Kondo lattice and antiferromagnetic behavior in quaternary CeTAl$_4$Si$_2$ (T~=~Rh, Ir) single crystals

1.3 MB·English

by  Arvind Maurya

APS/123-QED
Kondo lattice and antiferromagnetic behavior in quaternary
CeTAl Si (T = Rh, Ir) single crystals
4 2
Arvind Maurya, R. Kulkarni, A. Thamizhavel and S. K. Dhar∗
Department of Condensed Matter Physics and Materials Science,
Tata Institute of Fundamental Research, Homi Bhabha Road, Colaba, Mumbai 400 005, India.
D. Paudyal
The Ames Laboratory, U.S. Department of Energy,
Iowa State University, Ames, Iowa 50011-3020, USA.
(Dated: May 12, 2015)
5
We report the synthesis and the magnetic properties of single crystalline CeRhAl Si and
4 2
1
CeIrAl Si and their non magnetic La-analogs. The single crystals of these quaternary compounds
0 4 2
were grown using Al-Si binary eutectic as flux. The anisotropic magnetic properties of the cerium
2
compounds were explored in detail by means of magnetic susceptibility, isothermal magnetization,

y electrical resistivity at ambient and applied pressures up to 12.6 kbar, magnetoresistivity and heat
a capacity measurements. Both CeRhAl Si and CeIrAl Si undergo two antiferromagnetic transi-
4 2 4 2
M tions,firstfromtheparamagnetictoanantiferromagneticstateatT =12.6Kand15.5K,followed
N1
by a second transition at lower temperatures T = 9.4 K and 13.8 K (inferred from the peaks in
N2
0 the heat capacity), respectively, in conformity with an earlier report in the literature. The para-
1 magnetic susceptibility is highly anisotropic and its temperature dependence in the magnetically
ordered state suggests the c-axis to be the relatively easy axis of magnetization. Concomitantly,

] isothermal magnetization at 2 K along the c-axis shows a sharp spin-flop transition accompanied
l
e by a sizeable hysteresis, while it varies nearly linearly with field along the [100] direction up to the
- highest field 14 T of our measurement. The electrical resistivity provides evidence of the Kondo
r
t interaction in both compounds, inferred from its −lnT behavior in the paramagnetic region and
s
thedecreaseofmagnetictransitiontemperaturewithpressure. Theheatcapacitydataconfirmthe
.
t bulknatureofthetwomagnetictransitionsineachcompound,andfurthersupportthepresenceof
a
m Kondo interaction by a reduced value of the entropy associated with the magnetic ordering. From
theheatcapacitydatabelow1K,thecoefficientofthelineartermintheelectronicheatcapacity,γ,
- is inferred to be 195.6 and 49.4 mJ/mol K2 in CeRhAl Si and CeIrAl Si , respectively classifying
d 4 2 4 2
these materials as moderate heavy fermion compounds. The main features of the magnetoresis-
n
o tivity measured at a particular temperature correlate nicely with the isothermal magnetization at
c the same temperature in these two isostructural compounds. We have also carried out an analysis
[ of the magnetization based on the point charge crystal electric field model and derived the crystal
electric field energy levels which reproduce fairly well the peak seen in the Schottky heat capacity
2
intheparamagneticregion. Further,wehavealsoperformedelectronicstructurecalculationsusing
v
(LSDA+U)approach,whichprovidephysicalinsightsontheobservedmagneticbehaviourofthese
0
two compounds.
5
2
PACSnumbers: 81.10.Fq,75.50.Ee,75.30.Kz,75.10.Dg,71.70.Ch,75.50.Ee
0
0
.
1 I. INTRODUCTION 1:1:4:2 compounds, with a local fourfold axial (4/mmm)
0 symmetry at the Eu site. These are a new addition
5 to several quaternary rare earth-based compounds al-
1
Recently, the synthesis and magnetic properties of ready known in the literature with 1:1:4:2 stoichiome-
:
v quaternary EuTAl Si (T = Rh and Ir) single crystals, try, which have been grown using aluminum as flux; for
4 2
Xi using the Al-Si binary eutectic as flux have been re- example, RNiAl4(NixSi2−x), EuNiAl4Si2, RNiAl4Ge2,
ported1,2. The two Eu compounds initially order into RAuAl4Ge2 and RAuAl4(AuxGe1−x)2 where R is a rare
ar an incommensurate amplitude modulated antiferromag- earth metal3,4. While most of the these compounds
netic state at TN1 = 11.7 and 14.7 K respectively, fol- adopt the rhombohedral YNiAl4Ge2-type structure5,
lowed by a second transition to an equal moment state the phases RAuAl4(AuxGe1−x)2 and EuAu1.95Al4Ge1.05
at lower temperature TN2. Though these two com- crystallize in the KCu4S3-type structure5. Both struc-
pounds prima-facie are antiferromagnetic, the isother- ture types are characterized by the slabs of “AuAl4X2
mal magnetization curves at low temperatures (below (X = Si or Ge)” or “AuAl4(AuxGe1−x)2” stacked along
T ) show a hysteresis right near the origin with a rem- the c-axis with layers of R atoms in between. The Ce
N2
nance; unlike any other antiferromagnetic material. The atoms in both CeAuAl4Ge2 and CeAuAl4(AuxGe1−x)2
EuTAl Si compoundsadoptanorderedderivativeofthe (x = 0.4) have been reported to be in a valence fluc-
4 2
ternary KCu S -type tetragonal, tP8, P4/mmm struc- tuating state3. This suggests the possibility of strong
