We calculated the nuclear spin-lattice relaxation rate in the Mg1-xAlxB2 system and found that the orbital relaxation mechanism dominates over the dipolar and Fermi-contact mechanisms in MgB2, whereas in AlB2 due to a smaller density of states and strong anisotropy of boron p orbitals the relaxation is completely determined by Fermi-contact interaction. The results for MgB2 are compared with existing experimental data. To validate the theory, nuclear resonance experiments for the studied diboride alloy system are needed

Antropov, Vladimir B.

Belashchenko, Kirill D.

Rashkeev, S.N.

English

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DigitalCommons@University of Nebraska - Lincoln 
Faculty Publications from Nebraska Center for 
Materials and Nanoscience 
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8-28-2001 
Anisotropy of conducting p states and 11B nuclear spin-lattice 
relaxation in Mg1-xAlxB2 
Kirill D. Belashchenko 
University of Nebraska-Lincoln, belashchenko@unl.edu 
Vladimir B. Antropov 
Ames Laboratory, US Department of Energy, antropov@ameslab.gov 
S.N. Rashkeev 
Vanderbilt University, Nashville, Tennessee 
Follow this and additional works at: https://digitalcommons.unl.edu/cmrafacpub 
 Part of the Nanoscience and Nanotechnology Commons 
Belashchenko, Kirill D.; Antropov, Vladimir B.; and Rashkeev, S.N., "Anisotropy of conducting p states and 
11B nuclear spin-lattice relaxation in Mg1-xAlxB2" (2001). Faculty Publications from Nebraska Center for 
Materials and Nanoscience. 26. 
https://digitalcommons.unl.edu/cmrafacpub/26 
This Article is brought to you for free and open access by the Materials and Nanoscience, Nebraska Center for 
(NCMN) at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Faculty 
Publications from Nebraska Center for Materials and Nanoscience by an authorized administrator of 
DigitalCommons@University of Nebraska - Lincoln. 
Anisotropy of conducting p states and 11B nuclear spin-lattice relaxation in Mg1ÀxAl xB2
K. D. Belashchenko,1 V. P. Antropov,1 and S. N. Rashkeev2
1Ames Laboratory, Ames, Iowa 50011
2Vanderbilt University, Nashville, Tennessee 37235
~Received 17 May 2001; published 31 August 2001!
We calculated the nuclear spin-lattice relaxation rate in the Mg12xAl xB2 system and found that the orbital
relaxation mechanism dominates over the dipolar and Fermi-contact mechanisms in MgB2, whereas in AlB2
due to a smaller density of states and strong anisotropy of boronp rbitals the relaxation is completely
determined by Fermi-contact interaction. The results for MgB2 are compared with existing experimental data.
To validate the theory, nuclear resonance experiments for the studied diboride alloy system are needed.
DOI: 10.1103/PhysRevB.64.132506 PACS number~s!: 76.60.Es, 74.70.Ad, 74.25.Jb
The discovery of superconductivity in MgB2 ~Ref. 1! has
stimulated a significant interest in the electronic structure of
intercalated boron compounds. For the superconductivity,
one of the most important parameters is the valueN(EF)
[N of the electronic density of states~DOS! at the Fermi
level in the normal state. Several groups have performed
local-density-functional~LDA ! calculations of this quantity
and the results scatter around 0.7 states/~eV f.u.!.2–4 Experi-
mentallyN can be determined in many different ways but the
nuclear spin-lattice relaxation~NSLR! rate 1/T1 measure-
ments represent an excellent opportunity to check experi-
mentally not only the totalN and its partial components but
also their anisotropy, i.e., the distribution between the in-
plane and out-of-planep orbitals. Experimental values of
TT15180, 155, and 165 K sec for
11B (m52.689mN) were
reported.5–7 These relaxation rates were interpreted in terms
of dipolar and orbital contributions due to the corresponding
Korringa ratio and the already known2–4 theoretical totalN.
