Contrasting chemical pressure effect on the moment direction in the Kondo semiconductor CeT$_2$Al$_{10}$ (T = Ru,Os)

1.3 MB·English

by  D. T. Adroja

Contrasting chemical pressure effect on the moment direction in the Kondo
semiconductor CeT Al (T = Ru,Os)
2 10
D. T. Adroja,1,2,∗ A. D . Hillier,1 C. Ritter,3 A. Bhattacharyya,1,2 D. D.
Khalyavin,1 A. M. Strydom,2,4 P. Peratheepan,2,5 B. F˚ak,3 M. M. Koza,3 J.
Kawabata,6 Y. Yamada,6 Y. Okada,6 Y. Muro,7 T. Takabatake,6 and J. W. Taylor1
1ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, OX11 0QX, United Kingdom
2Highly Correlated Matter Research Group, Physics Department,
University of Johannesburg, Auckland Park 2006, South Africa
3Institute Laue- Langevin, BP 156, 6 Rue Jules Horowitz 38042, Grenoble Cedex, France
5
4Max Planck Institute for Chemical Physics of Solids, No¨thnitzerstr. 40, 01187 Dresden, Germany
1
0 5Department of Physics, Eastern University, Vantharumoolai, Chenkalady 30350, Sri Lanka
2 6Department of Quantum Matter, ADSM and IAMR,
Hiroshima University, Higashi-Hiroshima 739-8530, Japan
n 7Faculty of Engineering, Toyama Prefectural University, Toyama 939-8530, Japan
a
(Dated: January 30, 2015)
J

9 TheopeningofaspingapintheorthorhombiccompoundsCeT2Al10 (T=RuandOs)isfollowed
2 byantiferromagneticorderingatTN =27Kand28.5K,respectively,withasmallorderedmoment
(0.29−0.34µB) along the c−axis, which is not an easy axis of the crystal field (CEF). In order
] to investigate how the moment direction and the spin gap energy change with 10% La doping in
l
e Ce1−xLaxT2Al10 (T = Ru and Os) and also to understand the microscopic nature of the magnetic
- ground state, we here report on magnetic, transport, and thermal properties, neutron diffraction
r
t (ND) and inelastic neutron scattering (INS) investigations on these compounds. Our INS study
s reveals the persistence of spin gaps of 7 meV and 10 meV in the 10% La-doped T = Ru and Os
.
t compounds, respectively. More interestingly our ND study shows a very small ordered moment
a
m of 0.18 µB along the b−axis (moment direction changed compared with the undoped compound),
in Ce0.9La0.1Ru2Al10, however a moment of 0.23 µB still along the c−axis in Ce0.9La0.1Os2Al10.
- ThiscontrastingbehaviorcanbeexplainedbyadifferentdegreeofhybridizationinCeRu2Al10 and
d
n CeOs2Al10, being stronger in the latter than in the former. Muon spin rotation (µSR) studies on
o Ce1−xLaxRu2Al10 (x = 0, 0.3, 0.5 and 0.7), reveal the presence of coherent frequency oscillations
indicatingalong−range magnetically orderedgroundstateforx=0to0.5, butanalmost temper-
c
[ ature independent Kubo−Toyabe response between 45 mK and 4 K for x = 0.7. We will compare
the results of the present investigations with those reported on the electron and hole−doping in

1 CeT2Al10.
v
7 PACSnumbers: 71.27.+a,75.30.Mb,75.20.Hr,25.40.Fq
9
4
7 I. INTRODUCTION (27 K) in CeRu Al [8, 15]. The broad maximum in
2 10
0 the susceptibility and its strong anisotropic behavior in
.
1 the paramagnetic state reveal the presence of strong hy-
Inrecentyears,the magneticandtransportproperties
0 bridization between 4f and conduction electrons as well
of Ce-based ternary compounds of type CeT Al (T =
5 2 10 as strong single ion anisotropy arising from the crystal
1 Fe, Ru and Os), which crystalline in the orthorhombic
field potential [16, 17].
: structure(space groupNo63Cmcm) [1], havegenerated
v
stronginterestinboththeoreticalandexperimentalcon- Further difference between the two systems appears
i
X densed matter physics [2–11]. This interest arose due to in the resistivity of the ordered state; the resistivity of
r the various ground states observed in this family of Ce- CeOs2Al10 displays a thermal activation-type temper-
a compounds. Anunusuallysharpphasetransitionnear27 ature dependence below 15 K while the resistivity of
K in the magnetic susceptibility of CeRu2Al10 has been CeRu2Al10 exhibits a metallic behavior below the phase
attributed to a spin-dimer formation [12, 13]. The re- transition down to 2 K. In spite of the comparable tran-
sistivity of CeRu Al exhibits a sharp drop near 27 K sition temperatures a fundamental contrast in the elec-
2 10
resemblinganinsulator-metaltransition[2]. A verysim- tronic disposition of the two compounds has been ex-
ilar phase transition, near 29 K, has been observed in posed in recent high-pressure studies [8]. Under a hy-
CeOs Al [8,14],butinthiscompoundthesusceptibil- drostatic pressure of 1.75 GPa the electrical resistivity
2 10
ity (along the a−axis) exhibits a broad maximum near of CeRu2Al10 changes in a way as closely to match the
45 K in contrast to a sharp drop at the phase transition overallbehaviorofthetemperaturedependentresistivity
of CeOs Al in zero applied pressure. Applying pres-
2 10
sureis awellrecognizedtuning methodofthe 4f−band
with respect to the Fermi energy (E ) in narrow-band
F
∗Electronicaddress: [email protected] systems. The results obtained for the two iso-electronic
2
compounds are therefore an indication that the center 2000 (a) Ce0.9La0.1Ru2Al10
of gravity of the 4f−band is lying on opposite sides of
the E : the 4f− spectral weight in CeRu Al is most 1000
F 2 10
likely close to but below the EF whereas in CeOs2Al10, units) 0
mthoere4fextbeannddedisnamtuorset olifktehlye 5adbobvaendthoef OEsFcodmuepatroedthtoe y (arb. 2000 300 K
the 4d band of Ru. The 3d transition metal compound nsit (b) Ce0.9La0.1Os2Al10
e
CeFe2Al10 exhibits Kondo insulating behavior with a Int 1000
transport−derivedgap of 15 K [3], while an NMR study
revealsamuchlargervalueofthegap,namely110K[18]. 0
Neutron diffraction studies of CeT Al (T=Ru and
2 10
20 40 60 80 100 120
Os) reveal a very small ordered moments, 0.34 µB and 2 (o)
0.29 µ , respectively, along the c−axis, which is not
B
the direction expected from the single ion crystal field FIG. 1: (Color online) (a) and (b) show Rietveld refinement
(CEF) anisotropy [5, 6, 19]. As the single ion crys- oftheneutronpowderdiffractionpatternofCe0.9La0.1T2Al10
tal field would prefer the moment along the a−axis in (T = Ru and Os) at 300 K collected using the D2B diffrac-
tometer with wavelength λ =1.594 ˚A. The circle symbols
both compounds, this indicates that the moment direc-
(black) and solid line (red) represent the experimental and
tion in these compounds is governed by the anisotropic
calculated intensities, respectively, and the line below (blue)
magnetic exchange and not by the CEF anisotropy. The
is the difference between them. Tick marks indicate the po-
inelastic neutron scattering (INS) study at 4.5 K on the sitions of Bragg peaks in theCmcm space group.
polycrystallinesamples of CeT Al (T=Ru, Os and Fe)
2 10
reveals a clear sign of a spin-gapformation of 8 meV, 11
meV and 12 meV, respectively [20, 21]. These gaps are ionanisotropy,andlargervaluesoftheorderedstatemo-
nearly temperature independent up to 24 K, but disap- ment, ≈ 1 µ [26].
