in a platinum crucible of volume 500 ml , the materials , 843 g of lead oxide ( pbo , 4n ); 978 g of bismuth oxide ( bi 2 o 3 , 4n ); 128 g of ferric oxide ( fe 2 o 3 , 4n ); 38 g of boron oxide ( b 2 o 3 , 5n ); 6 . 0 g of terbium oxide ( tb 4 o 7 , 3n ); 7 . 0 g of holmium oxide ( ho 2 o 3 , 3n ); 18 g of gallium oxide ( ga 2 o 3 , 3n ); and 4 . 2 g of aluminum oxide ( al 2 o 3 , 3n ), were laid . the crucible was set at a predetermined position in a precision vertical tubular electric furnace , and was heated at 1000 ° c . to melt the mixture . the melt mixture was fully stirred to be evenly mixed , and then cooled down to the melt temperature of 775 ° c . to obtain a melt for raising a bismuth - substituted iron garnet single crystal . by a conventional procedure , the surface of thus obtained melt was made in contact with the one surface of a ( 111 ) garnet single - crystal substrate : ( gdca ) 3 ( gamgzr ) 5 o 12 ( lattice constant : 12 . 493 ± 0 . 002 å ) of 480 μm in thickness , and the epitaxial growth was continued while maintaining the melt temperature of 775 ° c . to obtain a ( hotbbi ) 3 ( fegaal ) 5 o 12 single - crystal film ( hotbbifegaalg single - crystal film ) of 47 μm in film thickness . then , the hotbbifegaalg single - crystal film was cut into the size of 1 mm × 3 mm to be measured with respect to magnetic characteristics . the measurement was carried out as the following . first , the hotbbifegaalg single - crystal film of 1 mm × 3 mm in size was positioned at the center of a magnet field generating device ( magnet ) comprising of a coil produced by magnatec co ., and then , as a magnet field being applied , a semiconductor laser beam of 0 . 786 μm was emitted to the hotbbifegaalg single - crystal film . and , by measuring the rotation angle of the polarization plane in the laser ray passed through the hotbbifegaalg single - crystal film , the applied magnetic field - dependent characteristics of the faraday rotation angle was studied . as the result , with respect to the hotbbifegaalg single - crystal film , the saturated magnetic field intensity and the hysteresis value were known ; the hysteresis curve similar to fig4 was obtained . that is , the magnetic characteristics of the hotbbifegaalg single - crystal film was the following : secondly , a permanent magnet being positioned and fixed on the hotbbifegaalg single - crystal film as shown in fig1 , the magnetic characteristics was measured similarly . the permanent magnet was a ferrite permanent magnet of 4000 ( g ) residual magnetic flux density and 1 mmφ × 1 mm in size . the ferrite permanent magnet was fixed on the corner of the faraday rotator by an epoxy adhesive , wherein the magnetization direction being normal to the film surface of the faraday rotator . the measured values of magnetic characteristics at the center of the faraday rotator are shown in fig1 . the magnetic hysteresis was eliminated in the plus zone ( opposite direction to the magnetization direction by the permanent magnet ) with respect to the applied magnetic field . that is , the magnetic characteristics of the hotbbifegaalg single - crystal film were the followings : except that the ferrite permanent magnet used in embodiment 1 was positioned as shown in fig1 , the magnetic characteristics of the hotbbifegaalg single - crystal film was measured in the same method as embodiment 1 . however , the two ferrite permanent magnets were positioned adversely to each other in their magnetization direction . the magnetic field characteristics measured at the center of the faraday rotator showed the characteristics described in fig1 . that is , their values were as follows : except that the rare - earth element - permanent magnet of 10000 ( g ) residual magnetic flux density and 1 mmφ × 1 mm in size was used instead of the ferrite permanent magnet in embodiment 2 , the measurement was carried out in the same method as embodiment 2 . the magnetic field characteristics measured at the center of the hotbbifegaalg single - crystal film showed the characteristics described in fig1 . that is , their values were as follows : ferrite permanent magnets of 4000 ( g ) residual magnetic flux density and 1 mm × 1 mm × 0 . 5 mm in size was fixed by an epoxy adhesive on the both ends of the hotbbifegaalg single - crystal film of 1 mm × 3 mm in size produced in embodiment 1 . the arrangement of the hotbbifegaalg single - crystal film and the magnet is shown in fig1 . the ferrite magnet was positioned such that the magnetization direction is normal to the film surface of the hotbbifegaalg single - crystal film . the measuring values of the magnetic characteristics at the center of the hotbbifegaalg single - crystal film are shown in fig1 . that is , their values were as follows : in a platinum crucible of volume 300 ml , the materials , 420 g of lead oxide ( pbo , 4n ); 490 g of bismuth oxide ( bi 2 o 3 , 4n ); 65 g of ferric oxide ( fe 2 o 3 , 4n ); 15 g of boron oxide ( b 2 o 3 , 5n ); 7 . 1 g of gadolimium oxide ( gd 2 o 3 , 3n ); 1 . 3 g of gallium oxide ( ga 2 o 3 , 3n ); and 3 . 8 g of aluminum oxide ( al 2 o 3 , 3n ), were laid . the crucible was set at a predetermined position in a precision vertical tubular electric furnace , and was heated at 1000 ° c . to melt the mixture . the melt mixture was fully stirred to be evenly mixed , and then cooled down to the melt temperature of 841 ° c . to obtain a melt for raising a bismuth - substituted magnetic garnet single crystal . by a conventional procedure , the surface of thus obtained melt was made in contact with the one surface of a ( 111 ) garnet single - crystal substrate : ( gdca ) 3 ( gamgzr ) 5 o 12 ( lattice constant : 12 . 493 ± 0 . 002 å ) of 480 μm in thickness , and the epitaxial growth was continued while maintaining the melt temperature of 841 ° c . the epitaxial growth brought out a ( gdbi ) 3 ( fegaal ) 5 o 12 single - crystal film ( gdbifegaalg single - crystal film ) of 26 μm in film thickness . then , the gdbifegaalg single - crystal film was cut into the size of 1 mm × 3 mm to be measured with respect to the magnetic characteristics ; the magnetic characteristics was measured by the just same method as embodiment 1 and showed the rectangular hysteresis described in fig6 . that is , their values are as follows : secondly , a permanent magnet was fixed on the gdbifegaalg single - crystal film of 1 mm × 3 mm in size , positioned as shown in fig1 , in the same method as embodiment 4 , the magnetic characteristics were measured similarly . the permanent magnet was the same ferrite permanent magnet as used in embodiment 4 , of 4000 ( g ) residual magnetic flux density and 1 mm × 1 mm × 0 . 5 mm in size . the measured values of the magnetic characteristics at the center of the gdbifegaalg single - crystal film are shown in fig1 . that is , their values were as follows : according to the p resent invention , the magnetic hysteresis can be erased with respect to a rare - earth iron garnet single - crystal film with large magnetic hysteresis which is an obstacle in using as a faraday rotator although the film has an extremely small saturated magnetic field intensity . as the result , an optical switch utilizing faraday effect and a magneto - optical sensor with a faraday rotator , wherein being applied a rare - earth iron garnet single - crystal film with a small saturated magnetic field intensity , have been enabled . pg , 24