Quantum Critical Scaling and origin of Non-Fermi-Liquid behavior in Sc$_{1-x}$U$_{x}$Pd$_3$

0.6 MB·English

by  Stephen D. Wilson

Quantum Critical Scaling and origin of Non-Fermi-Liquid behavior in Sc U Pd
1−x x 3
Stephen D. Wilson,1 Pengcheng Dai,1,2,∗ D. T. Adroja,3 S.-H. Lee,4
J.-H. Chung,4,5 J. W. Lynn,4 N. P. Butch,6 and M. B. Maple6
1 Department of Physics and Astronomy, The University of Tennessee, Knoxville, Tennessee 37996-1200, USA
2 Condensed Matter Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
3 ISIS Facility, Rutherford Appleton Laboratory, Didcot, Oxon OX11 0QX, United Kingdom
4 NIST Center for Neutron Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
5 5 Department of Materials Science and Engineering,
0
University of Maryland, College Park, Maryland 20742, USA
0
6 Department of Physics and Institute for Pure and Applied Physical Sciences,
2
University of California, San Diego, La Jolla, California 92093-0319, USA

n
a We use inelastic neutron scattering to study magnetic excitations of Sc1−xUxPd3 for U concen-
J trations (x = 0.25, 0.35) near the spin glass quantum critical point (QCP). The excitations are
1 spatially incoherent, broad in energy (E = ¯hω), and follow ω/T scaling at all wave vectors inves-
tigated. Since similar ω/T scaling has been observed for UCu5−xPdx and CeCu6−xAux near the

] antiferromagnetic(AF)QCP,wearguethattheobservednonFermiliquid(NFL)behaviorinthese
l f-electronmaterialsarisesfromthecriticalphenomenanearaT =0Kphasetransition,irrespective
e
- of thenature of the transition.
r
t
s PACSnumbers: 75.40.Gb,71.27.+a,71.10.Hf
.
t
a
m The breakdown of Fermi-liquid theory has been ob- the Γ doublet ground state is more consistent with the
3
- servedinaclassofstronglycorrelatedf-electronmateri- x=0.45 data and the x=0.2 compound has a degener-
d
als, followingthe originaldiscoveryof this so-callednon- ate Γ and Γ groundstate. In this case,the QKEcould
3 5
n
o Fermi-liquid (NFL) behavior in the Y1−xUxPd3 pseu- be the predominant cause of NFL behavior [15].
c dobinary alloy in 1991 [1, 2, 3, 4]. In spite of intensive In this Letter, we report neutron scattering experi-
[ theoreticalandexperimentaleffortsoverthe pastdecade ments on Sc1−xUxPd3 (x = 0.0, 0.25, 0.35). We show
[5,6,7,8,9,10,11,12,13],itisstillunclearwhetherthe thatmagneticexcitationsattheNFLconcentration(x=
1
v observed NFL behavior is an intrinsic property [14, 15] 0.35) do not form the distinct CEF excitations seen in
′′
4 or extrinsic property associated with metallurgical in- Y0.55U0.45Pd3. Instead, the susceptibility χ (q,ω,T) at
0 homogeneity in these materials [16]. Models describing all probed wave vectors (q), temperatures (T), and en-
0
this anomalous NFL behavior include single-ion physics ergies (¯hω) obeys ω/T scaling indicative of a T = 0 K
1
of noninteracting local magnetic moments [5, 6], close second order phase transition. While such behavior is
0
5 proximity to a T =0 K second-orderphase transition or also observed in the NFL compounds CeCu6−xAux [20],
0 quantum critical point (QCP) [7, 8, 9, 10], and disorder UCu5−xPdx [21,22],andCe(Rh0.8Pd0.2)Sb[23]nearan-
t/ induced effects [11, 12, 13]. tiferromagnetic (AF) QCP, χ′′(q,ω,T) in Sc1−xUxPd3
a We studied Sc1−xUxPd3 because this system has (x = 0.35) is wave vector independent with no spatial
m
a phase diagram and NFL properties similar to correlations and obeys ω/T scaling over a much wider
d- Y1−xUxPd3, but with a nearly homogeneousU distribu- energy range with a different critical exponent. There-
tion in the ScPd matrix [14]. While the U inhomogene- fore, the dynamics of isolated U ions are responsible for
n 3
o ity in Y1−xUxPd3 is unlikely the main cause of the NFL the temperature and energy scaling, suggesting that the
c behavior [15], neutron scattering experiments seeking to NFL behavior originates from the spin-glass phase tran-
:
v provide constraints on various microscopic models have sition suppressed to near zero temperature.