B
pear suddenly at 27 K, 39 K and 75 K respectively [22]. Koyabasiet. al. [27] and Nishioka et. al. [8] suggested
Above these temperatures, the INS response becomes that the phase transition at T is not due to simple
N
very broad, of quasi-elastic-type. Very recently inelas- RKKY interactions as it is not possible to describe the
tic neutron scattering investigation on single crystals of behavior of Ce1−xGdxRu2Al10 and Ce(Fe1−xRux)2Al10.
CeRu2Al10, CeOs2Al10 and CeFe2Al10 have been per- Kondo et. al. [28] found that TN is suppressed by the
formed [20, 21, 23]. Well defined gapped spin waves are application of a magnetic field as well as by La substi-
observed in CeRu2Al10 and CeOs2Al10 that can well be tution on the Ce site in CeRu2Al10. Considering these
explained by anisotropic exchange interactions. Even in interesting observations [29, 30] found with electron and
the paramagnetic state of CeFe2Al10 (no magnetic or- hole doped CeRu2Al10 and CeOs2Al10, it is timely to
dering observed down to 50 mK) the neutron study re- investigate the effect of chemical pressure (La or Y dop-
vealsadispersivegappedmagneticexcitationshavingthe ing) on the Ce site in CeT Al (T = Ru and Os) using
2 10
same propagation vector k = (1, 0, 0) as observed in microscopic techniques such as neutron diffraction, in-
CeRu2Al10, suggesting that these magnetic excitations elastic neutron scattering and µSR measurements. We
in the Kondo insulating state have some connection to therefore present in this paper our results of such mea-
the spinwaveobservedinthe magneticallyorderedstate surements on La-substituted Ce1−xLaxT2Al10 (T = Ru
of CeT2Al10 (T = Ru and Os) [20, 21]. andOs)toshedlightonthenatureofthephasetransition
The effects of electron (Ir/Rh) and hole (Re) doping and the ground state of the Ce ion in these compounds.
on the transition metal site in CeT Al (T = Ru and Our study is motivated by the highly unusual magnetic
2 10
Os) have been investigated, through magnetization, re- ordering in the Ru and Os compounds of the CeT Al
2 10
sistivity, muon spin rotation (µSR), and neutron scat- series, with questions about the enigmatic behavior first
tering (both elastic and inelastic) [10, 11, 24]. These posed by Nishioka et. al. [8]. Moreover, in the special
studiesshowthegeneraltrendthatthehybridizationbe- class of Kondo insulator materials, the Ru and Os com-
tween 4f−electrons and conduction electrons increases pounds are to date the only cases where such a strongly
withhole-doping,whiletheCe-4f electronsbecomemore hybridized and unstable f−shell condenses into a long-
localized with electron-doping. On hole-doping the spin range magnetic ordered ground state.
gap and the antiferromagnetic order with an anoma- The effect of La and Y substitution on the parent
lous direction of the magnetic moment (i.e. moment ei- compound CeRu Al has been investigated before by
2 10
ther along c−axis or b−axis) not governed by the single threegroupsbystudyingmagneticandtransportproper-
ion crystal field anisotropy (this prefers moment along ties[27,29,30]. La(Y)hasabigger(smaller)ionicradius
a−axis) survive with small ordered state moments of compared to Ce and hence La substitution expands the
0.18−0.23µ [6, 24, 25]. In contrast to this, electron lattice corresponding to negative chemical pressure and
B
doping destabilizes the spin gap formation and the an- Ysubstitutioncontractsthelatticecorrespondingtothat
tiferromagnetic ordering becomes normal with moment to positivechemicalpressure. The results areinteresting
directions along the a−axis e.g. governed by the single but unexpected [27, 29]. With increasing La concentra-
3
tion x in Ce1−xLaxRu2Al10, the transition temperature
is progressively shifting to lower temperature and van-
ishes near the critical composition x ≈ 0.7 [30, 31]. ol) 5
Surprisingly Y−substitution leads as cwell to a decrease u/m 560 kOe TN (a) TN (b)
fboofertTwpNeoesnritaixtvhe=ecrh0te.hm4ainacnatdlop0ar.e5nss[i3un1rc]er.,eaaTsnhedisadsbiseoahnpaepveiwoaorrusclasdundnexdopetnebclyet -3 (10em 34 130500.0T (K)N 0.4Ce1-xL0a.8xRu2Al10 10 CkeO0.9Lea0.1Os2Al10 34
understood by a simple magnetic phase transition, sug- x
gesting that the change in the valence of Ce ion plays K)
an important role in the mysterious phase transition 0 3 (c) (d)
0 2
[31, 32]. The high-field magnetization measurements on (3
Ce1−xLaxRu2Al10 (x=0and0.25)performedbyKondo T)/ 2
et. al. [28]revealedthatthelong-rangeorderdisappears (
Ce0.9La0.1Ru2Al10 Ce0.9La0.1Os2Al10
at a critical fields H = 50 and 37 T for x = 0 and 0.25, 1
c 1
respectively. 1 10 T(K) 1001 10 T(K) 100
2 )
mol K0.6 CLaeR0.9uL2aA0l.11R0u2Al10 (e) CLaeO0.9sL2aA0l.11O0s2Al10 (f) 00..68
From the single crystal susceptibility measurements J/0.4
Tanida et. al. have proposed that 10% La doping in T ( 0.4
/0P.2
CeRu Al changes the direction of the ordered state C 0.2
2 10
moment from the c−axis found in undoped system to 0.0 0.0
0 10 20 30 0 10 20 30
the b−axis, the hard axis of magnetization. Application
T(K) T(K)
of a pressure of 0.3 GPa changes the moment back to
the c−axis [33]. However,magnetic susceptibility data
FIG. 2: (Color online) (a-b) Temperature dependence of dc
can only give indirect information on the ordered state magnetic susceptibility χ(T) Ce1−xLaxT2Al10 with x = 0.1
momentdirectionandcanbeerroneousifanisotropicex- (T = Ru and Os). Inset shows the variation of TN with La
change interactions are dominating over the single ion composition for Ce1−xLaxRu2Al10 [29]. (c-d) Semilogarith-
crystal field anisotropy. They cannot give a direct mea- mic plot of electrical resistivity vs temperature. (e-f) Tem-
sureofthevalueoftheorderedstatemoment. Theunan- peraturevariationofspecificheatCP dividedbytemperature
swered question remains what is happening to the spin for Ce1−xLaxT2Al10 (T = Ru and Os) (open symbol) with
gap formation and its energy scale as the direction of non magnetic counterpart LaRu2Al10 and LaOs2Al10 (solid
line).
