Abstract

A Faraday Effect sensor with Nd2Fe14B biasing magnetic film was described. Ta/Nd2Fe14B/Ta films were grown by magnetron sputtering method. The magnetic domain in the sensor with the Nd2Fe14B biasing magnetic film can persist its distribution. The average linearity error of Faraday Effect sensor with biasing magnetic film decreased from 1.42% to 0.125% compared with non-biasing magnetic film, and the measurement range increased from 820 Oe to 900 Oe.

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  1. S. Saito, Y. Fujii, K. Yokoyama, J. Hamasaki, and Y. Ohno, “The laser current transformer for EHV power transmission lines,” IEEE J. Quantum Electron. 2(8), 255–259 (1966).
    [CrossRef]
  2. P. Ripka, “Electric current sensors: a review,” Meas. Sci. Technol. 21(11), 112001 (2010).
    [CrossRef]
  3. B. Yi, B. C. B. Chu, and K. S. Chiang, “Magneto-optical electric-current sensor with enhanced sensitivity,” Meas. Sci. Technol. 13(61–N), 63 (2002).
  4. Y. N. Ning, Z. P. Wang, A. W. Palmer, K. T. V. Grattan, and D. A. Jackson, “Recent progress in optical current sensing techniques,” Rev. Sci. Instrum. 66(5), 3097–3011 (1995).
    [CrossRef]
  5. J. G. Bai, G.-Q. Lu, and T. Lin, “Magneto-optical current sensing for applications in integrated power electronics modules,” Sens. Actuators A Phys. 109(1-2), 9–16 (2003).
    [CrossRef]
  6. N. Itoh, Y. Yoshikawa, H. Minemoto, and S. Ishizuka, “Optical magnetic field probe sensor with high accuracy using iron garnet films,” in proceeding of the eleventh International Conference on Optical Fiber Sensors,” Advanced Sensing Photonics (Japan Society of Applied Physics, Sapporo, 1996), pp. 638–641.
  7. O. Kamada, “Magneto-optical properties of (BiGdY) iron garnets for optical magnetic field sensors,” J. Appl. Phys. 79(8), 5976–5978 (1996).
    [CrossRef]
  8. O. Kamada, H. Minemoto, and N. Itoh, “Magneto-optical properties of (BiGaY)3Fe5O12 for optical magnetic field sensors,” J. Appl. Phys. 75(10), 6801–6803 (1994).
    [CrossRef]
  9. N. Itoh, H. Minemoto, D. Ishiko, and S. Ishizuka, “Optical magnetic field sensors with high linearity using Bi-substituted rare earth iron garnets,” IEEE Trans. Magn. 31(6), 3191–3193 (1995).
    [CrossRef]
  10. V. Neu, A. Anane, S. Wirth, P. Xiong, S. A. Shaheen, and F. J. Cadieu, “Design optimization for a SmCo-biased colossal magnetoresistive thin film device,” J. Appl. Phys. 87(9), 5350 (2000).
    [CrossRef]
  11. H. Guerrero, R. Perez del Real, R. Fernandez de Caleya, and G. Rosa, “Magnetic field biasing in Faraday effect sensors,” Appl. Phys. Lett. 74(24), 3702–3704 (1999).
    [CrossRef]
  12. F. Dumas-Bouchiat, L. F. Zanini, M. Kustov, N. M. Dempsey, R. Grechishkin, K. Hasselbach, J. C. Orlianges, C. Champeaux, A. Catherinot, and D. Givord, “Thermomagnetically patterned micromagnets,” Appl. Phys. Lett. 96(10), 102511 (2010).
    [CrossRef]
  13. M. Ohkoshi, “Formation and stability of small-size bubbles in garnet films,” J. Appl. Phys. 92(1), 370–373 (2002).
    [CrossRef]
  14. M. Mino and H. Yamazaki, “Magnetic domain structure in thin film under alternate magnetic field,” J. Magn. Magn. Mater. 272–276, E509–E510 (2004).
    [CrossRef]

2010

P. Ripka, “Electric current sensors: a review,” Meas. Sci. Technol. 21(11), 112001 (2010).
[CrossRef]

F. Dumas-Bouchiat, L. F. Zanini, M. Kustov, N. M. Dempsey, R. Grechishkin, K. Hasselbach, J. C. Orlianges, C. Champeaux, A. Catherinot, and D. Givord, “Thermomagnetically patterned micromagnets,” Appl. Phys. Lett. 96(10), 102511 (2010).
[CrossRef]

