Table Of ContentNMR in the normal and in the superconducting state of MgB and comparison with
2
AlB
2
S. H. Baek,1 B. J. Suh,2 E. Pavarini,3 F. Borsa,1,3 R. G. Barnes,1 S. L. Bud’ko,1 and P. C. Canfield1
1Department of Physics and Astronomy and Ames Laboratory, Iowa State University, Ames, IA 50011
2 2Department of Physics, the Catholic University of Korea, Puchon, 420-743, Korea
0 3Department of Physics “A. Volta” and Unita’ INFM di Pavia, Via Bassi 6, I27100 Pavia, Italy
0 (Dated: February 1, 2008)
2
11BNMRmeasurementshavebeenperformed in11BenrichedMgB2 powdersamples inexternal
n fields of 0.813, 1.55, 4.7 and 7.2 T both in the normal phase and in the superconducting phase. A
a
previously unreported dipolar Pake doublet has been observed in the quadrupole perturbed NMR
J
spectrum. TheKnightshiftcanthusbeaccuratelydeterminedbynarrowingthelinewiththeMagic
4 AngleSpinning(MAS)technique. Resultsof Knightshift (K) andrelaxation rates (1/T1) for both
2 11B and 27Al nucleiare reported also for AlB2. The comparison of thedata in thetwo compounds
shows the dramatic drop of the density of states at the boron site in AlB2 with respect to MgB2.
]
n The experimental values for K and 1/T1 are in most cases in good agreement with the theoretical
o values obtained from first principles calculations. The recovery of thenuclear magnetization below
c Tc in random powder samples is non-exponential due to the anisotropy of the upper critical field.
- Theexponentialdropof1/T1inthesuperconductingphaseobservedbyKotegawaetal.isconfirmed
r
herebut not thecoherence peak.
p
u
PACSnumbers: 74.25.Nf,74.70.Ad
s
.
t
a
m I. INTRODUCTION initio calculations.
-
d After the discovery of superconductivity1 in MgB
2
n
with T ∼ 39 K and subsequent observation of boron II. EXPERIMENTAL DETAILS AND SAMPLE
o c
isotope effect2,3 confirming that MgB is a phonon- PREPARATION
c 2
[ mediated BCS superconductor, much effort have been
devoted to this intermetallic compound up to date due MgB crystallizes in the hexagonal AlB type struc-
2 2 2
v to its remarkably high Tc among BCS superconductors. ture,whichconsistsofalternatinghexagonallayersofMg
0 Nuclear Magnetic Resonance (NMR) is a suitable mi- atoms and graphite-like honeycomb layers of B atoms.
5 croscopic tool to investigate the electronic structure in Powder samples were prepared with the method de-
4 the normal state, the structure of the gap and the flux scribed in Ref. [2]. X-ray powder diffraction measure-
1 line lattice in the superconducting state.4 This justi- ments confirmed the hexagonal unit cell of MgB .1,2
2
0 fies the large number of studies by both 11B and 25Mg MagnetizationmeasurementsdoneatH =2.5mTyielda
2
0 NMR in MgB2 which havealreadyappearedin the liter- transitiontemperature Tc =39.2 K with a shielding vol-
ature.5,6,7,8,9,10,11 ume fraction close to 100 %.2,12,13 We have investigated
/
at Regarding the 11B NMR, there is substantial agree- several samples from different batches of polycrystalline
m mentaboutthemeasurementsofthequadrupolecoupling 11B enriched MgB in order to check the reproducibility
2
constantν andaboutthenuclearspin-latticerelaxation of the data. Also we have performed measurements in
- Q
d rate,1/T ,inthenormalphase. Ontheotherhandthere samplesfromthesamebatchbothinbulkandinpowder
1
n is considerable controversy concerning the 11B Knight ground to different particle size. No substantial differ-
o
shifts in the normal phase and about the temperature ences were observed in the NMR measurements in the
c
dependenceof1/T inthesuperconductingphase. Inthe different samples. The onset of superconductivity was
: 1
v present paper, we report new results for the 11B NMR alsodeterminedbymonitoringthe detuning ofthe NMR
i
X spectrum in the normal phase and an accurate determi- circuit occurring at the irreversibility temperature, Tirr.