the ordered state moment of Ce La Ru Al changes
0.9 0.1 2 10
to the b−axis from the c−axis as in CeRu Al . In or-
2 10
der to answer these questions we have carried out neu-
II. EXPERIMENTAL DETAILS
trondiffractionandinelasticneutronscatteringmeasure-
ments on Ce La Ru Al . The neutron diffraction
0.9 0.1 2 10
study provides direct information on the direction as on ThepolycrystallinesamplesofCe1−xLaxRu2Al10 (x=
the magnitude of the orderedmoment. Inelastic neutron 0, 0.1, 0.3, 0.5 and 0.7), Ce0.9La0.1Os2Al10, LaRu2Al10
scattering gives direct information about the magnitude andLaOs2Al10 werepreparedbyargonarcmeltingofthe
of the spin-gap energy, its temperature and wave-vector stoichiometric constituents with the starting elements,
(Q) dependency. Ce/La 99.9% (purity), Ru/Os 99.9% and Al 99.999%.
◦
The samples were annealed at 800 C for seven days in
anevacuatedquartzampoule. The sampleswerecharac-
In order to gain further information on the micro- terizedusingpowderX-raydiffractionorneutrondiffrac-
scopicchangeinthemagnetismwehaveperformedmuon tion (on D2B diffractometer at ILL, Grenoble) at 300 K
spin rotation measurements on Ce1−xLaxRu2Al10 (x = and were found to be dominantly single-phase (see Fig.
0, 0.3,0.5 and0.7) alloys. µSR is anexceptionally sensi-
tive microscopic probe of cooperative magnetic ordering
phenomena and is thus ideally suited to our compounds
where previous studied had alluded very small magnetic TABLE I: Lattice parameters of Ce1−xLaxT2Al10 (T = Ru,
Os) for x = 0 , 0.1 refined from the neutron diffraction data
moment values. Our neutron diffraction study reveals a
collected at 300 K in theorthorhombic Cmcm space group.
long−range magnetically ordered ground state in both
Ce0.9La0.1Ru2Al10 and Ce0.9La0.1Os2Al10 compounds. Compounds a (˚A) b (˚A) c (˚A) V (˚A)
More interestingly the ordered Ce moment of 0.18 µ
is along the b−axis in the former, but along the c−axBis CeRu2Al10 9.1246 10.2806 9.1878 861.9 [34]
with a value of 0.23 µ for the latter. Our INS study Ce0.9La0.1Ru2Al10 9.1224 10.2749 9.1865 861.066
B
revealsthe presence ofa well defined spin gapsof 7 meV CeOs2Al10 9.138 10.2662 9.1694 861.686 [3]
at 2 K in Ce0.9La0.1Ru2Al10 and 10 meV at 4.5 K with Ce0.9La0.1Os2Al10 9.1412 10.2668 9.1898 862.474
considerable reduced intensity in Ce La Os Al .
0.9 0.1 2 10
4
Ce La Os Al samples were performed using the
0.9 0.1 2 10
high neutron flux D20 diffractometer at ILL, Greno-
0.4 ble, France using constant wavelengths of 1.3 ˚A or 2.41
(a)
˚A. The powder samples were mounted in a 10 mm di-
2K)0.3
ol ameter vanadium can, which was cooled down to 2 K
m
J/ using a standard He-4 cryostat. The program FULL-
T (0.2
C/4f PROF [35] was used for Rietveld refinements and group
theoretical calculations were performed with the aid of
0.1
the Sarah/ISOTROPYsoftware [36, 37].
0.0 The inelastic neutron scattering measurements
Ce0.9La0.1Ru2Al10
4(b) Ce0.9La0.1Os2Al10 between 2 K and 35 K on Ce0.9La0.1Ru2Al10,
Ce La Os Al , CeRu Al , LaRu Al and
K) 0.9 0.1 2 10 2 10 2 10
mol 3 LaOs2Al10 (15 g sample) were carried out using
J/ the MARI time-of-flight (TOF) chopper spectrome-
(mag 2 ter at ISIS Facility, while on Ce La Ru Al and
S 0.9 0.1 2 10
LaRu Al additional data were collected on the IN4
1 2 10
TOF chopper spectrometer at ILL, Grenoble, France.
0 On MARI the samples were wrapped in a thin Al-foil
0 5 10 15 20 25 30
T(K) and mounted inside a thin-walled cylindrical Al-can,
which was cooled down to 4.5 K inside a top-loading
FIG.3: (Coloronline)(a)Temperaturevariationofmagnetic
closed-cycle-refrigerator (TCCR) with He-exchange gas
specific heat C4f for Ce0.9La0.1T2Al10 (T = Ru, Os). (b) around the samples. The measurements were performed
Calculated magnetic entropyas a function of temperature.
with an incident neutron energy E of 25 (20) meV,
i
with an elastic resolution (at zero energy transfer) of
1). Magneticsusceptibility measurementsweremade us- 1.1 meV (0.8 meV) (FWHM). On IN4 the samples were
ing a Magnetic Property Measurement System (MPMS) wrapped in a thin Al-foil, which was cooled down to 2
superconducting quantum interference device (SQUID) K inside a standard He-4 cryostatwith He-exchange gas
magnetometer (Quantum Design). Electrical resistivity around the samples. The measurements were performed
by the four probe method and heat capacity by the re- with an incident neutron energy Ei of 16.9 meV, with
laxation method were performed in a Quantum Design anelasticresolution(at zeroenergytransfer)of1.1 meV
Physical Properties Measurement System (PPMS). (FWHM).
The µSR experiments were carried out using the
MUSRspectrometerinlongitudinalgeometryattheISIS
muon source, UK. At the ISIS facility, a pulse of muons III. RESULTS AND DISCUSSIONS
is produced every 20 ms and has a FWHM of ≈ 70 ns.
These muons are implanted into the sample and decay A. Bulk properties
with a half-life of 2.2 µs into a positron which is emit-
ted preferentially in the direction of the muon spin axis.
