Relevance of ferromagnetic correlations for the Electron Spin Resonance in Kondo lattice systems

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by  Cornelius Krellner

Relevance of ferromagnetic correlations for the Electron Spin Resonance in Kondo
lattice systems
C. Krellner, T. F¨orster, H. Jeevan, C. Geibel, and J. Sichelschmidt
Max Planck Institute for Chemical Physics of Solids, D-01187 Dresden, Germany
(Dated: February 2, 2008)
ElectronSpinResonance(ESR)measurementsoftheferromagneticKondolatticesystemCeRuPO
showawelldefinedESRsignalwhichisrelatedtothemagneticpropertiesoftheCe3+ moment. In
contrast, noESRsignal could beobserved in theantiferromagnetic homologue CeOsPO. Addition-
ally, we detect an ESR signal in a further ferromagnetic Yb compound, YbRh,while it was absent
in a number of Ce or Yb intermetallic compounds with dominant antiferromagnetic exchange, in-
8
dependentlyof thepresenceof astrong Kondointeraction or theproximitytoa (quantum)critical
0
point. Thus,theobservationofanESRsignalinaKondolatticeisneitherspecifictoYbnortothe
0
proximity of a quantum critical point, but seems to be connected to the presence of ferromagnetic
2
fluctuations. These conclusions not only provide a basic concept to understand the ESR in Kondo
n lattice systems even well below the Kondo temperature as observed in the heavy fermion metal
a
J YbRh2Si2 but point out ESR as a prime method to investigate directly the spin dynamics of the
Kondoion.
8
PACSnumbers: 71.27.+a,75.20.Hr,76.30.-v

]
l
e
- Heavy fermion intermetallic compounds with concen- now, no results or arguments allowing a discrimination
r
t trated4f-and5f-ionsshownoElectronSpinResonance between these scenarios were reported. Thus, the origin
s
. (ESR) signal. This common belief was experimentally for the observability of the ESR signal in the these two
t
a wellestablishedandwasjustifiedbythestrongelectronic compounds remained a mystery.
m correlations which arise from the hybridization between Recently, we have shown the CeTPO (T=Ru, Os) com-
- 4f- or 5f-electrons and conduction electrons. An ESR pound series to be an interesting class of Ce-based
d
investigation of the Kondo ions’ spin dynamics seemed Kondolattice systems atthe borderbetweenintermetal-
n
onlyto be possibleindirectly by additionallydopedESR lic and oxide materials, presenting a layered structure
o
c probespins,usuallyGd3+ [1,2],analogoustothe princi- and strong tendency to ferromagnetism.[9] For CeRuPO
[ pleofNMRinthesesystems. However,the denseKondo apronounceddecreaseoftheelectricalresistivityattem-

1 lattice systems YbRh2Si2 and YbIr2Si2 pose a remark- peratures below 50 K indicates the onset of coherent
v able exception. They exhibit an ESR signal with clear Kondo scattering which is confirmed by an enhanced
1 propertiesoflocalYb3+ momentsand,mostsurprisingly, thermopower. ThereferencecompoundLaRuPOneither
9 thesignalisobservablebelowtheKondotemperatureTK shows signatures of the Kondo effect nor of magnetism
1 wherethelocalYb3+ momentsbecomescreenedbecause of the Ru atoms.[9] The temperature and magnetic field
1
of pronounced Kondo interactions.[3, 4] As both com- dependence of magnetic susceptibility and specific heat
.