In this paper we perform a more careful theoretical analysis
of NSLR in MgB2. However, the direct numerical compari-
son with experiment for one single system may not be suffi-
cient to verify the theory, and studies of trends in a sequence
of related systems are usually much more credible. There-
fore, we also studied the NSLR in Mg12xAl xB2 that is the
only known diboride alloy with substitution in the Mg sub-
lattice and a rather wide range of solubility.8 In addition,
earlier studies2–4 have shown that in this system the two-
dimensional~2D! boron bands are gradually filled with Al
doping. Hopefully, the studies of NSLR in this system may
provide valuable information about the genesis of anisotropy
of electronic states at the Fermi level.
Below we evaluate the relaxation rates for MgB2 and
AlB2 compounds using an LDA calculation, and for the in-
termediate concentrations we used the rigid band approxima-
tion with MgB2 bands. We will show that in MgB2 the or-
bital mechanism is the leading term in NSLR, whereas the
Fermi-contact mechanism is dominating in AlB2. Our calcu-
lated total relaxation rate in MgB2 is in fair agreement with
experiments,5–7 thus indicating that the calculatedN in
MgB2 is basically correct, whereas in AlB2, due to high an-
isotropy and low DOS of boronp states, we predict a much
smaller relaxation rate fully determined by the Fermi-contact
mechanism.
The standard technical details of the Linear muffin-tin or-
bital calculations are similar to those described in Refs. 2 and
3. In addition, we carefully checked the sensitivity of the
results to the parameters of calculations. We used different
exchange-correlation potentials and inputs with different ra-
dii of the B sphere~both with and without empty spheres!.
Our values of DOS fors andp orbitals on theB site in MgB2
and AlB2 are listed in Table I. One can see that in MgB2 all
p orbitals on theB site have a sizable DOS, while in AlB2
only pz orbital is significant withNpx'0.1Npz . The s com-
ponent in AlB2 becomes relatively more important compared
to MgB2 resulting in the dominance of the Fermi-contact
NSLR in AlB2, as we will show below. In both materials the
contribution ofd states to NSLR is very small. As for the Mg
site, thes component ofN is the most important, and we
expect that the NSLR on25Mg is controlled by the Fermi-
contact mechanism. However, in this paper we will focus on
the 11B NSLR.
To calculateT1 according to a general prescription one
has to estimate thêr 23& l expectation values for different
orbitals and the electronic density at the nucleusws
2(0)/4p.
We found that the convergence of the total NSLR rate with
respect to the boron sphere radius in thissp system is worse
compared tod metals~from r B52.3a0 to r B52.4a0 the total
T1
21 decreases by;15%). The uncertainty is mostly related
to the value of̂ r 23&pNp .
In our calculations we used the largestr B that were pos-
sible without a significant distortion of the band structure,
2.4a0 for MgB2 and 2.1a0 for AlB2. For these radii we have
^(a0 /r )
3&p51.11 in MgB2 and 1.37 in AlB2. For compari-
son, the atomic value9 for ^(a0 /r )
3&p in B is 0.78. The elec-
tronic densities on the nucleusa0
3ws
2(0)/4p for MgB2 and
AlB2 were, respectively, 2.68 and 3.02.
The contributions to the11B relaxation rate for the poly-
crystalline sample calculated using the general formulas10 for
the hexagonal crystal are given in Table II. The in-plane and
TABLE I. Partial DOS for s and p orbitals at B site, 1023
(eV spin atom)21.
s pz px
MgB2 3.4 50 36
AlB2 3.3 19 1.9
PHYSICAL REVIEW B, VOLUME 64, 132506
0163-1829/2001/64~13!/132506~3!/$20.00 ©2001 The American Physical Society64 132506-1
out-of-planep orbitals in MgB2 have similar densities of
states, and hence the relative magnitude of orbital and dipo-
lar contributions to NSLR is close to the 3/10 rule forp
states in a cubic crystal described by Obata.10 The Fermi-
contact contribution is also important and amounts to 30% of
the orbital term. The contributions from thed partial waves
to the dipole and orbital relaxation rates are small~ t the
order of 1%! due to the low diagonal and off-diagonal den-
sities of states (Nd /Np)
2;0.02 and (Npd /Np)
2;0.05. The
quadrupole contribution to NSLR is negligible due to a
rather small11B quadrupole moment.
