Abstract

We present a detailed formulation to describe far-infrared reflection and transmission from a ferroelectric film at normal incidence. The formalism begins with the Gibbs free energy per unit area and the Landau–Khalatnikov equations of motion. To take size and surface effects in the film into account, boundary values and possible spatial variation in polarization are included in the free-energy expression, which leads to the existence of two additional parameters, D and δ. The inclusion of D leads to the presence of another spin-wave type of optical mode in addition to the normal polariton type of waves in the dispersion curves and the appearance of the spin-wave mode fringes in the reflectivity curves. Reflection curves for various values of δ are illustrated, and the results show that the effects of these two parameters are distinctively different in reflectivity. Far-infrared reflectivity measurements are proposed here as a tool to determine surface and size effects in ferroelectric thin films.

© 2001 Optical Society of America

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  1. W. L. Zhong, Y. G. Wang, and P. L. Zhang, “Phase transitions in finite-size ferroelectrics,” Ferroelectr. Rev. 1, 131–193 (1998).
  2. D. R. Tilley and B. Zeks, “Landau theory of phase transitions in thick films,” Solid State Commun. 49, 823–827 (1984).
  3. L. H. Ong, J. Osman, and D. R. Tilley, “Landau theory of second-order phase transitions in ferroelectric films,” Phys. Rev. B 63, 144109, 1–10 (2001).
  4. J. F. Scott, H. M. Duiker, P. D. Beale, B. Pouligny, K. Dimmler, M. Parris, D. Butler, and S. Eaton, “Properties of ceramic KNO3 thin-film memories,” Physica B 150, 160–167 (1988).
  5. E. K. Tan, J. Osman, and D. R. Tilley, “First-order phase transitions in ferroelectric films,” Solid State Commun. 116, 61–65 (2000).
  6. Ph. Ghosez and K. M. Rabe, “Microscopic model of ferroelectricity in stress-free PbTiO3 ultrathin films,” Appl. Phys. Lett. 76, 2767–2769 (2000).
  7. T. Tybell, C. H. Ahn, and J.-M. Triscone, “Ferroelectricity in thin perovskite films,” Appl. Phys. Lett. 75, 856–858 (1999).
  8. K. H. Chew, J. Osman, R. L. Stamps, D. R. Tilley, and J. F. Webb, “Theory of far infrared spectroscopy for ferroelectric size effects,” Integr. Ferroelectr. 23, 161–186 (1999).
  9. K. H. Chew, S. Alwi, D. R. Tilley, J. Osman, and J. F. Webb, “Optical transmission through ferroelectric thin films as a probe of surface terms,” Ferroelectrics 230, 209–214 (1999).
  10. Y. Ishibashi, “Structure and physical properties of domain walls,” Ferroelectrics 104, 299–310 (1990).
  11. J. Osman, Y. Ishibashi, and D. R. Tilley, “Calculation of nonlinear susceptibility tensor components in ferroelectrics,” Jpn. J. Appl. Phys. 37, 4887–4893 (1998).
  12. S. C. Lim, J. Osman, and D. R. Tilley, “The gyromagnetic Fabry–Pérot resonator. II. dipole–exchange effects,” J. Phys. Condens. Matter 10, 1891–1907 (1998).
  13. W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge University, Cambridge, UK, 1989).
  14. M. G. Cottam, D. R. Tilley, and B. Zeks, “Theory of surface modes in ferroelectrics,” J. Phys. C 17, 1793–1823 (1984).
  15. R. N. Philp and D. R. Tilley, “Exciton polaritons in thin films,” Phys. Rev. B 44, 8170–8180 (1991).
  16. M. Lui, C. A. Ramos, A. R. King, and V. Jaccarino, “Antiferromagnetic standing-spin-wave resonance in epitaxial films of MnF2,” J. Appl. Phys. 67, 5518–5520 (1990).
  17. M. G. Cottam and D. R. Tilley, Introduction to Surface and Superlattice Excitations (Cambridge University, Cambridge, UK, 1986).
  18. S. A. Feiven and T. J. Parker, Department of Physics, University of Essex, Colchester, UK (private communication, 1994).
  19. K. Abraha and D. R. Tilley, “Theory of far-infrared reflectivity and surface magnetic polaritons of rare-earth magnets,” Infrared Phys. Technol. 35, 681–699 (1994).
  20. R. W. Boyd and J. E. Sipe, “Nonlinear optical susceptibilities of layered composite materials,” J. Opt. Soc. Am. B 11, 297–303 (1994).
  21. G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. R. Weller-Brophy, “Enhanced nonlinear optical response of composite materials,” Phys. Rev. Lett. 74, 1871–1874 (1995).