1 poundsarelocatedveryclosetoaquantumcriticalpoint evidence ferromagnetic (FM) order at TC = 15K. Thus,
0
8 [5, 6] the ESR signal was initially thought to be a direct CeRuPO (TK ≃ 10K) seems to be a rare example of
verificationofthe localizedmomentscenarioofquantum a f-electron based FM Kondo lattice [9], along further
0
: criticality [3]. However, the consequences of this signal d-electron based Kondo lattice systems [10]. In con-
v
forunderstandingthephysicsclosetoaquantumcritical trast, CeOsPO shows antiferromagnetic (AFM) order at
i
X pointinparticularorfortheKondoionphysicsingeneral TN =4.4K,despiteonlyminorchangesinlatticeparam-
r remained unclear. A plausible explanation would be the eters and electronic configuration. Therefore, CeRuPO
a
inherent difference between Yb- and Ce- based Kondo and CeOsPO are ideally suited to study the difference
lattices, the former one presenting a much stronger lo- between FM and AFM Kondo lattices. We present ESR
cal character allowing for a narrow observable ESR line. results on these new Ce-based systems and discuss the
Another mechanism could be based on the presence of ESR of further Ce- or Yb- based compounds with ei-
ferromagneticfluctuations,sinceYbRh2Si2 andYbIr2Si2 ther ferro- or antiferromagnetic exchange and different
seem to be unique cases of Kondo lattice systems close strength of the Kondo interaction. The results demon-
to a criticalpoint with strong ferromagneticfluctuations strate that the above mentioned unexpected ESR obser-
anda concomitantstronglyenhancedspinsusceptibility. vationinheavyfermionmetalsisrestrictedneithertoYb-
Such a scenario is supported by previous ESR reports based compounds nor to compounds close to a quantum
about how exchange enhanced spin susceptibility leads critical point, nor to compounds with a strong Kondo
to a reduced ESR line broadening [7] compared to the interaction. Instead, they indicate that the observability
line broadening in simple ferromagnetic systems like Fe of the ESR signal in a dense Kondo lattice is connected
or Ni [8] in their paramagnetic regime. However, until withthepresenceofFMcorrelationsbetweentheKondo
2
cation. The different nature of magnetic correlations in
CeRuPO and CeOsPO seems to be the only difference
whichis relevantfor the ESRobservation. In fact, many
oftheirpropertiesaresimilar: thepreparationmethodis
identical, the lattice parameters are very close, and the
disorder effect on the electrical resistivity is comparable.
Thedashedline inFig.1fits the CeRuPOspectrumwith
a metallic Lorentzian line shape (including the effects of
the counter rotating component of the linearly polarized
microwavefield). Theobservedasymmetryofthelinein-
dicates the metallic character of the sample powder and
reflectsa penetrationdepth being smallerthanthe grain
size [11].
Fig. 2 shows the temperature dependence of the ESR
spectra which is distinctly different for temperatures
FIG. 1: ESR spectra of polycrystalline samples of CeRuPO above and below TC. This difference indicates that the
(TC = 15 K) and CeOsPO (TN = 4.4 K). Dashed line repre- observed ESR reflects the bulk magnetic properties of
sentsafittothedatawithametallicLorentzianlineshapeat CeRuPO.Above TC, the resonancefield is strongly tem-
g=2.6. Spectra were taken with same instrument settings. perature dependent and varies between 310 mT at 15 K
and210mTat24K.Withdecreasingtemperature,when
entering the FM phase, the ESR signal splits into a low
ions. field (LF) and high field (HF) component. Both show a
We used polycrystalline samples of CeTPO (T=Ru, Os) pronounced temperature dependence of their resonance
whose preparation and characterization was described fields BrLeFs,HF(T) which shift in opposite directions. The
in Ref.[9]. X-ray powder diffraction and energy dis- decrease of BrLeFs(T) with decreasing temperature reflects
persive X-ray measurements confirmed the formation of thedevelopinginternalmagneticfieldsbecauseoftheon-
single phase CeTPO. The tetragonal crystal structure setofFMorder. TheHFcomponentismuchlessintense
(P4/nmm)contains alternatinglayersof OCe4 and TP4 and gets visible below ≈13 K (see dashed line fit in Fig.