The values ofT1
21 obtained in such manner correspond to
the theoretical ‘bare’ partial boronN whereas the actualT1
21
contains different terms enhanced according to the corre-
sponding susceptibilities. To estimate the possible range of
enhancement, we calculated the total enhancement coming
from the spin susceptibility only~which is the case for
AlB2). We estimated the effective Stoner exchange param-
eter I[DE/m51.7 eV from the splitting of the bands at the
G point in the external magnetic field. The corresponding
Stoner enhancement of the uniform susceptibility in the 3D
case may be written11 as S53/@(12NI)(322IN)#'(1
2IN)2a with a'1.62, while in the 2D case the enhance-
ment is described by the same formula witha52. In our
case due to the mixed 2D and 3D character of the bands it is
not clear what value ofa should be used, but the difference
in the result fora51.62 and 2.0 is less than 10%. We used
a51.9 resulting in the enhancement ofT1
21 by approxi-
mately 60%~Table II!. The obtained ‘bare’ and enhanced
values provide a range of possible NSLR rates for MgB2 that
should be compared with the experimental rates5–7 of 56
31024–6431024 (K sec)21. The fact that such simple es-
timate may give a faster relaxation compared to experiments
suggests a possible importance of unique effects resulting in
the lowering of the effective boronN.
The roles of the three NSLR mechanisms are very differ-
ent in AlB2 where no traces of superconductivity have been
found and where no experimental data are available. Accord-
ing to our theoretical estimation, due to the sharp decrease of
the boronp component ofN compared to MgB2 and its very
strong anisotropy~see Table I!, the orbital and dipolar con-
tributions to NSLR become very small, and the NSLR in
AlB2 is completely dominated by the Fermi-contact mecha-
nism. This conclusion may be verified experimentally by
studying the Korringa ratio. The resulting Stoner-enhanced
NSLR rate in AlB2 is more than three times smaller than in
MgB2 ~see Table II!. We should note that the strong anisot-
ropy of boronp states in AlB2 on this stage is a theoretical
prediction and more experimental information is needed to
confirm it.
We also calculated the NSLR rate in Mg12xAl xB2 in the
rigid band approximation with MgB2 bands. From Fig. 1 one
can see how the roles of different mechanisms of NSLR
change with doping. The sharp decrease ofN in the 2D
sheets of the Fermi surface with doping3 leads to the corre-
sponding lowering of all contributions to NSLR, and at the
point of the complete filling of these 2D bands we expect a
very largeT1. Experimental verification of this sharp depen-
dence ofT1 on doping in this alloy may be a crucial test of
our understanding of the electronic structure of this system
and is highly desirable. Together with the nuclear quadrupole
resonance data~which is related to the anisotropy of total
charges on differentp orbitals! such measurements should
help to build a general picture of anisotropy ofp orbitals.
The above calculations have been done for a polycrystal-
line sample. Because single crystals are becoming available,
we include our estimations of the anisotropy in the angular
dependence of NSLR rate10 A1B sin2 u. For MgB2 we ob-
tained B/A'20.06, so that the NSLR is nearly isotropic.
The NSLR rate in AlB2 is isotropic because it is determined
by isotropic Fermi-contact mechanism.
