mon-
triggers a shake-up of low energy modes on neighboring
ney,S.Nishimoto,S.Singh,A.Revcolevschi,J.-S.Caux,
Co atoms. Within the model, even quite weak interac-
L. Patthey, H. M. Rønnow, J. van den Brink, and T.
tions with a 4T2 multiplet charge excitation are shown Schmitt, Nature 485, 82 (2012).
to transform its line shape by causing low energy excita- [14] M. M. van Schooneveld, R. Kurian, A. Juhin, K. Zhou,
tions to appear stochastically on different atomic neigh- J. Schlappa, V. N. Strocov, T. Schmitt, and F. M. F. de
bors of the scattering site. Based on this, we anticipate Groot, J. Phys. Chem. C 116, 15218 (2012).
[15] L. A. Wray, W. Yang, H. Eisaki, Z. Hussain, Y.D.
that future high resolution studies may identify Poisson-
Chuang, Phys. Rev. B 86, 195130 (2012).
like line shapes for highly localized charge excitations in
[16] A tetragonal distortion beneath the N´eel temperature is
other materials that have a large low energy density of
unlikely to be resolvable in our spectra [17].
states, such as many mid-transition metal oxides (e.g. [17] Matrix elements and higher order modeling factors are
cobaltates and manganites). reviewed in the online Supplemental Material.
[18] G. van der Laan, E. Arenholz, R. V. Chopdekar and Y.
Acknowledgements:
Suzuki, Phys. Rev. B 77, 064407 (2008).
TheAdvancedLightSourceissupportedbytheDirec- [19] G. Srinivasan and M. S. Seehra, Phys. Rev. B 28, 6542
tor, Office of Science, Office of Basic Energy Sciences, of (1983).
theU.S.DepartmentofEnergyunderContractNo. DE- [20] J. Sakurai, W. J. L. Buyers, R. A. Cowley, and G.
Dolling, Phys. Rev. 167, 510 (1968).
AC02-05CH11231. Work at Brookhaven National Labo-
[21] M.D.RechtinandB.L.Averbach,Phys.Rev.B5,2693
ratory was supported by the U.S. Department of Energy
(1972).
under No. DEAC02-98CH10886.
[22] P. J. van der Zaag, L. F. Feiner, R. M. Wolf, J. A.
Borchers,Y.Ijiri,andR.W.Erwin,Phys.B:Cond.Mat.
276, 638 (2000).
[23] Y.-D. Chuang, J. Pepper, W. McKinney, Z. Hussain, E.
Gullikson,P.Batson,D.Qian,andM.Z.Hasan,J.Phys.
[1] P.Kuiper,J.-H.Guo,ConnyS˚athe,L.-C.Duda,J.Nord- Chem. Solid 66, 2173 (2005).
gren, J. J. M. Pothuizen, F. M. F. de Groot, and G. A. [24] B. L. Henke, E. M. Gullikson, and J. C. Davis, Nuclear
Sawatzky, Phys. Rev. Lett. 80, 5204 (1998). Data Tables 54, 181 (1993).
[2] F.M.F.deGroot,P.Kuiper,andG.A.Sawatzky,Phys. [25] Theinter-d-orbitaland3p-3dSlater-Condonparameters
Rev. B 57, 14584 (1998). aresetto80%and65%ofatomicvalues(64%and52%of
[3] G. Ghiringhelli, N. B. Brookes, E. Annese, H. Berger, Hartree-Fock). The d-orbital spin orbit coupling param-
C. Dallera, M. Grioni, L. Perfetti, A. Tagliaferri, and L. eter is set to 0.06eV with no core hole and 0.07eV when
Braicovich, Phys. Rev. Lett. 92, 117406 (2004). a 3p core hole is present, and the 3p spin orbit coupling
[4] M. Z. Hasan, E. D. Isaacs, Z.-X. Shen, L. L. Miller, K. strength is set to 1.5eV.