Toexplainthe overallbulk propertiesofthe title com-
Thesepositronsaredetectedandtimestampedinthede-
pounds, we present here their magnetic susceptibility,
tectors which are positioned before, F, and after, B, the
electric resistivity, and specific heat data with emphasis
sample. The positron counts, NF,B(t), have the func- on the magnetic phase transitions. Figs. 2 (a−f) show
tional form
the temperature dependent magnetic susceptibility, elec-
tricalresistivity,and heatcapacity of Ce La Ru Al
0.9 0.1 2 10
N (t)=N (0)e−t/τµ(1±G (t)) (1) and Ce0.9La0.1Os2Al10. The magnetic susceptibility
F,B F,B z χ(T)ofCe La Ru Al exhibitsaclearpeaknear23.0
0.9 0.1 2 10
K, which is due to an antiferromagnetic ordering of Ce
where G (t) is the longitudinal relaxation function.
z
moments. On the other hand χ(T) of Ce La Os Al
G (t) is determined using 0.9 0.1 2 10
z
exhibits a broadmaxima near40 K anda kink near 21.7
K.Theformerisduetoanopeningofthespingap,while
G (t)=(N (t)−αN (t))/(N (t)+αN (t)) (2) thelatteris duetothe onsetofthe antiferromagneticor-
z F B F B
dering. Averysimilarbehaviorofχ(T)[10]withabroad
whereαisacalibrationconstantwhichwasdetermined maximum at 31 K (due to spin gap formation) above
at 35 K by applying a small transverse field (≈ 20 Oe) T = 23 K is observed for CeRu Re Al . The in-
N 1.96 0.06 10
andadjustingits valueuntilthe resultingdampedcosine verse magnetic susceptibilities of Ce La Ru Al and
0.9 0.1 2 10
signal was oscillating around zero. The powdered sam- Ce La Os Al exhibitCurie-Weissbehaviorbetween
0.9 0.1 2 10
ples were mounted onto a 99.995+%pure silver plate. 50 K and 300 K. A linear least-squares fit to the data
The low temperature neutron diffraction measure- yields an effective magnetic moment µ = 2.12 µ
eff B
ments at 1.5 K and 35 K on Ce La Ru Al and and a paramagnetic Curie temperature θ = −95 K for
0.9 0.1 2 10 p
5
Then ρ(T) of Ce La Ru Al exhibits a peak near
0.9 0.1 2 10
T and remains metallic at low temperature, while for
N
Ce0.9La 0.1Ru2Al10/CeRu1.94Re0.06Al10 CeRu2Al10/CeOs2Al10 Ce0.9La 0.1Os2Al10/CeOs1.94Re0.06Al10 Ce La Os Al the ρ(T) showsa slope change at T ,
0.9 0.1 2 10 N
but still increases with further decrease in the tempera-
~0.2µµµµB ~0.3µµµµB ~0.2µµµµB ture down to 2 K. This contrasting behavior of the low
temperature resistivity is similar to that observed in the
c
undoped compounds [14, 15]. It is interesting to note
a that the resistivity of slightly electron-(8% Ir) and hole-
b
(2% Re) doped CeOs Al exhibits metallic behavior in
2 10
all directions below T [24].
N
Figs. 2 (e) and (f) show the heat capacity di-
vided by temperature C /T vs T of Ce La Ru Al
P 0.9 0.1 2 10
and Ce La Os Al along with their respective non-
0.9 0.1 2 10
magnetic phonon reference compounds, LaRu Al and
2 10
LaOs Al . The heat capacity of Ce La Ru Al ex-
2 10 0.9 0.1 2 10
hibits a λ−type anomaly near T , while the anomaly
N
is considerably suppressed in Ce La Os Al . A
0.9 0.1 2 10
rapid suppression of the heat capacity anomaly near
T was also observed both in CeRu Re Al and
N 1.94 0.06 10
CeOs Re Al [11,24]. Byfittingthehightempera-
1.96 0.04 10
tureheatcapacity(aboveT )toC /T=γ+βT2,wehave
N P
estimated the Sommerfeld coefficient γ = 0.125 J/mol-
K2 and β= 3.5×10−4 J/mol-K4 for Ce La Ru Al
0.9 0.1 2 10
andγ =0.121J/mol-K2 andβ =5.6×10−4 J/mol-K4 for
Ce La Os Al . Theobservedvaluesofγ forboththe
FIG. 4: (Color online) Rietveld refinements of the mag- 0.9 0.1 2 10
compounds are smaller than those observedfor undoped
netic intensity of Ce1−xLaxT2Al10 (T = Ru, Os) along with compounds, γ = 0.2 J/mol-K2 for CeRu Al and γ =
Ce(Ru/Os1−xRex)2Al10 (x = 0.03) obtained as a difference 0.541J/mol-K2 forCeOs Al ,indicating2hea1v0yfermion
between thediffraction patternscollected at 1.5K and35K. 2 10
The circle symbols (red) and solid line represent the exper- behavior in the undoped compounds. From the value of
imental and calculated intensities, respectively, and the line β = (12π4/5) (nNAkB/Θ3D), where NA and kB have the
below(blue)isthedifferencebetweenthem. Tickmarksindi- usual meaning, and n = 13 is the number of atoms per
catethepositions of Bragg peaksforthemagneticscattering f.u., weestimatedthe DebyetemperaturetoΘ =416K
D
with the k= (1, 0, 0) propagation vector. The upper panel and355 K for Ce La Ru Al and Ce La Os Al
0.9 0.1 2 10 0.9 0.1 2 10
showsthemagneticstructuresoftheLa-doped(foundinthis respectively. Fig. 3 (a) shows the magnetic heat ca-
paper),Ce(Ru/Os1−xRex)2Al10 (x=0.03) andCeT2Al10 (T pacityvariationwithtemperature forCe La Ru Al
0.9 0.1 2 10
=RuandOs)samples. Forclarity,onlyCeandRu/Reatoms
and Ce La Os Al . The weak anomaly for the for-
are shown (top). 0.9 0.1 2 10
mer at temperature below 5 K may be attributed to im-
puritycontribution. ThevalueofmagneticentropyS
mag
[Fig. 3(b)]at30Kis3.5J/mol-KforCe La Ru Al
Ce La Ru Al and µ = 2.58 µ and θ = −175 0.9 0.1 2 10
0.9 0.1 2 10 eff B p and 3.55 J/mol-K for Ce La Os Al , which is much
K for Ce La Os Al . The value of the magnetic 0.9 0.1 2 10
0.9 0.1 2 10 smaller than Rln(2) = 5.76 J/mol-K. The reduced mag-
moment suggests that the Ce atoms are in their nor-
neticentropycanbeexplainedonthe basisoftheKondo
mal Ce3+ valence state in both the compounds. The
effect. We also estimated the gap in the spin wave by
negative value of θ is in agreement with AFM order-
p fitting C data below T , and we find gaps 50 K
ing,anegativesignfortheexchangeinteractions,and/or mag(T) N
for Ce La Ru Al and 60 K for Ce La Os Al ,
the presence of the Kondo effect. The larger negative 0.9 0.1 2 10 0.9 0.1 2 10
whose values are approximately half of those reported
value of θ of Ce La Os Al compared to that of
p 0.9 0.1 2 10 for the undoped compounds [8].