In conclusion, we have performed LDA calculations for
the NSLR rate in the Mg12xAl xB2 system. We found that the
rbital mechanism of relaxation dominates over the spin-
dipolar and Fermi-contact ones in MgB2, because the boron
p orbitals at the Fermi level are distributed nearly isotropi-
cally and have a large DOS. Strong anisotropy and low den-
sity of p states at the Fermi level in AlB2 results in the
dominance of the Fermi-contact NSLR mechanism. With the
values of 0.7~0.5! st./eV for the bare total~boron partial!
DOS at the Fermi level for MgB2 and 1.7 eV for the effec-
tive Stoner exchange parameter, reasonable agreement is ob-
tained with the experimental NSLR rates. However, we em-
phasize a relatively weak radial convergence of the NSLR
rate in this system compared to the well-studiedd metals,
TABLE II. Contributions to (TT1)
21 @1024/(K sec)#.
Fermi
contact Orbital Dipole Total
Stoner
enhanced Experiments
MgB2 12 30 9 51 81 56
5,646,617
AlB2 21 1 1 23 26
FIG. 1. Different contributions to the total11B relaxation rate in
Mg12xAl xB2. Thick solid line, orbital; dashed, dipolar; thin solid,
Fermi contact.
BRIEF REPORTS PHYSICAL REVIEW B 64 132506
132506-2
and a common uncertainty related to the estimate of the en-
hancement factor. Still, we strongly believe that the obtained
results related to the relative importance of different NSLR
mechanisms are qualitatively correct. According to our cal-
culation, the NSLR rate strongly depends on the concentra-
tion in the Mg12xAl xB2 system, and the experimental studies
of this dependence are highly desirable for the understanding
of the anisotropy of boronp states.
When this paper was completed we became aware that
similar results for NSLR in MgB2 were independently ob-
tained in Ref. 12, where theT1 on
25Mg and the Knight
shifts were also computed. We believe that the discrepancy
in the Fermi-contact term is mainly due to the significantly
larger boron sphere radius used in our calculations.
We are grateful to I. Mazin and F. Borsa for valuable
discussions. This work was carried out at the Ames Labora-
tory, which is operated for the U.S. Department of Energy by
Iowa State University under Contract No. W-7405-82. This
work was supported by the Director for Energy Research,
Office of Basic Energy Sciences of the U.S. Department of
Energy.
1J. Nagamatsuet al., Nature~London! 410, 63 ~2001!.
2J. Kortus, I. I. Mazin, K. D. Belashchenko, V. P. Antropov, and L.
L. Boyer, Phys. Rev. Lett.86, 4656~2001!.
3K. D. Belashchenko, M. van Schilfgaarde, and V. P. Antropov,
cond-mat/0102290~unpublished!.
4J. M. An and W. E. Pickett, Phys. Rev. Lett.86, 4366~2001!; G.
Satta, G. Profeta, F. Bernardini, A. Continenza, and S. Massidda,
Phys. Rev. B~to be published 1 September 2001!.
5H. Kotegawa, K. Ishida, Y. Kitaoka, T. Muranaka, and J. Akim-
itsu, cond-mat/0102334~unpublished!.
6A. Gerashenko, K. Mikhalev, S. Verkhovskii, T. D’yachkova, A.
Tyutyunnik, and V. Zubkov, cond-mat/0102421~unpublished!.
7J. K. Jung, S. H. Baek, F. Borsa, S. L. Bud’ko, G. Lapertot, and P.
C. Canfield, Phys. Rev. B64, 012514~2001!.
8J. S. Sluskyet al., Nature~London! 410, 343 ~2001!.
9S. Fraga, K. M. S. Saxena, and J. Karwowski,Handbook on
Atomic Data~Elsevier, Amsterdam, 1976!.
10Y. Obata, J. Phys. Soc. Jpn.18, 1020 ~1963!; A. Narath, Phys.
Rev.162, 320~1967!; T. Asada and K. Terakura, J. Phys. F: Met.
Phys.12, 1387~1982!.
11B. S. Shastry and E. Abrahams, Phys. Rev. Lett.72, 1933~1994!.