2004

M. Mino and H. Yamazaki, “Magnetic domain structure in thin film under alternate magnetic field,” J. Magn. Magn. Mater. 272–276, E509–E510 (2004).
[CrossRef]

2003

J. G. Bai, G.-Q. Lu, and T. Lin, “Magneto-optical current sensing for applications in integrated power electronics modules,” Sens. Actuators A Phys. 109(1-2), 9–16 (2003).
[CrossRef]

2002

B. Yi, B. C. B. Chu, and K. S. Chiang, “Magneto-optical electric-current sensor with enhanced sensitivity,” Meas. Sci. Technol. 13(61–N), 63 (2002).

M. Ohkoshi, “Formation and stability of small-size bubbles in garnet films,” J. Appl. Phys. 92(1), 370–373 (2002).
[CrossRef]

2000

V. Neu, A. Anane, S. Wirth, P. Xiong, S. A. Shaheen, and F. J. Cadieu, “Design optimization for a SmCo-biased colossal magnetoresistive thin film device,” J. Appl. Phys. 87(9), 5350 (2000).
[CrossRef]

1999

H. Guerrero, R. Perez del Real, R. Fernandez de Caleya, and G. Rosa, “Magnetic field biasing in Faraday effect sensors,” Appl. Phys. Lett. 74(24), 3702–3704 (1999).
[CrossRef]

1996

O. Kamada, “Magneto-optical properties of (BiGdY) iron garnets for optical magnetic field sensors,” J. Appl. Phys. 79(8), 5976–5978 (1996).
[CrossRef]

1995

Y. N. Ning, Z. P. Wang, A. W. Palmer, K. T. V. Grattan, and D. A. Jackson, “Recent progress in optical current sensing techniques,” Rev. Sci. Instrum. 66(5), 3097–3011 (1995).
[CrossRef]

N. Itoh, H. Minemoto, D. Ishiko, and S. Ishizuka, “Optical magnetic field sensors with high linearity using Bi-substituted rare earth iron garnets,” IEEE Trans. Magn. 31(6), 3191–3193 (1995).
[CrossRef]

1994

O. Kamada, H. Minemoto, and N. Itoh, “Magneto-optical properties of (BiGaY)3Fe5O12 for optical magnetic field sensors,” J. Appl. Phys. 75(10), 6801–6803 (1994).
[CrossRef]

1966

S. Saito, Y. Fujii, K. Yokoyama, J. Hamasaki, and Y. Ohno, “The laser current transformer for EHV power transmission lines,” IEEE J. Quantum Electron. 2(8), 255–259 (1966).
[CrossRef]

Anane, A.

V. Neu, A. Anane, S. Wirth, P. Xiong, S. A. Shaheen, and F. J. Cadieu, “Design optimization for a SmCo-biased colossal magnetoresistive thin film device,” J. Appl. Phys. 87(9), 5350 (2000).
[CrossRef]

Bai, J. G.

J. G. Bai, G.-Q. Lu, and T. Lin, “Magneto-optical current sensing for applications in integrated power electronics modules,” Sens. Actuators A Phys. 109(1-2), 9–16 (2003).
[CrossRef]

Cadieu, F. J.

V. Neu, A. Anane, S. Wirth, P. Xiong, S. A. Shaheen, and F. J. Cadieu, “Design optimization for a SmCo-biased colossal magnetoresistive thin film device,” J. Appl. Phys. 87(9), 5350 (2000).
[CrossRef]

Catherinot, A.

F. Dumas-Bouchiat, L. F. Zanini, M. Kustov, N. M. Dempsey, R. Grechishkin, K. Hasselbach, J. C. Orlianges, C. Champeaux, A. Catherinot, and D. Givord, “Thermomagnetically patterned micromagnets,” Appl. Phys. Lett. 96(10), 102511 (2010).
[CrossRef]

Champeaux, C.

F. Dumas-Bouchiat, L. F. Zanini, M. Kustov, N. M. Dempsey, R. Grechishkin, K. Hasselbach, J. C. Orlianges, C. Champeaux, A. Catherinot, and D. Givord, “Thermomagnetically patterned micromagnets,” Appl. Phys. Lett. 96(10), 102511 (2010).
[CrossRef]

Chiang, K. S.

