Gapless quantum excitations from an Ice-like Splayed Ferromagnetic ground state in stoichiometric Yb2Ti2O7

2.4 MB·

by  J. Gaudet

Gapless quantum excitations from an Ice-like Splayed Ferromagnetic ground state in
stoichiometric Yb Ti O .
2 2 7
J. Gaudet,1 K. A. Ross,2,3,∗ E. Kermarrec,1 N. P. Butch,3 G. Ehlers,4 H. A. Dabkowska,5 and B. D. Gaulin1,5,6
1Department of Physics and Astronomy, McMaster University, Hamilton, ON L8S 4M1 Canada
2Institute for Quantum Matter and Department of Physics and Astronomy,
Johns Hopkins University, Baltimore, Maryland 21218, USA
3NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
4Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
5Brockhouse Institute for Materials Research, Hamilton, ON L8S 4M1 Canada
6Canadian Institute for Materials Research, 180 Dundas Street West, Toronto, Ontario M5G 1Z8, Canada
(Dated: January 21, 2016)
6
The ground state of the quantum spin ice candidate magnet Yb Ti O is known to be sensitive
1 2 2 7
to weak disorder at the ∼ 1 % level which occurs in single crystals grown from the melt. Powders
0
producedbysolidstatesynthesistendtobestoichiometricanddisplaylargeandsharpheatcapacity
2
anomalies at relatively high temperatures, T ∼ 0.26 K. We have carried out neutron elastic and
C
n inelastic measurements on well characterized and equilibrated stoichiometric powder samples of
a Yb Ti O which show resolution-limited Bragg peaks to appear at low temperatures, but whose
2 2 7
J
onset correlates with temperatures much higher than T . The corresponding magnetic structure
C
0 is best described as an ice-like splayed ferromagnet. The spin dynamics in Yb Ti O are shown to
2 2 7
2 be gapless on an energy scale < 0.09 meV at all temperatures, and organized into a continuum of
scattering with vestiges of highly overdamped ferromagnetic spin waves present. These excitations

] differ greatly from conventional spin waves predicted for Yb Ti O ’s mean field ordered state,
l 2 2 7
e but appear robust to weak disorder as they are largely consistent with those displayed by non-
- stoichiometriccrushedsinglecrystalsandsinglecrystals,aswellasbypowdersamplesofYb Ti O ’s
r 2 2 7
st sister quantum magnet Yb2Sn2O7.
.
t PACSnumbers: 75.25.-j,75.10.Kt,75.40.Gb,71.70.Ch
a
m
- I. INTRODUCTION µ H ∼0.5 T into a polarized phase that is character-
d 0 C
izedbyresolution-limitedspinwaves14. Linearspinwave
n
o theory using anisotropic exchange produces an excel-
Pyrochlore magnets of the form A B O have been of
c 2 2 7 lent description of the high field spin wave dispersion
[ greattopicalinterestasboththeAandBsublatticesin- and intensities, and the resulting microscopic Hamilto-
dependently form networks of corner-sharing tetrahedra,
nianhasbeenusedinhightemperatureseriesexpansions
1
one of the canonical crystalline architectures supporting
v which accurately describe the magnetization and heat
geometricalfrustrationinthreedimensions1,2. Thecubic
9 capacity of Yb Ti O in absolute units22. Yb Ti O ’s
2 2 7 2 2 7
rareearthtitanates,oftheformRE Ti O havebeenes-
3 2 2 7 spin Hamiltonian contains 4 symmetry-allowed near-
1 peciallyrelevantasmanymagneticRE3+ionscanoccupy neighbour anisotropic exchange terms and it has been
5 the A-site of the structure and where the non-magnetic
proposed that the largest of these is J , which ferro-
0 Ti4+ occupy the B-site. This pyrochlore family can also zz
magnetically couples together local z, or Ising compo-
1. be relatively easily produced in both powder and single nents of spin12. These z-components are aligned directly
0 crystal form3–5. One of the family members, Yb2Ti2O7, into or out of the tetrahedra, and this combination of
6 has been particularly topical as it has been proposed as
S = 1/2 spins, the spin Hamiltonian, and the py-
1 a realization of quantum spin ice6–16. It displays a net eff
rochlore lattice would then be responsible for the quan-
v: ferromagnetic Curie-Weiss constant of ∼ 0.6 K17,18, and tum spin ice phenomenology. Somewhat different phe-
i crystal field (CF) effects give rise to a CF ground state
X doubletattheYb3+sitemadeupofprimarilym =±1/2 nomenology has also been discussed in which Jzz is less
J dominant23.