12E. Pavarini and I. I. Mazin, cond-mat/0105350~unpublished!.
BRIEF REPORTS PHYSICAL REVIEW B 64 132506
132506-3


Anisotropy of conducting \u3ci\u3ep\u3c/i\u3e states and \u3csup\u3e11\u3c/sup\u3eB nuclear spin-lattice relaxation in Mg\u3csub\u3e1-x\u3c/sub\u3eAl\u3csub\u3ex\u3c/sub\u3eB\u3csub\u3e2\u3c/sub\u3e

DigitalCommons@University of Nebraska

University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Faculty Publications from Nebraska Center for Materials and Nanoscience Materials and Nanoscience, Nebraska Center for (NCMN) 8-28-2001 Anisotropy of conducting p states and 11B nuclear spin-lattice relaxation in Mg1-xAlxB2 Kirill D. Belashchenko University of Nebraska-Lincoln, belashchenko@unl.edu Vladimir B. Antropov Ames Laboratory, US Department of Energy, antropov@ameslab.gov S.N. Rashkeev Vanderbilt University, Nashville, Tennessee Follow this and additional works at: https://digitalcommons.unl.edu/cmrafacpub  Part of the Nanoscience and Nanotechnology Commons Belashchenko, Kirill D.; Antropov, Vladimir B.; and Rashkeev, S.N., "Anisotropy of conducting p states and 11B nuclear spin-lattice relaxation in Mg1-xAlxB2" (2001). Faculty Publications from Nebraska Center for Materials and Nanoscience. 26. https://digitalcommons.unl.edu/cmrafacpub/26 This Article is brought to you for free and open access by the Materials and Nanoscience, Nebraska Center for (NCMN) at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Faculty Publications from Nebraska Center for Materials and Nanoscience by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. Anisotropy of conducting p states and 11B nuclear spin-lattice relaxation in Mg1ÀxAl xB2K. D. Belashchenko,1 V. P. Antropov,1 and S. N. Rashkeev21Ames Laboratory, Ames, Iowa 500112Vanderbilt University, Nashville, Tennessee 37235~Received 17 May 2001; published 31 August 2001!We calculated the nuclear spin-lattice relaxation rate in the Mg12xAl xB2 system and found that the orbitalrelaxation mechanism dominates over the dipolar and Fermi-contact mechanisms in MgB2, whereas in AlB2due to a smaller density of states and strong anisotropy of boronp rbitals the relaxation is completelydetermined by Fermi-contact interaction. The results for MgB2 are compared with existing experimental data.To validate the theory, nuclear resonance experiments for the studied diboride alloy system are needed.DOI: 10.1103/PhysRevB.64.132506 PACS number~s!: 76.60.Es, 74.70.Ad, 74.25.JbThe discovery of superconductivity in MgB2 ~Ref. 1! hasstimulated a significant interest in the electronic structure ofintercalated boron compounds. For the superconductivity,one of the most important parameters is the valueN(EF)[N of the electronic density of states~DOS! at the Fermilevel in the normal state. Several groups have performedlocal-density-functional~LDA ! calculations of this quantityand the results scatter around 0.7 states/~eV f.u.!.2–4 Experi-mentallyN can be determined in many different ways but thenuclear spin-lattice relaxation~NSLR! rate 1/T1 measure-ments represent an excellent opportunity to check experi-mentally not only the totalN and its partial components butalso their anisotropy, i.e., the distribution between the in-plane and out-of-planep orbitals. Experimental values ofTT15180, 155, and 165 K sec for11B (m52.689mN) werereported.5–7 These relaxation rates were interpreted in termsof dipolar and orbital contributions due to the correspondingKorringa ratio and the already known2–4 theoretical totalN.In this paper we perform a more careful theoretical analysisof NSLR in MgB2. However, the direct numerical compari-son with experiment for one single system may not be suffi-cient to verify the theory, and studies of