B. Yi, B. C. B. Chu, and K. S. Chiang, “Magneto-optical electric-current sensor with enhanced sensitivity,” Meas. Sci. Technol. 13(61–N), 63 (2002).

Chu, B. C. B.

B. Yi, B. C. B. Chu, and K. S. Chiang, “Magneto-optical electric-current sensor with enhanced sensitivity,” Meas. Sci. Technol. 13(61–N), 63 (2002).

Dempsey, N. M.

F. Dumas-Bouchiat, L. F. Zanini, M. Kustov, N. M. Dempsey, R. Grechishkin, K. Hasselbach, J. C. Orlianges, C. Champeaux, A. Catherinot, and D. Givord, “Thermomagnetically patterned micromagnets,” Appl. Phys. Lett. 96(10), 102511 (2010).
[CrossRef]

Dumas-Bouchiat, F.

F. Dumas-Bouchiat, L. F. Zanini, M. Kustov, N. M. Dempsey, R. Grechishkin, K. Hasselbach, J. C. Orlianges, C. Champeaux, A. Catherinot, and D. Givord, “Thermomagnetically patterned micromagnets,” Appl. Phys. Lett. 96(10), 102511 (2010).
[CrossRef]

Fernandez de Caleya, R.

H. Guerrero, R. Perez del Real, R. Fernandez de Caleya, and G. Rosa, “Magnetic field biasing in Faraday effect sensors,” Appl. Phys. Lett. 74(24), 3702–3704 (1999).
[CrossRef]

Fujii, Y.

S. Saito, Y. Fujii, K. Yokoyama, J. Hamasaki, and Y. Ohno, “The laser current transformer for EHV power transmission lines,” IEEE J. Quantum Electron. 2(8), 255–259 (1966).
[CrossRef]

Givord, D.

F. Dumas-Bouchiat, L. F. Zanini, M. Kustov, N. M. Dempsey, R. Grechishkin, K. Hasselbach, J. C. Orlianges, C. Champeaux, A. Catherinot, and D. Givord, “Thermomagnetically patterned micromagnets,” Appl. Phys. Lett. 96(10), 102511 (2010).
[CrossRef]

Grattan, K. T. V.

Y. N. Ning, Z. P. Wang, A. W. Palmer, K. T. V. Grattan, and D. A. Jackson, “Recent progress in optical current sensing techniques,” Rev. Sci. Instrum. 66(5), 3097–3011 (1995).
[CrossRef]

Grechishkin, R.

F. Dumas-Bouchiat, L. F. Zanini, M. Kustov, N. M. Dempsey, R. Grechishkin, K. Hasselbach, J. C. Orlianges, C. Champeaux, A. Catherinot, and D. Givord, “Thermomagnetically patterned micromagnets,” Appl. Phys. Lett. 96(10), 102511 (2010).
[CrossRef]

Guerrero, H.

H. Guerrero, R. Perez del Real, R. Fernandez de Caleya, and G. Rosa, “Magnetic field biasing in Faraday effect sensors,” Appl. Phys. Lett. 74(24), 3702–3704 (1999).
[CrossRef]

Hamasaki, J.

S. Saito, Y. Fujii, K. Yokoyama, J. Hamasaki, and Y. Ohno, “The laser current transformer for EHV power transmission lines,” IEEE J. Quantum Electron. 2(8), 255–259 (1966).
[CrossRef]

Hasselbach, K.

F. Dumas-Bouchiat, L. F. Zanini, M. Kustov, N. M. Dempsey, R. Grechishkin, K. Hasselbach, J. C. Orlianges, C. Champeaux, A. Catherinot, and D. Givord, “Thermomagnetically patterned micromagnets,” Appl. Phys. Lett. 96(10), 102511 (2010).
[CrossRef]

Ishiko, D.

N. Itoh, H. Minemoto, D. Ishiko, and S. Ishizuka, “Optical magnetic field sensors with high linearity using Bi-substituted rare earth iron garnets,” IEEE Trans. Magn. 31(6), 3191–3193 (1995).
[CrossRef]

Ishizuka, S.

N. Itoh, H. Minemoto, D. Ishiko, and S. Ishizuka, “Optical magnetic field sensors with high linearity using Bi-substituted rare earth iron garnets,” IEEE Trans. Magn. 31(6), 3191–3193 (1995).
[CrossRef]

Itoh, N.