Tsutsui,T.Tohyama,andS.Maekawa,Science288,1811 [26] The CTM4XAS code maintained at
(2000). http://www.anorg.chem.uu.nl/CTM4XAS/ performs
[5] S.G.Chiuzbaˇian,G.Ghiringhelli,C.Dallera,M.Grioni, identical multiplet diagonalization, and was used as the
P.Amann,X.Wang,L.Braicovich,andL.Patthey,Phys. source for Hartree-Fock Slater Condon parameters.
Rev. Lett. 95, 197402 (2005). [27] CoO: phase diagram, crystal structure, lattice pa-
[6] L. J. P. Ament, F. Forte, and J. van den Brink, Phys. rameters. Madelung, O., Ro¨ssler, U., Schulz, M.
Rev. B 75, 115118 (2007). (ed.). SpringerMaterials - The Landolt-Brnstein
[7] S.G.Chiuzbaˇian,T.Schmitt,M.Matsubara,A.Kotani, Database (http://www.springermaterials.com). DOI:
G.Ghiringhelli,C.Dallera,A.Tagliaferri,L.Braicovich, 10.1007/10681735 500.
V. Scagnoli, N. B. Brookes, U. Staub, and L. Patthey, [28] Spectroscopy of Transition Metal Ions on Surfaces, Bert
Phys. Rev. B 78, 245102 (2008). M. Weckhuysen, Leuven University Press, 2000.
[8] F. Forte, L. J. P. Ament and J. van den Brink, Phys. [29] K.Okada,A.Kotani,H.Ogasawara,Y.SeinoandB.T.
Rev. B 77, 134428 (2008). Thole, Phys. Rev. B 47, 6203 (1993); H. Ogasawara, A.
[9] G. Ghiringhelli, A. Piazzalunga, C. Dallera, T. Schmitt, Kotani,andB.T.Thole,Phys.Rev.B50,12332(1994).
V. N. Strocov, J. Schlappa, L. Patthey, X. Wang, H. [30] Adomain-dependentZ2degreeoffreedominthespinori-
Berger, and M. Grioni, Phys. Rev. Lett. 102, 027401 entationofnearestneighborcobaltatomsisnotrelevant
(2009). to the calculation results.
[10] L. J. P. Ament, M. van Veenendaal, T. P. Devereaux, J. [31] R. Skomski, X. Wei, and D. J. Sellmyer, J. Appl. Phys.
P. Hill, and J. van den Brink, Rev. Mod. Phys. 83, 705 103, 07C908 (2008).
(2011). [32] P. Calabrese and J. Cardy, Phys. Rev. Lett. 96, 136801
[11] M. M. Sala, V. Bisogni, L. Braicovich, C. Aruta, G. (2006); M. A. Cazalilla, Phys. Rev. Lett. 97, 156403
Balestrino, H. Berger, N. B. Brookes, G. M. De Luca, (2006); M. Rigol, V. Dunjko, V. Yurovsky, and M. Ol-
D. Di Castro, M. Grioni, M. Guarise, P. G. Medaglia, shanii, Phys. Rev. Lett. 98, 050405 (2007).
F.M.Granozio,M.Minola,M.Radovic,M.Salluzzo,T.
Schmitt, and G. Ghiringhelli, New J. Phys. 13, 043026
SSuupppplleemmeennttaall mmaatteerriiaall:: mmaattrriixx eelleemmeennttss aanndd hhiigghheerr oorrddeerr mmooddeelliinngg ffaaccttoorrss
((DDaatteedd:: AApprriill 2233,, 22001133))
TThhiisssseeccttiioonnaaddddrreesssseesseexxppeerriimmeennttaallccaalliibbrraattiioonnffaaccttoorrssaannddhhiigghheerroorrddeerrmmooddeelliinnggccoonnssiiddeerraattiioonnss
tthhaatt mmaayy bbee ooff iinntteerreesstt ffoorr ffuuttuurree hhiigghh rreessoolluuttiioonn RRIIXXSS ssttuuddiieess..
