Samples of aligned MgB(2) crystallites have been prepared, allowing for the first time the direct identification of an upper critical field anisotropy H(ab)(c2)/H(c)(c2) = xi(ab)/xi(c) approximately 1.7, with xi(o,ab) approximately 70 A, xi(o,c) approximately 40 A, and a mass anisotropy ratio m(ab)/m(c) approximately 0.3. A ferromagnetic background signal was identified, possibly related to the raw materials purity.865974-

Avila, M A

Cardoso, C A

Coelho, A A

de Lima, O F

Ribeiro, R A

Physical Review Letters

English

Repositorio da Producao Cientifica e Intelectual da Unicamp

VOLUME 86, NUMBER 26 P H Y S I C A L R E V I E W L E T T E R S 25 JUNE 2001
5974Anisotropic Superconducting Properties of Aligned MgB2 Crystallites
O. F. de Lima, R. A. Ribeiro, M. A. Avila, C. A. Cardoso, and A. A. Coelho
Instituto de Física “Gleb Wataghin,” UNICAMP, 13083-970, Campinas, SP, Brazil
(Received 15 March 2001)
Samples of aligned MgB2 crystallites have been prepared, allowing for the first time the direct identifi-
cation of an upper critical field anisotropy Habc2 Hcc2  jabjc  1.7, with jo,ab  70 Å, jo,c  40 Å,
and a mass anisotropy ratio mabmc  0.3. A ferromagnetic background signal was identified, possibly
related to the raw materials purity.
DOI: 10.1103/PhysRevLett.86.5974 PACS numbers: 74.25.Ha, 74.60.Ec, 74.60.Jg, 74.70.AdThe recent discovery of superconductivity at 39 K in
magnesium diboride MgB2 [1] has brought new excite-
ment to the area of basic and applied research on super-
conducting materials. The observation of an isotope effect
[2], a BCS-type energy gap measured by scanning tun-
neling spectroscopy [3], as well as band structure studies
[4,5], points to a phonon-mediated superconductivity in
MgB2. Some reports [6,7] have suggested that MgB2 has
an isotropic (or 3D) behavior, based on measurements done
in polycrystalline samples. However, other studies [8,9]
have also discussed its possible anisotropic nature. The
relatively high values reported for the critical current den-
sity [6,10] Jc are possibly indicating the absence of weak
link problems, which are well known in the high-Tc mate-
rials. While polycrystalline MgB2 is very easy to grow and
is a readily available reagent, good-sized single crystals of
this material have not yet been reported, and their develop-
ment promises to be a greater challenge. Here we present
results from samples of aligned MgB2 crystallites that es-
tablish the anisotropy of the upper critical field Hc2, thus
implying an anisotropic character for other superconduct-
ing properties, e.g., the energy gap, coherence length j,
field penetration depth l, and Jc.
In this work, a weakly sintered sample of MgB2 was pre-
pared, starting with a stoichiometric mixture of 99.5 at. %
pure boron and 99.8 at. % pure magnesium, both in chips
form (Johnson Matthey Electronics). The loose mixture
was sealed in a Ta tube under Ar atmosphere, which was
then encapsulated in a quartz ampoule and put into the fur-
nace. The compound formation was processed by initially
holding the furnace temperature at 1200 ±C for 1 h, fol-
lowed by a decrease to 700 ±C (10 ±Ch), then to 600 ±C
(2 ±Ch), and finally to room temperature at a rate of
100 ±Ch. The weakly sintered product was easily crushed
and milled employing mortar and pestle. Using a stereomi-
croscope we could observe a very uniform powder consist-
ing mainly of shiny crystallites, with aspect ratios ranging
from 2 to 5. This is mainly due to the main surface size
distribution ranging from 5 to 40 mm for the larger linear
dimension, since the crystallites’ thickness is very regu-
lar, around 2 mm. The powder was then sieved into a
range of particle sizes between 5 20 mm, which allows
the crystallites fraction to be maximized to almost 100%.0031-90070186(26)5974(4)$15.00Small amounts of the powder were then patiently spread
on both sides of a small piece of paper, producing an al-
most perfect alignment of the crystallites, as shown in the
scanning electron microscopy (SEM) picture in the up-
