Magnetic and superconducting properties of Cd2Re2O7: Cd NMR and Re NQR

4 Pages·0.17 MB·English

by  O. Vyaselev

Magnetic and superconducting properties of Cd Re O : Cd NMR and Re NQR.
2 2 7
O. Vyaselev,1,2 K. Arai,1 K. Kobayashi,1 J. Yamazaki,1 K. Kodama,1 M. Takigawa,1 M. Hanawa,1 and Z. Hiroi1
1Institute for Solid State Physics, University of Tokyo 5–1–5 Kashiwanoha, Kashiwa, Chiba 277–8581, Japan
2Institute of Solid State Physics Rus. Ac. Sci., Chernogolovka Mosc. Distr., 142432 Russia
(Dated: February 1, 2008)
2
0
WereportCdNMRandReNQRstudiesonCd2Re2O7,thefirstsuperconductoramongpyrochlore
20 oxides(Tc ≃1 K). ReNQRspectrumatzeromagneticfieldbelow100Krulesoutanymagneticor
charge order. The spin-lattice relaxation rate below Tc exhibits a pronounced coherence peak and
n behaves within the weak–coupling BCS theory with nearly isotropic energy gap. Cd NMR results
a point to moderate ferromagnetic enhancement at high temperatures followed by rapid decrease of
J thedensity of states below the structural transition temperature of 200 K.

4
1
Thepyrochloretransitionmetaloxideswiththe chem- ant electron systems.

n] icalformulaA2B2O7 knownfordecadeshaverecentlyat- In this letter we describe the microscopic informa-
o tracted renewed interest. A and B sublattices both form tion on the magnetic and superconducting properties of
c a network of corner–sharing tetrahedra. The geometry Cd Re O obtainedfromthenuclearmagneticresonance
2 2 7
- ofsuchalattice causesstrongfrustrationofmagneticin- (NMR)atCdsitesandthenuclearquadrupoleresonance
r
p teraction when occupied by local moments, resulting in (NQR)atResites. Theprocedureofgrowingsinglecrys-
u
largedegeneracyofthe lowenergystatesandanomalous tals of Cd Re O has been described earlier [3]. NMR
2 2 7
s
. magnetic behavior [1]. Interplay between strong corre- measurementsweredone onasingle crystalin the exter-
t
a lation and geometrical frustration in itinerant electron nalfieldof10.47T.ForNQR,a crystalwascrushedinto
m systems is a challengingissue. For example,largedegen- powder. Standardspin–echopulse techniques wereused,
- eracy due to frustration is considered to be crucial also including inversion–recovery to measure spin–lattice re-
d
for the heavy–electron behavior of the spinel compound laxation rate.
n
o LiV2O4 [2], where V sites form the identical pyrochlore We first discuss the low-temperature NQR results on
c lattice. Recent investigations of pyrochlores including Re sites. NQR spectra of 185Re and 187Re nuclei, both
[ 5d transition metal elements have led to the discovery withspin5/2,havebeenobtainedbelow100K.Measure-

of the superconductivity, for the first time among py- ments at higher temperatures were hampered by short
1
v rochlore oxides, in Cd2Re2O7 below Tc ≃ 1 K [3, 4, 5] spin–spinrelaxationtime. The spectra at5 K areshown
5 and unusualmetal–insulatortransitionin Cd2Os2O7 [6]. in Fig. 1 where the top and the bottom panels corre-
1 spond to ±3/2 ↔ ±1/2 and ±5/2 ↔ ±3/2 transitions,
2 Besides superconductivity, Cd2Re2O7 shows an un- respectively. NQR frequency of spin 5/2 nucleus can be
1
0 usual phase transition at 200 K [3, 7, 8]. Although com- expressed as [18]: ν±3/2,±1/2 ≈ νQ[1 + (59/54)η2] and
2 plete structural determination below 200 K is yet to be ν±5/2,±3/2 ≈ 2νQ[1 − (11/54)η2], where νQ ∝ Vzz =
0 done, X–ray studies proposed a second–order transition
/ from the high–temperature (high–T) cubic Fd¯3m space
t
a group to the low–T cubic F¯43m space group [7], accom-
m paniedbylossofinversionsymmetryatReandCdsites. 38 39 40 41 42 43 44 45
- The transition also causes a large change of electronic
d properties [3, 8]. The resistivity shows almost no T– s) 3/2<-> 1/2
on dependence near room temperature but drops abruptly Unit
c below 200 K. The magnetic susceptibility also decreases b.
v: steeply below 200 K, while at higher temperatures it (Ar 1 87Re 1 8 5 R e
Xi snheoawrs30o0nlKy.wMeaokreTo–vdere,peankdiennkceinwritehsisatibvritoyadnemaarx1im20umK Area
r o 5 / 2 < -> 3/ 2
a indicates an additional phase transition [7, 9]. Results ch
of band structure calculations [10, 11] indicate that the E
n
material is a compensated semi-metal with two electron pi
S
(one hole) Fermi surfaces centeredcentered at the Γ (K) 187Re 185Re