nationoftheKnightshiftbyusingtheMagicAngleSpin- This type of measurement corresponds to probing the
r
a ning (MAS) technique. We also find an explanation for temperature dependence of the radio frequency (rf) sur-
thediscrepanciesintheresultsof1/T belowT reported face resistance.5 Thus, as the magnetic field is increased
1 c
by different authors, based on the strong anisotropy of the transition region broadens due to the dissipation as-
the upper critical field in MgB . sociated with flux line motion below T , and at 7.2 T
2 c
Since NMR in metals probes the density of states nodetuningcanbeobservedalthoughthemagnetization
(DOS) at the Fermi level, we have performed measure- measurements indicate a Tc =23 K at 7 T.5 The transi-
ments of both 11B and 27Al NMR in AlB2 in order to tion temperature at 4.7 T was found to be Tc = 27.5 K
comparetheDOSinthetwocompounds. Finallytheex- and at 1.55 T, Tc =34 K.
perimental results for Knight shifts and relaxation rates 11B and 27Al NMR and spin-relaxationmeasurements
in both MgB and AlB have been compared with ab- were performed with home built Fourier transform (FT)
2 2
2
pulse spectrometers operating at variable frequencies.
The π/2 radio frequency (rf) pulse length was typically
6 µs. The Magic Angle Spinning (MAS) experiment was
performedwithahomebuiltspinningprobewithamax-
imum spinning frequency of about 10 kHz.
III. 11B NMR IN MgB IN THE NORMAL
2
STATE
The 11B NMR spectrum in MgB powder samples is
2
complicated by the simultaneous presence of first and
secondorderquadrupoleinteractions,anisotropicKnight
shiftandapreviouslyunnoticeddipolarsplittingwhichis
particularlyevidentin11Bisotopicallyenrichedsamples.
Inthefollowingweanalyzethedifferentspectralfeatures,
anecessarystepinordertoextractreliableNMRparam-
eters.
FIG. 1: Room-temperature 11B NMR spectrum for MgB2
powder sample showing both the central line transition and
A. Quadrupole interactions the two singularities of the distribution of satellite transi-
tions. The inset shows the temperature dependence of the
Thecomplete11BNMRspectrumwasdeterminedina quadrupolecoupling constant derived from the spectrum.
7.2 T external field by performing the Fourier transform
of half of the solid echo following a (π/2) −τ −(π/2)
0 90
pulse sequence. In order to cover the whole spectrum where νL is the nuclear Larmor frequency. Because of
three separate spectra were recorded at resonance fre- the inverse Larmor frequency dependence in Eq. 2 the
quencies centered at the three lines and added together. two singularities can be resolved only at low magnetic
The result is shown in Fig. 1. Each rf pulse has a band- field as shown in Fig. 2(a). At lower fields (1.55 and
widthofabout100kHz. Since thespectrumisthe result 0.813 T), the second order quadrupole splitting is well
ofirradiationatonlythreedifferentfrequencies,theparts resolved and each singularity is split into a doublet. If
of the spectrum in between the peaks may be distorted one takes the middle point of each doublet, the distance
but this does not affect the conclusions. The separation betweensingularitiesis ingoodagreementwith thatcal-
of the symmetric satellite lines is due to first and second culated from Eq. 2 and the value of νQ determined from
order quadrupole interactions. For spin I = 3/2, with the separation of the satellite lines i.e. δν =32.7 kHz at
electric quadrupole moment Q and for an axially sym- 0.813 T [see Fig. 2(b)]. One unexpected feature is that
metric electric field gradient tensor (EFG) with maxi- the two singularities are each split into a field indepen-
mum component q the separation is14 dentdoublet. Athigherfields(4.7and7.2T),thesecond
orderquadrupolesplittingisnegligibleandonlyonePake
e2qQ
∆ν =ν (3cos2θ−1) with ν = (1) doublet is shown.
Q Q
2h
where θ is the angle between the principal axis of the
EFG tensor and the applied field H .