i reached different conclusions. According to Lea, Leask, Our experiments were performed on the HET time-
X
and Wolf [17], the cubic crystalline electric field (CEF) of-flight spectrometer at the UK ISIS spallation neutron
ar of ScPd3 splits the U4+ J = 4 multiplet into Γ4 and Γ5 source [19], and on the BT-2 and cold neutron SPINS
triplets, a Γ singlet, and a Γ doublet. If the single- triple-axisspectrometersattheNISTCenterforNeutron
1 3
ion based two-channel quadrupolar Kondo effect (QKE) Research(NCNR).TheHETdatawerecollectedwithin-
is responsible for the NFL behavior in Y U Pd [1], cident beam energies (E ) of both 18 meV and 65 meV
0.8 0.2 3 i
the U4+ ground state should be a nonmagnetic Γ with for a range of temperatures, and a vanadium standard
3
magnetic Γ and Γ excited states [5]. In contrast, was used to normalize the scattering intensity to abso-
5 4
polarized triple-axis neutron-scattering experiments on lute units. The magnetic scattering in U-doped materi-
Y1−xUxPd3 reveal a magnetic ground state for x=0.45 alswasdeterminedbycomparingthescatteringintensity
and possibly for x = 0.2, thus precluding the possibility withthatofthenonmagneticScPd parentcompoundfor
3
of a QKE [18]. However, based on subsequent neutron 18meVdata,andby subtractionofa parent-compound-
time-of-flight measurements, Bull et al. [19] argue that generatedmappingbackgroundfor65meVdata[19,24].
2
Fig. 1) | Q | (Å-1)
0 .5 1 1.5 2
18 10
)Vem( ygrenE 11118646420 Intensity a-240)20 | Q |1 (Å-1) 2 STc=.6 55UK,. 3H5PETd3 6842Vem bm( ytis netnIΩ1-
2 ) 1-
0 0
8 b) Sc UPd X = 0
1-)V 6 T=1 -5x Kx, H3ET XX == ..3255
e 4
m
Ω1- 2
b
m
( ytisnetn 60 c) 1X5320 00=K0 00KK ,K 5 K Sc.65U.35Pd3
I 4 X30=00 ,K 100 K
2
0
-15 -10 -5 0 5 10 15
Energy (meV)
FIG. 2: (a) q-integrated (0 < q < 2.5 ˚A−1) S(ω,T) for
FIG. 1: (a) E-q image of Sc1−xUxPd3 (x= 0.35) at 5 K for x = 0.35 with Ei=65 meV. Open triangles show the map-
Ei = 18 meV. The inset shows E-integrated [E = 3-6 meV pingbackground,andvertical dashedlinesare theresolution
(blue);6-9meV(green);9-12meV(black)]q-cutsat5K.(b) half-widthof1.65meV.(b)Netmagneticscatteringatvarious
Theq-integrated(0<q<2.5˚A−1)S(ω,T)forx=0.0,0.25, temperatures. (c) Calculated CEF S(ω,T) for two possible
and0.35. Thedashedlineshowstheexpectedmagneticscat- ground states: magnetic Γ5 and nonmagnetic Γ3.
tering for x=0.25 assuming simple U-concentration scaling.
(c)Theq-integrated(0<q<1.5˚A−1)S(ω,T)forx=0.35at
various temperatures. Dashed lines on the E <0 side reflect K(Fig. 1b). Whiletheoutcomeshowsclearmagneticre-
detailed balance expectations calculated from the magnetic
sponseforthetwodopedsystems,thescatteringisbroad
scattering on the E > 0 side. Grey, vertical dashed-lines
andfeaturelesswithnoevidenceforlocalizedCEFstates.
show the resolution half-width of 0.433 meV.
Inaddition,themagneticscatteringdoesnotfollowtheU
concentration scaling. Assuming that the magnetic fluc-
To study the low-energy spin dynamics, we used SPINS tuations in Sc1−xUxPd3 scale linearly with the U solute
with final neutron energy fixed at E = 5 meV. An in- concentration, one would expect scattering for x = 0.25
f
cident beam collimation of 80′ was used followed by a asthedashedlineinFig. 1b. Theactualscatteringfrom
cold Be filter and a radial collimator after the sample. the x = 0.25 concentration instead almost lies directly
We alsocollecteddata using polarizedneutronsonBT-2 ontopofthenonmagneticparentbackgroundwithmuch
to separate the magnetic signal from nuclear spin inco- less magnetic signal. We note that similar behavior has
herent scattering. For the experiment, we prepared 18 also been observed in Y1−xUxPd3 [19].
g polycrystalline samples of Sc1−xUxPd3 (x = 0, 0.25, Since the Sc1−xUxPd3 x = 0.25 compound is nearly
0.35) through arc-melting techniques [14]. The lattice nonmagnetic and does not exhibit strong NFL features
parametersofthese cubic Cu Austructure materialsare [15],we focusonthe NFL x=0.35compoundandstudy
3
a=b=c=4.01˚A for x=0.35 and3.99 ˚A for x=0.25. the temperature evolution of the magnetic scattering.
