Electron Spin Resonance of the Yb 4f moment in Yb(Rh1-xCox)2Si2

1.8 MB·English

by  T. Gruner

Electron Spin Resonance of the Yb 4f moment in Yb(Rh Co ) Si
1−x x 2 2
T. Gruner, J. Sichelschmidt,∗ C. Klingner, C. Krellner, C. Geibel, and F. Steglich
Max Planck Institute for Chemical Physics of Solids, D-01187 Dresden, Germany∗
(Dated: January 25, 2012)
TheevolutionofspindynamicsfromthequantumcriticalsystemYbRh Si tothestabletrivalent
2 2
Yb system YbCo Si was investigated by Electron Spin Resonance (ESR) spectroscopy. While the
2 2
Kondotemperaturechangesbyoneorderofmagnitude,allcompositionsofthesinglecrystallinese-
riesYb(Rh Co ) Si showwelldefinedESRspectrawithaclearYb3+characterfortemperatures
1−x x 2 2
below≈20K.WithincreasingCo-contenttheESRg-factoralongthec-directionstronglyincreases
indicating a continuous change of the ground state wave function and, thus, a continuous change
2
ofthecrystalelectricfield. ThelinewidthpresentsacomplexdependenceontheCo-contentandis
1
0 discussed in terms of the Co-doping dependence of the Kondo interaction, the magnetic anisotropy
2 andtheinfluenceofferromagneticcorrelationsbetweenthe4f states. Theresultsprovideevidence
that,forlowCo-doping,theKondointeractionallowsnarrowESRspectradespitethepresenceofa
n
large magnetic anisotropy, whereas at high Co-concentrations, the linewidth is controlled by ferro-
a
magneticcorrelations. Apronouncedbroadeningduetocriticalcorrelationsatlowtemperaturesis
J
only observed at the highest Co-content. This might be related to the presence of incommensurate
4
magnetic fluctuations. [published in Phys. Rev. B 85, 035119 (2012)]
2

PACSnumbers: 76.30.Kg;75.20.Hr;71.27.+a;75.30.Gw
]
l
e
-
r I. INTRODUCTION fined crystal electric field (CEF) levels was evidenced by
t susceptibility14, M¨oßbauer results15, inelastic neutron-
s
. scattering experiments16, specific heat measurements17
t
a The heavy fermion metal YbRh2Si2 shows thermo- as well as by photoemission spectroscopy11. The Co-
m dynamic and transport properties which, at low tem- ion itself remains non-magnetic because of a strong Co-
- peratures, are determined by the hybridization of 4f Si hybridization.14 In the magnetically ordered state
d states and conduction electrons resulting in a Kondo of YbCo Si a complex magnetic phase diagram with
n interaction with a single-ion Kondo temperature TK (cid:39) significan2t b2asal-plane anisotropy is evidenced by the
o 25 K.1,2 Besides its quite remarkable magnetic behav- magnetoresistance12 and magnetization data18. Pow-
c
[ iors, like weak antiferromagnetic (AFM) order below der neutron diffraction revealed a complex magnetic
TN =72mK,afieldinducedAFMquantumcriticalpoint structure with two phases with different propagation
1 at Bc = 60 mT, and a highly enhanced Sommerfeld- vectors.19 A first-order phase transition from an in-
v Wilson ratio,1 the existence of a well-defined Electron commensurable arrangement of moments below T into
2 N
2 Spin Resonance (ESR) signal at temperatures below TK a commensurable one below TL = 0.9K < TN was
0 with pronounced Yb3+ Kondo-ion character triggered identified.13 For YbRh Si the stronger 4f-conduction
2 2
5 newtheoreticalstudiesofthedynamicalpropertiesoflo- electron hybridization leads to a small deviation of the
1. calanditinerantmagnetisminKondolatticesystems.3–6 valency from the trivalent state. Photoemission spec-
0 In these theories the origin of the resonance was inti- troscopy results suggested a mean valency of ∼ 2.9.20
2 mately connected to the Kondo interaction and strong Yet, the magnetic structure of YbRh Si is not known
2 2
1 ferromagnetic correlations. The relevance of both ef- due to its very small ordered moment. Some hints could
v: fects were experimentally verified by ESR results on Lu- be obtained from the knowledge of the magnetic struc-
Xi udpiluontedCoYbdRophi2nSgi2(,x7 E≤SR0.1e8x)p,8eraimndentthseuEndSeRrporfetshsuerfeerarnod- tcuomrepionunYdbsCmo2aSgin2etsiicncsetruwcittuhrinesaanreisoofetelenctcrloonseiclysreerliaetsedof.