0 B. Dipolar doublet
In a powder pattern the two singularities in the satel-
lite distribution occur at θ = 90◦. Thus from the spec-
As shown in Fig. 2(a) at high fields, where the second
trum in Fig. 1 we obtain ν = 835 ± 10 kHz. The
Q orderquadrupoleeffectsbecomenegligible,the11BNMR
quadrupole coupling constant is almost temperature in-
spectrum is formed by a doublet. At low fields one can
dependent as shown in the inset of Fig. 1. A small in-
clearly resolve two doublets, one for each singularity in
creaseinthe quadrupolecouplingconstantwithdecreas-
the quadrupolepowderpattern. The splitting istemper-
ing temperature was observed in 111Cd perturbed angu-
ature and field independent and results from the near-
lar γγ–correlation(TDPAC) experiments6 and is consis-
est neighbor nuclear dipolar interaction of 11B nuclei in
tent with the effect of lattice vibrations.15
the planar honeycomb lattice structure. In such a struc-
In the presence of second order quadrupole effects the
ture each 11B nucleus is strongly coupled to three near-
central line transition is shifted. For axially symmetric
est neighbors resulting in three equivalent Pake pairs.16
EFG this results in a powder pattern with two singular-
A single dipolar pair gives rise to a Pake doublet in the
ities separated by
NMR spectrum with frequencies:
25ν2
Q
δν = 48νL (2) ν± =νL±νD(3cos2θ′−1) (3)
3
FIG. 2: (a) Central line transition of 11B NMR spectrum for
powder sample of MgB2 at several representative magnetic
fields. (b) Spectrum at 0.813 T. The distance between the
middlepointofeachdoubletcorrespondstothesecondorder FIG. 3: Magic angle spinning (MAS) experiment in MgB2
quadrupolesplitting, δν. powder sample at 4.7 T. Spinning frequencies are shown at
theright side of the figure.
with
anisotropic Knight shift may be inferred from the asym-
3 γµ
νD = 22πa3 (4) metric broadening of the NMR line.17 Since our mea-
surements are limited to a maximum field of 7.2 T no
where θ′ is the angle formed by the magnetic field with measurable anisotropic Knight shift could be detected.
the vectorjoining the twointeractingnuclei, µis the nu- The isotropic Knight shift, K, is measurable but very
clearmagneticmomentandaistheinternucleardistance. small. Its measurement is further complicated by the
In the presence of three interacting pairs one has to dipolar splitting discussed above. In order to obtain a
sum over the different angles and take the powder av- reliable value of K we performed a magic angle spinning
erage including the second order quadrupole interaction (MAS) experiment18 at room temperature in a field of
and the anisotropic Knight shift interaction. The situ- 4.7 T. As shown in Fig. 3, the dipolar splitting is totally
ation was analyzed previously in connection with mea- removedforaspinningfrequencyof8kHzaswellaspart
surementsin intermetalliccompounds ofthe C32(AlB ) of the dipolar broadening and of the quadrupole broad-
2
structure.17 The conclusion was reached that in the C32 ening. From the resulting narrow line we obtain K =80
structure the resonance line in the presence of all the ppm with respect to a reference solution of NaBH4. If
aboveinteractionscanbedescribedintermsoftheangle the Knight shift is referred to the BF3 solution, which
θ formedbythe magnetic fieldandthec axialsymmetry is the compound used by chemists as the “zero chemical
axisperpendiculartotheB plane. Thusitwaspredicted shift”,19 one obtains K =40±10 ppm.
that the θ = 90◦ singularity in the quadrupole pattern
should be split into two lines separated by ∆ν = 3ν
90 D
while the intermediate angle singularity should be split
D. Nuclear spin-lattice relaxation rate
into two lines separated by ∆ν = 2ν . From the in-
1 D
spectionofFig.2(b)onecanseethattheratioofthetwo
splittings is in reasonableagreementwith the abovepre- Forthecaseofsaturationofthe centralline ofthe11B
diction. Furthermore, by using in Eq. 4 γ = 13.66×2π NMR spectrum with a single rf pulse (or short sequence
MHz/T, µ = Iγh/2π and the measured value ν = of pulses) and for magnetic relaxation mechanism, the
D
4.00±0.50kHz(at0.813T),oneobtainstheB-Bnearest recovery of the nuclear magnetization after a time t fol-
neighbordistancea=1.72±0.08˚Ainagreementwiththe lowing saturation is given by:20
known value of 1.782 ˚A.
M(∞)−M(t)
=0.1exp(−2Wt)+0.9exp(−12Wt) (5)
M(∞)
C. Knight shift
wherewedefinethenuclearspinlatticerelaxationrateas
In order to determine the Knight shift, both isotropic 1/T =2W. Theresultsforthetemperaturedependence
1
and anisotropic parts, measurements should be made of 1/T are shown in Fig. 4. As can be seen, a field
1
at very high magnetic fields (H ≫ 10 T) where the independent linear temperature dependence is observed
second order quadrupole effects are negligible, and the in the normal phase yielding T T =170 sK.
1
4
FIG. 4: Temperature dependence of 1/T1 for 11B in MgB2 FIG. 5: Comparison of 1/T1 for 11B and for 27Al in AlB2
at external fields 1.55, 4.7 and 7.2 T. The line is the Kor- powder sample. T1T for 27Al is 400 times smaller than the
ringa law with T1T =170 sK. The three arrows indicate the valuefor 11B.
superconducting transition temperatures at each field which
are 23, 27.5 and 34 K respectively. In the inset, (T1T)−1103
is plotted against temperature.
temperature dependence yields for 27Al T T = 3.5 sK
1
which is 400 times smaller than the value for 11B.