point of the Re-5d(t ) bands. The electronic structure
2g
74 76 78 80 82 84 86
near the Fermi level is sensitive to structural distortion.
Frequency (MHz)
While it is proposedthat a structuraltransitionmay oc-
curtoremovelargespindegeneracyoflocalizedmoments
on a pyrochlore lattice [12], relation between structure FIG. 1: Re NQR spectra at 5 K. Top panel: ±3/2 ↔ ±1/2
transition. Bottom panel: ±5/2↔±3/2 transition.
and electronic propertiesis largelyunexploredfor itiner-
2
∂2V/∂z2 isthelargestprincipalvalueoftheelectricfield

gradient (EFG) tensor at the nuclear position, V is the
electrostatic potential, and η = |V −V |/|V | is the
xx yy zz
asymmetryparameter. Applyingtheseexpressionstothe
100
measuredspectraonefindsν =40.4MHzat5K,gradu-
Q )
1
ally decreasing with temperature to 37.6 MHz at 100 K, -S
(
adnepdenηd=enc0e.1.66±0.002 without noticeable temperature 7-1T 1
8
1
A sharp line for each NQR transition of both Re iso-
topesimmediatelyruleoutnon–uniformchargedistribu-
tion among Re sites such as charge density wave states.

Because of the large quadrupole moments of 185,187Re
10
and high sensitivity of the EFG to the local charge dis- 1 2
1/T (K-1)
tribution of 5d electrons,any non–uniform charge distri-
bution should give rise to broadening or splitting of the
FIG. 2: 187Re spin–lattice relaxation rate vs inverse tem-
NQR lines. We can also rule out any magnetic order,
perature. The solid line is the fit to the weak coupling BCS
since1µ ofspinmomentin5d statetypicallygivesthe
B theory with δ/∆=0.22, ∆(T = 0)=1.80 K, and Tc=0.98 K.
hyperfinefieldof100T.Thusevenatinymomentwould The dashed lines represent thecases with δ/∆=0.27 or 0.17
have caused the Zeeman splitting of the NQR spectra.
Re sites possess three–fold rotation symmetry both in
thehigh–T Fd¯3mstructureorintheF¯43mstructure,the fit was obtained for δ/∆=0.22, ∆(T = 0)=1.80 K, and
latter being proposed by X–ray for the structure below T =0.98KasshownbythesolidlineinFig.2. Theratio
c
200K[7]. SinceEFGis asecondranksymmetrictensor, ∆(T = 0)/T =1.84 is close to the weak coupling BCS
c
it must be axially symmetric in these cases. Therefore, value 1.75, justifying our analysis. The dashed lines in
the non–zero value of η implies further lowering of sym- Fig. 2 indicates that the height of the coherence peak
metry at least in the temperature range below 100 K. is sensitive to distribution of the gap. The fitted value
Fig. 2 shows the spin–lattice relaxation rate 187T−1 of δ/∆ puts the upper limit for the gap variation, since
1
of 187Re nuclei measured on the ±5/2 ↔ ±3/2 NQR any damping ofthe quasi-particleswill also suppress the
transition at zero magnetic field as a function of inverse coherence peak.
temperature. Therelaxationwasconfirmedtobeofmag- Let us now turn to the NMR results on Cd sites. The
netic(notquadrupolar)originatseveraltemperaturesby Knight shift, K, and the spin–lattice relaxation rate,
observing that the ratio of T−1 for the two Re isotopes 111T−1 were measured for 111Cd nuclei (spin 1/2) using
1 1
isequaltothe squaredratioofthe nuclearmagneticmo- a single crystal. In the high temperature Fd¯3m struc-
ments. ture, three–fold rotation symmetry at Cd sites should