r magnetic Kondo lattice CeRuPO.9,10 In this paper we first present the ESR results of
a
RecentlythecompoundseriesYb(Rh1−xCox)2Si2wasin- YbCo2Si2 and analyze the data in the context of fur-
vestigated for the whole concentration range 0 ≤ x ≤ 1. ther experimental results. We continue with the series
Whereas the crystal structure remains tetragonal (space Yb(Rh Co ) Si where we found a sensitive depen-
1−x x 2 2
group I4/mmm) the magnetic, thermal, and transport dence of the ESR parameters on the Co -content.
propertiesshowclearvariationswithx:11–13itwasshown
that the Kondo interaction can largely be suppressed
by substituting Rh with the smaller isoelectronic Co
II. EXPERIMENTAL DETAILS
which, at the same time, enhances T and the size of
N
the ordered moment, thus stabilizing the AFM order by
suppressing the Kondo screening.11 For YbCo Si with For our ESR measurements we used clean In-flux
2 2
T = 1.7 K a stable trivalent Yb state with well de- grownsinglecrystalsofYb(Rh Co ) Si whichallhad
N 1−x x 2 2
2
their c-axis perpendicular to the main surface of the
platelet-shaped crystals. Thermal and magnetic proper- values g (5K) = 2.84±0.03 and g (5K) = 1.53±0.02
⊥ (cid:107)
ties as well as electrical resistivity have been thoroughly the intensity should vary by a factor of (g /g )2 = 3.4.
⊥ (cid:107)
investigated and were described elsewhere.11 The origin of this discrepancy which is even more pro-
ESR detects the absorbed power P of a magnetic mi- nounced in YbIr Si and YbRh Si 24 remains unclear.
2 2 2 2
crowave field b as a function of a transverse external The observed g-values nicely agree with the values ex-
mw
static magnetic field B. To improve the signal-to-noise
(cid:1)
ratio,alock-intechniqueisusedbymodulatingthestatic
fidPel/dd,Bw.hicThhyeieEldSsRthmeedaseurirveamtievnetsofwtehreerpeseorfnoarnmceedsiwgnitahl (cid:2)(cid:1) (cid:10)(cid:1)(cid:8)(cid:5)(cid:23)(cid:9)(cid:1)(cid:2) (cid:10)(cid:1)(cid:5)(cid:23)(cid:3) -factorg22..05 B ^(cid:1)c B(cid:2)(cid:1)(cid:1)(cid:12)(cid:10)(cid:12) c(cid:1)(cid:5)(cid:23)
R
a standard continuous wave spectrometer at X-band fre- ES1.5
quencies (ν ≈ 9.4GHz) by using a cylindrical resonator its) (cid:2)(cid:1)(cid:1)(cid:10)(cid:1)(cid:8)(cid:5)(cid:23)(cid:9)(cid:1)(cid:2) (cid:10)(cid:1)(cid:8)(cid:5)(cid:23)(cid:3) 0 45 90 13(cid:1)5(cid:1)(cid:2)(cid:18)(cid:19)(cid:20)(cid:4)1(cid:3)80
in TE012 mode or, for temperatures down to 1.5 K, a . un (cid:16)(cid:17)(cid:11)(cid:22) (cid:14)(cid:21)
split-ring resonator. The temperature was varied be- rb (cid:6) (cid:6)
tween 1.5K ≤ T ≤ 16K using 4He-flow-type cryostats. (a T (cid:1)(cid:10)(cid:1)(cid:7)(cid:13)
B
TheESRmeasurementsatQ-bandfrequencies(34GHz) /d
P
turned out to provide much less definite spectra. Their d (cid:2)(cid:1)(cid:1)(cid:10)(cid:1)(cid:5)(cid:23)(cid:9)(cid:1)(cid:2)(cid:1)(cid:10)(cid:1)(cid:5)(cid:23)(cid:3)
linewidths and g-factors are found to be comparable to
the X-band results regarding temperature dependencies
and absolute values. 0 .0 0 .2 0 .4 (cid:1) 0 .6 0 .8
B (cid:2)(cid:15)(cid:3)
All recorded ESR spectra were analyzed by fitting them
with a metallic Lorentzian line shape.21 From these fits
FIG.1: (coloronline)ESRspectraofYbCo Si atT =5Kfor
the following ESR parameters were extracted: linewidth 2 2
the field orientation B ⊥ c-axis (Θ = 90◦ and η-orientation
∆B (HWHM), the ESR g-factor (as given by the res-
ofthebasalplanetothemicrowavemagneticfield)andB(cid:107)c-
onance field B in the resonance condition hν =
res axis(Θ=0◦). SolidlinesindicateLorentzianlines(Θ=90◦:
gµB·Bres), the asymmetry parameter α (describing same resonance field and linewidth for η = 0◦,90◦). Inset
the dispersive contribution in metallic samples), and shows the Θ-dependence of the resonance-field-calculated g-
the intensity√(spin susceptibility, given by the area ∝ factorwithuniaxialbehaviorindicatedbythesolidline. Peak
amp·∆B2· α2+1 under the ESR absorption). at 0.325 T arises from background signals of the resonator.