ThevariousNMRparametersforbothMgB andAlB
IV. 11B AND 27Al NMR IN AlB2 aresummarizedinTab.I. TheconstantS liste2dinTab.2I
is given by S = (γ /γ )2h/(8π2k ) and the Korringa
e n B
The room temperature 11B NMR spectrum on the ratio R is defined as R=K2T T/S.
1
powder sample of AlB is very similar to the one shown
2
in Fig. 1 for MgB . From the separation of the satel-
2
lite lines one derives a quadrupole coupling frequency V. COMPARISON OF THEORY AND
νQ = 540±10 kHz somewhat smaller than the one in EXPERIMENTS IN MgB2 AND AlB2
MgB . Thecentraltransitionlinewidth atroomtemper-
2
ature is about 19 kHz and it hides the dipolar splitting
In order to understand the microscopic origin of the
discussed for the case of MgB2 due to the stronger dipo- relaxation, and thus also the differences between AlB2
lar interaction with the 27Al nuclei present in AlB2. By and MgB , a comparison between experimental and ab-
2
spinning the sample at 10 kHz we obtain a MAS NMR initio calculated values of Knight shifts and relaxation
line 2 kHz wide. The Knight shift value with respect
rates is highly desirable. Recently, first principles calcu-
to a reference solution of BF3 measured from the MAS lationofthe relaxationrates21,22 andthe Knightshifts21
spectrum is found to be K =−10±5 ppm. Finally, the were performed for MgB . In Ref. [22] the relaxation
2
1/T1 measurements as a function of temperature shown rates were calculated for AlB2 as well. In the present
inFig.5yieldaKorringalawwithT1T =1400sKi.e.al- work we calculate K and 1/T1T for AlB2 by using the
most one order of magnitude greater than in MgB2. methoddescribedinRef.[21],andcomparetheresultsfor
The roomtemperature 27Al (I =5/2)NMRspectrum MgB and AlB . Our calculations are based on density
2 2
in AlB2 is composed of a central transition line 23 kHz functional theory (DFT) in the local density approxima-
wide and a poorly-resolved powder pattern originating tion (LDA). We adopt the tight binding linear-muffin-
from the two satellite pairs over a spectral distribution tin-orbital (LMTO) method23 in the atomic-spheres-
of about 200 kHz. From the fit of the NMR spectrum to approximation (LMTO47 Stuttgart code). The density
a computer simulated spectrum with a Gaussian dipolar ofstatesmatrix(Eq.2ofRef.[21])andthepartialdensity
width of 7.5 kHz one can derive a quadrupole coupling of states, N , (with L = lm, where l is the orbital an-
L
constantνQ =80±10kHz. Itisassumedthattheelectric gular momentum quantum number, and m = −l,···,l)
fieldgradienthasaxialsymmetryasforthe11Bsite. The were calculated by using the linear tetrahedron method.
Knight shift was measured from the position of the cen- We found that the results already converged very well
tral line transition (which has a negligible second order with a mesh of 481 irreducible k points. In order to ob-
quadrupole broadening). The Knight shift with respect tain accurate wavefunctions at the Fermi level, the lin-
to a AlCl3 aqueous solution is K =880±20 ppm. ear partial wave expansion was performed with ǫν ≡ǫF,
The27Al1/T resultsasafunctionoftemperatureare where ǫ is the Fermi level and ǫ the expansionenergy.
1 F ν
showninFig.5togetherwiththe11Bresults. Thelinear Furtherdetailsaboutthemethodemployedcanbefound
5
MgB2 AlB2
25Mg [Ref. 7] 11B 27Al 11B
K (ppm) 242±4a +40 ± 10b +880 ± 20c −10 ± 5b
T1T (sK) 1090 170 3.5 1400
S (sK) 7.03×10−5 2.57×10−6 3.88×10−6 2.57×10−6
R 0.95 0.102 ± 0.05 0.7 ± 0.03 0−0.12
νQ (kHz) 222 (1.5) 835 (10) 80 (10) 540 (10)
TABLE I: Summary of the various NMR parameters for both MgB2 and AlB2. The Korringa ratio, R, is defined as R =
K2T1T/S. Resultsfor 25Mg NMR were taken from Ref. [7].
aReferencesolutionMgCl2
bReferencesolutionBF3
cReferencesolutionAlCl3
in Ref. [21]. and K(B)∼21/37 ppm. For the relaxation time, it was
In Tab.II andTab. III, we showthe calculatedK and shown21thattheStonerenhancementfactorisabout1.6.