r eigenvectors and local XY anisotropy19–21. Yb Ti O is
a 2 2 7
therefore a good realization of quantum S =1/2 spins
eff While the general phase behaviour for an anisotropic
decorating a network of corner-sharing tetrahedra - the
exchange Hamiltonian of the form which describes
pyrochlore lattice.
Yb Ti O in zero magnetic field has exotic quantum
2 2 7
The microscopic spin Hamiltonian for Yb Ti O has spinliquidandCoulombferromagneticmeanfieldground
2 2 7
been estimated using neutron spectroscopic measure- states present within it24,25, the mean field ground state
ments of spin waves in its high field polarized state12. predicted on the basis of Yb Ti O ’s spin Hamiltonian
2 2 7
While the zero field phase of Yb Ti O does not show is a simple ferromagnet with a mean field phase transi-
2 2 7
well defined spin waves in single crystals, a magnetic tion of T ∼ 3 K12. A broad “hump” in Yb Ti O ’s
MF 2 2 7
field applied along the [1-10] direction pushes Yb Ti O experimentally-determined heat capacity (C ) is ob-
2 2 7 P
through a quantum phase transition or crossover near served at ∼ 2 K, roughly co-incident with the calculated
2
T , however there are no indications of order observed ments is Ising-like, rather than XY-like in stoichiometric
MF
above a sharp C anomaly which occurs near T ∼ 0.26 Yb Ti O , and this may be related to the effectiveness
P C 2 2 7
K in stoichiometric powders of Yb Ti O 11,26. Taking of disorder at this low ∼ 1 % level21.
2 2 7
the sharp C anomaly at face value for an indication It is therefore important to fully characterize powder
P
of the ferromagnetic phase transition predicted by mean samples of Yb Ti O which are known to be stoichio-
2 2 7
field theory, this indicates that T is suppressed by a metric and to display sharp C anomalies at T =0.26
MF P C
factorof∼12byquantumfluctuations,geometricalfrus- K; that is to use this as a benchmark for understand-
tration, or both. However, there are strong indications ing the zero field ground state of pristine Yb Ti O . In
2 2 7
thatYb Ti O ’szerofieldphasebelowT ∼0.26Kisfar this work, we report elastic and inelastic neutron scat-
2 2 7 C
removedfromaconventionalferromagnet. Todatethere tering results from the same two powder samples pre-
are experimental studies which support a relatively sim- viously studied by neutron diffraction28 and which are
pleferromagneticgroundstate6,8, butalsostudieswhich knowntobestoichiometricYb Ti O andtheCSCwith
2 2 7
show extensive diffuse neutron scattering covering all of composition Yb Ti O with x=0.046. In addi-
2+x 2−x 7−y
reciprocal space10, no changes in the spin relaxation ob- tion, we report a comparison between the spin dynam-
servedwhencoolingbelowthesharpC anomalyinµSR ics measured on a stoichiometric powder of Yb Ti O ,
P 2 2 7
studies from stoichiometric samples27, and no evidence the CSC powder, a single crystal of Yb Ti O grown
2 2 7
for the conventional spin waves that are expected as the by the floating zone technique, and a powder sample of
normal modes of the magnetically-ordered state in any Yb Ti O ’s sister pyrochlore magnet, Yb Sn O . We
2 2 7 2 2 7
sample13,14,23. show that stoichiometric Yb Ti O displays resolution-
2 2 7
An interesting feature of Yb Ti O ’s exotic zero mag- limited magnetic Bragg scattering at low temperatures,
2 2 7
netic field ground state is its sensitivity to weak disor- howeverthesepersisttoamuchhighertemperaturescale
der28,29. The sharp CP anomaly observed at TC∼0.26 than TC=0.26 K. Nonetheless, looking only at the low
K in stoichiometric powder samples, is observed to be temperatureBraggintensities,werefineastaticmagnetic
broader and to occur at lower temperatures in all single structure which is best described as an ice-like splayed
crystal samples measured to date29. The CP anomalies ferromagnet with an ordered moment of 0.90(9)µB. The
can occur as low as ∼ 0.15 K in single crystals grown spin dynamics at the lowest temperatures in stoichio-
from floating zone image furnace techniques, may not metric Yb2Ti2O7 in zero field are indeed far removed
obviously occur at any temperature, or may appear as from conventional spin waves. They are gapless on an
multiple peaks at lower temperatures. energy scale < 0.09 meV at all wave vectors, and char-
acterizedbyacontinuumofscatteringwithabandwidth
Intheinterestofunderstandingthemicroscopicstruc-
of ∼ 1 meV. Vestiges of very overdamped ferromagnetic
ture and defects responsible for the differences between
spin waves can be seen in the inelastic scattering, which
powder samples grown by solid state synthesis, and sin-
itself is temperature independent below T ∼ 3 K.