Ce La Ru Al suggests a stronger hybridization in
0.9 0.1 2 10
theformer. TheinsetintheFig. 2(a)showstheLacom-
position dependence of TN of Ce1−xLaxRu2Al10, which
reveals that T decreases almost linearly and becomes IV. NEUTRON DIFFRACTION
N
zero near x≥0.7 [12, 29]. In this critical region of com-
positionstheheatcapacityexhibits ariseatlowtemper- Figs. 1 (a) and (b) show the neutron diffraction pat-
ature suggesting the presence ofnon-Fermi-liquid(NFL) terns for Ce La Ru Al and Ce La Os Al , col-
0.9 0.1 2 10 0.9 0.1 2 10
behavior close to a quantum critical point (QCP) [29]. lectedat300KontheD2Binstrumentinthehighresolu-
Figs. 2(c) and (d) show the electrical resistivity ρ(T) tionmodewhichbothareconsistentwiththeCmcmsym-
ofCe La Ru Al andCe La Os Al samples,re- metryandcanbe satisfactorilyfitted withthe structural
0.9 0.1 2 10 0.9 0.1 2 10
spectively. At high temperature ρ(T) of both sam- modelproposedearlier[1]. Thestructuralparametersfor
ples increases with decreasing temperature up to T . both samples are listed in Table I. A comparison of the
N
6
thefactthatthemagneticneutrondiffractionintensityis
proportional to the square of the ordered moment com-
30
20 4.5 K CLaeRRuu22AAll1100 (a) 4.5 K CLaeOOss22AAll1100 (b) potohneernhtapnedrpinenCdeiculLaratoOtsheAslcatsteevreinraglvmeacgtonre.ticOBnrathgge
1) 0.9 0.1 2 10
-u. 10 peaks were observed including the (0, 1, 0) one and the
1 f. relativeintensitiesofthesepeaksareverysimilartothose
-eV 30 Ce0.9La0.1Ru2Al10 (c) (d) observedinCeRu2Al10, indicatingthatthe momentsare
-1sr m 20 2 K LaRu2Al10 4.5 K CLaeO0.9sL2aA0l.11O0s2Al10 pmreonbtabdliyreactloionngs,thaellct−heaxoibs.seIrnvesdpimteaogfntehtiecdBiffraegregnptemakos-
mb 10 in Ce0.9La0.1Ru2Al10 and Ce0.9La0.1Os2Al10 can be in-
)( 30 dexed based on the same propagation vector k = (1, 0,
(SQ, 20 123005 KKK Ce0.9La0.1Ru2Al10 (e) 3L0a K(4.5 K) (f) 0), which is identical to that found in pure CeRu2Al10
La(2 K) Ce0.9La0.1Os2Al10 [4]. It is to be notedthat the propagationvectork = (0,
10 1, 0) proposed for CeOs Al is equivalent to k = (1, 0,
2 10
0) as they are both related by the allowed (h+k even)
-5 0 5 10 -10 0 10 reciprocal translation G = (-1, 1, 0).
Energy transfer (meV)
In the qualitative refinement of the magnetic struc-
FIG. 5: (Color online) Q-integrated (0≤Q≤2.5 ˚A) intensity tures, we employed a method whereby combinations of
versus energy transfer of (a-b) CeT2Al10 (T = Ru and Os) axialvectorslocalizedonthe4c(Ce)site(asCeisonlythe
measuredontheMARIspectrometer(c-f)Ce0.9La0.1Ru2Al10 magnetic atom) and transforming as basis functions of
and Ce0.9La0.1Os2Al10 measured on the IN4 spectrometer the irreducible representations of the wave vector group
along with the nonmagnetic phonon reference compounds are systematically tested. The symmetry analysis yields
LaT2Al10 (T=RuandOs)(redhalffilledcircles), measured thatthereduciblemagneticrepresentationisdecomposed
with respective incident energy of Ei = 20 meV. For IN4 we intosixone-dimensionalrepresentations,labeledY+ (i=
havemade cutsin scattering angle between 13◦ to 43◦. 2,3,4)andY− (i=1,2,3). TheY+ representationsiresult
i i
in a ferromagnetic (FM) alignment of the Ce moments
within the primitive unit cell, along different crystallo-
−
latticeparametersofthedopedcompoundswiththepar- graphicdirections. Onthe otherhand, Y transformCe
i
entonesshowsthat10%LadopinginCeRu Al results moments which are AFM coupled within the primitive
2 10
inavolumecontractionof0.001,while10%Ladopingin unit cell. We refined the difference data (1.5 K−35 K)
CeOs Al increases the volume by 0.001. This can be usingthethreeAFMstructures(withthemomentsalong
2 10
compared to the volume contraction of 0.10% observed a−, b− and c−axes) given by Y− representations. The
i
in 3% Re-doped (or hole doped) CeRu Al , where the bestfittothe datawasobtainedwithaCeorderedstate
2 10
ordered state moment of 0.20 µ is along the b−axis. It momentof0.18(2)µ AFM coupledalongthe b−axisfor
B B
is generally agreed that hole-doping in both CeRu Al Ce La Ru Al [see Fig. 4, where the magnetic unit
2 10 0.9 0.1 2 10
and CeOs Al increases the hybridization [10, 25]. cells are shown], while an orderedmoment of 0.23(1)µ
2 10 B
along the c−axis was obtained for Ce La Os Al .
To investigate the magnetic structure, we carried out 0.9 0.1 2 10
neutrondiffractionmeasurementsontheD20instrument Itisinterestingto comparethese valuesofthe ordered
at 1.5 K and 35 K (12 hours each temperature) on statemomentswiththosefoundintheundopedsystems,
Ce La Ru Al and Ce La Os Al . At 1.5 K we 0.34(2)µ for CeRu Al and0.29(2)µ for CeOs Al
0.9 0.1 2 10 0.9 0.1 2 10 B 2 10 B 2 10
observed very weak magnetic Bragg peaks at scattering both along the c−axis [10, 11]. This comparison shows
angles away from the nuclear Bragg peaks, which con- areductionoftheorderedmomentin10%Ladopedsys-
firmed the long−rangeantiferromagnetic ordering of the tems, which might be due to a change in the Ce valence
Ce moment at 1.5 K in both compounds. To see the with La-doping as proposed in Ref. [32]. The different
magnetic Bragg peaks clearly, we plotted the difference directions of the orderedstate moment in 10% La doped
between the 1.5 K and 35 K data for both compounds, CeRu Al and CeOs Al is a surprising observation
2 10 2 10
whichareshowninFig. 4,alongwiththeir3%Redoped and can be only explained by assuming a different de-
counterparts(see Refs [10,25] for details of the neutron greeofhybridization(weakintheformermaterial). This
diffraction experiment of these materials). The impor- meansthat10%La-dopedCeOs Al seesanisotropicex-
2 10
tant observation is the qualitatively similar diffraction changeinteractionswhicharestillsimilarto those inthe
patterns between the La and Re doped compositions. undoped compound preserving hence the moment direc-
The absence of the magnetic (0, 1, 0) peak near 10.3 tion. It should be possible to change the moment direc-
˚AinbothCe La Ru Al andCeRu Re Al in- tion as well in La−doped CeOs Al to the b−axis by
0.9 0.1 2 10 1.94 0.06 10 2 10
dicates the ordered moments to be along the b−axis, in increasingthe Lacontentupto 20or30%inCeOs Al .