2001 (1)

L. H. Ong, J. Osman, and D. R. Tilley, “Landau theory of second-order phase transitions in ferroelectric films,” Phys. Rev. B 63, 144109, 1–10 (2001).

2000 (2)

E. K. Tan, J. Osman, and D. R. Tilley, “First-order phase transitions in ferroelectric films,” Solid State Commun. 116, 61–65 (2000).

Ph. Ghosez and K. M. Rabe, “Microscopic model of ferroelectricity in stress-free PbTiO3 ultrathin films,” Appl. Phys. Lett. 76, 2767–2769 (2000).

1999 (3)

T. Tybell, C. H. Ahn, and J.-M. Triscone, “Ferroelectricity in thin perovskite films,” Appl. Phys. Lett. 75, 856–858 (1999).

K. H. Chew, J. Osman, R. L. Stamps, D. R. Tilley, and J. F. Webb, “Theory of far infrared spectroscopy for ferroelectric size effects,” Integr. Ferroelectr. 23, 161–186 (1999).

K. H. Chew, S. Alwi, D. R. Tilley, J. Osman, and J. F. Webb, “Optical transmission through ferroelectric thin films as a probe of surface terms,” Ferroelectrics 230, 209–214 (1999).

1998 (3)

W. L. Zhong, Y. G. Wang, and P. L. Zhang, “Phase transitions in finite-size ferroelectrics,” Ferroelectr. Rev. 1, 131–193 (1998).

J. Osman, Y. Ishibashi, and D. R. Tilley, “Calculation of nonlinear susceptibility tensor components in ferroelectrics,” Jpn. J. Appl. Phys. 37, 4887–4893 (1998).

S. C. Lim, J. Osman, and D. R. Tilley, “The gyromagnetic Fabry–Pérot resonator. II. dipole–exchange effects,” J. Phys. Condens. Matter 10, 1891–1907 (1998).

1995 (1)

G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. R. Weller-Brophy, “Enhanced nonlinear optical response of composite materials,” Phys. Rev. Lett. 74, 1871–1874 (1995).

1994 (2)

R. W. Boyd and J. E. Sipe, “Nonlinear optical susceptibilities of layered composite materials,” J. Opt. Soc. Am. B 11, 297–303 (1994).

K. Abraha and D. R. Tilley, “Theory of far-infrared reflectivity and surface magnetic polaritons of rare-earth magnets,” Infrared Phys. Technol. 35, 681–699 (1994).

1991 (1)

R. N. Philp and D. R. Tilley, “Exciton polaritons in thin films,” Phys. Rev. B 44, 8170–8180 (1991).

1990 (2)

M. Lui, C. A. Ramos, A. R. King, and V. Jaccarino, “Antiferromagnetic standing-spin-wave resonance in epitaxial films of MnF2,” J. Appl. Phys. 67, 5518–5520 (1990).

Y. Ishibashi, “Structure and physical properties of domain walls,” Ferroelectrics 104, 299–310 (1990).

1988 (1)

J. F. Scott, H. M. Duiker, P. D. Beale, B. Pouligny, K. Dimmler, M. Parris, D. Butler, and S. Eaton, “Properties of ceramic KNO3 thin-film memories,” Physica B 150, 160–167 (1988).

1984 (2)

D. R. Tilley and B. Zeks, “Landau theory of phase transitions in thick films,” Solid State Commun. 49, 823–827 (1984).

M. G. Cottam, D. R. Tilley, and B. Zeks, “Theory of surface modes in ferroelectrics,” J. Phys. C 17, 1793–1823 (1984).

Abraha, K.