tetrahedra. Itisworthtopointoutthatdespitethepres- 2). BrHeFs(T) shifts to higher fields with decreasing tem-
ence of oxygen the compounds show pronounced metal- perature,continuingthetemperaturebehavioroftheres-
lic properties with a residual resistivity ρ0 = 1.5µΩcm onancefield atT >TC. This is unusual,since one would
for CeRuPO. ESR probes the absorbed power P of a notexpecttheresonancefieldtoincreasewhenapproach-
transversal magnetic microwave field as a function of an ingandenteringtheFMorderedstate. Insteaditshould
external, static magnetic field B. To improve the signal- inverselyfollowthe temperaturedependence ofthe mag-
to-noiseratio,weusedalock-intechniquebymodulating netization (taken at the ESR X-band field) [12]. Mag-
the static field, which yields the derivative of the res- netization and preliminary ESR results on a CeRuPO
onance signal dP/dB. The ESR experiments were per- singlecrystalshowthatthisunusualtemperaturedepen-
formedatX-bandfrequencies(ν ≈9.4GHz)andattem- dence is due to a complex anisotropy,with the single ion
peratures between 5 K≤T ≤ 125K. The measuredESR anisotropybeingoppositetotheexchangeanisotropy.[13]
spectracouldbefittedwithaLorentzianlineshape. Here A detailed ESR study is going on and shallbe presented
wediscuss the lineshapeparameterslinewidth (∆B) and in a dedicated forthcoming paper.[14] In the paramag-
resonancefield(Bres)which determines aneffective ESR netic regime, at T = 20 K, the resonance field corre-
g-factor (g = hν/µBBres). In case of a local ESR spin sponds to an effective ESR g factor of 2.6. This value is
probe in a metallic environment ∆B measures the spin- close to the expected value from the Γ6 wavefunction of
spin relaxationrate of the local spin, whereas g is deter- a Ce3+ ion (J =5/2) in tetragonal point symmetry.
mined both by the magnitude of the local moment and TothebestofourknowledgeanESRsignalduetodense
the static magnetic field at the spin site. Ce3+ magneticmomentsinanenvironmentwithconduc-
Fig. 1 shows the main result of our ESR measurements tion electrons has only been reported for the Kramers
on CeTPO (T=Ru, Os) at temperatures just above the salt CeP [15]. There the Ce3+ resonance originates from
respective magnetic ordering. The ESR investigationsof transitions within the excited Γ8 quartet. Note, that al-
both compounds were performed with the same instru- thoughCePshowsAFMcorrelationswithananomalyin
ment parameters and almost the same sample masses. magnetic susceptibility at TN ≃9 K FM interactions are
For CeRuPO, which shows FM correlations, a well de- indicated by a positive Weiss temperature. This is also
fined and intense ESR signal could easily be observed reflectedintheCurie-WeissbehavioroftheESRg factor
whereas the AFM correlatedCeOsPO is absolutely ESR with a positive Weiss temperature. Several ESR investi-
silent, even when using the largest instrument amplifi- gationsofdilutedCe3+ inmetalshavebeenperformedin
3
passingTCistypicalfortheonsetofmagneticorderingof
theESRprobespins: thespinfluctuationtimeincreases,
CeRuPO theexchangenarrowingmechanismgetslesseffectiveand
inhomogeneous broadening gains influence, leading to a
4.5 K
strong increase of the linewidth. The relatively sudden
8.5 K
linewidth increase immediately below TC indicates that
9.5 K
the effect of atomic disorder or short range magnetic
order is negligible for the ESR linewidth. A broaden-
11.5 K ing which occurs already at temperatures far above TC
s) was attributed to effects of atomic disorder in various
nit 12.5 K rare earth containing FM intermetallic compounds [12].
u
B (arb. B0 (.T5) TC tThheerinefvoerset,igtahteedobCseeRrvuePdO∆sBa(mTp)lebeishaavifoerrrionmdaicganteetswthitaht
d 13.5 K a high grade of homogeneity.