N. Itoh, H. Minemoto, D. Ishiko, and S. Ishizuka, “Optical magnetic field sensors with high linearity using Bi-substituted rare earth iron garnets,” IEEE Trans. Magn. 31(6), 3191–3193 (1995).
[CrossRef]

O. Kamada, H. Minemoto, and N. Itoh, “Magneto-optical properties of (BiGaY)3Fe5O12 for optical magnetic field sensors,” J. Appl. Phys. 75(10), 6801–6803 (1994).
[CrossRef]

Jackson, D. A.

Y. N. Ning, Z. P. Wang, A. W. Palmer, K. T. V. Grattan, and D. A. Jackson, “Recent progress in optical current sensing techniques,” Rev. Sci. Instrum. 66(5), 3097–3011 (1995).
[CrossRef]

Kamada, O.

O. Kamada, “Magneto-optical properties of (BiGdY) iron garnets for optical magnetic field sensors,” J. Appl. Phys. 79(8), 5976–5978 (1996).
[CrossRef]

O. Kamada, H. Minemoto, and N. Itoh, “Magneto-optical properties of (BiGaY)3Fe5O12 for optical magnetic field sensors,” J. Appl. Phys. 75(10), 6801–6803 (1994).
[CrossRef]

Kustov, M.

F. Dumas-Bouchiat, L. F. Zanini, M. Kustov, N. M. Dempsey, R. Grechishkin, K. Hasselbach, J. C. Orlianges, C. Champeaux, A. Catherinot, and D. Givord, “Thermomagnetically patterned micromagnets,” Appl. Phys. Lett. 96(10), 102511 (2010).
[CrossRef]

Lin, T.

J. G. Bai, G.-Q. Lu, and T. Lin, “Magneto-optical current sensing for applications in integrated power electronics modules,” Sens. Actuators A Phys. 109(1-2), 9–16 (2003).
[CrossRef]

Lu, G.-Q.

J. G. Bai, G.-Q. Lu, and T. Lin, “Magneto-optical current sensing for applications in integrated power electronics modules,” Sens. Actuators A Phys. 109(1-2), 9–16 (2003).
[CrossRef]

Minemoto, H.

N. Itoh, H. Minemoto, D. Ishiko, and S. Ishizuka, “Optical magnetic field sensors with high linearity using Bi-substituted rare earth iron garnets,” IEEE Trans. Magn. 31(6), 3191–3193 (1995).
[CrossRef]

O. Kamada, H. Minemoto, and N. Itoh, “Magneto-optical properties of (BiGaY)3Fe5O12 for optical magnetic field sensors,” J. Appl. Phys. 75(10), 6801–6803 (1994).
[CrossRef]

Mino, M.

M. Mino and H. Yamazaki, “Magnetic domain structure in thin film under alternate magnetic field,” J. Magn. Magn. Mater. 272–276, E509–E510 (2004).
[CrossRef]

Neu, V.

V. Neu, A. Anane, S. Wirth, P. Xiong, S. A. Shaheen, and F. J. Cadieu, “Design optimization for a SmCo-biased colossal magnetoresistive thin film device,” J. Appl. Phys. 87(9), 5350 (2000).
[CrossRef]

Ning, Y. N.

Y. N. Ning, Z. P. Wang, A. W. Palmer, K. T. V. Grattan, and D. A. Jackson, “Recent progress in optical current sensing techniques,” Rev. Sci. Instrum. 66(5), 3097–3011 (1995).
[CrossRef]

Ohkoshi, M.

M. Ohkoshi, “Formation and stability of small-size bubbles in garnet films,” J. Appl. Phys. 92(1), 370–373 (2002).
[CrossRef]

Ohno, Y.

S. Saito, Y. Fujii, K. Yokoyama, J. Hamasaki, and Y. Ohno, “The laser current transformer for EHV power transmission lines,” IEEE J. Quantum Electron. 2(8), 255–259 (1966).
[CrossRef]

Orlianges, J. C.

F. Dumas-Bouchiat, L. F. Zanini, M. Kustov, N. M. Dempsey, R. Grechishkin, K. Hasselbach, J. C. Orlianges, C. Champeaux, A. Catherinot, and D. Givord, “Thermomagnetically patterned micromagnets,” Appl. Phys. Lett. 96(10), 102511 (2010).
[CrossRef]

Palmer, A. W.