K. Abraha and D. R. Tilley, “Theory of far-infrared reflectivity and surface magnetic polaritons of rare-earth magnets,” Infrared Phys. Technol. 35, 681–699 (1994).

Ahn, C. H.

T. Tybell, C. H. Ahn, and J.-M. Triscone, “Ferroelectricity in thin perovskite films,” Appl. Phys. Lett. 75, 856–858 (1999).

Alwi, S.

K. H. Chew, S. Alwi, D. R. Tilley, J. Osman, and J. F. Webb, “Optical transmission through ferroelectric thin films as a probe of surface terms,” Ferroelectrics 230, 209–214 (1999).

Beale, P. D.

J. F. Scott, H. M. Duiker, P. D. Beale, B. Pouligny, K. Dimmler, M. Parris, D. Butler, and S. Eaton, “Properties of ceramic KNO3 thin-film memories,” Physica B 150, 160–167 (1988).

Boyd, R. W.

G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. R. Weller-Brophy, “Enhanced nonlinear optical response of composite materials,” Phys. Rev. Lett. 74, 1871–1874 (1995).

R. W. Boyd and J. E. Sipe, “Nonlinear optical susceptibilities of layered composite materials,” J. Opt. Soc. Am. B 11, 297–303 (1994).

Butler, D.

J. F. Scott, H. M. Duiker, P. D. Beale, B. Pouligny, K. Dimmler, M. Parris, D. Butler, and S. Eaton, “Properties of ceramic KNO3 thin-film memories,” Physica B 150, 160–167 (1988).

Chew, K. H.

K. H. Chew, J. Osman, R. L. Stamps, D. R. Tilley, and J. F. Webb, “Theory of far infrared spectroscopy for ferroelectric size effects,” Integr. Ferroelectr. 23, 161–186 (1999).

K. H. Chew, S. Alwi, D. R. Tilley, J. Osman, and J. F. Webb, “Optical transmission through ferroelectric thin films as a probe of surface terms,” Ferroelectrics 230, 209–214 (1999).

Cottam, M. G.

M. G. Cottam, D. R. Tilley, and B. Zeks, “Theory of surface modes in ferroelectrics,” J. Phys. C 17, 1793–1823 (1984).

Dimmler, K.

J. F. Scott, H. M. Duiker, P. D. Beale, B. Pouligny, K. Dimmler, M. Parris, D. Butler, and S. Eaton, “Properties of ceramic KNO3 thin-film memories,” Physica B 150, 160–167 (1988).

Duiker, H. M.

J. F. Scott, H. M. Duiker, P. D. Beale, B. Pouligny, K. Dimmler, M. Parris, D. Butler, and S. Eaton, “Properties of ceramic KNO3 thin-film memories,” Physica B 150, 160–167 (1988).

Eaton, S.

J. F. Scott, H. M. Duiker, P. D. Beale, B. Pouligny, K. Dimmler, M. Parris, D. Butler, and S. Eaton, “Properties of ceramic KNO3 thin-film memories,” Physica B 150, 160–167 (1988).

Fischer, G. L.

G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. R. Weller-Brophy, “Enhanced nonlinear optical response of composite materials,” Phys. Rev. Lett. 74, 1871–1874 (1995).

Gehr, R. J.

G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. R. Weller-Brophy, “Enhanced nonlinear optical response of composite materials,” Phys. Rev. Lett. 74, 1871–1874 (1995).

Ghosez, Ph.

Ph. Ghosez and K. M. Rabe, “Microscopic model of ferroelectricity in stress-free PbTiO3 ultrathin films,” Appl. Phys. Lett. 76, 2767–2769 (2000).

Ishibashi, Y.

J. Osman, Y. Ishibashi, and D. R. Tilley, “Calculation of nonlinear susceptibility tensor components in ferroelectrics,” Jpn. J. Appl. Phys. 37, 4887–4893 (1998).

Y. Ishibashi, “Structure and physical properties of domain walls,” Ferroelectrics 104, 299–310 (1990).

Jaccarino, V.