Above T in the region 1 – 5 K, 187T−1 is practi- give rise to the axially symmetric Knight shift, K =
c 1
callylinearintemperature,187(T T)−1=127(Sec·K)−1. K +K (1−3cos2θ), where θ is angle between the
1 iso ax
Just below T , 187T−1 increases sharply exhibiting a external field and the [111] direction. This angular de-
c 1
strong coherence peak [13] with a maximum of about pendencewasobservedabove200K.Uponcoolingbelow
245 (Sec·K)−1 at ∼ 0.88 K, which is twice as large as the structural transition temperature (200 K) the line
just above T . Below 0.8 K the relaxationrate decreases splits in two. The average shift of the split lines follows
c
following an activated T–dependence. the same angular dependence and thus the values of the
It is well known that a coherence peak in the T– isotropic (K ) and the axial (K ) parts of the shift
iso ax
dependence of T−1 is easily depressed when magnitude were determined as a function of temperature. Since the
1
ofthesuperconductinggapvariessubstantiallyortheor- splittingisverysmall(lessthan0.018%),theconclusions
derparameterchangessignovertheFermisurface. Thus ofthe followinganalysisdo notdependonthe validityof
the observed well–pronounced coherence peak provides such averaging.
a clear evidence for nearly isotropic s–wave supercon- In Fig. 3a, K is plotted against temperature (bot-
iso
ducting gap. Nodeless gap in this material have been tom axis) or magnetic susceptibility, χ (top axis). The
recently inferred also from specific heat data [14] and axial part K (not shown in the figure) is –0.042% at
ax
µSR[15,16]measurementsofthepenetrationdepth. We 300 K, much smaller than K , and decreases only by
iso
have fitted the data to the BCS expression, considering 0.01% upon cooling down to 4 K, indicating that the
distribution of the gapdue to possible variationoverthe dominant hyperfine field comes from the Cd s–states
Fermi surface [17]. We assumed a uniform distribution hybridized with the Re 5d conduction states. Simi-
of the gap between ∆ − δ and ∆ + δ and δ/∆ to be lar to the magnetic susceptibility χ [3], K decreases
iso
independent of temperature. The T-dependence of ∆ is rapidly below 200 K. The shift is generally expressed
assumedtofollowtheweakcouplingBCStheory. Agood as K = K +K (T), where the first term is the T–
iso 0 s
3
known to be satisfied, T TK2 =(γ /γ )2(h¯/4πk )≡S,
c (x10-4 emu/mol Re) 1 s e n B
where γ and γ are respectively electronic and nuclear
e n
0 0.4 0.8 1.2 1.6 2.0 2.4
gyromagnetic ratios. In real metals, the ratio
c
.5 a) 0 K =S/(T TK2) (1)
α 1 s
.4
%) providesausefulmeasureofmagneticcorrelation[20,21].
( Since (T T)−1 probes the dynamical susceptibility aver-
o .3 1
K is agedovertheBrillouinzone,itcanbeenhancedbyeither
11 .2 ferromagnetic (FM) or antiferromagnetic (AF) spin cor-
1
relations, while only FM correlation strongly enhances
.1
the spinshift. Thus, generallyspeaking,the value ofKα
0 being much smaller (larger)than unity is a signature for
substantial FM (AF) correlation.
-1K) 1.2 b ) ThSeolviadluceircolfesKin ∼Fig0..248sahbowoveth2e00T–KdeppoeinndtsentcoemofodKeαr-.
1 α
-c ate FM enhancement. The sudden increase of K below
e 0.8 α
S
( 200 K can be accounted for by loss of DOS as explained
T-1 ) below. However,there is a broad peak in Kα near 60 K,