III. EXPERIMENTAL RESULTS AND
3 .0
DISCUSSION r2 .5 B ^ c
to
c
YbT(Rheh1E−SxRCorxe)s2oSnia2n(cxe =fiel0d...d1i)spalapyrsonfoorutnhceedwahnoilseosteroripeys SR g-fa12 ..50 B || c
upon rotating the crystalline c-axis from parallel (Θ = E
1 .0
0fi◦e)ldt.owaTrhdisspceornpfiernmdiscutlhaer (lΘoca=l c9h0a◦r)acttoerthoefmthagenesitgic- 0 .5 T N Y b C o 2 S i2 B || c
nal and verifies a typical resonance feature of Yb-ions 0 .4
)
which are located on lattice sites with tetragonal point (T0 .3
symmetry.22,23 B(cid:1) B ^ c
0 .2
0 2 4 6 8 1 0 1 2 1 4 1 6
T (K )
A. YbCo Si
2 2
FIG. 2: (color online) Temperature dependence of linewidth
Fig.1 shows typical ESR spectra of YbCo Si for se-
2 2 ∆B and ESR g-factor of YbCo2Si2 above the antiferromag-
lected directions of the static magnetic field B (an- neticorderingtemperatureT forthefieldorientationB ⊥c-
N
gle Θ) and the microwave magnetic field bmw (angle axisandB(cid:107)c-axis. Dashedlinesing(T)showsthemeanfield
η). All spectra could be well described by a metal- expectationasdeducedfromχ(T). Here,alargercrystalthan
lic Lorentzian lineshape (solid line). Within experimen- the one of Fig. 1 was used, hence yielding stronger lines and
tal accuracy linewidth and resonance field remain un- a higher data accuracy.
changedifthec-axisisrotatedfromc⊥b (η =0◦)to
mw
c(cid:107)b (η = 90◦). Interestingly, in that case, the ESR pected from the saturation magnetization18: gm = 3.0
mw ⊥
intensity only varies by a factor of 1.5. This is not ex- (µ⊥ (cid:39) 1.5µB) and g(cid:107)m = 1.2 (µ(cid:107) (cid:39) 0.6µB). These g-
pected from the considerable uniaxial anisotropy shown factors can be well accounted for by a CEF model using
in the inserted graph for c ⊥ b : With the observed agroundstatedoubletwithaΓ symmetryandastrong
mw 7
3
Y b ( R h C o ) S i
1 -x x 2 2
mixing of |±3/2> and |∓5/2> wave functions.17 The
deviationsoftheESRg-valuesfromgm arepartlydueto
the pronounced temperature dependence of the g-values 1
as shown in Fig. 2. As a consequence of the anisotropic 0 .6 8
) 0 .5 8
interactions between the Yb-ions the internal magnetic its 0 .3 8
n
field leads to a temperature dependent shift of the res- . u
rb 0 .2 1 5
onance fields. This can reasonably be described by a (a
molecular field model25,26 /dB 0 .1 8
P
d
(cid:18) θ(cid:107)−θ⊥(cid:19)12 0 .0 7
g (T) = g0 · 1− (1) 0 .0 3
⊥ ⊥ (cid:18) θT(cid:107)−−θθ⊥⊥(cid:19) x = 0 T = B 2 .^7 Kc
g (T) = g0· 1+ (2)
(cid:107) (cid:107) T −θ(cid:107) 0 .0 0 .2 0 .4 0 .6
B (T )
as shown by the dashed lines in Fig. 2. Here, the
FIG.3: (coloronline)EvolutionoftheESRspectra(symbols,
Weiss temperatures θ⊥,(cid:107) are obtained by a Curie-Weiss
backgroundsubtracted)byvariationoftheCoconcentration
[χ = C/(T −θ)] plot of the susceptibilities χ⊥,(cid:107) below
for the field orientations B ⊥ c and b ⊥ c. Solid lines
T = 6 K measured at the resonance magnetic fields of mw
depict metallic Lorentzian line shapes.