1/T T. The results for MgB are taken from Ref. [21]. Thus the total relaxation times are: T T(Mg)∼ 625 sK
1 2 1
Let us discuss first the case of MgB2. The 11B orbital and T1T(B) ∼ 169 sK. These results are in quite good
relaxation rate is about 3 times larger than the dipole- agreement with experimental data.
dipole,andabout10timeslargerthantheFermi-contact LetusnowdiscussthecaseofAlB . Inthiscompound
2
term. As explained in Ref. [21], the reasonis the follow- the B p bands are fully occupied, and only B p bands
σ π
ing. In MgB2 the B pσ and B pπ bands are all at the are at the Fermi level. In addition |φs(0)|2/4π ∼2.87a30
Fermilevel: the partialdensity ofstates Npx,y (σ bands) andNs ∼0.003states/eV/spin/B,hr−3i11 ∼1.45a30 and
and Npz (π bands) are, respectively, Npx =Npy ∼0.035 Np ∼ 0.0216 states/eV/spin/B. With these numbers we
states/eV/spin/B, and Npz ∼ 0.045 states/eV/spin/B. find F ∼ 2.3; terms with l > 1 give a small contribution
On the contrary, there are very few B s electrons close to F, because the radial integrals decrease quickly when
to ǫF (Ns ∼ 0.002 states/eV/B). An approximate for- l increasesandbecause,inthecaseofB,Nl isverysmall
mula for the ratio between the Fermi-contact and the for l > 1. Thus F is considerably larger than 1, and
orbital/dipole-dipole coupling constants is given by21 theFermicontactinteractionisthedominantmechanism
of relaxation for 11B (see Tab. III). The same happens
F = 2 |φs(0)|2Ns . (6) for 27Al, for which we find |φs(0)|2/4π ∼ 2.96a30 and
3Pl>0hr−3illNl Ns ∼0.0362states/eV/spin,hr−3i11 ∼1.74a30andNp ∼
0.0325 states/eV/spin/B, and therefore F ∼16.
Here φl(r) is the l radial solutions of the Schr¨odinger Inordertounderstandbetterthenumericalresultsfor
m=l
equationatenergyǫν andNl ≡Pm=−lNlm. Inaddition AlB2, we calculate analytically the contact shift and re-
hr−3ill ≡ R(|φl(r)|2/r−3)r2dr and φs(0) ≡ φl=0(r = 0), laxation rates for a model Hamiltonian which includes
wherer =0isthepositionofthenucleus. InthecaseofB only B s and Al s states. Within this model, the Knight
it was found21 F ∼0.35. Thus F is considerablysmaller shift is given by K ∼ µ2B(4/3)|φs(0)|2Ns, and the re-
than 1, and the Fermi contact interaction (which usu- laxation rate can be obtained from the Korringa rela-
ally dominates overthe orbitaland dipole-dipole mecha- tion. We find K(Al) ∼ 645 ppm, K(B) ∼ 52 ppm
nisms) gives only a small contribution to the relaxation and 1/T1T(Al) ∼ 107 · 10−3/(sK), 1/T1T(B) ∼ 1.05 ·
rate. Moreover, it was found21 that N = N ∼ N . 10−3/(sK), in very good agreement with the first princi-
px py pz
ForamodelHamiltonianwhichincludesonlyBporbitals ples values of Tab. II and Tab. III.
andforwhichN =N =N =N /3,onecanshowan- Theab-initiototalKnightshifts(Tab.II)areK(Al)∼
px py pz p
alytically21 that the ratio between orbital/dipole-dipole 644/647ppmandK(B)∼42/66,andthetotalrelaxation
relaxationrate is about 3.3. This explains the numerical times (Tab. III) are T1T(Al) ∼ 9 sK and T1T(B) ∼ 602
results obtained for B in MgB . sK. The agreement between first principle results and
2
The case of 25Mg is different: the ratio F is consider- experimental data is quite good for Al. In the case of
ably largerthan one (F ∼5)andthus the Fermicontact Bthe calculatedrelaxationtime isabout2timessmaller
interaction is expected to dominate. Tab. III shows that thantheexperimentaldata. Similarresultswerefoundin
this actually happens: the orbital and the dipole-dipole Ref.[22]. Thisdiscrepancycouldsuggestthat,inthecase
termsaremuchsmallerthantheFermicontactcontribu- of AlB2, LDA tends to slightly overestimate the Fermi-
tion. contact interaction at B nucleus.