gle crystals grown from the melt by floating zone tech- MF
niques, neutron diffraction studies were carried on both
powder and crushed single crystal (CSC) samples, that
II. EXPERIMENTAL DETAILS
were known to display different C behaviour at low
P
temperature28. The conclusions were that, while the
powder sample was stoichiometric Yb Ti O , the CSC The powder samples employed in this study were the
2 2 7
was characterized as exhibiting weak “stuffing” wherein same samples previously studied by Ross et al28. 10
a small proportion of excess Yb3+ resides on the Ti4+ grams of stoichiometric Yb Ti O and 8 grams of the
2 2 7
site, and the composition of the crushed single crystal CSC powder, Yb Ti O with x = 0.046, were
2+x 2−x 7+y
was Yb Ti O with x = 0.046. Note that this separately loaded in aluminum sample cans with cop-
2+x 2−x 7+y
defect level is close to the limit of detectability by con- per lids under 10 atms of helium exchange gas. This
ventional diffraction techniques. This study was greatly method of loading powder samples is known to provide
aided by the fact that Ti displays a negative coherent good thermal contact to the cold finger of the dilution
neutron scattering length, hence there is significant neu- refrigerator, and maintains thermal conductivity below
tron contrast for Yb, which has a positive coherent neu- 1K by enabling enough superfluid Helium to coat the
tronscatteringlength,occupyingtheTisite. Inandofit- powder grains31. The 4 gram single crystal of Yb Ti O
2 2 7
self,sensitivityofthegroundstatetosuchweakdisorder (producedinafloatingzoneimagefurnacefollowingsim-
is a remarkable result, as conventional three dimensional ilar procedures to those used to grow other single crys-
ordered states are not sensitive to disorder at such a low tal titanate pyrochlores) was mounted on an aluminum
level. For example, the phase transition to non-collinear holder.
Ψ antiferromagneticorderinEr Ti O isnotsamplede- Elastic neutron scattering measurements were carried
2 2 2 7
pendent, and has been studied as a function of magnetic outontheSPINStripleaxisinstrumentattheNISTCen-
dilution and shown to be consistent with conventional terforNeutronResearch. SPINSusedpyrolyticgraphite
three dimensional percolation theory30. A recent study as both monochromator and analyzer, and 80’ collima-
of the Yb3+ crystal field excitations in Yb Ti O sug- tors before and after the sample, producing a 5.0 meV
2 2 7
gests that the anisotropy of Yb3+ in defective environ- elastically scattered beam with an energy resolution of
3
0.25 meV. Cooled beryllium filters placed before and af-
ter the sample helped to eliminate higher harmonic con-
tamination. ThesamplewasfirstcooledtoT=8Kwhere
scans of the (111), (002), (220), (113) and (222) Bragg
peaks were collected. Afterwards, the sample was cooled
down to 100mK and sat at this temperature for 2 hours
before collecting measurements at the same Bragg posi-
tions as above. Finally, the sample was warmed up to
700mKwhereanotherscanofthesameBraggpeakswas
also collected.
Inelastic neutron scattering measurements were also
performed on both the stoichiometric powder as well as
the CSC, stuffed powder using the time-of-flight disk
chopper spectrometer (DCS) at NIST32. For these mea-
surements, monochromatic incident neutrons of wave-
length of 5˚A were employed, giving an energy resolution
at the elastic position of 0.09 meV. Empty can measure-
ment have been used as a background for these data.