CCOONNTTEENNTTSS
EExxppeerriimmeennttaall ccaalliibbrraattiioonn 22
SSuurrffaaccee aanndd bbuullkk llaattttiiccee ddiissttoorrttiioonn iinn CCooOO 22
TThheerrmmaall cchhaannggeess iinn iinntteennssiittyy mmaattrriixx eelleemmeennttss 22
RReeffeerreenncceess 22
2
EXPERIMENTAL CALIBRATION
CalibrationofenergylossvaluesacrosstheCCDwasperformedseparatelyforeachmeasurementconfiguration(each
incident energy) to ensure accuracy. Scattering intensity measured at each pixel was normalized by a roughly unitary
factor representing the energy scale per pixel, which was non-uniform across the CCD, to ensure that intensity in the
final spectra accurately represents the density of scattered photons per unit energy. Intensity was also normalized by
the incident photon flux and the beamline/spectrometer efficiency vs. energy curves.
SURFACE AND BULK LATTICE DISTORTION IN CoO
CoO undergoes a tetragonal lattice distortion that is expected to broaden lineshapes beneath 290K [1]. It appears
empirically that this effect is small, because low temperature excitation onset lineshapes are quite sharp, and higher
energy lineshapes are similar at high and low temperature. The tetragonal distortion has been approximated with a
crystal field term of D =0.02eV at T=10K in recent literature [2], which is likely larger than occurs in the T=90K
S
measurements here, and is greatly mitigated by the dominant L.L multiplet interaction terms. Including Ds=0.02eV
causes splitting of just 11meV in leading edge states of the 4T excitation, which is small relative to the experimental
2
lineshape of 70meV.
Asimilartetragonallatticedistortionwillmanifestintrinsicallywithinafewnanometersofthecrystalsurface. The
RIXS energy loss features from 4.2nm diameter CoO nanoparticles have recently been shown to be shifted to <10%
lower energies relative to bulk CoO excitations [2]. Atoms near the surface termination of a large crystal exis∼t in a
far more bulk-like environment, however this trend suggests that surface relaxation could slightly broaden the energy
gain side of M-edge RIXS excitations relative to intrinsic bulk line shapes. Strong surface effects are not expected, as
the measured [010] face is non-polar and bulk-like properties (e.g. z-axis dispersion) are observed from photoemission
on CoO with roughly 1/10th the measurement penetration depth of M-edge RIXS [3].
THERMAL CHANGES IN INTENSITY MATRIX ELEMENTS
Because lattice expansion and electronic Boltzmann factors both affect the starting electronic state of the RIXS
scattering process, they have a visible effect on the expected intensity of peak features which can also be used to
identify if thermal changes in the electronic state are accurately captured by the model. Table I summarizes these
matrixelementsforthecurvesinFig. 2ofthemaintext, andshowsthatthethermalizedmultipletmodelreproduces
the intensity change in all curves to within 3% statistical error.
A B C D E
Data 0.88 0.87 0.86 0.90 0.82
Model 0.86 0.84 0.89 0.90 0.82
Lattice 0.99 1.04 1.00 0.95 0.92
TABLE I. Intensity matrix element change (90K 320K): The ratio of peak heights at T=320K and T=90K
→
(I(320K/I(90K)) for the data in Fig. 2(c) of the main text is compared with the thermalized multiplet model, and with a
simulation of lattice distortion only.
[1] H. P. Rooksby and N. C. Tombs, Nature 167, 364 (1951).
[2] M. M. van Schooneveld et al., J. Phys. Chem. C 116, 15218 (2012).
[3] Z.-X. Shen, J. W. Allen, P. A. P. Lindberg, D. S. Dessau, B. O. Wells, A. Borg, W. Ellis, J. S. Kang, S.-J. Oh, I. Lindau
and W. E. Spicer, Phys. Rev. B 42, 1817 (1990).