With a Stoner enhancement factor of about 1.33 (cal- Finally,wepointoutthatinAlB thedensityofstates
2
culated ab-initio in Ref. [21]), the following results were intheB planeisstronglyreducedwithrespecttoMgB .
2
foundforthetotalKnightshifts: K(Mg)∼361/341ppm The reason is that in AlB the σ bands are well below
2
6
MgB2 dipole (xy) dipole(z) orbital Fermi contact core Total (xy/z) Experiment
B -4 8 0 27 -7 16/28 40±10
Mg 5 -10 0 260 3 271/256 242±4
AlB2 dipole (xy) dipole(z) orbital Fermi contact core Total (xy/z) Experiment
B -8 16 0 61 -11 42/66 −10±5
Al 1 -2 0 660 -15 644/647 880±20
TABLE II: Knight shifts in ppm in MgB2 and AlB2 (without Stoner factor). The label α= x,y,z indicates the direction of
theexternal magnetic field. Results for MgB2 are taken from Ref. [21].
MgB2 dipole orbital Fermi-contact core Total Experiment
B 0.8 2.6 0.28 0.02 3.7 5.9
Mg 0.01 0.02 1.0 0.0001 1.0 0.92
AlB2 dipole orbital Fermi-contact core Total Experiment
B 0.086 0.132 1.4 0.04 1.66 0.71
Al 0.115 0.370 105 0.05 105 286
TABLE III: Relaxation rates in 10−3/(sK) in MgB2 and AlB2 (without Stoner factor). Results for MgB2 are taken from
Ref. [21].
ǫ , while in MgB they cross the Fermi level. We find
F 2
N +N ∼0.0046 and N ∼0.017 states/eV/spin/B,
px py pz
while for MgB N + N ∼ 0.07 and N ∼ 0.045
2 px py pz
states/eV/spin/B was found.21
VI. 11B NMR IN MgB IN THE
2
SUPERCONDUCTING PHASE
Althoughthemainemphasisofthepresentpaperison
theelectronicpropertiesofMgB inthe normalphase,it
2
is worthwhile to present and discuss here the 11B NMR
results obtained in the superconducting phase mostly to
point out the limitations incurred in the NMR experi-
ments in polycrystalline samples.
Regarding the Knight shift, one can conclude that no
meaningful measurements of K can be performed below FIG. 6: 1/T1 results for 11B in a powder and in a sintered
Tc in a powder sample. In fact the Knight shift is very bulk sample of MgB2 below Tc.
small compared to the line broadening due to the mag-
netic field distribution of the flux line lattice.8 Further-
more the correction for the shift due to the diamagnetic observed in the data taken in an external field of 1.55 T
shielding in the superconducting phase cannot be esti- but not in the data at 4.7 T and 7.2 T. The explana-
mated accurately in a powder sample as a result of the tion for this is easily found in the strong anisotropy of
distribution of shapes of the particles e.g.distribution of the upper criticalfield, H . The powders utilized in the
c2
demagnetization factors. present experiment have Hmax/Hmin = γ ≈ 6 whereby
c2 c2
The temperature dependence of 1/T below T allows the maximum critical field pertains to the particles with
1 c
inprincipletoobtaininformationaboutthepairingsym- the field in the ab plane.26,27 In a detuning experiment
metryandthestructureofthe superconductinggap.24,25 one detects the superconducting transition of the parti-
In fact the ratio of the relaxation rates in the supercon- cleswhichhavethehigheruppercriticalfield(seearrows
ducting phase andthe normalphase,(1/T )/(1/T ), is in Fig. 4). On the other hand in the NMR experiment
1s 1n
related to the density of states in the superconducting the stronger signal arises from the particles which are
phase and should decrease below T either exponentially orientedinsuchawayastohavetheloweruppercritical
c
or with a power law depending on the pairing symme- field. This is a consequence of the strongly reduced rf
try and/or the structure of the gap.9 As can be seen in penetration length and consequently reduced NMR sig-
Fig. 4 a decrease of the relaxation rate below T can be nal, in the superconducting particles. Thus the results
c
7
T as claimed by Kotegawa et al.9 It is noted that from
c
the data in the inset of Fig. 4 and Fig. 7 there appears
to be a enhancementof(T T)−1 overthe Korringavalue
1
of the normal phase starting at T and extending to low
c
temperature. This effect, which is barely outside the ex-
perimental error, is not presently understood. One may
speculate that the measured 1/T in Fig. 4 is an aver-
1
age of the relaxation of nuclei in particles in the normal
phase and particles in the superconducting phase with
H perpendicular to the ab plane in which the relaxation
is enhanced by the presence of flux lines.4 More detailed
measurements as a function of magnetic field are needed
to elucidate this point.