2 10
contrast with the parent CeRu Al compound as well However, the absolute value of the moment would cer-
2 10
aswiththeCe(Ru Fe ) Al series,wherethemoments tainly reduce further with increased doping making its
1x x 2 10
were found to be along the c−axis [10]. The conclusion experimental detection difficult. The question remains
about the b−axis moment direction comes directly from why−despite having a smaller hybridization the ordered
7
moment in Ce La Ru Al is smaller in comparison this could be the zero frequency mode observed in sev-
0.9 0.1 2 10
to that found in Ce La Os Al . A possible explana- eralmagneticallyorderedheavyfermionsystems[38,39].
0.9 0.1 2 10
tion could be that the Kondo effect along the b−axis is To understand this, spin wave measurements on single
stronger than along the c−axis, which might screen the crystals of Ce La Ru Al are highly desirable. On
0.9 0.1 2 10
moment value. the other hand within the resolution of the MARI ex-
periment we could not see any clear sign of a low energy
excitation at 4.5 K in Ce La Os Al ; this excitation
0.9 0.1 2 10
was also absent in CeOs Al from the high resolution
V. INELASTIC NEUTRON SCATTERING 2 10
STUDY INS study [3].
Now we discuss the temperature dependence of the
spingapexcitation. ForCe La Ru Al withincreas-
With the dramatic and contrasting changes observed 0.9 0.1 2 10
ing temperature to 10 K no dramatic changes were ob-
in the moment direction and its absolute value in 10%
served in the spectra, but at 20 K the spin gap en-
La-doped CeRu Al and CeOs Al it would be inter-
2 10 2 10 ergy decreases to 5.5 meV and its width increases to
esting to investigate directly the spin gap formation in
1.26 meV. Further increase in the temperature to 25 K
thesecompoundsusinginelasticneutronscattering. Fur-
thermore, Kawabata et. al. [24] reported that the sup- (same response at 30 K) the inelastic response contin-
ues to broaden. The data show two components, a low
pression of T is well correlated with the gap energy ∆
N energy/quasi-elastic component with narrow linewidth
as a function of electron-(Ir) and hole-(Re) doping and
and a second, distinctly broader component. The Q-
they conclude that the presence of the hybridizationgap
dependent integrated intensity of Ce La Ru Al be-
isindispensablefortheAFMorderatunusuallyhighT 0.9 0.1 2 10
N tween 5 and 8 meV at 2 K nearly follows the Ce3+ mag-
in CeOs Al . Thus the information on the spin gap en-
2 10 neticformfactorsquared(F2(Q),figurenotshown),very
ergy scale in Ce La Ru Al and Ce La Os Al
0.9 0.1 2 10 0.9 0.1 2 10 similar to that observed in pure CeRu Al [6]. The ob-
is very important. Therefore, we briefly report the INS 2 10
served single ion type response of Ce La Ru Al in
spectra, which give direct information of the spin gap 0.9 0.1 2 10
the magnetic orderedstate could be due to the fact that
energy, below and above T of Ce La Ru Al and
N 0.9 0.1 2 10 theobservedspinwavescatteringintensityinCeRu Al
Ce La Os Al andalsoofCeRu Al andCeOs Al 2 10
0.9 0.1 2 10 2 10 2 10 singlecrystalisstrongernearthezoneboundaryandcon-
for comparison in this section. A detailed report on the
sidering the presence of powder averaging effect could
inelastic neutron scattering investigations on CeT Al
2 10 give single-ion type behavior. It is to be noted that the
(T = Fe, Ru and Os) compounds can be found in Ref.
single-ion type response is also observed in the inelastic
[3].
response of the spin gap system CeRu Sb (no mag-
Fig. 5 displays the inelastic neutron scattering spec- 4 12
netic ordering down to 2 K), which does not exhibit any
tra of 10% La-doped compounds with that of undoped
long-range magnetic ordering down to 50 mK [40]. On
compounds at two temperatures at low−Q measured on
the other hand, the deviation from a single-ion response
the MARI and IN4 spectrometers. There is a clearmag-
is observed in the spin gap system CeFe Sb , where it
netic excitation centered around 7 meV and 10 meV in 4 12
was proposed that the intersite interactions between Ce
Ce La Ru Al and Ce La Os Al , respectively
0.9 0.1 2 10 0.9 0.1 2 10 and Fe are playing an important role [41]. As the spin
which may be comparedto the 8 meV and 11 meV exci-
gapsinCeOs Al andCeRu Al openupbelow(orjust
tations found in the parent compounds CeRu Al and 2 10 2 10
2 10 above)the magneticorderingtemperatureonewouldex-
CeOs Al ,respectively[3,10,11]. Thevalueofthepeak
2 10 pect that the spin gap energy and its intensity would be
position can be taken as a measure of the spin gap en-
stronglyQ−dependent,butthisisnotthecase. Further-
ergy in these compounds. These results show that in
more, with increasing temperature to 30 K the response
both 10% La doped systems, despite the moment direc-
ofCe La Os Al alsobecomesverybroadandthein-
tionbeingdifferentandtheorderedstatemomentsbeing 0.9 0.1 2 10
tensitydecreasesconsiderably[Fig. 5(f)]comparedwith
reduced,averysmallchangeinthespingapenergyscale
4.5 K.
is observed. On the other hand the intensity of the spin
gap does not change much in Ce La Ru Al , while
0.9 0.1 2 10
a dramatic reduction in the intensity of the spin gap is
VI. MUON SPIN RELAXATION
observed in Ce La Os Al . An interesting observa-
0.9 0.1 2 10
tionistheexistenceofaclearlowenergyresponseatlow
Q in Ce La Ru Al at 2 K. This signal is not ob- Figs. 6(a−f) shows the zero-field (ZF) µSR spectra at
0.9 0.1 2 10
served in the non-magnetic phonon reference compound various temperatures of Ce1−xLaxRu2Al10 (x = 0, 0.3,
LaRu Al , which confirms its magnetic origin. Further 0.5 and 0.7). The left hand side figures show the spec-
2 10
thehighresolutionINSstudyonCeRu Al byJ.Robert traatlowtemperatures,whiletherighthandsidefigures
2 10
et. al. [21] did not reveal any clear sign of the low en- showthespectraathightemperature. Itisinterestingto
ergyorquasi-elasticexcitationat11K.Thisrevealsthat seethedramaticchangeinthetime-evolutionoftheµSR
thelowenergyexcitationinCe La Ru Al hassome spectrawithtemperatureforallcompositions,exceptfor
0.9 0.1 2 10
relation with changes in the moment direction from the x=0.7. At35K(or4.5K)weobserveastrongdamping
c−axis to the b−axis. It is an open question whether at shorter time, and the recovery at longer times for all
8
0.2 (a) 1.4 K 35 K (b)
11 K
2
23 K
x=0.0
4
0.1
1
0.0x=0.0 2
0.2 (c) 1.4 K 35 K (d) z)
4.0 K H
(a) (b)
9.8 K M
0 0
y (
metr0.1 ncy 2 x=0.3 2 -1 s)
m e
Asy00..02 x=0.3 1.2 K (e) 4.5 K (f) equ 1 1 (
2.5 K r
F
(c) (d)
0.1 0 0
0.6 x=0.5
x=0.5 2
0.0
0 2 4 0 4 8 12 0.4

0.2 44 mK (g) 4.0 K (h) 1
0.2

(e) (f)
0.1 0.0 0
0 10 20 30 0 10 20 30
x=0.7
0.0 T (K)
0 4 8 12 0 4 8 12
Time ( s)
FIG. 7: (Color online) The temperature dependenceof (a, c,
FIG.6: (Coloronline)Thetimeevolutionofthemuonspinre- e) muon precession frequency/internal field at the muon site
laxationinCe1−xLaxRu2Al10forvarioustemperatures(above inCe1−xLaxRu2Al10. (b,d,f)thedepolarizationrateσ. The
and below TN) in zero field. The solid line is a least-squares solid line in (c, e) is fit to thedata using Eq. (4) (see text).