0.46 T and 0.35 T for χ⊥ and χ(cid:107), respectively: θ⊥ =
(−2.1±0.2)K and θ(cid:107) = (−0.8±0.2)K. Furthermore
we used g0 = gm = 2.96 and g0 = gm = 1.2. Al-
⊥ ⊥ (cid:107) (cid:107)
though the dashed lines in Fig. 2 do not agree perfectly for T = 5 K. The anisotropy of both quantities reduces
withthedatathey,however,reflectthecorrecttendency. with increasing x. Note, that ∆B shows a narrowing
(cid:107)
Namely, towards low temperatures the g-values tend to with increasing Co-doping, providing evidence that the
merge each other which is a consequence of θ(cid:107) > θ⊥. relaxation due to disorder is not the dominant broad-
Note, in YbIr2Si2 θ(cid:107) < θ⊥ and thus we observed a mu- ening mechanism. The relaxation rate which is deter-
tual divergent behavior of g⊥(T) and g(cid:107)(T).24 mined by Γ = µBg∆B shows no clear anisotropy but a
h
The temperature dependence of the ESR linewidth remarkable increase with increasing x up to ≈0.5 and a
clearly differs at low temperatures from the linewidth slight decreasing tendency with further increasing x up
behaviors of YbIr2Si2 and YbRh2Si2 where a continu- to 1. Both g⊥ and g(cid:107) evolve with x with no pronounced
ous decrease or a saturation towards low temperatures anomalies, especially around x = 0.5 where T shows
N
was observed27,28. As shown in Fig. 2 the linewidth of a minimum.11 The inset of Fig. 4 provides a compari-
YbCo2Si2startstoincreasebelowT ≈8Kindicatingthe son of the measured g-values at T =5 K (symbols) with
effect of critical spin fluctuations due to magnetic order thoseexpectedforthetwopossibleKramersdoublets22,23
below TN ≈1.7 K. Above T ≈8 K the linewidth contin- with irreducible representations Γ6 or Γ7. The experi-
uously increases, similar to YbIr2Si2 and YbRh2Si2. For mental values are close to the theoretical values for ei-
T > 16 K the ESR signal is too weak and too broad to ther Γ or Γ doublets for all Co-contents. Thus, the
6 7
be detected. A comparison of X-band with Q-band data ESR g-values can be well accounted for by a localized
of YbCo2Si2 shows no change in linewidth and g-value model. However, these results do not allow a clear dis-
regarding absolute value and temperature dependence. tinction between Γ and Γ . The latter was established
6 7
for the ground state of YbRh Si by angle-resolved pho-
2 2
toemission investigations of the energy dispersion of the
B. Yb(Rh1−xCox)2Si2 crystal-field-split 4f states29 and by an analysis of the
quadrupole moment30. Furthermore, the analysis of all
Figure 3 presents the ESR signals of the series availabledataonYbCo2Si2 usingastandardCEFmodel
Yb(Rh1−xCox)2Si2 at T = 2.7 K and for the magnetic indicate a Γ7 ground state for YbCo2Si2 too.17 All these
field B ⊥ c-axis, i.e. the orientation at which the res- resultsindicateasmoothandcontinuousevolutionofthe
onance field is the smallest. All depicted spectra show crystalelectricfieldfromYbRh2Si2 toYbCo2Si2 without
welldefinedmetallicLorentzianshapes. Theratioofdis- change of the symmetry of the ground state doublet.
persion to absorption varies between 0.64 and 1 without Theevolutionofthelinewidthanditstemperaturede-
clear relation to the x values which may be explained by pendence is shown in Fig. 5. Different characteristic be-
experimental reasons like different resonator filling fac- haviorssuggestthreetemperatureregimes: alineartem-
tors. peratureregimewhichseparatesaregimebelowT ≈4K,
Linewidth and resonance field show an overall contin- characterized by tendencies to saturation or to low tem-
uous change with the Co-content x as shown in Fig. 4 perature broadening, from a regime above T ≈ 12 K
4

g ^
3 3 0 0 3 0 0
ctor2 GG 7 x = 1 0.68 0.38 0.215 0 -3 .0 ^ 2 5 0 0.12 2 5 0
- fa 6 -3 .5 g 2 0 0 x=1 2 0 0
gESR 01 g || -1 .5 -1 .0 -0 .5 g || B (mT)(cid:1)^1 5 0 0.27 0.070.18 00..6588 1 5 0 B (mT)(cid:1)^
1 0 0 1 0 0
1 .2 (cid:1)B || Y b ( R h 1 -x C o x ) 2 S i2 0.215 0.38 0.27
(T)0 .8 T = 5 K 5 0 0.03 x = 0 Y b (R h 1 -xC o x)2 S i2 5 0
B(cid:1)0 .4 0 0
(cid:1)B ^ 0 4 8 1 2 1 6 0 4 8 1 2 1 6
T (K ) T (K )
0 .0
1 0
FIG. 5: (color online) Temperature dependence of the
) linewidth ∆B for the field orientation B ⊥ c-axis. Dashed
z
H 5 G lines show for x = 0.27 the maximum linear increase. The
(G G || solidline√describesthelowtemperaturepartofthex=1data
G ^ witha1/ T −T +∆B +b(T−T )behavior(b=8mT/K),
L 0 L
0 0 .0 0 .2 0 .4 0 .6 0 .8 1 .0 see main text Sec. IV.