T1(10.4 zaenrdoavtalluoweserfotremKp0edraoteusrnesotKcαhadnegceretahsiess.beChhaoviicoer,ofwnhoicnh-
11 is already evident in Fig. 3 since 111(T1T)−1 keeps de-
0 creasing whereas K(T) becomes nearly flat below 50 K.
0 100 200 300
T (K) InordertoexaminetowhatextentthebehaviorofKα
is explained by T–dependence of DOS, we utilize a sim-
FIG. 3: (a): Isotropic part of 111Cd Knight shift vs tem- ple RPA expression with a free–electron–like dispersion
oftheconductionband. Thisanalysisismainlyforquali-
perature (circles – bottom axis), and vs magnetic suscepti-
bility (squares – top axis). (b): Temperature dependence of tativepurposesincespecificfeatureofthemultipleFermi
(T1T)−1 at 111Cd sites. surfacesof Cd2Re2O7 [10, 11] is not considered. We also
neglect possible variation of the matrix elements of the
contactinteractionoverthe Fermisurface. Althoughthe
good proportionality between K and χ supports such a
independent chemical shift and the second term is the
simple situation, careful examination would be required
T–dependent spin shift from conduction electrons. Like-
in future in the light of realistic Fermi surface and wave
wise χ = χ +χ (T), where the first term is the sum of
0 s
functions. The Stoner enhancement factor of the spin
the diamagnetic and the orbital (Van Vleck) susceptibil-
susceptibility
ity. AsshowninFig.3,linearrelationwasfoundbetween
K and χ in the whole temperature range, yielding
iso 1/(1−α)=χ /(2µ2ρ ), α=Uρ , (2)
the hyperfine coupling constant A = N µ K /χ = s B 0 0
hf A B s s
17.9 T/µ . Since the chemical shift of Cd in a non–
B whereρ istheDOSattheFermilevelandU denotesthe
0
magnetic and non–metallic substance is typically 0.01 %
Coulomb repulsion, is related to K by RPA as [20, 21]
α
or less [19] and much smaller than the observed value of
Kiso, we assume K0=0 in the following analysis. We 1 (1−α)2xdx
then obtain χ0 = 0.75 × 10−4 emu/mole Re, leading Kα,RPA =2Z [1−αG(x)]2, (3)
to χ = 1.65 × 10−4 emu/mole Re at 300 K. From 0
s
the standard value for the diamagnetic susceptibility G(x) = 0.5{1+(1−x2)/(2x)}ln|(1+x)/(1−x)|. Ap-
χbidliiaty=is−e0s.t7im6×ate1d0−a4seχmorub/=mo1l.e51R×e,1t0h−e4oermbiuta/lmsoulseceRpet.i- tpalyinin1g/(e1q.−(α3))=to7t.h3eatex3p0e0riKm.enTthailsdvaatluaeoifsKcoαm,pwaeraobble-
In Fig. 3b, is shown the T–dependence of 111(T T)−1 to the enhancement factor of 4.4 obtained from the cal-
1
measured for Hk[001]. At some temperatures 111T was culated DOS value for the room temperature structure
1
measured for Hk[110] and found to be isotropic. We (0.58eV−1 perRe[10])andtheexperimentalvalueofχ
s
found that 111(T T)−1 also shows rapid reduction be- obtained above.
1
low 200K, indicating that the phase transition at 200 K WenowdeterminetheT–dependenceofDOSorαfrom
causes sudden loss of the density of states (DOS). For the experimental data of χ (T) by using eq. (2), χ ∝
s s
non–interacting electrons, when the spin shift and the α/(1−α), withthe initialconditionthat1/(1−α)=7.3
spin–lattice relaxation are both due to contact interac- at T=300 K. We then calculate K using eq. (3).
α,RPA
trion with unpaired s–electrons,the Korringa relation is The results are shown by the circles in Fig. 4. One can
4
tuations.