4 3
ture, which leads to quaternary and truly stoichiometric hybridization between the Ce-4f-orbitals and the itin-
2
erant electrons in these structure-types, which is known alytical x-ray diffractometer. The stoichiometry was
to lead to a variety of anomalous ground states, such as checked by semiquantitative analysis performed by en-
Kondo lattices, heavy fermions with huge effective elec- ergy dispersive analysis by x-rays (EDAX). Well ori-
tron masses, magnetically ordered states with reduced ented crystals were cut appropriately by an electric dis-
saturation moments6,7. The N´eel temperature in some chargecuttingmachinefordirectiondependentmeasure-
heavy fermion, antiferromagnetic Kondo lattices can be ments. The magnetization data were measured in a
tuned to zero using pressure as an external parame- QuantumDesignSuperconductingQuantumInterference
ter, which leads to a quantum phase transition where Device (SQUID) magnetometer and Vibration Sample
the Fermi-Landau description of quasiparticles breaks Magnetometer (VSM) in the temperature range 1.8 to
down8. It was therefore of interest to explore the for- 300 K and fields up to 14 T. The electrical resistivity,
mation of other RTAl Si (T = Rh and Ir) compounds, magnetoresistivity and the heat capacity were measured
4 2
in particular for R = Ce. We have been able to grow the in a Quantum Design Physical Properties Measurement
single crystals for R = Ce and Pr and in this report we System (PPMS). Heat capacity measurements down to
give a detailed description of properties of two Ce com- 100 mK were performed using the dilution insert of QD-
pounds, usingthetechniquesofmagnetization, electrical PPMS. A piston-cylinder type pressure cell fabricated
resistivity in zero and applied magnetic fields, and un- from MP35N alloy was used to measure the resistivity
der externally applied pressure, and heat capacity. We upto 12.6 kbar. A teflon capsule covering sample plat-
find that both CeTAl Si (T = Rh and Ir) compounds form, holding two samples and one Sn wire as manome-
4 2
are dense Kondo lattice antiferromagnets, each under- ter,wasfilledwithDaphneoil,whichishydrostaticpres-
going two magnetic transitions like the Eu-analogs. We sure medium. The dimension of capsule is such that it
havesupplementedourexperimentaldatawithelectronic fits exactly inside the 5 mm bore of the cell. A feed
structurecalculationsforCeTAl Si (T=Rh,IrandPt) through made out of beryllium copper alloy was used
4 2
employingthelocalspindensityapproximationincluding for providing electrical contacts to the sample and Sn
Hubbard U-onsite electron-electron correlation. manometer. A cernox temperature sensor and a heater
Whilethismanuscriptwasunderpreparation,Ghimire intheformofmanganinwiremountedoverthecellwere
et al.9 have reported the anisotropic susceptibility and fedtoaCryoconPIDtemperaturecontroller. A5mAdc
resistivity, and the low temperature heat capacity (1.8 current derived from Keithley current source was passed
to 30 K) of CeMAl Si (M = Rh, Ir, Pt) compounds9. through samples and the generated voltage was read out
4 2
Our observation of two antiferromagnetic transitions in by a sensitive nanovoltmeter. All the resistivity mea-
these two compounds (M = Rh and Ir) is in confor- surements were done in the standard four probe configu-
mity with their results. Ghimire et al. allude to the ration. Temperature controller, current source and volt-
presence of Kondo interaction and the opportunity to meter were interfaced to a computer via GPIB and data
explore strongly correlated electron behaviour in these acquisition was automated by a Labview programme.
quaternary compounds. Our low temperature heat ca-
pacity data (below 1 K) reveal moderately heavy elec-
tron masses. Our more extensive magnetization data, III. RESULTS AND DISCUSSION
andmagnetoresistivityrevealsomeadditionalfeaturesin
thepropertiesofthethesetwocompounds. Ourresistiv- A. Structure
itydataatambientpressureshowthepresenceofKondo
interactioninthesecompounds,furthersupportedbythe The compositions obtained from EDAX analysis con-
resistivity data under externally applied pressure, where firmedthestoichiometricratioof1:1:4:2towithin1at.%
we observe a suppression of TN with pressure, which is for each element. The powder x-ray diffraction patterns
a standardfeature of Ce-Kondolatticespredicted by the ofCeTAl Si (T=RhandIr)aresimilartothoseofEu-
4 2
Doniach’s phase diagram10. In a more recent paper, us- analogs, and no extra peaks due to any parasitic phases
ingpowderneutrondiffraction,Ghimireet al.11 havede- were found. A Rietveld refinement using FullProf soft-
termined that the antiferromagnetic structure in both
CeRhAl Si and CeIrAl Si is A-type with propagation
4 2 4 2
vector k=(0,0,1/2) along the c-axis. TABLEI: Latticeconstantsaandc,andunitcellvolumeV
of CeRhAl Si and CeIrAl Si as determined from the x-ray
4 2 4 2
powder diffraction pattern.