P / At temperatures above TC, ∆B(T) reflects the typical
d
0.0 ESR behavior of a magnetic moment in a metallic host
15 20
T (K) [19]. ∆B(T) increases linearly with ≃ 10 mT/K in a
14.5 K small region up to ≈ 18 K whereas at higher tempera-
tures an exponential increase dominates. A small ampli-
15.5 K
tudeandalargelinewidthmakesthesignalundetectable
forT >∼24K.Averysimilarbehaviorof∆B(T)isfound
17.5 K for diluted Ce3+ in cubic LaAs, for instance [18].
20 K Our comparison of the ESR properties of CeTPO
(T=Ru,Os)providesafirstevidenceforaconnectionbe-
0.0 0.4 0.8 1.2 1.6
tweenthe observabilityof the ESRline andthe presence
B (T)
of ferromagnetic correlations. We obtained more exper-
imental arguments for this conclusion by investigating
FIG.2: ESRspectraofpowdersamplesofCeRuPObelowand furtherYborCe basedintermetalliccompoundswithei-
above TC =15 K. Dotted lines represent metallic Lorentzian ther FM or AFM correlations and different strength of
line fits. Below TC a low field and a high field component the Kondo interaction (see Tab. I). Besides the posi-
of the ESR line develops as shown with two Lorentzian lines
(dashedline). Inset: T-dependenceoftheESRlinewidth∆B tiveESRobservationsinYbRh2Si2andYbIr2Si2(I-type)
(squares). Theopen circles refer to thehigh field component [3, 4] which both exhibit strong FM correlations (as in-
which appears below TC. dicated, e.g., by an enhanced Sommerfeld-Wilson ratio)
[6, 23] we found an ESR signal in yet another Yb-based
compound with FM correlations, YbRh. However, in
thecubicmonopnictideswithaΓ7groundstatemultiplet contrast to both above mentioned heavy fermion com-
[16, 18]. It turned out that Ce3+ ESRis hardto observe pounds, Kondo-type features are neither found in the
because ofasmallΓ7−Γ8 splitting andthe concomitant electricalresistivitynorinthespecificheatofYbRh. FM
large linewidth contribution from the excited CEF level. order of Yb3+ magnetic moments below TC = 1.2 K is
The inset of Fig.2 shows the temperature dependence confirmed by magnetic susceptibility and magnetization
of the linewidth below TC (solid symbols: LF compo- measurementsaswellasbythefielddependenceoftheor-
nent; open circles: HF component) and above TC where dering temperature. [17] We investigatedpolycrystalline
only one single, well defined line (see line-fit in Fig.1) YbRh (CsCl structure) and observed a clean and well
could be observed. Within the temperature range where defined ESR signal within our accessible temperature
theHFcomponentcanbeobserveditslinewidthchanges range 3-30 K. The linewidth (minimum ∆B = 220 mT
only weakly whereas the linewidth of the LF component at T = 3 K) shows a temperature dependence typical
showsanextremebroadeningtowardslowtemperatures. for local moments in metals. The ESR g-value reaches a
We therefore suspect that the two components refer to constantvalue of 2.55 for T ≥10 K which is comparable
different in-plane and out-of-plane magnetic properties to the g-values for Yb3+ in cubic monopnictides [18].
ofCeRuPO.ThisanisotropybecomesapparentbelowTC We looked for an ESR line in further Ce- and Yb-based
andthustheESRsignalofpolycrystallinesamplessplits. compounds, with different strength of the Kondo inter-
Within the FM phase no hysteresis effects could be ob- action, but all with dominant antiferromagnetic correla-
servedinthe ESRspectra. This absenceis probablydue tions. Although the measurements were performed on
to the weakness of the hysteresis effect in magnetization high quality single crystals in a wide temperature range
measurements at 2 K of oriented powder [9]. around TK and / or the magnetic ordering temperature,
ThestronglinewidthincreaseoftheLFcomponentwhen wedidnotobserveanESRsignalinanyofthesesystems
4
TABLE I: Intermetallic compounds with predominating AFM or FM spin correlations investigated by X-band ESR.”Kondo”
denotes a Kondolattice behavior in ρ(T) or otherproperties.