trends in a sequenceof related systems are usually much more credible. There-fore, we also studied the NSLR in Mg12xAl xB2 that is theonly known diboride alloy with substitution in the Mg sub-lattice and a rather wide range of solubility.8 In addition,earlier studies2–4 have shown that in this system the two-dimensional~2D! boron bands are gradually filled with Aldoping. Hopefully, the studies of NSLR in this system mayprovide valuable information about the genesis of anisotropyof electronic states at the Fermi level.Below we evaluate the relaxation rates for MgB2 andAlB2 compounds using an LDA calculation, and for the in-termediate concentrations we used the rigid band approxima-tion with MgB2 bands. We will show that in MgB2 the or-bital mechanism is the leading term in NSLR, whereas theFermi-contact mechanism is dominating in AlB2. Our calcu-lated total relaxation rate in MgB2 is in fair agreement withexperiments,5–7 thus indicating that the calculatedN inMgB2 is basically correct, whereas in AlB2, due to high an-isotropy and low DOS of boronp states, we predict a muchsmaller relaxation rate fully determined by the Fermi-contactmechanism.The standard technical details of the Linear muffin-tin or-bital calculations are similar to those described in Refs. 2 and3. In addition, we carefully checked the sensitivity of theresults to the parameters of calculations. We used differentexchange-correlation potentials and inputs with different ra-dii of the B sphere~both with and without empty spheres!.Our values of DOS fors andp orbitals on theB site in MgB2and AlB2 are listed in Table I. One can see that in MgB2 allp orbitals on theB site have a sizable DOS, while in AlB2only pz orbital is significant withNpx'0.1Npz . The s com-ponent in AlB2 becomes relatively more important comparedto MgB2 resulting in the dominance of the Fermi-contactNSLR in AlB2, as we will show below. In both materials thecontribution ofd states to NSLR is very small. As for the Mgsite, thes component ofN is the most important, and weexpect that the NSLR on25Mg is controlled by the Fermi-contact mechanism. However, in this paper we will focus onthe 11B NSLR.To calculateT1 according to a general prescription onehas to estimate thêr 23& l expectation values for differentorbitals and the electronic density at the nucleusws2(0)/4p.We found that the convergence of the total NSLR rate withrespect to the boron sphere radius in thissp system is worsecompared tod metals~from r B52.3a0 to r B52.4a0 the totalT121 decreases by;15%). The uncertainty is mostly relatedto the value of̂ r 23&pNp .In our calculations we used the largestr B that were pos-sible without a significant distortion of the band structure,2.4a0 for MgB2 and 2.1a0 for AlB2. For these radii we have^(a0 /r )3&p51.11 in MgB2 and 1.37 in AlB2. For compari-son, the atomic value9 for ^(a0 /r )3&p in B is 0.78. The elec-tronic densities on the nucleusa03ws2(0)/4p for MgB2 andAlB2 were, respectively, 2.68 and 3.02.The contributions to the11B relaxation rate for the poly-crystalline sample calculated using the general formulas10 forthe hexagonal crystal are given in Table II. The in-plane andTABLE I. Partial DOS for s and p orbitals at B site, 1023(eV spin atom)21.s pz pxMgB2 3.4 50 36AlB2 3.3 19 1.9PHYSICAL REVIEW B, VOLUME 64, 1325060163-1829/2001/64~13!/132506~3!