II. EXPERIMENT a c V
(˚A) (˚A) (˚A3)
CeRhAl Si 4.223(2) 8.048(2) 143.54(2)
The single crystals of CeTAl Si and LaTAl Si were 4 2
4 2 4 2 CeIrAl Si 4.236(3) 8.043(2) 144.34(2)
grown by following the same experimental protocol as 4 2
described in ref. 1 for the Eu-compounds. Their Laue
patterns were recorded using a Huber Laue diffractome- ware12 based on the EuIrAl Si -type tetragonal crystal
4 2
ter, while the phase purity was inferred from the pow- structure was performed. The obtained lattice parame-
der x-ray diffraction pattern collected using a PAN- ters a and c are listed in Table I and are in good agree-
3
ment with the values reported in ref. 9. It may be noted
TABLE II: Effective moment and paramagnetic Curie tem-
that similar to Eu compounds1 the lattice parameter a
perature in CeRhAl Si and CeIrAl Si along the principal
is larger but c is slightly shorter in Ir analog compared 4 2 4 2
crystallographic directions.
to that of Rh analog but overall the unit cell volume of
CeIrAl4Si2 is slightly larger than that of the Rh-analog, CeRhAl4Si2 CeIrAl4Si2
which is in accordance with the larger atomic volume of µeff(µB/f.u.) θp(K) µeff(µB/f.u.) θp(K)
Ir. H (cid:107) [100] 2.65 −155 2.62 −140
H (cid:107) [001] 2.35 7.1 2.43 4
B. Magnetic susceptibility and magnetization
T exhibits hysteresis thereby indicating that the tran-
N2
The magnetic susceptibility, χ(T), of CeRhAl Si and sition at T has a first order character (Figs. 1e-f).
4 2 N2
CeIrAl Si below 300 K is shown in the main panel of The hysteresis is weaker at lower fields and it increases
4 2
Figs. 1 (a) and 1 (b), for field (0.3 T) applied along with increment in magnetic field till spin flop field. The
the [100] and [001] directions, respectively. The inverse changeinT andT withfieldappliedalong[100]and
N1 N2
susceptibility in the temperature range 1.8 to 300 K is [001] directions has been summarized in the phase dia-
plotted in the insets of Fig. 1(a) and (b). The suscepti- gramsshowninFigs.1gand1h. Criticalpointsobtained
bility is highly anisotropic in the paramagnetic region from isothermal magnetization vs. magnetic field (MH),
in both compounds and a fit of the Curie-Weiss law, electrical resistivity as a function of field (RH) and tem-
χ = C to the high temperature data (100-300 K), perature (RT) measurements are also shown which are
represeTn−teθpd by the solid lines, furnishes the Curie-Weiss in consonance with each other. It may be noted that the
parameterswhicharelistedinTableII.Theeffectivemo- phase boundary separating two antiferromagnetic states
ments are close to the Ce3+-free ion moment value of AF1 and AF2 for H (cid:107) [001] is of first order character
2.54 µ /Ce. The highly anisotropic nature of the sus- as inferred from the susceptibility and magnetoresistiv-
B
ceptibility is clearly reflected by the respective values of itydata. Also,TNssuppressfasterforfieldappliedalong
paramagneticCurietemperatureθ whicharemorethan the easy axis viz. [001].
p
one order of magnitude larger for H (cid:107) [100] in both The isothermal magnetization at 2 K is linear up
compounds. In conformity with the trivalent nature of to 14 T along [100] while there is a sharp spin-flop
the Ce ions, the compounds order antiferromagnetically (metamagnetic-like) transition revealed by two closely
at T = 13.3 and 16 K, and T = 9.4 and 13.8 K for spaced jumps in the magnetization along the [001]-
N1 N2
T = Rh and Ir, respectively, close to the values reported directionbeginningat5.3(6.4)TforCeRh(Ir)Al Si (see
4 2
in ref. 9. It may be noted that the absolute value of the Figs. 2a and 2b). The former behaviour is typical of
polycrystalline averaged θ (−100 and −68 K) is sub- an antiferromagnet when the moments are perpendicu-
p
stantially higher than T . We believe it to be primarily lar to the field. The field dependence thus clearly marks
N1
duetothecrystalelectricfieldandanisotropicKondoin- the easy and the hard-axes of magnetization. This is in
teraction (vide infra) which contribute negatively to θ . conformity with neutron diffraction in which magnetic
p
In the simplest collinear two-sublattice antiferromagnet, moments aligned antiferromagnetically along the c-axis
the χ along the hard direction is temperature indepen- below T is inferred11. The magnetization attains a
⊥ N2
dent below T while χ gradually decreases to zero as value of 0.95 and 1.14 µ /Ce at 14 T along the c-axis in
N (cid:107) B
T→0. A weak temperature dependence of χ along [100] CeRhAl Si and CeIrAl Si respectively, which is lower
4 2 4 2
in the two compounds indicates a hard ab-plane. than the saturation moment of Ce3+ (2.14 µ /Ce). We
B
It may be noted that the anisotropy in χ100] and attributethelowervaluestothecombinedeffectsofcrys-
[
χ001] persists in our data(Figs. 1a and 1b)upto 300 K. talelectricfieldandpartialquenchingoftheCemoments
[
Ontheotherhandinref.9thetwocrosseachothernear due to Kondo screening. We note that the magnetiza-
275 K in CeIrAl Si . Such a crossover, prima-facie indi- tion at 14 T at 2 K is lower in the Rh-analogue, which is
4 2
catesachangeintheeasyaxisofmagnetizationwithtem- consistent with its higher Kondo temperature, TK (vide
perature. However, in the crystal electric field analysis infra). Themagnetizationat2Kin14Tisnotyetsatu-
of the magnetization data (vide infra), the values of the rated and is lower than the values determined in ref. 11.