M. Lui, C. A. Ramos, A. R. King, and V. Jaccarino, “Antiferromagnetic standing-spin-wave resonance in epitaxial films of MnF2,” J. Appl. Phys. 67, 5518–5520 (1990).

Jenekhe, S. A.

G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. R. Weller-Brophy, “Enhanced nonlinear optical response of composite materials,” Phys. Rev. Lett. 74, 1871–1874 (1995).

King, A. R.

M. Lui, C. A. Ramos, A. R. King, and V. Jaccarino, “Antiferromagnetic standing-spin-wave resonance in epitaxial films of MnF2,” J. Appl. Phys. 67, 5518–5520 (1990).

Lim, S. C.

S. C. Lim, J. Osman, and D. R. Tilley, “The gyromagnetic Fabry–Pérot resonator. II. dipole–exchange effects,” J. Phys. Condens. Matter 10, 1891–1907 (1998).

Lui, M.

M. Lui, C. A. Ramos, A. R. King, and V. Jaccarino, “Antiferromagnetic standing-spin-wave resonance in epitaxial films of MnF2,” J. Appl. Phys. 67, 5518–5520 (1990).

Ong, L. H.

L. H. Ong, J. Osman, and D. R. Tilley, “Landau theory of second-order phase transitions in ferroelectric films,” Phys. Rev. B 63, 144109, 1–10 (2001).

Osaheni, J. A.

G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. R. Weller-Brophy, “Enhanced nonlinear optical response of composite materials,” Phys. Rev. Lett. 74, 1871–1874 (1995).

Osman, J.

L. H. Ong, J. Osman, and D. R. Tilley, “Landau theory of second-order phase transitions in ferroelectric films,” Phys. Rev. B 63, 144109, 1–10 (2001).

E. K. Tan, J. Osman, and D. R. Tilley, “First-order phase transitions in ferroelectric films,” Solid State Commun. 116, 61–65 (2000).

K. H. Chew, S. Alwi, D. R. Tilley, J. Osman, and J. F. Webb, “Optical transmission through ferroelectric thin films as a probe of surface terms,” Ferroelectrics 230, 209–214 (1999).

K. H. Chew, J. Osman, R. L. Stamps, D. R. Tilley, and J. F. Webb, “Theory of far infrared spectroscopy for ferroelectric size effects,” Integr. Ferroelectr. 23, 161–186 (1999).

S. C. Lim, J. Osman, and D. R. Tilley, “The gyromagnetic Fabry–Pérot resonator. II. dipole–exchange effects,” J. Phys. Condens. Matter 10, 1891–1907 (1998).

J. Osman, Y. Ishibashi, and D. R. Tilley, “Calculation of nonlinear susceptibility tensor components in ferroelectrics,” Jpn. J. Appl. Phys. 37, 4887–4893 (1998).

Parris, M.

J. F. Scott, H. M. Duiker, P. D. Beale, B. Pouligny, K. Dimmler, M. Parris, D. Butler, and S. Eaton, “Properties of ceramic KNO3 thin-film memories,” Physica B 150, 160–167 (1988).

Philp, R. N.

R. N. Philp and D. R. Tilley, “Exciton polaritons in thin films,” Phys. Rev. B 44, 8170–8180 (1991).

Pouligny, B.

J. F. Scott, H. M. Duiker, P. D. Beale, B. Pouligny, K. Dimmler, M. Parris, D. Butler, and S. Eaton, “Properties of ceramic KNO3 thin-film memories,” Physica B 150, 160–167 (1988).

Rabe, K. M.

Ph. Ghosez and K. M. Rabe, “Microscopic model of ferroelectricity in stress-free PbTiO3 ultrathin films,” Appl. Phys. Lett. 76, 2767–2769 (2000).

Ramos, C. A.

M. Lui, C. A. Ramos, A. R. King, and V. Jaccarino, “Antiferromagnetic standing-spin-wave resonance in epitaxial films of MnF2,” J. Appl. Phys. 67, 5518–5520 (1990).

Scott, J. F.