Figure 1 summarizes HET results with E = 18 meV The most striking feature of the data is the tempera-
i
for Sc1−xUxPd3 at x = 0, 0.25, 0.35, where we probed ture independence on the neutron energy loss side of the
excitations in the energy range between 3 and 13 meV. spectra, while the neutron energy gain side obeys de-
Thescatteringforx=0.35intheenergy-momentum(E- tailedbalance as shownin Fig. 1c. To confirmthat such
q) space probed (Fig. 1a) shows a broad continuum of behavior indeed arises from the U magnetic moment, we
intensitywithnopeakattheexpectedAForderingwave performedacarefulstudyofthetemperaturedependence
vector for Y0.55U0.45Pd3 marked as the vertical dashed of the nonmagnetic ScPd3 and found that the nonmag-
line [18]. Different energy-integratedcuts at 5 K (see in- neticscatteringistemperatureindependentbelow100K
set of Fig. 1a) show no modulation at any wavevector, and increases only slightly at 300 K (Fig. 1c).
different from that of Y1−xUxPd3 (Fig. 10 of Ref. [19]). To determine the magnetic excitations of the x=0.35
ToseeifthescatteringinFig. 1aismagnetic,wecompare compound above 13 meV, we increased E = 65 meV at
i
q-integratedenergy cuts for all three concentrations at 5 the HET. Fig. 2a shows the scattering at T = 5 K for
3
T = 5 K using BT-2 at NCNR. The flipping ratios for
both horizontal and vertical guide fields are ∼20. By
subtracting vertical field intensity from that in horizon-
tal field, we confirmed the presence of elastic magnetic
scattering [18, 25]. To further prove that the observed
excitations are from U moments, we show in Fig. 3c the
wave vector dependence of the magnetic scattering from
bothHETandSPINSexperimentsnormalizedtotheex-
pected U4+ and U3+ magnetic form factors. The data
are clearly consistent with U magnetic scattering.
The absence of any characteristicq and E scale in the
magnetic excitations of the x = 0.35 compound sug-
gests that isolated U ions are responsible for the ob-
servedspindynamicalbehavior. Theuniquetemperature
independent form of the magnetic scattering S(q,ω,T)
bears a remarkable resemblance to that of UCu5−xPdx,
where the excitations at all q, and for limited temper-
atures and energies (< 25 meV) accessed display the
same type of NFL ω/T scaling [21, 22]. The mea-
sured S(q,ω,T) is related to the imaginary part of the
′′
dynamical susceptibility, χ (q,ω,T), via S(q,ω,T) =
FIG. 3: (a) Energy scans at fixed q = 1.3 ˚A−1 for x = 0.35 χ′′(q,ω,T)/[1 − exp(−¯hω/k T)], where [n(ω) + 1] =
B
and 0.0 on SPINS. Dashed vertical lines show the resolution
1/[1−exp(−¯hω/k T)] is the Bose population factor. In
halfwidth of 0.12 meV. (b) (q,E) map of magnetic fluctu- B
′′
calculating χ (q,ω,T) for the various temperatures, we
ations for x = 0.35 at 1.4 K. The dashed grey line shows
theAForderingwavevectorof(0.5,0.5,0) forY0.55U0.45Pd3 find that χ′′ multiplied by T1/5 collapses onto a single
[18]. (c) q-dependence of magnetic excitations. Solid lines curve for all data sets as a function of ω/T.
showcalculatedmagneticformfactorsforU3+ andU4+ ions. Figure 4 showsthe outcome ofour analysis,where the
SPINS data have been scaled to the absolute scale of
the HET data through normalizing the elastic incoher-
boththe x=0.35compoundandthe nonmagneticback- ent scattering of x = 0.0 and 0.35. In the final plot, all
ground [19, 24]. The resulting difference spectra at sev- data have been corrected for their magnetic form factor
eral temperatures are shown in Fig. 2b. Similar to Fig. dependence, which is critical for the time-of-flight data
1c, the magnetic excitations are broad, temperature in- because of the coupled E-q values. The obtained scaling
dependent,andextendupto50meV.Ifexcitationsfrom exponent of 1/5 represents a purely empirical analysis;
the Umomentsinthe x=0.35compoundhavelocalized however, slight deviations from this value induce sub-
states at ∼6 meV and ∼36 meV as in the AF ordered stantial discontinuities in the resulting ω/T scaling plot.