Y. N. Ning, Z. P. Wang, A. W. Palmer, K. T. V. Grattan, and D. A. Jackson, “Recent progress in optical current sensing techniques,” Rev. Sci. Instrum. 66(5), 3097–3011 (1995).
[CrossRef]

Perez del Real, R.

H. Guerrero, R. Perez del Real, R. Fernandez de Caleya, and G. Rosa, “Magnetic field biasing in Faraday effect sensors,” Appl. Phys. Lett. 74(24), 3702–3704 (1999).
[CrossRef]

Ripka, P.

P. Ripka, “Electric current sensors: a review,” Meas. Sci. Technol. 21(11), 112001 (2010).
[CrossRef]

Rosa, G.

H. Guerrero, R. Perez del Real, R. Fernandez de Caleya, and G. Rosa, “Magnetic field biasing in Faraday effect sensors,” Appl. Phys. Lett. 74(24), 3702–3704 (1999).
[CrossRef]

Saito, S.

S. Saito, Y. Fujii, K. Yokoyama, J. Hamasaki, and Y. Ohno, “The laser current transformer for EHV power transmission lines,” IEEE J. Quantum Electron. 2(8), 255–259 (1966).
[CrossRef]

Shaheen, S. A.

V. Neu, A. Anane, S. Wirth, P. Xiong, S. A. Shaheen, and F. J. Cadieu, “Design optimization for a SmCo-biased colossal magnetoresistive thin film device,” J. Appl. Phys. 87(9), 5350 (2000).
[CrossRef]

Wang, Z. P.

Y. N. Ning, Z. P. Wang, A. W. Palmer, K. T. V. Grattan, and D. A. Jackson, “Recent progress in optical current sensing techniques,” Rev. Sci. Instrum. 66(5), 3097–3011 (1995).
[CrossRef]

Wirth, S.

V. Neu, A. Anane, S. Wirth, P. Xiong, S. A. Shaheen, and F. J. Cadieu, “Design optimization for a SmCo-biased colossal magnetoresistive thin film device,” J. Appl. Phys. 87(9), 5350 (2000).
[CrossRef]

Xiong, P.

V. Neu, A. Anane, S. Wirth, P. Xiong, S. A. Shaheen, and F. J. Cadieu, “Design optimization for a SmCo-biased colossal magnetoresistive thin film device,” J. Appl. Phys. 87(9), 5350 (2000).
[CrossRef]

Yamazaki, H.

M. Mino and H. Yamazaki, “Magnetic domain structure in thin film under alternate magnetic field,” J. Magn. Magn. Mater. 272–276, E509–E510 (2004).
[CrossRef]

Yi, B.

B. Yi, B. C. B. Chu, and K. S. Chiang, “Magneto-optical electric-current sensor with enhanced sensitivity,” Meas. Sci. Technol. 13(61–N), 63 (2002).

Yokoyama, K.

S. Saito, Y. Fujii, K. Yokoyama, J. Hamasaki, and Y. Ohno, “The laser current transformer for EHV power transmission lines,” IEEE J. Quantum Electron. 2(8), 255–259 (1966).
[CrossRef]

Zanini, L. F.

F. Dumas-Bouchiat, L. F. Zanini, M. Kustov, N. M. Dempsey, R. Grechishkin, K. Hasselbach, J. C. Orlianges, C. Champeaux, A. Catherinot, and D. Givord, “Thermomagnetically patterned micromagnets,” Appl. Phys. Lett. 96(10), 102511 (2010).
[CrossRef]

Appl. Phys. Lett.

H. Guerrero, R. Perez del Real, R. Fernandez de Caleya, and G. Rosa, “Magnetic field biasing in Faraday effect sensors,” Appl. Phys. Lett. 74(24), 3702–3704 (1999).
[CrossRef]

F. Dumas-Bouchiat, L. F. Zanini, M. Kustov, N. M. Dempsey, R. Grechishkin, K. Hasselbach, J. C. Orlianges, C. Champeaux, A. Catherinot, and D. Givord, “Thermomagnetically patterned micromagnets,” Appl. Phys. Lett. 96(10), 102511 (2010).
[CrossRef]

IEEE J. Quantum Electron.

