Physica C 470 (2010) 1856–1859

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Physica C
journal homepage: www.elsevier.com/locate/physc

Large and spatial magnetic ﬁeld modulation using superconducting bulk
magnet and silicon steel
H. Fujishiro *, D. Furuta, K. Yaegashi, T. Naito, N. Yoshimoto
Faculty of Engineering, Iwate University, 4-3-5 Ueda, Morioka 020-8551, Japana r t i c l ei n f o

Article history:
Available online 16 May 2010
Keywords:
Magnetic modulation
Magnetic force
Superconducting bulk magnet
Magnetic circuit
The Moses effecta b s t r a c t
As an application of superconducting bulk magnets to a solution growth of organic semiconductor ﬁlms
by means of ‘‘the Moses effect”, we have investigated the realization of the spatially modulated magnetic
ﬁeld using two-aligned superconducting bulk magnets and silicon steel bundles. Two bulks were magnetized by pulsed ﬁelds with an opposite magnetic polarity of over 2 T and were magnetically coupled withthe three pairs of the ferromagnetic bundles stacked by thin silicon steel sheets with a narrow open gap.
To maximize the magnetic force in the gap, we measured systematically the spatial magnetic ﬁeld modulation DB and the magnetic force coefﬁcient BdB/dx, as functions of the thickness of the bundles (W), thespace between the bundles (S) and the open gap width (G). As a result, DB = 0.76 T and BdB/dx = 500 T2/m
were realized in the gap under the conditions of W = 1.4 mm, S = 6 mm and G = 1 mm.
Ó 2010 Elsevier B.V. All rights reserved.

1. Introduction
Recently, electronic devices using organic semiconductors suchas pentacene and oligothiophens have been widely developed because of a low-cost and low-temperature fabrication process onlarge and ﬂexible substrates [1–3]. However, in general, the electron
mobility le in organic semiconductors is fairly smaller than that of
crystalline silicon and other inorganic semiconductors because oflarge amount of crystal defects and a misalignment of the crystallites. A solution growth of organic semiconductors is a promisingtechnique for the practical applications because of the growth undera quasi-equilibrium condition. To realize the high le in the grownﬁlm, it is necessary to grow the large crystallites and to align thecrystal axes by some techniques. We have so far investigated thecrystal growth of organic semiconductors from solution phase [4],and have applied magnetic ﬁeld higher than 2 T to the solution byusing a superconducting bulk magnet. The thickness of the diamagnetic solvent such as tetra-hydrofurane (THF) became very thin bymeans of ‘‘the Moses effect” [5] and the single-crystalline ﬁlm of organic semiconductor started to grow preferentially from the edge ofthe thin solution layer because of a supersaturation. As a result, thegrown thin ﬁlm can be highly oriented along the magnetic gradient[6]. If the solution growth is performed under a deep and spatially
minute magnetic ﬁeld on the substrate, the highly oriented growth
pattern of the organic semiconductor can be fabricated by ‘‘the micro-Moses effect” [7] without any photolithography processes,
which reproduces the magnetic pattern.
* Corresponding author. Tel./fax: +81 19 621 6363.
E-mail address: fujishiro@iwate-u.ac.jp (H. Fujishiro).
0921-4534/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.physc.2010.05.222