per part of Fig. 1. The lower part of this figure shows
an x-ray diffraction pattern (u-2u scan) from a sample of
the crystallite-painted paper, displaying only the (001) and
(002) reflections coming from the MgB2 phase. A lattice
parameter c  3.518 6 0.008 Å was evaluated from these
two peak positions. The two small impurity peaks marked
with asterisks were indexed as SiO2. The inset in Fig. 1
FIG. 1. Top: SEM picture showing the well aligned crystallites
and intercrystallite material. Bottom: x-ray diffraction pattern
showing only the (001) and (002) peaks of MgB2, plus two
spurious peaks indexed as SiO2. Inset: rocking curve (v scan)
for the (002) peak, showing an angular spread of about 4.6±
along the crystallites’ c axis.© 2001 The American Physical Society
VOLUME 86, NUMBER 26 P H Y S I C A L R E V I E W L E T T E R S 25 JUNE 2001shows a rocking curve (v scan) for the (002) peak that
reveals an angular spread around 4.6±, associated with a
small misalignment of the crystallites’ c axis.
Electron microprobe analysis done on four different
areas between the MgB2 crystallites revealed the follow-
ing average concentration (in at. %) of elements: O (62.9),
C (22.2), Ca (9.48), Si (1.48), Mg (1.44), Al (1.37),
K (0.09), Fe (0.50), Cr (0.21), and Ni (0.09). The first
eight elements in this list were found also in the com-
position analysis made on the same type of paper used
(Canson, ref. 4567-114). Microprobe analysis done also
on the initial Mg and B revealed a few small precipitates,
smaller than 10 mm and containing up to 8 at. % Fe, only
in the Mg chips. This confirms the expectation of Fe be-
ing a common impurity [11] in commercial Mg and sets
a general concern on its possible effects. The average
composition found on top of several crystallites, normal-
ized to the whole MgB2 formula unit, was Mg (30.80),
O (2.20), Ca (0.17), Si (0.07), and Fe (0.06). Although
boron contributes with a fraction of 66.6 at. %, it does not
show up in the microprobe analysis because it is too light.
The contaminants found on top of the crystallites most
possibly came from a surface contamination caused by
the alignment technique, which required vigorous rubbing
on top of the powder, using a steel tweezers tip to spread
the crystallites uniformly. This is corroborated by a fur-
ther analysis done on top of several as-grown crystallites,
which detected only Mg and a small amount of O (possibly
from MgO). This result is consistent with the very small
solid solubility limit of about 0.004 at. % Fe in Mg, which
is known to occur [12] at the solidification temperature
of 650 ±C. The intercrystallite type of rubbish shown in
Fig. 1 is attributed mainly to the paper abrasion, which
produces a varied distribution of irregular grains of paper
fragments. In order to characterize the superconducting
and magnetic properties of the aligned crystallites, we
mounted several samples consisting of a pile of five small
squares 3 3 3 mm2 cut from the crystallite-painted
paper and glued with Araldite resin. Each one of these
samples contains a number of crystallites estimated to
be around 6.5 3 105, totalizing an effective volume of
0.065 mm3, which is reasonably close to 0.060 mm3 that
was evaluated from the expected slope of 214p for the
diamagnetic shielding at H  0.
Figure 2 shows the anisotropic signature of the Hc2T 
line in the field interval 0 # H # 40 kOe. The values
were taken from the transition onset of the real compo-
nent x 0 of ac susceptibility, measured using a PPMS-9T
machine (Quantum Design), with an excitation field of
amplitude 1 Oe and frequency 5 kHz. The inset shows an
enlarged view of the x 0T  curves for H k ab (open sym-
bols) and H k c (solid symbols), the field orientation par-
allel to the ab plane and parallel to the c axis, respectively.
The x 0T  as well as the MT  (inset of Fig. 3) measure-
ments, for H  10 Oe, show sharp transitions at the same
critical temperature Tc  39.2 K. The dashed lines con-
necting points in Figs. 2–4 are only guides to the eyes.20 22 24 26 28 30 32 34 36 38 40
0
10
20
30
40
50
60
H
c2
  