Inelastic neutron scattering measurements on the single FIG. 1: The temperature dependence of the (111) and (113)
Bragg peaks.– Panels a) and c) show the elastically scattered
crystal of Yb Ti O were performed using the cold neu-
tron chopper2spe2ct7rometer (CNCS)33 at the Spallation neutronintensityasafunctionofthemomentumtransfer|Q(cid:126)|
around the (111) and (113) Bragg peaks respectively. Panels
Neutron Source (SNS) at Oak Ridge National Labora-
b) and d) shows the subtraction between the different |Q(cid:126)|
tory. For this time-of-flight experiment, the single crys-
cutsatdifferenttemperatures. Aclear,|Q(cid:126)|-resolution-limited
tal was mounted in a dilution refrigerator and aligned
increase of the elastic scattering at these two Bragg peaks is
with the [HHL] plane in the horizontal plane. An inci-
observed and is representative of the data used to model the
dentneutronenergyof3.3meVwasemployedwhichgave
magnetic structure of stoichiometric Yb Ti O . Error bars
2 2 7
an energy resolution of 0.1 meV at the elastic position.
represent one standard deviation.
Samplerotationmethodswereemployedwhereinthesin-
gle crystal sample was rotated 360◦ about the vertical
direction in 1◦ steps. The background is approximated
8 K data set for (113), respectively. Similar elastic scat-
usingameasurementdoneunderthesameconditionsbut
tering measurements were also carried out at the (220)
without the sample. Magnetic and structural refinement
Bragg position. The magnetic intensities extracted from
were performed using SARAh Refine34 and FullProf35.
these differences are listed in Table I, where we see that
for all of the (111), (113) and (222) Bragg positions, the
increase in scattering, relative to T=8 K, is 3.2(4) %,
III. RESULTS AND DISCUSSION 3.3(5) %, and 3.6(6) %, respectively. Relative to T=0.7
K,themagneticintensityatT=0.1Kisincreasedbyonly
A. Elastic neutron scattering and magnetic ∼ 1.3 % at the (111) Bragg position. We also note that
structure determination: the differences in the elastic scattering have the same Q-
lineshape as the original Bragg scattering, implying that
Fig.1 shows elastic neutron scattering data taken on the corresponding magnetic order is long range, with a
the stoichiometric powder sample of Yb Ti O using correlation length exceeding 80 ˚A.
2 2 7
SPINS. No magnetic Bragg peaks were observed at Ignoring for the time being the fact that the magnetic
nuclear-disallowed positions upon cooling below T , and order parameter does not go to zero above T =0.26 K,
C C
consequentlywefocusedourattentiononnuclear-allowed we can nonetheless refine a magnetic structure based on
Bragg peaks typical of Q=0 magnetic structures. Fig.1 therelativeintensitiesofthedifferencesinBraggscatter-
a) and b) show the (111) Bragg peak at three temper- ing between T=0.1 K and 8 K. This difference is plotted
atures: T = 0.1 K (below T ), T=0.7 K (above T ), as a function of |Q| in Fig.2 a), along with the best fit to
C C
and T=8 K, which is above both the T calculated for a model for a canted or splayed ferromagnet of the form
MF
Yb Ti O on the basis of its microscopic spin Hamilto- depicted in the inset of Fig.2 b). This generalized struc-
2 2 7
nian,aswellabovethehighertemperature“hump”inits ture has the Yb moments along a [100] direction, but
C near ∼ 2 K. Fig.1 c) shows the corresponding elastic also allows for a canting angle, θ, which can be either
P
scattering at the (113) Bragg position at T=0.1 K and towards (+) or away from (-) the local [111] direction,
T=8 K. Elastic scattering at both wave vectors is domi- that is the direction pointing into or out of the tetra-
nated by nuclear contributions, but a weak temperature hedron. A collinear [100] ferromagnet would correspond
dependent magnetic contribution is identified as can be to a canting angle of zero, while the ordered spin ice
seen in Fig.1 b) and d) which show T=0.1 K − T=0.7 K ground state, in which all moments point directly into
andT=0.7K−T=8Kdatasetsfor(111)andaT=0.1− or out of the tetrahedra, would correspond to θ=54.7◦.