In this paper, we have investigated the realization of spatiallymodulated magnetic ﬁeld. Two-aligned superconducting bulk magnets higher than 2 T, which had the usable surface on both sides inopen space, were magnetically coupled with the ferromagnetic
bundles of silicon steel sheets with a narrow open gap. To maximize
the spatial magnetic ﬁeld modulation in the gap, we measured themagnetic ﬁeld proﬁles, as functions of the thickness of the bundles(W), the space between the bundles (S), and the open gap width (G).
2. Experimental procedure
Fig. 1 shows the schematic view of the experimental setup andthe dimension of the apparatus. Highly c-axis oriented SmBaCuO
and YBaCuO bulk disks (Dowa Mining Corp.) 45 mm in diameterand 15 mm in thickness were tightly fastened with the brass bar
from the side face and the bar was attached to the cold stage ofa Gifford McMahon (GM) cycle helium refrigerator. The distance
between the bulk centers was 60 mm. The bulks were cooled to40 K in a vacuum sheath and the pulse ﬁelds of Bex = 5.5 T were applied twice for each bulk using the split-type pulse coil dipped inliquid N2. The polarity of the applied pulse ﬁelds was opposite
for each bulk, and the maximum trapped ﬁelds were +2.36 T and1.80 T at the top surface of the vacuum sheath just on theSmBaCuO and YBaCuO bulk disk, respectively. Nearly the same
magnitude of the trapped ﬁeld was observed on the rear surfaceof the vacuum sheath with an opposite polarity. The detailed magnetizing process is described elsewhere [8].
Two bulk magnets were magnetically coupled with the threepaths of grain-oriented silicon (electrical) steel bundles with a narrow open gap. The silicon steel sheets (JFE Steel Corp.) with

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Fig. 1. The experimental setup and the dimensions of the apparatus used in this study.

0.35 mm in thickness were stacked up to four sheets and the thickness of the bundles (W) was changed from 0.35 mm to 1.4 mm. The
permeability lm and the saturation moment Bs are 5.3  104 and2.03 T, respectively. The bundles were separated using spacers
made by acrylic plates and the space between the bundles (S)was changed from 3 mm to 9 mm. The width of the open gap (G)was changed from 1 mm to 6 mm. The spatial magnetic modulation in the gap was measured as functions of the W, S and G values
using a Tesla meter (F.W. BELL 5080).
3. Results and discussion
Fig. 2 shows the x dependence of the magnetic ﬁeld B(x) in thegap for various thicknesses of the bundles W under the conditionsof G = 2 mm and S = 6 mm. The magnetic ﬁeld modulation changes
depending on the W value. Hereafter, we deﬁne the magnitude of
the magnetic ﬁeld modulation DB as the difference between theFig. 2. The x dependence of the magnetic ﬁeld B(x) in the gap for various
thicknesses of the silicon steel bundles W under the conditions of G = 2 mm,
S = 6 mm.

maximum magnetic ﬁeld Bmax at the central bundle and the local
minimum magnetic ﬁeld Bmin in the neighbor (DB = Bmax–Bmin).
For smaller W value, the Bmax value was small because of the small
cross section of the silicon steel bundles and, therefore, the DB value was also small. On the other hand, the DB value increases concomitantly with increasing W. The trapped ﬁeld proﬁle of theSmBaCuO bulk on the vacuum sheath is also shown in the rightaxis of ordinates in Fig. 2 as a dotted line. The maximum trapped
ﬁeld was 2.36 T. The shape of B(x) was conical and B(x) decreased
with increasing distance from the bulk center. The trapped ﬁeld
proﬁle of the YBaCuO bulk on the vacuum sheath was also a conicalshape.
Fig. 3 shows the x dependence of the magnetic ﬁeld B(x) in thegap for various S values under the conditions of W = 1.4 mm and
G = 2 mm. The Bmax value was independent of the S value. However, the Bmin value decreases concomitantly with increasing S. Because the measured B(x) in the gap was overlapped by themagnetic ﬁeld contributed from the neighbor bundles. As a result,Fig. 3. The x dependence of the magnetic ﬁeld B(x) in the gap for various spaces
between bundles S under the conditions of W = 1.4 mm and G = 2 mm.

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H. Fujishiro et al. / Physica C 470 (2010) 1856–1859