dominant CEF parameter B0 are negative in both com-
2
poundsandcomparablemakingtheanisotropiccrossover One can observe a clear hysteresis in the vicinity of
along the crystallographic axis unlikely. spin-flop transition. The hysteretic behaviour is also ob-
The magnetic field dependence of susceptibility served in the temperature dependence of magnetic sus-
(M/H) below T was investigated at a few fields and ceptibility (mentioned above) and electrical resistivity
N1
the data are plotted in Figs. 1(c-f). The T decreases (vide infra), revealing the presence of first order field
N
as the applied field is increased, as commonly observed induced effect. The spin-flop field value and the magne-
in antiferromagnets. However, the decrease is more sub- tization decrease with the increase of temperature. The
stantial for H (cid:107) [001] which is relatively the easy axis of magnetization for H (cid:107) [100] is relatively insensitive to
magnetization. Themagnetizationinbothcompoundsat the variation in temperature as inferred from Figs. 2(c)
4
50 6
CHe R= h0A.3l 4TSi2600 HH //// [[100001]] (a) CHe =Ir 0A.3l4 STi2 600 H // [001] (b)
H // [100]
-30emu/mol) 25 -1χ (mol/emu)420000 Curie Weiss fit -20emu/mol) 3 -1χ(mol/emu)420000 Curie Weiss fit
1 1
χ( 00 100 T (K2)00 300 χ( 00 100 200 300
T (K)
0 0
0 100 200 300 0 100 200 300
Temperature (K) Temperature (K)
14 12
(c) (d)
CeRhAl4Si2 0.1T
1T
mol) 58TT mol) 11
u/ 10T u/
m m
-30e12 H // [100] -30e
1 1
(H H ( 10 1T CeIrAl4Si2
M/ M/ 35TT H // [100]
8T
10T
10 9
0 10 20 0 5 10 15 20
Temperature (K) Temperature (K)
120 10
(e) 1T (f)
CeIrAl4Si2 3T
H // [001] 5T
mol) mol) 66.T4T
mu/ mu/ 66..68TT
e60 e 5 7T
-30 -20
(1H 12TT (1H
M/ 3T M/
CeRhAlSi 4T
0.02 emu/mol H // [0014] 2 4.2T
5.5T
0 0
0 10 20 0 10 20
Temperature (K) Temperature (K)
15 (g) 15 (h)
H // [001] MT H // [001] J // [100] RH H // [001] MT H // [001] J // [100] RH
H // [001] MH H // [001] J // [100] RT H // [001] MH H // [001] J // [100] RT
H // [100] MT H // [100] MT
10 CeRhAl4Si2 10 CeIrAl4Si2
T) )
( T
H H (
5 5
AF2 AF1 PM AF2 AF1 PM
0 0
0 10 20 0 10 20
T (K) T (K)
FIG. 1: (Color online) Magnetic susceptibility and inverse susceptibility (in inset) up to 300 K of (a) CeRhAl Si and (b)
4 2
CeIrAl Si . ThedependenceofM/H onfieldisshownin(c-f)forH (cid:107)[100]andH (cid:107)[001],respectively. In(e)and(f)single
4 2
colorplotsshowZFC(zerofieldcooled),FCC(fieldcooledcooling)andFCH(fieldcooledheating)datarevealingfieldinduced
first order nature of transition at T . Magnetic phase diagrams of (g) CeRhAl Si and (h) CeIrAl Si derived from magne-
N2 4 2 4 2
tization (MT, MH) and magnetoresistivity (RT, RH) data (vide infra). AF1, AF2 and PM represents two antiferromagnetic
and paramagnetic phases, respectively.
5
1.0 (a) 1.2
(b)
2K
CeRhAlSi
4 2 5K
Ce) H // [001] e) 182KK
µ/B 2K /CB 0.8 15K
on ( 0.5 58KK 1.0 µn ( H // [001]
Magnetizati 12K µM (/Ce)B0.5 2K HH //// [[100001]] agnetizatio 0.4 CeIrAl4Si2 µM (/Ce)B100...284 2HHK //// [[010010]]
0.00 2 4 6 8 10 12 14 M 0.00 2 4 6 8 10 12 14
H (T) H (T)
0.0 0.0
0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
Magnetic Field (Tesla) Magnetic Field (Tesla)
0.4 0.4
(c) (d)
0.30
CeIrAlSi
H [100] 4 2
Ce) CeR h2A Kl4Si2 Ce) /Ce)B 0.25 8K H // [100]
µ/B 150 K K µ/B µM ( 0.20
n ( 0.2 n ( 0.2
o o 0.15
zati zati 8 10H (T)12 14 25KK
eti eti 8K
n n
g g 10K
Ma Ma 15K

0.0 0.0
0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
Magnetic Field (Tesla) Magnetic Field (Tesla)
FIG.2: (Coloronline)Isothermalmagnetizationcurvesatselectedtemperaturesfor(a)CeRhAl Si and(b)CeIrAl Si along
4 2 4 2
[001]direction. Theinsetsshowthedataat2KforH(cid:107)[001]andH(cid:107)[100]. (c)and(d)showthedataatselectedtemperatures
for H (cid:107) [100]. The inset in (d) reveals two weakly first order changes which are also seen in the magnetoresitance data.(see
Fig. 7).
and 2(d). The inset in Fig. 2(d) reveals two weakly hys- similar low values of RRR. Our values of resistivity are
tereticregionsinthemagnetizationofCeIrAl Si at8K. also significantly higher than reported in ref. 9. Though
4 2
our single crystals looked good superficially, there may
bemicro-voidsandmicro-crackswhichleadtohigherob-
C. Electrical Resistivity served resistivity. While ρ[001] decreases as the tempera-
tureisdecreasedbelow300K,ρ showsaslightnega-
[100]
tivetemperaturecoefficientabove100K.The4f-derived
Figs. 3(a-d) show the zero-field electrical resistivity
part of the resistivity ρ is calculated by subtracting
ρ(T) data of CeRhAl Si (left panels) and CeIrAl Si 4f
4 2 4 2
the ρ(T) data of La-analog from the corresponding Ce-
(right panels) for the current density J parallel to [001]
compound,whichisalsoshowninFigs.3(a)and3(b)and
and [100] directions, respectively. The corresponding
replotted in 3(c) and 3(d) on a semi-logarithmic scale.
data for the non-magnetic La-reference compounds are
ρ reveals a negative logarithmic temperature depen-
also plotted. While anomalies at T and T for 4f
N1 N2
dence along both directions which is a hallmark of the
J (cid:107) [001] are visible either in the ρ vs T or dρ/dT vs T
Kondo interaction. The high temperature peak in ρ
plots (not shown), the ρ for J (cid:107) [100] shows a sudden 4f
in range 100-200 K, which arises due to the interplay of
change of slope only at T .