4
finementsofthesemagneticstructuresaresummarizedin
Table I, where we have calculated the expected increases
in Bragg scattering at each of (111), (113) and (222) for
two different Q=0 magnetic structures. The splayed XY
ferromagnet, with a negative canting angle, is known to
describeYb Ti O ’ssisterpyrochloremagnetYb Sn O
2 2 7 2 2 7
(θ∼-10◦)36,whilethesplayedspinicestructurehasbeen
reported in some studies of single crystal Yb Ti O but
2 2 7
with a smaller splay angle (θ ∼ 1◦)6,8. Fig.2 b) shows
how the goodness of fit parameter (χ2) vary as a func-
tion of splay angle for this model of splayed or canted
ferromagnets.
Fig.3 shows the temperature dependence of the (111)
Bragg intensity from the stoichiometric powder sample
of Yb Ti O , relative to T=0.7 K. This data set was
2 2 7
collected while warming from 100mK to 700mK with a
warmingrateof1mK/min. Forreference,weoverploted
theelasticscatteringperviouslymeasurednearthe(111)
position in single crystal Yb Ti O (note: both curves
2 2 7
are scaled to their intensities at 100 mK, after subtract-
ing their intensities at 700 mK). It is clear that these
temperaturedependenciesmirroreachother. Wealsoin-
cludedC asmeasuredonapowdersampleofYb Ti O
P 2 2 7
with T =0.26 K. One can see that these magnetic in-
C
tensities do not resemble a conventional order parame-
ter with T =0.26 K. The elastic intensities are approx-
C
imately constant up to ∼ 0.35 K, and then begin to de-
crease.
FIG. 2: Intensity of elastic magnetic scattering vs. Q and
the corresponding fit to the splayed Ice ferromagnet – a) the
best fit of the model for a splayed Ice ferromagnet to the
difference of elastic neutron scattering intensity at 100 mK
and 8 K (i.e., the magnetic elastic scattering) is shown. The
model employed is a splayed ferromagnet (a Q=0 structure
with a net moment along the cubic axes) on the pyrochlore
lattice,withsplayangleofθ=14(5)◦andanorderedmoment
of0.90(9)µ . Note: theerrorbarsarenotshowninthisfigure
B
for clarity, but are taken into account as weights in the least
squaredfittingofthemodel. b)thegoodness-of-fitparameter,
χ2,asafunctionofsplayangleisshown. Theinsettob)shows
an illustration of the best fit magnetic structure model on a
pair of tetrahedra.
FIG. 3: The temperature dependence of the elastic scattered
intensity at |Q(cid:126)|=(111).– The scattered elastic neutron inten-
A negative canting angle gives an XY splayed ferromag-
sity, relative to T=700mK at |Q(cid:126)|=(111) shows similar tem-
net. The best fit, shown as the solid line in Fig.2 a),
perature dependence for both a previously measured single
corresponds to a splayed ice-like ferromagnetic ground
crystal (data taken from Ross et al.14) and for the stoichio-
state with a positive canting angle of 14 ± 5◦, and an
metric powder sample of Yb Ti O (this work). With in-
2 2 7
ordered moment (relative to 8 K) of 0.90(9) µ . The
B creasing temperature, the elastic magnetic scattering begins
saturated moment determined by DC magnetization is to fall around T = 0.35 K, and decreases approximately lin-
1.75 µB which compared to the order moment we ob- earlyabovethistemperature. ThespecificheatanomalyTC∼
tained gives a spin polarization of 51 %. Note that, as 0.26KforarepresentativepowdersampleofYb Ti O (data
2 2 7
shown in Fig.1 b), most of the decrease in the Bragg taken from ref Ross et al.28) is shown for reference, and re-
scattering on raising the temperature occurs above 0.7 vealstherelativeinsensitivityofthetemperaturedependence
K, more than a factor of two above T =0.26 K. Our re- of the elastic scattering to the specific heat anomaly.