VII. SUMMARY AND CONCLUSIONS
Fromtheanalysisofthe11BNMRspectruminthenor-
FIG. 7: The plot of the ratio of 1/T1 in thesuperconducting
phaseandthenormalphaseagainstT/Tc. Theshortandlong mal phase of isotopically enriched MgB2, we have found
components of the relaxation rate at 4.7 T were obtained by evidence for a field independent splitting of the line due
fittingthe data toEq. 5 with two different values of W. to the nuclear dipolar interaction (Pake doublet). By
averaging out the dipolar interaction with Magic Angle
Spinning,wehaveobtainedreliablevaluesfortheKnight
in Fig. 4 for fields of 4.7 T and 7.2 T pertain mostly to shiftsfor11BinbothMgB2 andAlB2. Boththedecrease
the particles which remain in the normal phase down to of K and more so of (T1T)−1 for 11B in AlB2 with re-
helium temperature. It should be noted that the results spect to MgB2 is in qualitative agreementwith a drastic
inaloosepowderandinapolycrystallinebulk(sintered) dropofthe DOSattheFermilevelattheBsiteinAlB2.
sample are the same as shown in Fig. 6. The ab-initio calculated values in Tab. II and III are in
Our results need to be reconciled with the 11B NMR excellentagreementwiththe experimentalonesinMgB2
data in MgB by Kotegawa et al.9 where it is reported providedthetheoreticalresultsaremultipliedbyaStoner
2
that 1/T decreases exponentially below T in powder enhancement factor of 1.33 for the Knight shift and 1.6
1 c
samplesforallfieldvaluesfrom1.35T upto4.42Twith for the relaxation rates.
a tiny coherence peak just below Tc. First it is noted ForthecaseofAlB2 theab-initiocalculatedvaluesare
that the samples used in Kotegawa’s experiments could ingoodagreementwiththeexperimentsonlyforthe27Al
haveamuchsmalleranisotropyoftheuppercriticalfield. data considering that the theoretical results in Tab. II
Recent resistivity measurements in MgB single crystals and III are still to be multiplied by the Stoner factor.
2
yieldananisotropyratiooftheuppercriticalfieldofonly However, for the B site in AlB2 the theoretical values
2.7.28 A second factor is that our measurements were for both K and (T1T)−1 are a factor of two bigger than
done by fitting the first 90 % of the recovery of the nu- the experimental values indicating that the LDA calcu-
clear magnetization which yields the short component lations overestimatethe Fermicontactinteractionatthe
only of the relaxation. On the other hand the results re- B nuclear site.
ported by Kotegawa et al. were obtained by fitting the Regarding the superconducting phase in MgB2, we
recovery of the magnetization with two components and conclude that it is very difficult to obtain reliable infor-
assuming that the long component only is the one per- mation for the NMR parameters (particularly the relax-
taining to the superconducting particles.29 By following ationrates)from polycrystallinesamples due to the ran-
the same procedure i.e. by fitting the recoveryof the nu- domorientationwithrespecttothe appliedfieldandthe
clear magnetization with Eq. 5 with two different values strong critical field anisotropy. In particular, we could
of W we find the results shown in Fig. 7. The long com- confirm qualitatively the exponential drop of 1/T1 vs T
ponent does indeed agree with Kotegawa’s data at high below Tc reported by Kotegawaet al.9 but we could not
field (4.7 T) and with our low field data (1.55 T) thus detectanyenhancementof1/T1justbelowTc (coherence
confirming the validity of the conclusions regarding the peak).
structure of the gap.9 However, the distribution of criti- One issue which remains to be investigated is the ef-
cal fields due to the random orientation of the particles fect on the nuclear relaxationrate of the flux line lattice
inapowdersampleintroduceslargeerrorsintheevalua- and flux line fluctuations in the superconducting phase
tion of1/T particularlyclose to T since the recoveryof which was detected qualitatively in the enhancement of
1 c
the magnetization is the superposition of curves, Eq. 5, T T below T (see the inset of Fig. 4) but which would
1 c
with different W values. Therefore it is very difficult to require aligned powder samples or single crystals to be
infer thepresenceofacoherencepeakin1/T justbelow investigated quantitatively.