C o -c o n te n t x
FIG. 4: (color online) Co-concentration dependence of the
by the dashed lines, all the g-data are characterized by a
ESRg-factor,linewidth∆B andrelaxationrateΓ= µBg∆B
h logarithmic downturn towards low temperatures. This
for the field orientations B ⊥,(cid:107) c-axis and for T = 5 K.
Solid lines are guides for the eyes. Insert: Evolution of g
factor anisotropy with Co-concentration in comparison with
the expected g factors (solid lines) which correspond to Γ6 3 .6 Y b ( R h 1 -x C o x ) 2 S i2
andΓ7groundstatesymmetriesforaYb3+ioninatetragonal x= 0 B ^ c 3 .4
crystal field.
3 .4 0.03 0.58
tor 0.07 3 .2 tor
wiTnhhfleeureleinncaeenaroafldinrdeeiltwaioxidnattahilobnlienvheiawaviidtohtrheofifbrrtsohtaedemxecnidiitndegldeiCtnedEmiFcpa-elterevasetlut.h3r1ee g ESR -fac33 ..02 00..1182 000...236788 23 ..80 g ESR -fac
regimeremindstoaKorringalawoflocal-momentrelax- 2 .8
ation toward conduction electrons. This is displayed in 0.215 x= 1 2 .6
Fig.5 by the linear dashed line for the x = 0.27 sample 2 .6
5 1 0 5 1 0
which among all samples displays the largest tempera- T (K ) T (K )
ture slope b = δ∆B /δT of 22 mT/K. The linearly
⊥ ⊥
extrapolated linewidth at zero-temperature has roughly
FIG. 6: (color online) Temperature dependence of the ESR
the same value for the samples with x≤0.27. With fur-
g-factor for the field orientation B ⊥ c-axis. Dashed lines
ther increasing x b⊥ decreases again and for x ≥ 0.68 is guidetheeyesandemphasizethetrendinthelowtemperature
approximately the same as for x = 0.03. In the temper- behavior.
ature regime below T ≈ 4 K a deviation from linearity
is observed for 0.07 ≤ x ≤ 0.27 8 and x ≥ 0.68. This is most nicely developed for x = 0 where it was re-
is most obviously seen for the x = 1 linewidth, showing latedtoasmallcharacteristicenergyforthegroundstate
a considerable broadening above the magnetic ordering Kramers doublet.5 Whereas in this low temperature re-
temperature. For 0.07 ≤ x ≤ 0.27 and x = 0.68 small gion the temperature variation is largest for x = 0.215
positive curvatures in the low temperature linewidth be- the absolute g-values steadily decrease with Co doping
haviorsratherseemtoindicateatendencyforsaturation. (see also Fig. 4), indicating the effect of changes in the
Thistendencywasdiscussedfor0.07≤x≤0.27interms crystal electric field. The influence of the first excited
of a relation between the zero-temperature linewidth to crystal-field levels may be seen in the decrease of the g-
the residual electrical resistivity.8 factors at higher temperatures, being quite sensitive to
ThebehavioroftheESRg-factorisshownonalogarith- the Co-content. Unfortunately, due to the insufficient
mic temperature scale in Fig. 6. In general, as indicated experimental accuracy, further information on these ex-
5

)4 0 0 0 .4 )
cited levels could not be obtained. T /K
TheESRintensityperYb-iondoesnotchangewithinex- (m.72 0 0 0 .2 (14f
perimental accuracy across the doping series. Previous B2 0 0 .0 /T
detailed investigations of the number of ESR active Yb D 1
spinsinYbRh Si haveshownthatall Ybionscontribute ) 2 0 0
to the ESR 2sig2nal.21 Hence, for Yb(Rh1−xCox)2Si2, T/K 1 0 (K)
whereanyevidenceforComagnetismisabsent,theESR (m -2 ^QW
properties are always determined by all Yb ions despite ^
b
1 .5
the large variation of the Kondo interaction with Co-
doping.11 1 .0 T N
)
(K0 .5 T
T L
0 .0
IV. DISCUSSION
0 .0 0 .2 0 .4 0 .6 0 .8 1 .0
C o - d o p in g x
Collecting information on the competition of the lo-
calKondoandtheintersiteRKKYexchangeinteractions
FIG.7: (coloronline)ComparisonofESRlinewidth∆B at
2.7