N2
Kondo interaction and crystal electric field levels, occurs
There is a considerable anisotropy in the resistivity, ρ
at different temperatures along the two directions. The
along [001] being larger compared to [100] in the entire
resistivitydatathusrevealthatthesetwoCe-compounds
temperature range. The residual resistivity ratio (RRR)
are dense anisotropic Kondo lattice antiferromagnets.
ρ /ρ is 17.8 and 29.9 for J (cid:107) [100] and [001], re-
300K 2K
spectively for CeIrAl Si , compared to its corresponding The Kondo behaviour of CeTAl Si compounds, in-
4 2 4 2
values of 3.2 and 3.4 in CeRhAl Si . While our RRR ferred above from the resistivity data at ambient pres-
4 2
for CeIrAl Si is comparable to the value reported by sure,wasprobedfurtherbymeasuringtheresistivityun-
4 2
Ghimireetal9, inCeRhAl Si ourRRR valuesarelower der pressure up to 12.6 kbar. According to the stan-
4 2
for reasons unknown to us. We repeated the measure- dard Doniach phase diagram of a magnetic Kondo lat-
ments on a second sample of CeRhAl Si but observed tice, pressure enhances the 4f-conduction band coupling
4 2
6
300 (a) 400 (b)
CeRhAl4Si2 J // [001] CeIrAl4Si2 J // [001]
m) 200 m) ρ4f [001]
cΩ ρ4f [001] Ω c 200 CeIrAlSi J // [100]
ρ (μ 100 CeRhAl4Si2 J//[100] ρ (μ ρ [100] 4 2
ρ [100] 4f
0 LaRhAl4Si2 J // [001] LaRhAl4Si24 fJ // [100] 0 LaIrAl4S Li2a JI r/A/ [l40S0i12 ]J // [100]
0 100 200 300 0 100 200 300
Temperature (K) Temperature (K)
200 400
(c) (d)
CeIrAlSi
CeRhAlSi ρ [001] 4 2 ρ [001]
4 2 4f 4f
)
) m
m c
c 100 ρ [100] Ω 200
Ω 4f μ
(μρ 4f (ρ 4f ρ [100]
4f
0 0
2 4 6 8 2 4 6 8 2 2 4 6 8 2 4 6 8 2
1 10 100 1 10 100
Temperature (K) Temperature (K)
FIG.3: (Coloronline)Electricalresistivityof(a)CeRhAl Si andLaRhAl Si ;(b)CeIrAl Si andLaIrAl Si alongthemajor
4 2 4 2 4 2 4 2
crystallographic directions. ρ is represented by solid lines. ρ (T) data plotted on logarithmic temperature scale are shown
4f 4f
in (e) and (f).
andtheKondotemperature, whichdecreasestheT . At val around T . Such a scaling relationship has been
N max
sufficiently high pressures when the Kondo interaction reported in some Kondo compounds13. Though T
max
dominates over the RKKY interaction, T approaches increaseswithpressureintheIr-analogueaswell, weob-
N
zeroleadingtoaquantumphasetransition. Fig.4shows served a substantial difference in the resistivity values
the resistivity of the two compounds at selected values particularly at higher temperatures taken at nearly the
of pressure. The pressure cell was simultaneously loaded samepressureintwodifferentruns(withoutaffectingthe
with the two compounds and numbers in parentheses in- transition temperature), while as in the Rh compound
dicate the order of data acquisition. The T in both theresistivityvaluesnearlymatched. Therefore,wehave
N2
compounds decreases with pressure, which is qualita- notshownthedatafortheIr-anologueathighertemper-
tively in consonance with the Doniach phase diagram. atures. Fig. 4d shows the T-P phase diagram of both
T decreases from 13.6 (at ambient pressure) to 8.2 compounds. It may be noted that T is not discernible
N2 N1
(6.2)Kat8.8(11.4)kbarinCeIrAl Si ,whileitdecreases inanyofourpressuredependentresistivitymeasurement
4 2
from 9.4 to 4.7 K at 8.8 kbar in CeRhAl Si . No appar- as the data were taken for J (cid:107) [100] where we see only
4 2
ent anomaly is observed at higher pressures in the two one transition (cf. Figs. 5c and 5d).
compoundsdownto1.8KbothinρversusT anddρ/dT
versus T plots. Data at lower temperatures and presum-
ably higher pressures are required to track the eventual
D. Magnetoresistance
decrease of T to 0 K.
N2
The resistivity data under pressure were measured up The variation of resistivity at selected values of mag-
to 300 K and the data for CeRhAl Si are shown in netic field at low temperatures is shown in Figs. 5(a-d).