 (
kO
e
)
T   (K)
 H // ab
 H // c
 Müller et al.
10 20 30
-0.20
-0.15
-0.10
-0.05
0.00
        H (kOe)
   0.01
   1.00
 10.00
 20.00
 30.00
 40.00
 
χ'
  
(a
rb
. 
u
n
its
)
T   (K)
FIG. 2. Upper critical field Hc2 vs temperature phase diagram,
for both sample orientations. The stars represent the Hc2 vs T
line from Ref. [13]. The inset shows the real component x 0
of the ac susceptibility vs temperature, measured at several dc
fields for both orientations. Open symbols are for the H k ab
curves and solid symbols for H k c.
Typically, some of the published data on the temperature
dependence [2,10,13,14] of Hc2T  agree with our result
for Hc2T  k ab. As an example, the data from Ref. [13]
are plotted in Fig. 2 as stars. This could simply mean
that in polycrystalline samples the transitions are broad-
ened, showing the onset at the highest temperature that
corresponds to the highest critical field available, which
is Hc2T  k ab.
-1 0 1 2 3 4
-30
-20
-10
0
10
20
30
40
T = 5 K  H // ab
 H // c
M
 (
G
)
H  (kOe)
-0.8
-0.6
-0.4
-0.2
0.0
10 20 30 40 50
H = 10 Oe
 ZFC
 FCC
 T  (K)
M
 (
G
)
FIG. 3. Magnetization loops at 5 K for both sample orienta-
tions, showing a superconducting hysteresis on a ferromagnetic
background. The inset shows a zero field cooling (ZFC) and a
field cooling measured on cooling (FCC) magnetization curve
for H  10 Oe. We see a sharp transition at Tc  39.2 K and
a relatively high (70%) recovery of diamagnetism for the FCC
curve.5975
VOLUME 86, NUMBER 26 P H Y S I C A L R E V I E W L E T T E R S 25 JUNE 2001-20 -10 0 10 20 30 40 50
-60
-40
-20
0
20
40
60
-0.8 -0.4 0.0 0.4 0.8
-12
-8
-4
0
4
8
12
T = 45 K
 H // ab
 H // c
M
 (
G
)
H (kOe)
M
 (
G
)
H (kOe)
FIG. 4. Magnetization loops at 45 K (above Tc) for both
sample orientations, showing the ferromagnetic behavior of our
sample. The inset shows the hysteretic behavior at low fields.
The ratio h  Habc2 H
c
c2, between the upper critical
field when H is applied parallel to the ab plane, and
when it is along the c direction, was evaluated at different
temperatures, producing h  1.73 6 0.03. Using the
Ginzburg-Landau mean field expression [15] jT  
jo1 2 TTc212 and the results for anisotropic situ-
ations [16,17] Hcc2T   fo2pj
2
ab and H
ab
c2 H
c
c2 
1´, where fo  2.07 3 1027 G cm2 is the quantum
of flux (in CGS units) and ´2  mabmc is the mass
anisotropy ratio, we find that jo,abjo,c  jabT 
jcT   h  1.73 and ´2  0.3. Since at T  27 K
we have Hcc2  20 kOe, this implies that jo,ab  70 Å
and jo,c  40 Å. The mass anisotropy ratio of MgB2
thus corresponds to a relatively small anisotropy when
compared to the highly anisotropic high-Tc cuprates [17],
such as YBa2Cu3O7 ´2  0.04 and Bi2Sr2CaCu2O8
´2  1024. We do not expect that a likely very small
bulk contamination of the crystallites could eventually
change their anisotropy values. In fact, our careful com-
position analysis has indicated that almost all contami-
nants are located in the region between the crystallites,
thus having a negligible chance to affect the underlying
mechanism of the superconducting condensation.
The magnetization curves MT and MH, displayed
in Figs. 3 and 4, were measured using a SQUID magne-
tometer (Quantum Design, model MPMS-5). The MH
curves (T  5 K) shown in Fig. 3 are intriguing in the
region 21 & H & 1 kOe, where the maximum shielding
and first field penetration (in the initial virgin state) oc-
cur. For jHj * 1 kOe the hysteretic curves in both field
directions look very similar. However, for jHj * 40 kOe
(not shown here) the magnetization difference between
the up and down curves DM becomes smaller than the
noise. Large fluctuations of the magnetic moment were
consistently observed in this field region, for three differ-5976ent samples and temperatures T  5, 10, 20 K, possibly
associated with the high creep rate and the fast drop of Jc
occurring at high fields [10,14,18,19]. Figure 4 shows a
clear signature of the ferromagnetic hysteresis loop mea-
sured at T  45 K, mainly attributed to the presence of Fe,
Cr, and Ni in the intercrystallite region. The inset displays
an enlarged view close to H  0 indicating that demag-
netization effects are also observed for the H k ab and
H k c orientations. In a recent detailed study [8] the oc-
currence of Fe contamination has already been identified,
through measurements of MgB2 samples made from com-
mercial powder supplied by a different company.
In view of the superimposed ferromagnetic signal in the