Compound AFM FM Kondo ESR signal
CeRuPO - X X Yes
CeOsPO X - X No
YbRh - X - Yes
YbRh2Si2 [20] - X X Yes[3]
YbIr2Si2 (I-type)[6] - X X Yes[4]
YbIr2Si2 (P-type) [6] X - X No
Yb4Rh7Ge6 [21] X - - No
YbNi2B2C [22] X - X No
CeCu2Si2 (S/A) X - X No
CeNi2Ge2 X - X No
CeCu6−xAux (x=0,0.1) X - X No
(see Tab. I). P-type tetragonal YbIr2Si2 [6] and cu- relaxation framework may apply as indicated from ESR
bic Yb4Rh7Ge6 [21], which both have been grown from experiments on Yb1−xLaxRh2Si2.[29]
In-flux as YbRh2Si2, display AFM ordering and exhibit We conclude that a substantial amount of experimen-
more stable Yb3+ moments than YbRh2Si2 (because of tal data indicates the importance of strong FM corre-
a weaker Kondo interaction). CeCu2Si2 (S/A type), lations among the ESR probed magnetic moments for
CeNi2Ge2 and CeCu6−xAux (x=0, 0.1) are three well the observability of an ESR signal in Kondo lattice sys-
established heavy fermion systems close to a quantum tems in general. This conjecture is most strongly sup-
critical point. However, the former two are expected to ported by the presence of an ESR signal in CeRuPO
presentaspindensitywavecriticalpoint,whilethelatter onlysincethedominantmagneticinteractionisswitched
is suspected to present a local quantum critical point. from AF (CeOsPO) to FM (CeRuPO) while keeping
Our results demonstrate that the observability of the structural properties and disorder effects practically un-
ESR line in a dense Kondo lattice system is neither con- changed. These results not only provide a firm exper-
nected with specific properties of Yb or Ce, nor to the imental basis for the understanding of the unexpected
strength of the Kondo interaction, nor to the proxim- ESRline inYbRh2Si2 [3]andYbIr2Si2 [4], butmoreim-
ity of a (quantum) critical point (and thus also not to portantly establish ESR as a new experimental tool for
the character of the critical point). In contrast, these adirectstudy ofthe Kondoionindense Kondosystems.
results give a strong evidence for the importance of fer- Since NMR and NQR cannot be performed on Ce and
romagnetic correlations for the narrowing of the ESR were yet not successful on Yb systems with strong mag-
line. This conclusion bears a strong analogy to the sit- netic correlations, our results establish ESR as a unique
uation in itinerant transition metal compounds. Itiner- localprobeforadirectinvestigationofthespindynamics
ant d-systems with FM correlations may show a strong oftheKondoion. ThestandardESRtechnique(X-band)
enhancement of their conduction electron susceptibil- is especially qualified for this purpose because the mag-
ity. This enhancement leads to an enhanced shift of netic field (≪ 1 T) is small enough to leave the Kondo
the ESR g-value as well as a reduced Korringa broad- stateundisturbed. Preliminaryinvestigationsonthefield
ening of the linewidth [7]. As a consequence an ESR and temperature dependence of the ESR response in
signal may even be observed from the conduction elec- YbRh2Si2 evidence e.g. a correlationbetween the evolu-
trons in the form of a collective conduction spin ESR tion of the g-factor and the evolution of thermodynamic
(CESR) with a linewidth which is narrowedby electron- properties [30]. Such investigations should give a deeper
electron exchange interactions.[25] Various examples of insight in the way the heavy quasiparticles are formed
CESR in enhanced spin-susceptibility metals have been upon lowering the temperature or the field.
reported: Pd [26] and TiBe2 [27] which both show en- We would like to thank J. Ferstl, M. Deppe, and O.
hanced Sommerfeld-Wilson ratios, and the weak itiner- Stockert for providing us single crystals of Yb4Rh7Ge6,
antferromagnetZrZn2[28]. However,wearenotawareof CeNi2Ge2, and CeCu6−xAux (x=0, 0.1), respectively.
anyexampleofastronglyanisotropicCESRandananal-
ogy to the ESR in Kondo lattice systems is not straight-
forward. Phenomenologically, the anisotropy may arise
fromthestrongcouplingbetweenthelocalmagneticmo-
ments andthe conductionelectronswhile a”bottleneck”
5
[15] C. Huang, K. Sugawara, and B. Cooper, in Int. Conf.
on Crystal Field Effects in Metals and Alloys, (Plenum
Press, New York,London, 1976), pp. 51–60.
[1] B. Elschner and A. Loidl, in Handbook on the Physics [16] K. Sugawara and C. Huang, J. Phys. Soc. Jap. 40, 295
andChemistryofRareEarths24,(ElsevierScienceB.V., (1976).
Amsterdam, 1997), Chap. 162. [17] H. Jeevan et al.,to be published.