4 2
Fig. 4c. The temperature T at which the resistivity For H applied along [100] and J (cid:107) [001] the resistiv-
max
attains its maximum value ρ increases from ∼ 108 at ity plots are qualitatively similar except that there is a
max
ambient pressure to 130 K at 12.6 kbar. Qualitatively, gradual downward shift of T with increasing field. In
N
the upward shift of T is in conformity with the in- CeIrAl Si , one sees two steps to the lower temperature
max 4 2
crease of T with pressure. The inset of Fig. 4c shows transition at fields of 10 and 12 T (Fig. 5b), which is
K
ρ/ρ scales with T/T in a reasonably large inter- consistentwithtwoweaklyfirstorderchangesseeninthe
max max
7
70 (a) 100 (b)
CeRhAlSi CeIrAlSi
4 2 4 2
J // [100]
J // [100]
60
)
m )
m
c
Ω 0 kbar (1) Ω c 50 02 .k6b kabra (r1 ()2)
μ
( 2.6 kbar (2) μ 6.6 kbar (3)
ρ 50 6.6 kbar (3) ρ( 8.8 kbar (4)

8.8 kbar (4) 9.4 kbar (6)
9.4 kbar (7) 10.6 kbar (5)
10.6 kbar (5) 11.4 kbar (8)
12.6 kbar (6) 12.6 kbar (7)
40 0
0 5 10 15 0 10 20
T (K)
T (K)
120 (c) 15 (d)

0 kbar J // [100]
1.9 kbar
2.6 kbar TN2CeIrAl4Si2
6.6 kbar 10 TN2CeRhAl4Si2
) 8.4 kbar
m
c 9.7 kbar K)
Ω 60 10.6 kbar (
μ 12.6 kbar 1.0 N
( T
ρ4f ρ4fmax 00..86 5
CeRhAl4Si2 /ρ 4f 00..42
J // [100] 0.0
0 1 T/T 2 3
0 max 0
2 4 6 8 2 4 6 8 2 0 5 10 15
1 10 100
T (K) Pressure (kbar)
FIG.4: (Coloronline)ElectricalresistivityunderhydrostaticpressureatlowtemperatureswhenJ (cid:107)[100]for(a)CeRhAl Si ,
4 2
(b)CeIrAl Si . Numbersinparenthesisdenotethetheorderinwhichpressurewasapplied. (c)4f-derivedelectricalresistivity
4 2
ofCeRhAl Si upto300Konlogarithmictemperaturescale,(d)variationofT withpressureinCeRhAl Si andCeIrAl Si
4 2 N2 4 2 4 2
when J (cid:107) [100].
magnetization(inset,Fig.2d). Ontheotherhandpromi- 2 K for field applied in the ab-hard plane is small and
nentchangesareseenforH (cid:107)[001]andJ (cid:107)[100]. T is attains a value of ∼ 3 % at 14 T. On the other hand
N
suppressed relatively faster with a substantial hysteresis for field applied along the easy-axis [001] the MR at its
in the field-range where spin-flop occurs, revealing first maximum is an order of magnitude larger. Initially the
order effects in conformity with the magnetization data. positive MR increases with field, jumps sharply at the
It may be noted that there is a slight kink at 8.6 and first step of the spin-flop attaining a maximum of 30%
11.2 K in 5.5 T and 6 T in CeRhAl Si and CeIrAl Si , atnearlythesecondstepandthendecreasessharplyand
4 2 4 2
respectively. The inset of Fig. 5(d) shows that T in becomes negative at higher fields. In the return cycle
N1
6 T has decreased to the temperature at which the kink the MR shows hysteresis in the spin-flop region, which
occurs in CeIrAl Si . Maybe the anomaly is present at corresponds nicely with the hysteresis in the magnetiza-
4 2
lower fields also but it is not discernible. Similar expla- tion (cf. Fig. 2). We have reported earlier simialr sharp
nationholdsincaseofCeRhAl Si . Theinsetalsoshows changesintheMRofEuNiGe whichisanantiferromag-
4 2 3
that there is a good agreement between the hysteresis in net with T of 13.2 K14.
N
the resistivity (on right scale) and M/H (on left scale)
For CeIrAl Si the MR for H (cid:107) [001] is qualitatively
data at 6 T field applied parallel to [001]. 4 2
similar (Figs. 6 (b) at low fields except that the MR in
MagnetoresistivityMRwasalsoprobedbyvaryingthe the spin-flop region is even larger and exceeds 100 %.
fieldfromzeroto14Tatselectedtemperatures,withthe Above the spin-flop the MR drops sharply but unlike
field and current density in various orientations and the CeRhAl Si it does not attain negative values and re-
4 2
results are plotted in Figs. 6 and 7. The magnetore- mains positive up to the highest field of 14 T. For field
sistance, MR is defined as MR = [ρ(H) − ρ(0)]/ρ(0). appliedintheab-hardplaneviz. J (cid:107)[100]andH (cid:107)[010];
With reference to Fig. 6(a) the MR of CeRhAl Si at J (cid:107)[001]andH (cid:107)[100]theMRispositivequalitatively
4 2
8
150 100
(a) (b)
CeRhAlSi
J // [001]4 2 CeIrAlSi
4 2
H // [100] J // [001]
120 H // [100]
m) m)
Ω c Ω c 50
μ μ 0T
ρ ( 0T ρ ( 5T
8T
90 5T
10T
10T
12T
10 μΩ cm 14T 14T
0
0 10 20 0 5 10 15 20
Temperature (K)
Temperature (K)
70 50
(c) (d)
CeRhAlSi
4 2 CeIrAlSi
J // [100] 4 2
J // [100]
H // [001] H // [001] 0T 5T
1T 6T
m) m) 4T 7T
μΩ c 50 0T μΩ-c 25 mol) 60 M/H 80 ρ
ρ ( 434.TT5T ρ ( 0 emu/-3 4200 ρ 6400 c (μΩ
2 μΩ cm 5.5T H (1 m)
6T M/ 0 20
0 10 20
30 0 T(K)
0 2 4 6 8 10 12 14 0 5 10 15 20
Temperature (K) Temperature (K)
FIG. 5: (Color online) Magnetic field dependence of ρ(T) of CeRhAl Si and CeIrAl Si in different configuration. In (a) and
4 2 4 2
(c) the in-field plots have been shifted upward by a constant offset for clarity.