is essential for understanding the magnetic behavior of T =2.7Kandlinewidthtemperatureslopeb between4and
⊥
Yb(Rh1−xCox)2Si2. The doping with Co enhances the 8K(9and13K;x=1)withthecharacteristictemperatureT4f
size of the ordered moment and stabilizes the AFM or- deduced from the 4f- specific heat and the low-temperature,
derbyweakeningtheKondointeraction.11 Theobserved in-plane Weiss temperature Θ⊥ of Yb(Rh Co ) Si (data
W 1−x x 2 2
ESR parameters show dependencies on the Co-content fromRef.11). Bottomframeshowsmagneticphasediagram11
which are sensitively related to the Kondo effect, to the asdeterminedfromanomaliesofχ(T)andC(T). Belowtem-
peraturesT andT magneticorderappearstobeincommen-
anisotropy induced by the crystal field as well as to the N L
surate and commensurate, respectively. While the transition
presenceandcharacterofmagneticphasetransitionsbe-
at T is always second-order, the transition at T is second
low the investigated temperature range. In the following N L
order for x≤0.22 and first-order for x>0.22.
this will be discussed by analyzing the linewidth param-
eters shown in Fig.7 in terms of the relevant magnetic
properties of Yb(Rh Co ) Si .
1−x x 2 2
We start with discussing the relation between the bution in ∆B (x).
2.7
linewidth and the characteristic temperature T de- At high Co-contents the ESR linewidth should be con-
4f
duced from the magnetic entropy which reflects the en- sidered in terms of a strongly suppressed T because
K
ergy scale of all exchange interactions acting on the T gets dominated by RKKY exchange interactions for
4f
lowest CEF doublet.11 We have chosen the linewidth x>0.6. A strongly reduced Kondo interaction is estab-
∆B at T = 2.7 K as one possible measure of the lishedfromphotoemissionspectroscopy: YbCo Si (with
2.7 2 2
spin fluctuations which dominate the linewidth at low T (cid:28)1K17)showsaratherweakinteractionbetweenthe
K
temperatures. As shown in the upper frame of Fig. 7 4f and the valence states in comparison to YbRh Si .11
2 2
∆B (x) and 1/T (x) show a similar behavior. For We discuss the role of the RKKY interactions for the
2.7 4f
low Co-contents this similarity suggests that a decrease linewidth in terms of ferromagnetic fluctuations which
of the Kondo energy scale T leads to an increase of wereshowntoplayanimportantrolefortheobservability
K
the ESR linewidth because T dominates T for Co- ofaspinresonanceinKondolatticesystems.9 Theevolu-
K 4f
concentrations x ≤ 0.38. In this respect it is impor- tion of ferromagnetic fluctuations in Yb(Rh Co ) Si
1−x x 2 2
tant to mention also the effect of anisotropy of the ex- are reflected, for instance, in the Weiss temperature Θ⊥
W
change interactions to the linewidth. It has been shown characterizingthein-planemagneticsusceptibilityatlow
that a collective spin mode of Kondo ions and conduc- temperatures. Θ⊥(x) shows a clear maximum around
W
tionelectronsenablesanarrowlinewidthinaKondolat- x=0.3,whereitevenchangessignandbecomespositive,
tice despite a strong magnetic anisotropy.5 Hence, de- indicating the dominance of ferromagnetic exchange in-
spite the anisotropy (as seen in the ratio of g (x)/g (x), teractions. As documented in the middle frame of Fig. 7
⊥ (cid:107)
Fig. 4) is largest at x = 0, there the linewidth reaches this behavior is well correlated with the in-plane linear
its smallest value, supporting the collective spin mode temperature slope of the linewidth, b (x). For low x we
⊥
model. Note, that with increasing x the increasing con- interpret this correlation, similar to ∆B (x), by a de-
2.7
tribution of disorder to the linewidth should be consid- creasing Kondo interaction up to x≈0.2.