/$20.00 ©2001 The American Physical Society64 132506-1out-of-planep orbitals in MgB2 have similar densities ofstates, and hence the relative magnitude of orbital and dipo-lar contributions to NSLR is close to the 3/10 rule forpstates in a cubic crystal described by Obata.10 The Fermi-contact contribution is also important and amounts to 30% ofthe orbital term. The contributions from thed partial wavesto the dipole and orbital relaxation rates are small~ t theorder of 1%! due to the low diagonal and off-diagonal den-sities of states (Nd /Np)2;0.02 and (Npd /Np)2;0.05. Thequadrupole contribution to NSLR is negligible due to arather small11B quadrupole moment.The values ofT121 obtained in such manner correspond tothe theoretical ‘bare’ partial boronN whereas the actualT121contains different terms enhanced according to the corre-sponding susceptibilities. To estimate the possible range ofenhancement, we calculated the total enhancement comingfrom the spin susceptibility only~which is the case forAlB2). We estimated the effective Stoner exchange param-eter I[DE/m51.7 eV from the splitting of the bands at theG point in the external magnetic field. The correspondingStoner enhancement of the uniform susceptibility in the 3Dcase may be written11 as S53/@(12NI)(322IN)#'(12IN)2a with a'1.62, while in the 2D case the enhance-ment is described by the same formula witha52. In ourcase due to the mixed 2D and 3D character of the bands it isnot clear what value ofa should be used, but the differencein the result fora51.62 and 2.0 is less than 10%. We useda51.9 resulting in the enhancement ofT121 by approxi-mately 60%~Table II!. The obtained ‘bare’ and enhancedvalues provide a range of possible NSLR rates for MgB2 thatshould be compared with the experimental rates5–7 of 5631024–6431024 (K sec)21. The fact that such simple es-timate may give a faster relaxation compared to experimentssuggests a possible importance of unique effects resulting inthe lowering of the effective boronN.The roles of the three NSLR mechanisms are very differ-ent in AlB2 where no traces of superconductivity have beenfound and where no experimental data are available. Accord-ing to our theoretical estimation, due to the sharp decrease ofthe boronp component ofN compared to MgB2 and its verystrong anisotropy~see Table I!, the orbital and dipolar con-tributions to NSLR become very small, and the NSLR inAlB2 is completely dominated by the Fermi-contact mecha-nism. This conclusion may be verified experimentally bystudying the Korringa ratio. The resulting Stoner-enhancedNSLR rate in AlB2 is more than three times smaller than inMgB2 ~see Table II!. We should note that the strong anisot-ropy of boronp states in AlB2 on this stage is a theoreticalprediction and more experimental information is needed toconfirm it.We also calculated the NSLR rate in Mg12xAl xB2 in therigid band approximation with MgB2 bands. From Fig. 1 onecan see how the roles of different mechanisms of NSLRchange with doping. The sharp decrease ofN in the 2Dsheets of the Fermi surface with doping3 leads to the corre-sponding lowering of all contributions to NSLR, and at thepoint of the complete filling of these 2D bands we expect avery largeT1. Experimental verification of this sharp depen-dence ofT1 on doping in this alloy may be a crucial test ofour understanding of the electronic structure of this systemand is highly desirable. Together with the nuclear quadrupoleresonance data~which is related to the anisotropy of totalcharges on differentp orbitals! such measurements shouldhelp to build a general picture of anisotropy ofp orbitals.The above calculations have been done for a polycrystal-line sample. Because single crystals are becoming available,we include our estimations of the anisotropy in the angulardependence of NSLR rate10 A1B sin2 u. For MgB2 we ob-tained B/A'20.06, so that the NSLR is nearly isotropic.The NSLR rate in AlB2 is isotropic because it is determinedby isotropic Fermi-contact mechanism.In conclusion, we have performed LDA calculations forthe NSLR rate in the Mg12xAl xB2 system. We