C
5
B. Inelastic Neutron scattering and gapless spin
excitations in the Yb Ti O ground state:
2 2 7
Inelasticneutronscatteringmeasurementswerecarried
outonourthreeYb Ti O samples(stoichiometricpow-
2 2 7
der, lightly stuffed CSC powder, and single crystal) us-
ing time-of-flight neutron spectrometers. Measurements
werecarriedoutonthestoichiometricYb Ti O powder
2 2 7
sample and the CSC lightly stuffed powder with compo-
sition Yb Ti O x = 0.046 using the DCS direct
2+x 2−x 7+y
geometry chopper spectrometer at NIST. The resulting
S(|Q(cid:126)|,E) for these two samples at T=0.1 K are shown
in Fig.4 a) and b). The corresponding [HHL] plane-
averaged data set (approximating a powder average) for
singlecrystalYb Ti O atT=0.1KisshowninFig.4c).
2 2 7
FIG. 5: Energy vs. |Q(cid:126)| slice of the mean-field calculation of
S(|Q(cid:126)|,E) for Yb Ti O .– S(|Q(cid:126)|,E) has been computed us-
2 2 7
ing an anisotropic spin 1/2 exchange Hamiltonian with the
exchange parameters determined by Ross et al.12. This cal-
culation successfully accounts for the spin wave spectrum in
thehighmagneticfield,polarizedstateatallwavevectors,but
doesnotresembletheinelasticneutronscatteringseeninFig.
4. In particular the measured inelastic magnetic scattering
is gapless at all wavevectors, while the calculated S(|Q(cid:126)|,E),
shown here, possesses a minimum gap of ∼ 0.25 meV.
¯hω ∼ Q2 and whose intensity peaks at small Q. This
continuumspinexcitationspectrumisverydifferentfrom
thatexpectedforspinwaveswithintheferromagnetically
orderedstatepredictedbymeanfieldtheoryonthebasis
oftheanisotropicexchangeHamiltoniandeterminedpre-
viously from the high field, polarized state. Fig.5 shows
the powder average of this theoretical spin wave spec-
trum broadened by the instrumental resolution, and one
clearly expects sharp and dispersing excitations. The
FIG. 4: S(|Q(cid:126)|,E) as measured for stoichiometric and predicted spin wave spectrum is gapped at all wave vec-
weakly stuffed Yb2Ti2O7 with comparison to Yb2Sn2O7.– tors, with a minimum gap of ∼ 0.25 meV at Q=0. Such
a) and b) show S(|Q(cid:126)|,E) measured on the stoichiometric
a gap would be easily observed with our inelastic mea-
Yb Ti O powder and the lightly stuffed CSC powder of
2 2 7 surements using DCS.
Yb Ti O with x=0.046, respectively, both at T=0.1
2+x 2−x 7+y While the spin excitation spectrum in stoichiomet-
K. c) shows the corresponding S(|Q(cid:126)|,E) measurement on
ric Yb Ti O is exotic, and quite distinct from the
single crystal Yb Ti O , also at T=0.1 K. Panel d) shows 2 2 7
2 2 7
S(|Q(cid:126)|,E) measured on powder Yb Sn O at T=0.1 K, by expectations of anisotropic spin wave theory, compar-
Dunet al.37. Allfourdatasetshave2had2 a7nemptycanback- ison to the measured spectrum in lightly stuffed CSC
Yb Ti O withx=0.046,inFig.4b),andtosingle
grounddatasetsubtractedfromthem,andhavehadintensi- 2+x 2−x 7+y
tiesscaledsuchthatthescatteringat|Q(cid:126)|=1˚A−1 andE=0.5 crystal Yb2Ti2O7, in Fig.4 c) which is also likely lightly
meV saturates the colour scale. stuffed, shows that is not particularly sensitive to weak
disorder. Theupperbandedgeofthecontinuumslightly
The inelastic spectral weight shown in Fig.4 is known softensinthelightlystuffedCSCsampleandsinglecrys-
to be magnetic in origin from its previously determined tal, and the vestiges of the overdamped ferromagnetic
field dependence, and from its temperature dependence spin waves are not as clear compared with the stoichio-
to be discussed shortly. We see that S(|Q(cid:126)|,E) in sto- metric Yb2Ti2O7 in Fig. 4 a). However, the continuum
ichiometric Yb Ti O at T=0.1 K is largely character- natureofthemagneticscatteringanditslackofagapat
2 2 7
ized by a continuum of scattering below an upper band any wave vector are common to all three samples.
edge of ∼ 1 meV, and it is gapless on a energy scale ThesefeaturesarealsocommontoS(|Q(cid:126)|,E)measured
<0.09 meV at all wave vectors measured. The inelas- onDCSunder∼identicalconditionsonapowdersample
tic scattering has some weak structure to it, resembling of Yb Sn O by Dun and co-workers shown in Fig.4 d).