45 150
(a) (b)
J // [100] H // [001]
CeRhAlSi
4 2 J // [100] H // [001] J // [100] H // [010]
30 2 K J // [100] H // [010] J // [001] H // [100] CeIrAl4Si2
J // [001] H // [100] 100 T = 2K
)
) %
%
(
R ( 15 MR
M
50
0
-15 0
0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
Magnetic Field (Tesla) Magnetic Field (Tesla)
FIG. 6: (Color online) Current and field-direction dependence of isothermal Magnetoresistance(MR) at 2 K upto 14 T of (a)
CeRhAl Si and (b) CeIrAl Si .
4 2 4 2
similarthethatofCeRhAl Si butitsmagnitudeismuch field is applied along the easy axis, it tends to suppress
4 2
larger. At 2 K the MR rises monotonically reaching 44 the spin fluctuations in one sublattice and increase in
and 115 %, respectively at 14 Tesla. The latter value the other. Typically, the MR resulting from the com-
is even larger than the peak value for H (cid:107) [001]. The bined fluctuations is positive15. In the spin-flop region
observed MR can be qualitatively explained by invoking the spins can be imagined to be in a canted state with
three contributions, i) the MR of an antiferromagnet, higher spin disorder resistivity. As the field is increased
ii) the Kondo contribution and iii) the positive contri- further leading to spin-flip where a saturated paramag-
bution due to the cyclotron motion of the conduction netic state is achieved, the MR becomes negative. A
electrons. In an antiferromagnet for T <<T when the magnetic field tends to suppress the Kondo scattering of
N
9
(a)
30 100 (b)
CeRhAl4Si2 HJ / // /[ 1[00001]] 80 CeIrAl4Si2 J // [100]
H // [001]
2K
%) 15 46KK %) 60 25KK
MR ( 111025KKK MR ( 40 111035KKK
0 20K 20
0
-15 -20
0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
4 (c) 150 (d)
25KK CeRhAl4Si2 2K CeIrAl4Si2
3 8K 5K T = 2K
%) 2 112050KKK %) 100 11820KKK JH / // /[ [010010]]
MR ( 1 H J //// [[010010]] MR ( 50 1250KK
0
0
-1
0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
6 (e) 60 (f)
5 25KK CeRhAl4Si2 CeI r2AKl4Si2 HJ / // /[ [100100]]
8K 5K
%) 4 1105KK %) 40 180KK
R ( 3 20K R ( 1125KK
M J // [100] M 20K
2 H // [010] 20

1
0 0
0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14
Magnetic Field (Tesla) Magnetic Field (Tesla)
FIG.7: (Coloronline)TemperaturedependenceofMR(H)inCeRhAl Si andCeIrAl Si . Thedatain(c)and(e)arelooking
4 2 4 2
scattered due to the relatively smaller values of the MR.
the conduction electrons leading to a negative MR. Ac- are 35.26 and 13.53 µΩcm for J (cid:107) [100]; the ratio de-
cording to Zlatic’s model, which is based on the single creases with increasing temperature. Therefore, it is ex-
center scattering picture, the MR has a negative mini- pected that the positive cyclotron MR at 2 K will be
mumatnearlyT =T /2,changessignataroundT /2π roughly nine times larger in CeIrAl Si . We speculate
K K 4 2
and has a positive maximum at T = 0 K16. Taking a that may be the reason why the MR remains positive in
T of nearly 10 K for CeRhAl Si (vide infra) the neg- the Ir-analogue at high fields while it is negative in the
K 4 2
ative minimum due to Kondo interaction should occur Rh-analogue.
around 5 K. In CeIrAl Si with a lower T , the negative
4 2 K
minimum should occur at even lower temperature. The The sharp upturn in the MR at spin flop and the as-
MRispositiveatthesetemperaturesindicatingthatthe sociated hysteresis shift to lower fields as the tempera-
contributionduetotheeffectofmagneticfieldonthean- ture is increased (Figs. 7 (a) and 7 (b)). The relatively
tiferromagnetic state to MR is dominant. The negative sharp peak in the MR at 2 K increasingly broadens at
MR of CeRhAl Si above 6 T may have a contribution higher temperatures, mimicking qualitatively the broad-
4 2
from the Kondo interaction while it would be relatively ened spin-flop region as the temperature is increased (cf
far lower in CeIrAl Si . As regards the positive contri- Figs. 2a and 2b). Above the spin flop, qualitatively the
4 2
bution from the cyclotron motion of the electrons, in a MR shows a similar field and temperature dependence
simple two-band model17 the MR is proportional to B2 intwocompounds. AsmentionedabovetheKondoscat-
where B is the field and inversely proportional to ρ(0)2. tering of the conduction electrons should be partially
The resistivities of CeRhAl Si and CeIrAl Si at 2 K quenched in a magnetic field leading to negative MR.