[2] H.-A.KrugvonNidda,M.Heinrich, andA.Loidl, in Re- [18] K. H. Wienand, B. Elschner, and F. Steglich, J. Magn.
laxation phenomena, (Springer, 2003), Chap. 2.2. Magn. Mat. 28, 234 (1982).
[3] J. Sichelschmidt, V. Ivanshin, J. Ferstl, C. Geibel, and [19] S. Barnes, Adv.Phys.20, 801 (1981).
F. Steglich, Phys. Rev.Lett. 91, 156401 (2003). [20] O. Trovarelli, C. Geibel, S. Mederle, C. Langhammer,
[4] J. Sichelschmidt, J. Wykhoff, H.-A. K. von Nidda, I. I. F. M. Grosche, P. Gegenwart, M. Lang, G. Sparn, and
Fazlishanov, Z. Hossain, C. Krellner, C. Geibel, and F. Steglich, Phys.Rev. Lett. 85, 626 (2000).
F. Steglich, J. Phys. Condens. Matter 19, 16211 (2007). [21] J.Ferstl,F.Weickert,andC.Geibel,J.Magn.Mag.Mat.
[5] P. Gegenwart, J. Custers, C. Geibel, K. Neumaier, 272-276, E71 (2004).
T. Tayama, K. Tenya, O. Trovarelli, and F. Steglich, [22] P. Bonville, J. Hodges, Z. Hossain, R. Nagarajan,
Phys.Rev.Lett. 89, 056402 (2002). S.Dhar,L.Gupta,E.Alleno,andC.Godart,Eur.Phys.
[6] Z.Hossain, C.Geibel, F.Weickert,T.Radu,Y.Tokiwa, J. B 11, 377 (1999).
H. Jeevan, P. Gegenwart, and F. Steglich, Phys. Rev. B [23] P. Gegenwart, J. Custers, Y. Tokiwa, C. Geibel, and
72, 094411 (2005). F. Steglich, Phys.Rev. Lett. 94, 076402 (2005).
[7] M. Peter, J. Dupraz, and H. Cottet, Helv. Phys. Acta [24] P. Gegenwart, J. Custers, T. Tayama, K. Tenya,
40, 301 (1967). C. Geibel, G. Sparn,N. Harrison, P.Kerschl, D. Eckert,
[8] B.R.CooperandF.Keffer,Phys.Rev.125,896(1962). K.-H. Muller, et al., J. Low Temp. Phys. 133, 3 (2003).
[9] C.Krellner,N.S.Kini,E.Bru¨ning,K.Koch,H.Rosner, [25] D. R. Fredkin and R. Freedman, Phys. Rev. Lett. 29,
M.Nicklas,M.Baenitz,andC.Geibel,Phys.Rev.B76, 1390 (1972).
104418 (2007). [26] P. Monod, J. Phys. Colloque C6 C6, 1472 (1978).
[10] K.S. Burch et al., Phys. Rev. Lett. 95, 046401 (2005); [27] D.Shaltiel,D.Ioshpe,A.Grayevsky,V.Zevin,andJ.L.
S. Kondo et al., Phys. Rev. Lett. 78, 3729 (1997); K. Smith, Phys.Rev. B 36, 4090 (1987).
Miyoshi et al., Phys. Rev. B 69, 132412 (2004); J.W. [28] W. M. Walsh, G. S. Knapp, J. L. W. Rupp, and P. H.
Allen et al.,Phys.Rev.B 41, 9013 (1990). Schmidt, J. Appl.Phys. 41, 1081 (1970).
[11] G. Feherand A.F. Kip, Phys.Rev. 98, 337 (1955).
[29] J. Wykhoff, J. Sichelschmidt, J. Ferstl, C. Krellner,
[12] R. H. Taylor and B. R. Coles, J. Phys. F: Met. Phys. 5,
C. Geibel, F. Steglich, I. Fazlishanov, and H.-A. Krug
121 (1975). von Nidda,Physica C 460-462, 686 (2007).
[13] C. Krellner and C. Geibel, J. Crystal Growth (2007),
[30] High field ESR experiments of YbRh2Si2 are presently
doi:10.1016/j.jcrysgro.2007.10.045.
underway.
[14] T. F¨orster et al.,to bepublished.