ered as well. A discrimination of Kondo- and disorder At this point it is worth to note that in compounds
contributions was qualitatively accomplished by a com- withnoKondolatticebehavior(verysmallKondoenergy
parisonofthelinewidth-resistivityrelationofpressurized scales) such as YbRh9 or YbCo Si narrow ESR lines
2 2
YbRh Si and Yb(Rh Co ) Si with x ≤ 0.18.8 The emerge from ferromagnetic correlated 4f spins whereas
2 2 1−x x 2 2
result suggests that disorder is not the dominant contri- antiferromagnetic correlations as in Yb Rh Ge 9 lead to
4 7 6
6

an ESR linewidth too broad to be observable. That 3 .6 x= 0 0 .6 B || c 2 .0 B || c
means, for Yb(Rh Co ) Si above x ≈ 0.2, the fer-
romagnetic correlat1i−oxns axm2ong2 the 4f moments presum- 0.07 0.030 .5 x= 0 .215 1 .5 x= 0 .68 x= 1
ably start to control the linewidth, preventing b (x) to 3 .4 1 .0 3 .4
⊥
gcaretetahfsuiignrhtghCeinrofli-nucocernnetcaeesneotdsf,wthnheaicrRrhoKwmKalyYinbeiesnteaexrrpaecetcaitlosenod.farMlolomowreeadonviebnry-, g -factor3 .2 0.120 .2 0 .3 00.6.388 0 .5 0.127.0 1 .5 3 .2 g -factor
an anisotropy g⊥(x)/g(cid:107)(x) being much smaller than for SR3 .0 0.18 3 .0 SR
lsoliwghCtloy-cdoenctreenatssin.gT(fhoirsxis>co0n.6si)streenlatxwatiitohnaractoen,ssteaenFtiogr. E 0.215 x= 1 E
4. Again,theserelationsbetweentheESRlinewidthand 2 .8 2 .8
the interplay of Kondo effect, RKKY interactions and Y b (R h 1 -xC o x)2 S i2 B ^ c
anisotropy support the theoretical basis describing the
2 4 2 4
spindynamicsintermsofacollectivespinmodeofKondo c (1 0 -6 m 3 /m o l)
ions and conduction electrons.5
Next, we consider the linewidth behavior towards low
FIG. 8: (color online) Relation between ESR g-factor and
temperatures. There, broadening contributions from
magnetic susceptibility χ with B ⊥ c-axis. Insets show the
magnetic fluctuations become important even far above
relationforB(cid:107)c-axis. Dashedlinesindicateamolecular-field
the magnetic transition temperature because the reso-
relationship as discussed in the text.
nance relaxation is very sensitive to the effect of critical
spin fluctuations.32 The type of magnetic order underly- x g⊥ λ⊥ (kOe/µ ) g(cid:107) λ(cid:107) (kOe/µ )
ingthemagneticphasediagraminFig. 7dependsonthe 0 B 0 B
0 3.78 -3.3 - -
Co-content. As a consequence, characteristic differences
0.215 3.63 -3.3 0.18 525
in the low-temperature ESR broadening can be identi-
fied for low and high Co concentrations, roughly sepa- 0.27 3.57 -2 - -
rated by the pronounced minimum of T near x = 0.5. 0.38 3.49 -2 - -
N
As can be seen in Fig. 5 for almost all investigated Co 0.68 3.35 -2 0.86 52
concentrations the ESR line gets continuously narrowed 1 3.05 -2 0.86 52
down to the lowest accessible temperatures. A consid-
erable ESR broadening toward low temperatures is only
seen for x = 1. However, the x = 0.68 sample may also TABLEI:Meanfieldparametersofgobtainedfromlinearfits
as shown by the dashed lines in Fig. 8.