the overlap was enhanced and the DB value decreased withdecreasing S. It is noteworthy that the magnitude of maximum B
value on the outer bundles was lower than Bmax on the central bundle because of the conical B proﬁle of the bulk superconducting
bulks as shown in Fig. 2.
Fig. 4 shows the x dependence of the magnetic ﬁeld B(x) in thegap for various widths of the open gap G under the conditions ofW = 1.4 mm and S = 6 mm. For a large G value, the magnetic connection becomes weak because of the leakage ﬂux in the magneticcircuit. As a result, DB and Bmax were small. With decreasing G value, DB increased sensitively. The maximum DB value of 0.76 T wasobtained in this study by the condition of G = 1 mm.
As mentioned above, the DB and Bmax values change dependingon the values of G, W and S. Figs. 5a and 5b summarizes the DB values as functions of W and S values for each G value. The DB value
increases with increasing W and also increases with increasing S.
Furthermore, the DB increases sensitively with decreasing G. Toenhance the magnetic modulation more and more, the W and S values might be increased. However, the enhancement of DB is restricted because of the ﬁnite diameter of the bulk magnets. The
Bmax value ought to be increased up to the saturation magnetization of the used silicon steel (=2.03 T).
Fig. 6 shows the analyses of the measured magnetic ﬁeld modulation proﬁle for the conditions of W = 1.05 mm, S = 6 mm andG = 2 mm. In the ﬁgure, closed circles show the measured modulation. The dotted line depicts the estimated background magneticFig. 6. The analyses of the measured magnetic ﬁeld modulation for the conditionsof W = 1.05 mm, S = 6 mm and G = 2 mm (see text).

ﬁeld proﬁle using a Gaussian function, which results from the leakage ﬂux passing though the spaces between the silicon steel bundles. The open circles show the contribution from the siliconsteel bundles, which are subtracted for the estimated background
proﬁle from the measured ones. The thin solid lines are the Gaussian ﬁts for the contribution from the each bundle. The measured
proﬁle can be reproduced by the contributions of both concentrated ﬂux to the bundles and the leakage ﬂux as shown in thethick bold line.
Figs. 7a and 7b show the magnetic gradient dB/dx and the magnetic force coefﬁcient BdB/dx proﬁles for the condition(W = 1.4 mm, S = 6 mm, G = 1 mm), at which DB was the largest in
this study. For comparison, those for the condition (W = 1.4 mm,S = 6 mm, G = 2 mm) and those on the vacuum sheath were alsoshown. The magnetic force FM is proportional to the magnetic force
coefﬁcient BdB/dx; not only the magnetic ﬁeld B, but also magnetic
ﬁeld gradient (grad B) generated on the bulk. The maximum values(dB/dx = 600 T/m, BdB/dx = 500 T2/m) for G = 1 mm are higher thanthose on the vacuum sheath. These speciﬁc values are about 10 times
as large as those for the Nd–Fe–B permanent magnet and are important parameters for the Moses effect. These values were drasticallysuppressed for G = 2 mm.

Fig. 4. The x dependence of the magnetic ﬁeld B(x) in the gap for various widths ofthe open gap G under the conditions of W = 1.4 mm and S = 6 mm.

Fig. 5. The magnitude of the magnetic modulation DB, as functions of W and S
values for each G value.

Fig. 7. Magnetic gradient dB/dx and the magnetic force coefﬁcient BdB/dx proﬁlesfor the condition (W = 1.4 mm, S = 6 mm, G = 1 mm), for which DB was the largest in
this study. The dB/dx and BdB/dx proﬁles for the condition (W = 1.4 mm, S = 6 mm,
G = 2 mm) and those on the vacuum sheath are also shown.

H. Fujishiro et al. / Physica C 470 (2010) 1856–1859

In summary, we investigated the realization of the spatiallymodulated magnetic ﬁeld using two-aligned superconducting bulk
magnets and silicon steel bundles. Two bulks were magnetizedalong opposite direction by pulsed ﬁelds and were magneticallycoupled with three pairs of the silicon steel bundles with a narrow
open gap. We studied systematically the spatially magnetic ﬁeld
modulation DB and the magnetic force coefﬁcient BdB/dx, as functions of the thickness of the bundles (W), the space between thebundles (S), and the open gap width (G). As a result, DB = 0.76 Tand BdB/dx = 500 T2/m were realized in the open gap. We plan to
apply the spatially magnetic modulation to the solution growthof organic semiconductors.
Acknowledgement
This work was partially supported by Japan Science and Technology Agency under a Research for Promoting TechnologicalSeeds 2008 (02–035).

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