Y0.55U0.45Pd3 [18, 19], one can calculate the expected For comparison, the scaling exponent of UCu5−xPdx is
temperature dependence of the CEF levels assuming ei- 1/3 [21, 22].
ther Γ5 [18] or Γ3 [19] as the zero-energy ground state Thediscoveryofω/T scalingintheNFLx=0.35com-
(Fig. 2c). The comparison of Figs. 2b and 2c reveals pound strongly suggests that the magnetic fluctuations
that both CEF models are incompatible with the data. inthissystemarisefromthecloseproximitytoaT =0K
If excitations in the NFL x = 0.35 are indeed nonlo- phase transition. Similar ω/T scaling was first identified
calized, one would expect to find magnetic scattering at in the NFL UCu5−xPdx system, but with much smaller
energies much less than 3 meV. Figure 3a shows energy energy range [21, 22]. The key difference, however, is
scans at q = 1.3 ˚A−1 for x = 0.35 and x = 0.0 using that Sc U Pd does not have any enhancement in
0.65 0.35 3
SPINS at NCNR. Consistent with results at higher en- themagneticscatteringaroundtheexpectedAFordering
ergies (Figs. 1 and 2), magnetic excitations between 0.4 vectorofhigherUconcentrations[18]. Whiletheantifer-
meV and 8 meV are broad,featureless, and temperature romagnetism in Y1−xUxPd3 compounds with x ≥ 0.41
independentfrom1.4Kto300K.Toseeifmagneticscat- may not control the spin dynamics for Sc U Pd ,
0.65 0.35 3
tering in x= 0.35 peaks at the same AF wave vector as our results are consistent with the observation that the
Y U Pd [18],wecarriedoutaseriesofenergyscans spin-glass transition temperatures of the NFL x = 0.35
0.55 0.45 3
at different wave vectors at T = 1.4 K. The outcome and0.3compounds aresuppressedclosetoT =0K[15].
shows no enhancement along any wave vectors probed SinceNFLbehaviorhaspreviouslybeenattributedtothe
(Fig. 3b). To see if there is magnetic scattering at an proximity of an AF QCP at T = 0 K in CeCu Au
5.9 0.1
arbitrary (q = 1.95 ˚A−1) elastic position, we performed [20],ourresultssuggestthatdetailsoftheT =0Kphase
polarized neutron beam measurements on x = 0.35 at transition are unimportant for the NFL behavior.
4
tureless in wave vector and energy. The absence of any
characteristic energy scale, other than the temperature
itself, suggests that the microscopic origin of the NFL
behavior lies with individual U ions near a T = 0 K
spin-glass phase transition. Therefore, the NFL prop-
erties in a wide variety of f-electron systems includ-
ing (Y,Sc)1−xUxPd3, UCu5−xPdx, CeCu6−xAux, and
Ce(Rh Pd )Sb can be described by a common physi-
0.8 0.2
cal picture, being near a T = 0 K quantum phase tran-
sition. Although the intrinsic disorder in these systems
is essential for establishing the spin-glass ground state
[11, 12, 13], it cannot be the main cause of the NFL
behavior.
We thank M. C. Aronson, H. J. Kang, and Q. Si for
FIG. 4: Scaling plot for Sc.65U.35Pd3. The 300K HET data helpful discussions. This work is supported by the US
exhibit a slight deviation due possibly to underestimation of
NSF DMR-0139882 and DOE DE-AC05-00OR22725 at
phonon contributions.
UT/ORNL, and by the US DOE DE-FG02-04ER46105
and NSF DMR-0335173 at UCSD.
Theoretically, the NFL behavior may arise from the
proximitytoaT =0Kspin-glassquantumphasetransi-
tion, although models in their present forms do not pre-
dict the observed ω/T scaling [7, 8, 9]. Recent exper- ∗ Electronic address: [email protected]
iments on Ce(Ru Rh ) Si [26] have attributed the [1] C. L. Seaman et al.,Phys. Rev.Lett. 67, 2882 (1991).
0.5 0.5 2 2
NFL behavior to the disorder near a spin glass QCP [2] B.AndrakaandA.M.Tsvelik,Phys.Rev.Lett.67,2886
(1991).