2 2 7
overdamped ferromagnetic spin waves which disperse as These measurements on Yb Sn O were previously pub-
2 2 7
6
% increase (111) % increase (113) % increase (222) Moment Size canting angle (θ) χ2
Measured 3.2(4) 3.3(5) 3.6(6) - - -
Collinear FM 3.2 4.5 5.6 1.1µ 0o 1.09
B
Splayed Ice FM 3.2 3.1 4.2 0.90(9)µ 14o ± 5o 0.99
B
TABLEI:A Comparison of the excess intensity in the measured Bragg peaks with model calculations for possible ferromagnetic
ground states.– The percent excess elastic intensity for the (111), the (113) and the (222) Bragg peaks are compared with
those calculated for a (100) collinear ferromagnet and a Splayed Ice ferromagnet (Fig.2 b)). The best agreement between the
observed excess intensity and such a model for canted ferromagnets is achieved with the Splayed Ice ferromagnet, and a splay
angle of 14 ± 5◦.The magnetic moment size at the Yb3+ site, based on the increase in Bragg intensity relative to 8 K, is also
given for the proposed ordered states.
FIG. 6: Energy cuts of S(|Q(cid:126)|,E) for the stoichiometric powder sample of Yb Ti O and the CSC Yb Ti O with
2 2 7 2+x 2−x 7+y
x=0.046.– Top panels : These 4 different panels show cuts through S(|Q(cid:126)|,E) of Yb Ti O , taken from Fig. 4 a), for different
2 2 7
ranges of |Q(cid:126)| and at different temperatures. Four different integrations in |Q(cid:126)| going from smaller |Q(cid:126)| in a) to larger |Q(cid:126)| in d)
have been applied, as indicated in the individual panels. No differences in the scattering is observed from T=2.5 K down to
T=0.1 K. Bottom panels : Same data and —Q(cid:126)— integrated cuts as in a) - d) but for Yb Ti O with x=0.046 taken
2+x 2−x 7+y
from Fig. 4 b).
lished37, albeit using a high temperature subtraction, as the precise details of the background subtraction. This
opposed to the empty can subtraction we employ here. low-Qregionofscatteringisthusavoidedinthefollowing
Yb Sn O cannotbegrownasasinglecrystalduetothe quantitative analysis shown in the energy scans of Fig.6.
2 2 7
volatilityoftheSnO startingmaterials,whichalsolikely These energy scans employ different Q-integrations, go-
2
implies some level of defects in its powders. ing from smaller Q to larger Q in panels Fig.6 a) - d)
forYb Ti O andFig.6e)-h)forYb Ti O and
2 2 7 2+x 2−x 7+y
Energy cuts through the S(|Q(cid:126)|,E) data sets for sto- x=0.046. Consistent with the detailed S(|Q(cid:126)|,E) maps,
ichiometric powder Yb2Ti2O7 and lightly stuffed CSC we see that pronounced inelastic shoulders are observed
with approximate composition Yb2+xTi2−xO7+y and atintermediateQ’s,asseeninFigs.6b)andc),andthese
x=0.046 are shown in Figs.6. While differences between arethevestigesoftheferromagneticspinwavesdiscussed
the four data sets of Fig.4 can be seen at Q ≤ 0.4 ˚A−1, earlier. Well defined ferromagnetic spin waves would
this low-Q region corresponds to the edge of the neu- show inelastic peaks which would disperse as E ∼ Q2.
tron detector bank closest to the incident beam, and is As seen on Fig.6 f) - g), the shoulders are considerably
thus the part of the data set that is most sensitive to
7
moreroundedinthelightlystuffedCSCsample,indicat- µ . However, the temperature dependence of the elastic
B
ingthatthevestigesoftheseoverdampedexcitationsare Bragg scattering does not correlate with the T =0.26 K
C
even further overdamped in the presence of weak disor- expected for such powder samples. Rather, this elastic
der. scatteringbeginstodissipateabove∼350mKandshows
TheenergycutsthroughS(|Q(cid:126)|,E)inFig.6,alsoshows continued decrease above 700 mK.