magnetization curves, we found it to be not reliable to dis-
cuss the expected anisotropy in Jc ~ DM, which could be
determined using the Bean model [20]. A rough estimate
for both field orientations gives Jc  106 Acm2 at H 
1.5 kOe and T  5 K (Fig. 3). This calculation neglects
the small influence of the ferromagnetic hysteresis and con-
siders the average crystallite geometry as described before.
However, an anisotropy between JcH k c and JcH k ab
should be expected. Indeed, independently of the differ-
ent regime of vortex pinning, Jc is predicted [17] to be
proportional to j2, leading to JcH k cJcH k ab 
jabjc  Habc2 H
c
c2.
A final cautionary observation has to be addressed to
the possibility that surface superconductivity could also
be occurring for H k ab, since coincidently the surface
nucleation field is [21] Hc3  1.7Hc2. However, we have
made several careful measurements of MH and x 0H,
as well as MT and x 0T , around the onset of transition,
and no signature [22] of a surface nucleation field was
found. This is consistent with the fact that our Habc2 T 
line agrees with several reported Hc2T  lines measured in
polycrystalline samples [2,10,13,14], which certainly did
not comply with the boundary condition [21,22] required
for surface nucleation in the ab planes, i.e., H k ab.
In conclusion, we have prepared samples of aligned
MgB2 crystallites that allowed, for the first time, the iden-
tification of an anisotropy for the upper critical field given
by Habc2 H
c
c2  1.73, implying an anisotropy of the coher-
ence length jabjc  1.73 and a mass anisotropy ratio
mabmc  0.3. This could be considered a mild aniso-
tropy when compared to the values found for the high-Tc
materials mabmc & 0.04. The influence of contami-
nants is requiring further work, aimed at a more complete
and reliable characterization of the MgB2 intrinsic proper-
ties. Naturally the production of a good-sized single crystal
of MgB2 is also highly desirable.
We are very grateful to S. Gama for supplying some
of the raw materials, to I. Torriani and C. M. Giles for
the x-ray diffractograms, and to D. Silva (IG-Unicamp)
for the SEM and microprobe analysis. This work is sup-
ported by the Brazilian science agencies FAPESP (Fun-
dação de Amparo a Pesquisa do Estado de São Paulo) and
CNPq (Conselho Nacional de Desenvolvimento Científico
e Tecnológico).
VOLUME 86, NUMBER 26 P H Y S I C A L R E V I E W L E T T E R S 25 JUNE 2001Note added.—Since this manuscript was submitted two
papers have appeared [23,24] showing results consistent
with our anisotropy data.
[1] J. Akimitsu, in Proceedings of the Symposium on Tran-
sition Metal Oxides, Sendai, 2001 (to be published);
J. Nagamatsu et al., Nature (London) 410, 63 (2001).
[2] S. L. Bud’ko et al., Phys. Rev. Lett. 86, 1877 (2001).
[3] G. Karapetrov et al., cond-mat/0102312.
[4] J. Kortus et al., cond-mat/0101446 v2.
[5] N. I. Medvedeva et al., cond-mat/0103157.
[6] D. C. Larbalestier et al., Nature (London) 410, 186 (2001).
[7] W. N. Kang et al., cond-mat/0103161.
[8] Y. Wang, T. Plackowski, and A. Junod, cond-mat/0103181.
[9] J. M. An and W. E. Pickett, cond-mat/0102391 v2.
[10] P. C. Canfield et al., Phys. Rev. Lett. 86, 2423 (2001).
[11] G. V. Raynor, The Physical Metallurgy of Magnesium and
Its Alloys (Pergamon, London, 1959), p. 441.[12] Binary Alloy Phase Diagrams, edited by T. B. Massalski
(ASM International, Materials Park, OH, 1990), 2nd ed.,
p. 1076.
[13] K.-H. Müller et al., cond-mat/0102517.
[14] D. K. Finnemore et al., Phys. Rev. Lett. 86, 2420 (2001).
[15] M. Tinkham, Introduction to Superconductivity (McGraw-
Hill, New York, 1996).
[16] L. N. Bulaevskii, V. L. Ginzburg, and A. A. Sobyanin, Zh.
Eksp. Teor. Fiz. 94, 355 (1988) [Sov. Phys. JETP 68, 1499
(1988)].
[17] G. Blatter et al., Rev. Mod. Phys. 66, 1125 (1994).
[18] Y. Bugoslavsky et al., Nature (London) 410, 563 (2001).
[19] H. H. Wen et al., cond-mat/0102436 v3.
[20] C. P. Bean, Rev. Mod. Phys. 36, 31 (1964).
[21] D. Saint-James and P. G. de Gennes, Phys. Lett. 7, 306
(1963).
[22] D. Saint-James, G. Sarma, and E. J. Thomas, Type II Su-
perconductivity (Pergamon, Oxford, New York, 1969).
[23] A. Handstein et al., cond-mat/0103408.
[24] F. Bouquet et al., cond-mat/0104206.5977


Anisotropic Superconducting Properties Of Aligned Mgb(2) Crystallites.

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Anisotropic Superconducting Properties Of Aligned Mgb(2) Crystallites.

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