In summary, Re NQR data below 100 K reveals no
sign of magnetic or charge order in Cd Re O . How-
2 2 7
ever, asymmetry of electric field gradient indicates lack

0.4 of three–fold rotational symmetry. The superconduct-
ingstateaccordingtothetemperaturedependenceofRe
Ka NQR spin–lattice relaxation rate, is apparently a weak–

coupling BCS case with a nearly isotropic energy gap.

Cd NMR data show moderate ferromagnetic enhance-
0.3
mentabove200K.Rapiddecreaseofthespinsusceptibil-
ity and111(T T)−1 below the structuralphase transition
1
0 50 100 150 200 250 300 at 200 K is accounted for by loss of the density of states
T (K) (DOS)downto 120K.The shiftandrelaxationratedata

at lower temperatures pose puzzles which remain to be
FIG. 4: Temperature dependence of Kα. Filled circles: clarified.
experimental data of Kα obtained from 111Cd (T1T)−1 and We would like to thank H. Harima and K. Ueda for
Kspin=Kiso using eqn. (1) Open circles: Kα,RPA calculated enlightening discussion. This work is supported by the
from eqs. (2, 3) and thedata of χs from ref. [3].
Grant–in–Aid for Scientific Research, No. 12–00037 and
No. 10304027from the Japan Society for the Promotion
seethatfromhightemperaturesdownto∼120Kthecal- of Science (JSPS), and No. 12046219, Priority Area on
culated K reproduces the experimental data fairly Novel QuantumPhenomena in Transition Metal Oxides)
α,RPA
well, supporting our assumption that loss of DOS is the fromtheMinistryofEducation,Culture,Sports,Science
majorcauseforthereductionofbothχ and111(T T)−1 and Technology Japan. The research activity of O.V. in
s 1
below 200 K. However, they diverge below 120K. The Japanis supportedby the JSPSPostdoctoralFellowship
anomalousbehavioratlow temperatures implies that ei- for Foreign Researchers in Japan.
ther ferromagnetic enhancement is restored or there is
additional suppression only for the dynamical suscepti-
bility.
We found that the ratio of T−1 at Re and Cd sites
1 [1] A. P. Ramirez et al.,Nature 399, 333 (1999).
is unexpectedly large. Hyperfine interaction between Re [2] C. Urano et al.,Phys. Rev.Lett.85, 1052 (2000).
nuclei and the 5d conduction electrons should be mainly [3] M. Hanawa et al.,Phys. Rev.Lett. 87, 187001 (2001).
due to core polarization effect, with typical magnitude – [4] H. Sakai et al.,J. Phys.-Cond. Mat. 13, L785 (2001).
120T/µ [22]. Fromthevaluesofthehyperfinecoupling, [5] R. Jin et al.,Phys. Rev.B 64, 180503 (2001).
B
the nuclear gyromagnetic ratio and the reduction factor [6] D. Mandrus et al.,Phys. Rev.B 63, 195104 (2001).
for the relaxation due to core polarization field [23], we [7] M. Hanawa et al.,cond-mat/0109050.
expecttheratio187T−1/111T−1tobe17. Experimentally [8] R. Jin et al.,cond-mat/0108402.
we obtain 187T−1/1111T−1=4120 at 5K. Possible reasons [9] Z. Hiroi, privatecommunication.
1 1 [10] H. Harima, J. Phys. Chem. Solids, to be piublished.
for this may be the following: (1) Orbital hyperfine field [11] D.J.Singh,P.Blaha, K.Schwarz,andJ.O.Sofo, cond-
gives large contribution to 187T−1. (2) The hyperfine mat/0108226.
1
coupling, in particular for Cd nuclei, is not uniform over [12] Y. Yamashita and K. Ueda, Phys. Rev. Lett. 85, 4960
the Fermi surface, i.e. some partof the Fermi surface do (2000).
notcoupleeffectivelytoCdnucleibutmakeslargecontri- [13] L. C. Hebel and C. P. Slichter, Phys. Rev. 113, 1504
(1959).
bution to the Re relaxation rate. The latter case points
[14] Z. Hiroi and M. Hanawa, cond-mat/0111126.
to non–trivial magnetic correlation among 5d electrons
[15] M. D.Lumsden et al.,cond-mat/0111187.
which does not manifest in the Cd relaxation data. [16] R. Kadono et al.,cond-mat/0112448
Finally, we comment on the large reported value of [17] D. E. MacLaughlin, Solid. State. Physics 31, 1 (1976).
the T-linear coefficient of the specific heat γ=15 mJ/K2 [18] A.Abragam,ThePrinciples of Nuclear Magnetism (Ox-
above T [3]. Our estimate of χ and the susceptibil- ford UniversityPress, 1961), p.251.
c 0
ity data in ref. [3] give χ = 7×10−5 emu/mole Re at [19] G. C. Carter, L. H. Bennett, and D. J. Kahan, Metallic
s
Shifts in NMR (Pergamon Press, 1977).
5 K. We then obtain the Wilson ratio R =0.34. Such a
W [20] T. Moriya, J. Phys. Soc. Japan 18, 516 (1963).
smallvalueofRW wouldnormallyimplystrongelectron– [21] A. Narath, Phys.Rev. 18, 516 (1963).
phonon coupling and appears to be incompatible with [22] M. Shaham, U. El-Hanany, and D. Zamir, Phys. Rev. B
the weak coupling superconductivity. A exotic possibil- 17, 3513 (1978).
itymaybethatthelargeγ isduetolowlyingexcitations [23] Y. Yafet and V. Jaccarino, Phys. Rev. 133, A1630
which do not contribute to χ , for example, orbital fluc- (1964).
s