1
8
Acknowledgments is operated for the U.S. Department of Energy by Iowa
State University under Contract W-7405-Eng-82. This
We thank J. K. Jung for his help in the beginning workatAmesLaboratorywassupportedbytheDirector
stageofthe experiment, P.CarrettaandTabakfor shar- forEnergyResearch,OfficeofBasicEnergyScience. One
ing some unpublished data on different samples and ofauthors(B.J.S.)acknowledgesthe supportbyKOSEF
V. Antropov for useful discussions. Ames Laboratory via electron Spin Science Center at POSTECH.
1 J. Nagamatsu, N. Nakagawa, T. Muranaka, Y. Zenitani, 14 A.Abragam,Principles of Nuclear Magnetism (Academic
and J. Akimitsu,Nature 410, 63 (2001). Press, London, 1961).
2 S.L.Bud’ko,G.Lapertot,C.Petrovic,C.E.Cunningham, 15 F.Borsa andA.Rigamonti,J.ofMagneticResonance20,
N.Anderson,andP.C.Canfield,Phys.Rev.Lett.86,1877 232 (1975).
(2001). 16 G. E. Pake, J. Chem. Phys. 16, 327 (1948).
3 D. G. Hinks, H. Claus, and J. D. Jorgensen, Nature 411, 17 D. R. Torgeson, R. G. Barnes, and R. B. Creel, J. Chem.
457 (2001). Phys. 56, 4178 (1972).
4 A.Rigamonti,F.Borsa,andP.Carretta,Rep.Prog.Phys. 18 E. Fukushima and S. B. W. Roeder, Experimental Pulse
61, 1367 (1998). NMR (Addison-Wesley Pub.Co, 1981).
5 J.K.Jung,S.H.Baek,F.Borsa,S.L.Bud’ko,G.Lapertot, 19 T.P.Onak,H.Landesman,R.E.Williams,andI.Shapiro,
and P.C. Canfield, Phys. Rev.B 64, 012514 (2001). J. Phys. Chem. 63, 1533 (1959).
6 A. V. Tsvyashchenko et al., Solid State Comm. 119, 153 20 E.R.AndrewandD.P.Tunstall,Proc.Phys.Soc.London
(2001). 78, 1 (1961).
7 M.Mali,J.Roos,A.Shengelaya,H.Keller,andK.Conder, 21 E. Pavarini and I. I. Mazin, Phys. Rev. B 64, 140504(R)
Cond-Mat/0111022 v2 (2001). (2001).
8 G.Papavassiliou,M.Pissas,M.Fardis,M.Karayanni,and 22 K.D.Belashchenko, V.P.Antropov,andS.N.Rashkeev,
C. Christides, Cond-Mat/0107511 (2001). Phys. Rev.B 64, 132506 (2001).
9 H. Kotegawa, K. Ishida, Y. Kitaoka, T. Muranaka, and 23 O.K.Andersen,Z.Pawlowska, andO.Jepsen,Phys.Rev.
J. Akimitsu,Phys. Rev.Lett. 87, 127001 (2001). B 34, R5253 (1986).
10 A.Gerashenko,K.Mikalhev,S.Verkhovskij,T.D’yachova, 24 L. C. Hebel and C. P. Slichter, Phys. Rev. 113, 1504
A. Tyutyunnik, and V. Zubkov, Cond-Mat/0102421 (1959).
(2001). 25 L. C. Hebel, Phys. Rev. 116, 79 (1959).
11 H. Tou, H. Ikejiri, Y. Maniwa, T. Ito, T. Takenobu, 26 S.L.Bud’ko,V.G.Kogan,andP.C.Canfield,Phys.Rev.
K. Prassides, and Y.Iwasa, Cond-Mat/0103484 (2001). B 64, 180506(R) (2001).
12 D.K.Finnemore, J.E.Ostenson,S.L.Bud’ko,G.Laper- 27 F. Simon et al., Phys. Rev.Lett 87, 047002 (2001).
tot, and P.C. Canfield, Phys. Rev.Lett 86, 2420 (2001). 28 S. Lee, H. Mori, T. Masui, Y. Eltsev, A. Yamamoto, and
13 P. C. Canfield, D. K. Finnemore, S. L. Bud’ko, J. E. Os- S. Tajima, J. Phys.Soc. Japan 70, 2255 (2001).
tenson, G. Lapertot, C. E. Cunningham, and C. Petrovic, 29 Y. Kitaoka, Private communication.
Phys. Rev.Lett. 86, 2423 (2001).