fit [using Eq. (3) (aboveTN) and Eq. (4) (below TN)]to the
data as described in thetext.
perature (35 K or 4.5/4 K) to Eq. (3), which suggests
that muon stopping sites are the same for all composi-
compositions,whichisatypicalmuonresponsetonuclear
tions. From a simple electrostatic potential calculations
moment,knownastheKubo−Toyabe[42],arisingdueto of CeRu Al Kambe et. al. [43] have proposed muon
2 10
a static distribution of the nuclear dipole moment. Here stoppingsiteat4a(0,0,0),whileKhalyavinet. al.[5]pro-
it arises from the La (stable isotope 138La, I=5, 0.09%
posed muon stopping site at 4c (0.5,0,0.25) (using elec-
abundance and 139La, I=7/2, 99.91% abundance), Ru
trostatic calculation of CeOs Al ). Further the Den-
2 10
(stable isotope 99Ru, I=5/2, 12.76% abundance, 101Ru ,
sity Functional Theoretical (DFT) calculation of muon
I=5/2, 17.06% abundance) and Al (I=5/2) nuclear mo-
stopping sites in Ce(Ru1−xRhx)2Al10 [44] supports both
ment contributions(I = 0 forCe, i.e. zero contribution).
muon sites equally possible as they are located at local
Abovethemagneticorderingtemperaturethe µSRspec-
minimumpositionsoftheelectrostaticpotential. Further
tra of all compounds (x = 0 to 0.7) can all be described
theDFTcalculationrevealedthatthemuonstoppingsite
bythefollowingequation(seeFig. 6,righthandfigures):
(orposition) estimatedfromthe potentialcalculationdo
not change much with Rh-doping [45] as there are no
Gz(t)=A0 1 + 2(1−(σt)2)e(−σt)2/2 e−λt+Abg (3) bsiitgesc.hanges in the potential around the suggested muon
3 3
(cid:2) (cid:3) Nowwediscussthemuonspectraatlowtemperatures.
where A is the initial asymmetry, σ/γ is the local As shown in the left side of Fig. 6, µSR spectra of x =
0 µ
field distribution, γ =13.55 MHz/T is the gyromagnetic 0, 0.3 and 0.5 compounds exhibit a clear sign of coher-
µ
ratioofthemuon,λistheelectronicrelaxationratearis- entfrequencyoscillationsconfirmingthelongrangemag-
ing fromelectronic moments andA is a constantback- neticorderingoftheCemoment. OntheotherhandµSR
bg
ground. It is assumed that the electronic moments give spectra of x = 0.7 at 44 mK reveals the same behavior
an entirely independent muon spin relaxationchannel in asthatobservedat4.0K,indicatesthenon-magnetic(or
real time. The value of σ was found to be 0.32(3) µs−1 paramagnetic) ground state. The result is in agreement
forallcompositionsfromfitting the spectraathightem- with the proposed phase diagram T vs x (La concen-
N
9
tration), reveals T ≈0 K for x ≥ 0.6 [see the inset in H = 9.6(20) Oe, α = 0.99(30) and β = 1.2(12). It is
N 0
Fig. 2 (a)]. For the other compositions, the spectra be- to be noted that due to limited temperature range the
low T are best described by two oscillatory terms and fit to lower field did not converge. It is interesting to
N
an exponential decay, as given by the following equation compare these values of the exponents with α = 1.47(2)
and β = 0.96 observed in CeRu Re Al [10]. The
1.94 0.06 10
largervalues of beta comparedto 0.5,expected from the
2
G (t)= A cos(ω t+φ)e−(σt)2/2+A e−λt+A (4) meanfieldtheorysuggeststhatmagneticinteractionsare
z i i 3 bg
complex in nature.
Xi=1
Now we compare the results of our neutron diffrac-
where ω=γµHint is the muon precession frequency tion and µSR of Ce0.9La0.1Ru2Al10 with that of
(Hint is the internal field at the muon site) and φ is the hole doped systems, Ce(Ru0.97Re0.03)2Al10 and
the phase. In Fig. 7 (left) we have plotted the inter- Ce(Os Re ) Al . The neutron diffraction study
0.97 0.03 2 10
nalfield(ormuonprecessionfrequency)atthemuonsite of Ce(Ru Re ) Al shows that the compound or-
0.97 0.03 2 10
as a function of temperature. This shows that the two ders antiferromagnetically with a propagation vector k
internalfields (or frequencies)appear just below 27 K in = (1,0,0) and the ordered state moment is 0.20(1) µ
B
x = 0, 12.5 K in x = 0.3 and 4.2 K in x = 0.5, showing along the b−axis, in sharp contrast with the ordered
a clear onset ofbulk long-rangemagnetic orderin agree- moment of 0.34−0.42µ along the c−axis observed in
B
ment with TN proposed in the inset of Fig. 2 (a). It is CeRu2Al10 (TN = 27 K) [25], which is very similar be-
interestingto note thateventhoughthe heatcapacityof haviour observed in Ce La Ru Al . The µSR study
0.9 0.1 2 10
x = 0.3 and 0.5 exhibits a very broad λ− type anomaly on Ce(Ru Re ) Al reveals the presence of one in-
0.97 0.03 2 10
nearTN [46],theµSRshowsatypicalsecondorderphase ternalfield(frequency)withvalueof80Oeat1.2K.The
transition that can be explained by mean field behav- observed single frequency in Ce(Ru Re ) Al can
0.97 0.03 2 10
ior. Further, the associated internal fields are found to be explained by the dipolar field calculation with muon
be very small in agreement with a small ordered mag- stoppingsite at4c. Ontheotherhandthe µSRstudyon
netic moment of the Ce3+ ion observed in the neutron Ce1−xLaxRu2Al10 (x = 0, 0.3 and 0.5) shows the pres-
diffractionforx=0 and0.1. The observedtwovaluesof ence of two frequencies.
internalfieldscanbe explainedonthe basisofthedipole
Further Ce(Os Re ) Al has been studied by
field calculation. It was found that Kambe’s suggested 0.97 0.03 2 10
muon spin relaxation and neutron diffraction measure-
positions correspondto the 4a sites which had the lower
ments. A long-range antiferromagnetic ordering of the
field and Khalyavin’s suggested positions correspond to
Ce sublattice with a substantially reduced value of the
the 4c sites which had the higher field. Further the tem-
magneticmoment0.18(1)µ alongthe c−axis(samedi-
peraturedependenceofσandthedifferencesbetweenthe B
rection as in the undoped system) has been found be-
twovaluesofσ alsoexhibitverysimilarbehaviorto that
low T = 21 K. On the other hand the electron dop-
of the internal fields. The value of λ was bound to be N
ing (i.e Ir and Rh) in CeRu Al and (Ir) in CeOs Al
nearly temperature independent for all values of x. 2 10 2 10
showalargeorderedmomentof≈1µ alongthea−axis.