4 2 4 2
The effect is maximum close to T /2 and decreases as
K
10
the temperature is increased. It may be noted that at 4, two peaks shift to lower temperatures in 5 T and they
6 and 10 K the MR in CeRhAl Si in a limited range virtuallydisappearin8Tabovethespin-flopfieldwhere
4 2
above 6 T becomes less negative than its corresponding the field induces a saturated paramagnetic state.
values at 2 K. A negative contribution from the Kondo TheheatcapacitydataofLaanalogistypicalofanon-
interactionthatdecreasesasthetemperatureisincreased magnetic reference compound. The plots of C/T vs. T2
above T may explain this. As the Kondo interaction is below5KforthetwoLa-compounds(notshown)arelin-
K
relatively weaker in the Ir-analogue, its contribution to earandafitofthestandardexpressionC/T = γ+βT2,
MRisnotsignificantenoughtocauseasimilarbehaviour where γ and β are the electronic and phononic part of
in CeIrAl Si . Possible differences in the positive MR the heat capacity, furnishes the following values, γ = 8.7
4 2
due to the cyclotron motion of the conduction electrons and 8.0 mJ/mol K2, β = 0.22 and 0.21 mJ/mol K4 for
between the two compounds decrease with the increase the Rh and Ir compounds, respectively. Our values of γ
of temperature. In the paramagnetic region the applied and β are comparable with those reported in ref. 9. The
fieldwilltendtosuppressresidualspinfluctuationslead- 4f-derived entropy S was calculated by the following
4f
ing to a negative MR as observed at 15 and 20 K in relation:
CeRhAl Si . Clearly several competing mechanisms are
4 2 (cid:90) C
contributing to MR which have slightly different com- S = 4fdT (1)
parative energy scales in the two compounds. 4f T
The MR in CeRhAl Si at selected temperatures, for
4 2 whereC wasobtainedbysubtractingtheheatcapacity
fieldsappliedintheab-plane,i.e. along[100]and[010]is 4f
of the La-analog from the corresponding Ce-compound
qualitatively similar for current density parallel to [001]
and making the usual assumption of lattice heat capac-
and [100], respectively (see, Figs. 7c and 7e). A rela-
itybeingidenticalfortheisotypicLaandCecompounds.
tively sharp upturn in MR is seen at 5 and 8 K around
Only64%(72%)ofentropyS foradoubletgroundstate
∼12and∼6T,respectively,whichismostlikelyarising 4f
with effective spin 1/2 (i.e. Rln2) is released up to T
from changes in the spin reorientation. In CeIrAl Si ,for N1
4 2 for CeRh(Ir)Al Si indicating the presence of Kondo in-
J (cid:107) [001] and H (cid:107) [100], we observe two steps with hys- 4 2
teraction in these materials, assuming insignificant short
teresis at 8 K which correlate well with the data shown
rangeorderaboveT . Theentropycorrespondingtofull
in the inset of (Fig. 2(d). A single step with hystere- N1
doublet ground state is recovered at temperature ∼32 K
sis is seen in the 10 K data; however no corresponding
(31 K).
anomaly is clearly seen in the magnetization. The MR
The Kondo behavior of resistivity together with the re-
in CeIrAl Si for J (cid:107) [100] and H (cid:107) [010] also shows
4 2 duced value of entropy at the magnetic transition tem-
some peculiar features. A field induced hysteresis ap-
perature T imply a partial quenching of the 4f-derived
pearsat5Karound 13T,whichsplitsintotwoat8and m
Ce magnetic moment by the Kondo interaction. In such
10 K at lower fields but vanishes again at 12 K. It may
cases the degeneracy of the ground state doublet is par-
be noted that the ratios of resistivities of the Rh and Ir
tiallyremovedbytheKondoeffect,andithasbeenshown
compounds at 2, 10 and 20 K for J parallel to [001] are
thatS (T )=S (T /T ),whereS istheentropyas-
nearly 6, 2.4 and 1.2, respectively. As mentioned above 4f m K m K 4f
sociated with the magnetic ordering and S is the en-
thepositiveMRduetothecyclotronmotionisexpected K
tropy at T due to the Kondo effect with the Kondo
to be much larger in the Ir analogue, particularly at low m
temperature of T 18. The specific heat and the entropy
temperatures. K
as a function of T/T for a spin 1/2 Kondo impurity is
K
known19, and the ratio T /T can be determined using
m K
thevalueofS . Usingthisprocedurewegetasingle-ion
4f
E. Heat Capacity Kondo temperature T of 14 and 10 K in CeRhAl Si
K 4 2
and CeIrAl Si , respectively. On the other hand if T is
4 2 m
TheheatcapacityofCeRh(Ir)Al Si wasmeasuredbe- takenasthetemperatureatwhichtheupturnintheheat
4 2
tween100mKand150Ktogainmoreinformationabout capacity begins than T of 12.3 and 7.7 K are obtained.
K
the magnetically ordered Kondo lattice state such as the Wewouldliketoemphasizethatthisproceduresassumes
entropy associated with the magnetic ordering, values of negligible short range order above the magnetic transi-
the coefficient of the linear term in the electronic heat tion and may therefore overestimate the Kondo temper-
capacity γ, which is proportional to enhanced electron ature. The Kondo temperature of a lattice is believed to
effective mass, and Kondo temperature. The heat ca- be lower than its value for a single impurity. The simple
pacity of nonmagnetic analogs LaRh(Ir)Al Si was also analysis presented here supports the picture of two mag-
4 2
measured between 2 and 150 K. The data are plotted in neticallyorderedcompoundswitharesidualweakKondo
Fig. 8. The heat capacity clearly exhibits two peaks in interactionwithaKondotemperaturelowerorcompara-
bothceriumcompounds(Figs.8(a)and8(b))confirming ble (in the case of Rh-analog) to the magnetic ordering
the occurrence of two bulk phase transitions. The peak temperature. It may also be noticed that the T of the
K
temperaturesareoverallingoodagreementwiththecor- Ir compound is lower than that of the Rh analog. This
responding peaks in the susceptibility. For CeIrAl Si suggestslargerelectroncorrelationeffectinCeRhAl Si ,
4 2 4 2
the heat capacity was also measured in 5 and 8 T. The which is amply confirmed by the low temperature heat