S. Saito, Y. Fujii, K. Yokoyama, J. Hamasaki, and Y. Ohno, “The laser current transformer for EHV power transmission lines,” IEEE J. Quantum Electron. 2(8), 255–259 (1966).
[CrossRef]

IEEE Trans. Magn.

N. Itoh, H. Minemoto, D. Ishiko, and S. Ishizuka, “Optical magnetic field sensors with high linearity using Bi-substituted rare earth iron garnets,” IEEE Trans. Magn. 31(6), 3191–3193 (1995).
[CrossRef]

J. Appl. Phys.

V. Neu, A. Anane, S. Wirth, P. Xiong, S. A. Shaheen, and F. J. Cadieu, “Design optimization for a SmCo-biased colossal magnetoresistive thin film device,” J. Appl. Phys. 87(9), 5350 (2000).
[CrossRef]

O. Kamada, “Magneto-optical properties of (BiGdY) iron garnets for optical magnetic field sensors,” J. Appl. Phys. 79(8), 5976–5978 (1996).
[CrossRef]

O. Kamada, H. Minemoto, and N. Itoh, “Magneto-optical properties of (BiGaY)3Fe5O12 for optical magnetic field sensors,” J. Appl. Phys. 75(10), 6801–6803 (1994).
[CrossRef]

M. Ohkoshi, “Formation and stability of small-size bubbles in garnet films,” J. Appl. Phys. 92(1), 370–373 (2002).
[CrossRef]

J. Magn. Magn. Mater.

M. Mino and H. Yamazaki, “Magnetic domain structure in thin film under alternate magnetic field,” J. Magn. Magn. Mater. 272–276, E509–E510 (2004).
[CrossRef]

Meas. Sci. Technol.

P. Ripka, “Electric current sensors: a review,” Meas. Sci. Technol. 21(11), 112001 (2010).
[CrossRef]

B. Yi, B. C. B. Chu, and K. S. Chiang, “Magneto-optical electric-current sensor with enhanced sensitivity,” Meas. Sci. Technol. 13(61–N), 63 (2002).

Rev. Sci. Instrum.

Y. N. Ning, Z. P. Wang, A. W. Palmer, K. T. V. Grattan, and D. A. Jackson, “Recent progress in optical current sensing techniques,” Rev. Sci. Instrum. 66(5), 3097–3011 (1995).
[CrossRef]

Sens. Actuators A Phys.

J. G. Bai, G.-Q. Lu, and T. Lin, “Magneto-optical current sensing for applications in integrated power electronics modules,” Sens. Actuators A Phys. 109(1-2), 9–16 (2003).
[CrossRef]

Other

N. Itoh, Y. Yoshikawa, H. Minemoto, and S. Ishizuka, “Optical magnetic field probe sensor with high accuracy using iron garnet films,” in proceeding of the eleventh International Conference on Optical Fiber Sensors,” Advanced Sensing Photonics (Japan Society of Applied Physics, Sapporo, 1996), pp. 638–641.

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Figures (7)

Fig. 1
Fig. 1

Garnet with Nd2Fe14B biasing magnetic film POM image. (b) Schematic drawing.

Fig. 2
Fig. 2

Schematic diagram of experimental set up.

Fig. 3
Fig. 3

XRD patterns for Garnet/Ta/Nd2Fe14B/Ta thin films deposited at 400 °C and annealed at 550 °C for 30 min.

Fig. 4
Fig. 4

Hysteresis loops at room temperature of Nd2Fe14B biasing magnetic film The loop shown in solid black boxes is for applied field perpendicular to the film plane and the in red circle is for field in the film plane.

Fig. 5
Fig. 5

POM image of magnetic domain in garnet at different Hext Hext = 0 Oe; (b)Hext = 400 Oe; (c)Hext = 0 Oe.

Fig. 6
Fig. 6

POM image of magnetic domain in garnet with biasing magnetic film at different Hext Hext = 0 Oe; (b)Hext = 400 Oe; (c)Hext = 0 Oe.

Fig. 7
Fig. 7

Faraday rotation angle of two types of sensor as a function of Hext.

Equations (3)

Equations on this page are rendered with MathJax. Learn more.

θ=VBL
σ= 1 n i=1 n [( H out H in )/ H in ] ×100
I φ ( θ F ) I φ ( θ F ) I 0 ο ( θ F ) I 0 ο ( θ ο ) = 2sin2φ tan θ F

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