showasimilarbroadeningatlowertemperaturesbecause
the linewidth temperature slope b is similar to the one
⊥
for x=1 at T >9 K. The linewidth of the samples with
Co concentrations 0.07≤x≤0.27 show deviations from
the temperature linearity below T ≈4 K. susceptibility8, pointing out a typical property of a lo-
The sensitivity of the ESR linewidth to the type of cal ESR probe. This feature was discussed in terms of
magnetic order in Yb(Rh1−xCox)2Si2 strongly resembles a molecular field model for YbIr2Si2 in Ref. 24 and
the observations from a local Gd3+ ESR in the heavy- for YbCo Si in Sec. IIIA. That means that internal
2 2
fermion compound Ce(Cu1−xNix)2Ge2. There, the na- magnetic fields lead to an effective g-factor geff which
tureofmagneticorderchangessignificantlyfromx≤0.5 is shifted from the ionic g-factor g depending on a
0
(local moment type magnetism) to x ≥ 0.5 (itinerant molecular-field parameter λ:
heavy-fermion band magnetism).33 The temperature de-
pendence of the Gd3+ linewidth could characterize the g =g [1+λχ(T)] (3)
eff 0
different ground states and, in particular, provide infor-
mation about Ce3+ spin-fluctuations and the scattering For Yb(Rh1−xCox)2Si2 the validity of this equation is
of conduction electrons at the Gd3+ spins (for which, nicely established as shown by the dashed lines in Fig. 8
with the values listed in Table I. The values g succes-
moreover,non-Fermiliquidbehaviorcouldbeidentified). 0
The effect of Ce3+ spin-fluctuations could be described sivelydecreasewithincreasingCo-content. Discrepancies
√
between these values and the values gm obtained from
bya1/ T dependence. InthecaseofYb(Rh Co ) Si
1−x x 2 2
the Yb3+ spin fluctuations lead to an increase of the saturationmagnetizationcouldbeduetoVan-Vleckcon-
tributionstothesusceptibility.22Thein-planemolecular-
linewidth, as clearly visible for the data of x = 1. As
√
field parameter λ⊥ which is sensitive to the interactions
shown by the solid line in Fig.5 a 1/ T dependence rea-
for the x−y components of the Yb-moments shows neg-
sonably describes the data.
ative values pointing to an antiferromagnetic exchange
Previous ESR investigations of YbRh Si under pres-
2 2
for the x − y components. An abrupt change from
sure and with Co-dopings x ≤ 0.18 have shown a
λ⊥ = −3.3kOe/µ for x ≤ 0.215 to λ⊥ = −2kOe/µ
close relationship between the g-factor and the magnetic B B
for x ≥ 0.27 could be related to a corresponding change
7
anisotropy (i.e. g /g is large) which is the case for
⊥ (cid:107)
in the magnetic structure. M¨ossbauer results on pure Yb(Rh Co ) Si with a small Co-content. Further-
1−x x 2 2
YbCo2Si2 indicate the ordered moment to be within the more, ourresultssuggestthatferromagneticcorrelations
basal plane.15 The out-of plane internal fields lead to a mayremainasthedominantmechanismfornarrowESR
ferromagnetic g-shift as shown in the insets of Fig. 8. lines when the Kondo interaction is strongly suppressed
There, positive and large molecular-field values λ(cid:107) de- and the magnetic anisotropy is sufficiently small, i.e., at
scribe the data. The strongly enhanced value of λ(cid:107) for highCo-contentsofYb(Rh Co ) Si . Thisisanewas-
1−x x 2 2
x=0.215 is a consequence of the small value of g(cid:107), since pect of the previously stated relevance of ferromagnetic
0
within a Heisenberg picture λ can be related to the ex- correlations among 4f spins for a narrow ESR in Kondo
change parameter J as λ ∝ J/g2. Hence, for x ≥ 0.68 lattice systems.
J(cid:107) is twice as large than for x=0.215 supporting an in- The character of the linewidth temperature dependence
crease of the ferromagnetic exchange with increasing x. towards low temperatures (T (cid:46) 4 K) is clearly different
Theseresultssuggestthattheexchangeforthezandthe for low and high Co-dopings. This indicates changes in
x-y components of the local moment are predominantly themagneticfluctuationsuponCo-dopingduetochanges
ferromagnetic and antiferromagnetic, respectively. in the AFM structure. These changes could also be
inferred from a change in the in-plane molecular-field
around x = 0.22 where the linearity between the mag-
V. CONCLUSION neticsusceptibilityχandtheESRg-valueschangesslope.
Moreover, this slope shows a different sign for g (χ) and
(cid:107)
The series Yb(Rh1−xCox)2Si2 show well defined ESR g⊥(χ)suggestingtheexchangeforthezandthex-ycom-
spectrawithpropertiestypicalforlocalYb3+ spins. The ponents of the moment to be predominantly ferromag-
ESR g-factor shows a distinct and uniform variation netic and antiferromagnetic, respectively.
with the Co-content and no indications for a change
in the symmetry of the ground state Kramers dou- Acknowledgements
blet could be found. The linewidth evolution with the
Co-content clearly reflects variations of both the mag-
netic order and the Kondo interaction. A strong reduc-
tion of the latter by Co-doping leads to a line broad- We thank F. Garcia, Hans-Albrecht Krug von Nidda
ening. This demonstrates that the Kondo interaction and B.I. Kochelaev for fruitful discussions and acknowl-
crucially determines the ESR linewidth in Kondo lat- edge the Volkswagen foundation (I/84689) for financial
tices, especially in the presence of a strong magnetic support.
∗ Electronic address: [email protected] 012035 (2010).
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