Nowexaminingthe temperaturedependence ofthein- B
Theobtainedresultrevealsthecrucialdifferencebetween
ternal fields, we can see that there is a dip in the inter-
electron- and hole-doping effects on the magnetic order-
nal field (see Fig. 7 top left), which occurs around15 K.
inginCeT Al (T=RuandOs). Theformersuppresses
Moreover,below15Kthefirstandthesecondcomponent 2 10
the anisotropic c−f hybridization and promotes local-
of the depolarization rates also increase (Fig. 7 right).
izedCe moments controlledby single ionanisotropy. On
In principle this could originate from various phenom-
thecontrary,thelatterincreasesthehybridization,keep-
ena related to a change in distribution of internal fields,
ing the dominantroleofthe anisotropicexchangeonthe
but a structural transition is a likely candidate in view
direction of the moments and shifts the system towards
of the structural instability reported on this system [2].
a delocalized nonmagnetic state [26].
To find out the value of criticalexponents and hence get
Finally, it should be pointed out that the obtained re-
more information on the nature of the magnetic tran-
sults pose a question about the role of the hybridiza-
sition, the temperature dependence of the internal field
tion and the crystal field effects in the reduced moment
was fitted [47]:
nature of the magnetic ground state in the undoped
CeT Al (T = Ru and Os) compounds. The behav-
2 10
T α β ior of the system under the hole doping, electron doping
H (T)=H 1− (5)
int 0 and chemical pressure (positive by Y-doping and neg-
(cid:18) (cid:18)T (cid:19) (cid:19)
N
ative by La-doping) along with the applied hydrostatic
Fitting the temperature dependent internal field of x pressurestudypointstothekeyroleofthehybridization
= 0.3 to Eq. (5) we obtained the value of the parame- in the anisotropic character of the exchange interactions
tersforhigher[andforlower]internalfield: T =12.9(3) observed in the undoped compound as well. This also
N
(same for both fields), H =16.5(3) Oe [11.8(7) Oe], α = implies the hybridization effect on the moments reduc-
0
1.65(6) [1.42(4)] and β = 0.81(3) [0.89(2)]. Fit for x = tion,attributedbyStrigariet. al.[48]tothecrystalfield
0.5 data fitting higher field we obtained T = 4.06(9), effects implicitly.
N
10
cating a long−range magnetic ground state in x = 0 to
TABLE II: A list of samples studied Ce1−xLaxT2Al10 (T = 0.5, but almost temperature independent Kubo-Toyabe
Ru, Os) for x = 0 , 0.1 and their transitions temperatures
response between 45 mK and 4 K for x = 0.7. The ab-
(TN =antiferromagneticorderingtemperature),groundstate
sence of temperature dependent relaxation rate in x =
magnetic moment (µAF) value and moment directions (µd)
∗ 0.7 despite of the logarithmic rise in the heat capacity
obtained from neutron diffraction study.( this work)
down to mK is an unusual behavior. One would expect
Compounds TN µAF µd Spin Gap that near a quantum phase transition, µSR will sense
(K) (µB) (meV) the presence of quantum fluctuations even in the para-
CeRu2Al10 [3] 27.0 0.34(2) c−axis [3] 8.0 magnetic NFL state. These µSR results are very similar
Ce0.9La0.1Ru2Al10 23.0 0.18(2) b−axis∗ 7.0 to that observed in YFe2Al10, where despite of NFL be-
CeOs2Al10 28.5 0.29(2) c−axis [3] 11 havior observed in the magnetic susceptibility and heat
Ce0.9La0.1Os2Al10 21.7 0.23(1) c−axis∗ 10 capacity,the µSRspectra[3]areindependentoftemper-
ature down to mK. A major achievement of this work
has been the finding offrequency oscillationsin our µSR
spectra up to x = 0.5, which for the first time estab-
VII. CONCLUSIONS lishes the onset of long-range magnetic ordering in the
La-doped compounds and the robust magnetic ordering
We have carried out a comprehensive study on in spite of the large and anisotropic c−f hybridization
Ce La T Al (T=RuandOs)usingthecomplemen- in this system. The temperature dependence of the µSR
0.9 0.1 2 10
tary techniques ofmagnetization,resistivity,heat capac- frequenciesandmuondepolarizationratesofx=0follow
ity, neutron diffraction, inelastic neutron scattering and an unusual behavior with further cooling of the sample
muon spin relaxation measurements to understand the below 18 K, pointing at the possibility of another phase
unusual behavior of the magnetic moment direction and transition below 15 K. On the other hand the tempera-
theopeningofaspingapbelowT . Theneutrondiffrac- ture dependence of the µSR frequencies andmuondepo-
N
tion study is unambiguous in confirming the long-range larization rates of x = 0.3 follows conventional behavior
magneticorderinthiscompound. Moreinterestinglyour expectedforasecondorderphasetransitioninthemean
NDstudyshowsaverysmallorderedmomentof0.18µ field theory.
B
along the b−axis in Ce La Ru Al , but a moment
0.9 0.1 2 10
of 0.23 µB along the c−axis in Ce La Os Al . This
0.9 0.1 2 10
contrasting behavior can be explained based on a differ- ACKNOWLEDGEMENT
entdegreeofhybridizationinCeRu Al andCeOs Al :
2 10 2 10
hybridizationisstrongerinthelatterthanintheformer. Some of us DTA/ADH would like to thank CMPC-
OurINSstudyrevealsthepresenceofaspingapof7meV STFC for financial support. The work at Hiroshima
and 10 meV in the 10% La-doped T = Ru and Os com- University was supported by KAKENHI (Grant No.
pounds, respectively. Interestingly the intensity of the 26400363)from JSPS, Japan. AMS thanks the SA-NRF
spin gap decreases dramatically in La-doped CeOs Al (Grant 78832)and UJ ResearchCommittee for financial
2 10
compound. support. A.B would like to acknowledge FRC of UJ,
Further we also present muon spin rotation study on NRF of South Africa and ISIS-STFC for funding sup-
Ce1−xLaxRu2Al10 (x=0,0.3,0.5and0.7),whichreveals port. We would like to thank P. Manuel, J. M. Mignot
the presence of two coherent frequency oscillations indi- and I. Watanabe for an interesting discussion.
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