[11, 12, 13]. On the other hand, disorder was found not
[3] M. B. Maple et al.,J. Low Temp. Phys. 99, 223 (1995).
to be the main cause for the NFL behavior in quantum [4] G. R.Stewart, Rev.Mod. Phys. 73, 797 (2001).
spin-glasses UCu5−xPdx at x=1.0 and 1.5 [27, 28]. As- [5] D.L.CoxandA.Zawadowski,Adv.Phys.47,599(1998).
suming that disorderdoes not play a major role [14, 15], [6] I.AffleckandA.W.W.Ludwig,Nucl.Phys.B360,641
onecanenvisionthreedifferentmicroscopicscenariosfor (1991).
the NFL behavior in (Y,Sc)1−xUxPd3. The first is the [7] S. Sachdev, N. Read and R. Oppermann, Phys. Rev. B
QKE [5], where one would expect localized spin excita- 52, 10286 (1995).
[8] A.M.SenguptaandA.Georges,Phys.Rev.B52,10295
tions with nonmagnetic Γ as the ground state. Inspec-
3
(1995).
tion of previous data for Y0.8U0.2Pd3 [18, 19] as well as [9] A. Georges et al., Phys.Rev.B 63, 134406 (2001).
Figs. 1-3 for Sc0.65U0.35Pd3 reveals no convincing ev- [10] Q. Si et al., Nature (London), 413, 804 (2001); Phys.
idence for localized states. In addition, there is clear Rev. B 68, 115103 (2003).
magnetic scattering at E = 0 meV, and the tempera- [11] E. Miranda et al., Phys.Rev.Lett. 78, 290 (1997).
ture dependence of magnetic excitations does not follow [12] A. H. Castro Neto et al., Phys. Rev. Lett. 81, 3531
the expectations of a simple CEF scheme (Figs. 1-3). (1998).
[13] D. R. Grempel and M. J. Rozenberg, Phys. Rev. B 60,
The second is the T = 0 K AF phase transition [2, 10].
′′ 4702 (1999).
However, χ (q,ω,T) displays localized moment dynam- [14] D. A. Gajewski et al.,Phys.Rev.B. 62, 5496 (2000).
ics with no evidence for U-U correlations (Fig. 1a) [29]. [15] R. P. Dickeyet al.,Phys.Rev. B. 68, 104404 (2003).
Instead, the data are consistent with ω/T scaling anal- [16] S. Su¨llow et al.,J. Alloys Compd. 215, 223 (1994).
ogous to UCu5−xPdx, and therefore can be understood [17] K. R. Lea et al.,J. Phys.Chem. Solids 23, 1381 (1962).
as manifestations of single-impurity critical scaling as- [18] P. Dai et al., Phys.Rev.Lett. 75, 1202 (1995).
sociated with a spin-glass phase transition suppressed [19] M. J. Bull et al.,Phys.Rev. B 57, 3850 (1998).
[20] A. Schr¨oder et al., Phys.Rev.Lett. 80, 5623 (1998).
to near 0 K [30]. The solid line in Fig. 4 shows the
[21] M. C. Aronson et al.,Phys. Rev.Lett. 75, 725 (1995).
theoretically proposed spin susceptibility scaling func- [22] M.C.Aronsonetal.,Phys.Rev.Lett.87,197205(2001).
tion χ′′(q,ω,T) = 1/[ATαF(ω/T)] with α = 1/5 and [23] J.-G. Park et al., J. Phys.: Condens. Matter 14, 3865
F(ω/T)=exp[αΨ(1/2−iω/2πT)][10,31]. Althoughno- (2002).
tabledeviationswiththeoppositesignfromUCu5−xPdx [24] A. P. Murani, Phys. Rev.B 28, 2308 (1983).
are seen for small ω/T [22], the model accurately de- [25] Intensities for horizontal and vertical fields are 679.7±
scribes the data over a remarkable ω/T range (Fig. 4). 8.2 and 655.7±7.4 counts/hour, respectively. The net
elastic magnetic scattering for x = 0.35 is then 48±22
In summary, we have used inelastic neutron scat- counts/hour at T =5 K and q=1.95 ˚A−1.
tering to show that magnetic excitations in the NFL [26] Y. Tabata et al.,Phys.Rev. Lett.86, 524 (2001).
Sc1−xUxPd3 (x = 0.35) compound are broad and fea- [27] D. E. MacLaughlin et al., Phys. Rev. Lett 87, 066402
5
(2001). [30] M. C. Aronson et al.,Europhys. Lett.40, 245 (1997).
[28] E. D.Bauer et al.,Phys. Rev.B 65, 245114 (2002). [31] We use this functional form although it was derived for
[29] The weak q-peak in Fig. 10a of Ref. [19] is then due to a AF QCP [10], not a spin-glass QCP.
theU-Uclustering in Y0.8U0.2Pd3 [16].