the temperature evolution of this inelastic scattering The zero field magnetic inelastic spectrum of sto-
from T=0.1 K, well below TC=0.26 K, to T=8 K, above ichiometric Yb2Ti2O7 is exotic. It shows a gapless,
TMF and the “hump” in CP near 2 K. This tempera- continuum form, at T=0.1 K, well below TC=0.26 K,
ture dependence is very similar for both the stoichio- with an upper band edge of ∼ 1 meV. No spin gap is
metric Yb2Ti2O7 and the lightly stuffed CSC powder observed at any wave vector to an upper limit of 0.09
sample, so we focus our discussion on the stoichiomet- meV, in contrast to the expectations of anisotropic
ric Yb Ti O energy cuts of S(|Q(cid:126)|,E) shown on the top spin wave theory within the ferromagnetically ordered
2 2 7
panels of Fig.6. It is worth noting that the temperature state predicted from the mean field model using the
evolutionofS(|Q(cid:126)|,E)onthenegativeenergyside,shows spin Hamiltonian derived from high field spin wave
clearevolutionofthescatteringfromT=0.8toT=0.3K, measurements. The continuum inelastic spectrum shows
implying that the stoichiometric Yb Ti O was equili- some weak structure, with vestiges of overdamped ferro-
2 2 7
brateddowntoatleast0.3K.Whilenoteasilyvisiblein magnetic spin waves present at small Q. The inelastic
Fig.6, there is a continued decrease in the inelastic scat- magnetic spectrum in stoichiometric Yb2Ti2O7 shows
tering near -0.1 meV from T=0.3 K to 0.1 K, strongly little or no temperature dependence up to temperatures
suggesting that the system equilibrated at all tempera- greater than 2.5 K, much larger than TC, and on the
tures measured. order ofTMF ∼ 3 K,and thetemperature characterizing
The most striking feature of the temperature depen- the high temperature “hump” in CP near 2 K. The
dence of S(|Q(cid:126)|,E) in Yb Ti O is that there is none for form of the magnetic inelastic scattering, its continuum
2 2 7
temperatureslessthan∼2.5K.Thatis,thegapless,con- nature and temperature dependence, is only slightly
tinuum form of S(|Q(cid:126)|,E) in stoichiometric Yb Ti O is influenced by weak stuffing, as is known to characterize
2 2 7
the non-stoichiometric CSC powder sample and single
maintainedthroughitslargeC anomalyatT =0.26K,
P C
up to 10 times this temperature. Changes in S(|Q(cid:126)|,E) crystal samples that were also measured.
only appear in the temperature range from 2.5 K to 8
K, consistent with a temperature evolution on the scale
of the calculated T ∼ 3 K, or the high temperature
MF
”hump” observed in T near 2 K. Very similar temper- Acknowledgments
C
ature dependence of S(|Q(cid:126)|,E) is observed for the lightly
stuffed CSC sample, as shown in the bottom panels of We wish to thank Jan Kycia for collaborations and
Fig.6. discussion related to heat capacity measurements. We
thankC.WiebeandH.Zhouformakingtheirdataavail-
able to this work. The neutron scattering data were re-
IV. CONCLUSIONS ducedusingMantid38andanalyzedusingDAVEsoftware
package39. Research using ORNL’s Spallation Neutron
New neutron scattering measurements on a stoichio- SourcewassponsoredbytheScientificUserFacilitiesDi-
metric powder sample of Yb Ti O reveal low temper- vision, OfficeofBasicEnergySciences, U.S.Department
2 2 7
ature magnetic Bragg peaks, overlapping with nuclear- of Energy. The NIST Center for Neutron Research is
allowed Bragg peaks. This elastic scattering is inter- supported in part by the National Science Foundation
preted in terms of a long range ordered, splayed spin under Agreement No. DMR-094472. Works at McMas-
ice static structure with a correlation length exceeding ter University was supported by the National Sciences
80˚A and an ordered moment, relative to 8 K, of 0.90(9) and Engineering Research Council of Canada (NSERC).
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