found that therbital mechanism of relaxation dominates over the spin-dipolar and Fermi-contact ones in MgB2, because the boronp orbitals at the Fermi level are distributed nearly isotropi-cally and have a large DOS. Strong anisotropy and low den-sity of p states at the Fermi level in AlB2 results in thedominance of the Fermi-contact NSLR mechanism. With thevalues of 0.7~0.5! st./eV for the bare total~boron partial!DOS at the Fermi level for MgB2 and 1.7 eV for the effec-tive Stoner exchange parameter, reasonable agreement is ob-tained with the experimental NSLR rates. However, we em-phasize a relatively weak radial convergence of the NSLRrate in this system compared to the well-studiedd metals,TABLE II. Contributions to (TT1)21 @1024/(K sec)#.Fermicontact Orbital Dipole TotalStonerenhanced ExperimentsMgB2 12 30 9 51 81 565,646,617AlB2 21 1 1 23 26FIG. 1. Different contributions to the total11B relaxation rate inMg12xAl xB2. Thick solid line, orbital; dashed, dipolar; thin solid,Fermi contact.BRIEF REPORTS PHYSICAL REVIEW B 64 132506132506-2and a common uncertainty related to the estimate of the en-hancement factor. Still, we strongly believe that the obtainedresults related to the relative importance of different NSLRmechanisms are qualitatively correct. According to our cal-culation, the NSLR rate strongly depends on the concentra-tion in the Mg12xAl xB2 system, and the experimental studiesof this dependence are highly desirable for the understandingof the anisotropy of boronp states.When this paper was completed we became aware thatsimilar results for NSLR in MgB2 were independently ob-tained in Ref. 12, where theT1 on25Mg and the Knightshifts were also computed. We believe that the discrepancyin the Fermi-contact term is mainly due to the significantlylarger boron sphere radius used in our calculations.We are grateful to I. Mazin and F. Borsa for valuablediscussions. This work was carried out at the Ames Labora-tory, which is operated for the U.S. Department of Energy byIowa State University under Contract No. W-7405-82. Thiswork was supported by the Director for Energy Research,Office of Basic Energy Sciences of the U.S. Department ofEnergy.1J. Nagamatsuet al., Nature~London! 410, 63 ~2001!.2J. Kortus, I. I. Mazin, K. D. Belashchenko, V. P. Antropov, and L.L. Boyer, Phys. Rev. Lett.86, 4656~2001!.3K. D. Belashchenko, M. van Schilfgaarde, and V. P. Antropov,cond-mat/0102290~unpublished!.4J. M. An and W. E. Pickett, Phys. Rev. Lett.86, 4366~2001!; G.Satta, G. Profeta, F. Bernardini, A. Continenza, and S. Massidda,Phys. Rev. B~to be published 1 September 2001!.5H. Kotegawa, K. Ishida, Y. Kitaoka, T. Muranaka, and J. Akim-itsu, cond-mat/0102334~unpublished!.6A. Gerashenko, K. Mikhalev, S. Verkhovskii, T. D’yachkova, A.Tyutyunnik, and V. Zubkov, cond-mat/0102421~unpublished!.7J. K. Jung, S. H. Baek, F. Borsa, S. L. Bud’ko, G. Lapertot, and P.C. Canfield, Phys. Rev. B64, 012514~2001!.8J. S. Sluskyet al., Nature~London! 410, 343 ~2001!.9S. Fraga, K. M. S. Saxena, and J. Karwowski,Handbook onAtomic Data~Elsevier, Amsterdam, 1976!.10Y. Obata, J. Phys. Soc. Jpn.18, 1020 ~1963!; A. Narath, Phys.Rev.162, 320~1967!; T. Asada and K. Terakura, J. Phys. F: Met.Phys.12, 1387~1982!.11B. S. Shastry and E. Abrahams, Phys. Rev. Lett.72, 1933~1994!.12E. Pavarini and I. I. Mazin, cond-mat/0105350~unpublished!.BRIEF REPORTS PHYSICAL REVIEW B 64 132506132506-3

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Anisotropy of conducting \u3ci\u3ep\u3c/i\u3e states and \u3csup\u3e11\u3c/sup\u3eB nuclear spin-lattice relaxation in Mg\u3csub\u3e1-x\u3c/sub\u3eAl\u3csub\u3ex\u3c/sub\u3eB\u3csub\u3e2\u3c/sub\u3e

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