J. F. Scott, H. M. Duiker, P. D. Beale, B. Pouligny, K. Dimmler, M. Parris, D. Butler, and S. Eaton, “Properties of ceramic KNO3 thin-film memories,” Physica B 150, 160–167 (1988).

Sipe, J. E.

G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. R. Weller-Brophy, “Enhanced nonlinear optical response of composite materials,” Phys. Rev. Lett. 74, 1871–1874 (1995).

R. W. Boyd and J. E. Sipe, “Nonlinear optical susceptibilities of layered composite materials,” J. Opt. Soc. Am. B 11, 297–303 (1994).

Stamps, R. L.

K. H. Chew, J. Osman, R. L. Stamps, D. R. Tilley, and J. F. Webb, “Theory of far infrared spectroscopy for ferroelectric size effects,” Integr. Ferroelectr. 23, 161–186 (1999).

Tan, E. K.

E. K. Tan, J. Osman, and D. R. Tilley, “First-order phase transitions in ferroelectric films,” Solid State Commun. 116, 61–65 (2000).

Tilley, D. R.

L. H. Ong, J. Osman, and D. R. Tilley, “Landau theory of second-order phase transitions in ferroelectric films,” Phys. Rev. B 63, 144109, 1–10 (2001).

E. K. Tan, J. Osman, and D. R. Tilley, “First-order phase transitions in ferroelectric films,” Solid State Commun. 116, 61–65 (2000).

K. H. Chew, S. Alwi, D. R. Tilley, J. Osman, and J. F. Webb, “Optical transmission through ferroelectric thin films as a probe of surface terms,” Ferroelectrics 230, 209–214 (1999).

K. H. Chew, J. Osman, R. L. Stamps, D. R. Tilley, and J. F. Webb, “Theory of far infrared spectroscopy for ferroelectric size effects,” Integr. Ferroelectr. 23, 161–186 (1999).

S. C. Lim, J. Osman, and D. R. Tilley, “The gyromagnetic Fabry–Pérot resonator. II. dipole–exchange effects,” J. Phys. Condens. Matter 10, 1891–1907 (1998).

J. Osman, Y. Ishibashi, and D. R. Tilley, “Calculation of nonlinear susceptibility tensor components in ferroelectrics,” Jpn. J. Appl. Phys. 37, 4887–4893 (1998).

K. Abraha and D. R. Tilley, “Theory of far-infrared reflectivity and surface magnetic polaritons of rare-earth magnets,” Infrared Phys. Technol. 35, 681–699 (1994).

R. N. Philp and D. R. Tilley, “Exciton polaritons in thin films,” Phys. Rev. B 44, 8170–8180 (1991).

M. G. Cottam, D. R. Tilley, and B. Zeks, “Theory of surface modes in ferroelectrics,” J. Phys. C 17, 1793–1823 (1984).

D. R. Tilley and B. Zeks, “Landau theory of phase transitions in thick films,” Solid State Commun. 49, 823–827 (1984).

Triscone, J.-M.

T. Tybell, C. H. Ahn, and J.-M. Triscone, “Ferroelectricity in thin perovskite films,” Appl. Phys. Lett. 75, 856–858 (1999).

Tybell, T.

T. Tybell, C. H. Ahn, and J.-M. Triscone, “Ferroelectricity in thin perovskite films,” Appl. Phys. Lett. 75, 856–858 (1999).

Wang, Y. G.

W. L. Zhong, Y. G. Wang, and P. L. Zhang, “Phase transitions in finite-size ferroelectrics,” Ferroelectr. Rev. 1, 131–193 (1998).

Webb, J. F.

K. H. Chew, J. Osman, R. L. Stamps, D. R. Tilley, and J. F. Webb, “Theory of far infrared spectroscopy for ferroelectric size effects,” Integr. Ferroelectr. 23, 161–186 (1999).

K. H. Chew, S. Alwi, D. R. Tilley, J. Osman, and J. F. Webb, “Optical transmission through ferroelectric thin films as a probe of surface terms,” Ferroelectrics 230, 209–214 (1999).

Weller-Brophy, L. R.

G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. R. Weller-Brophy, “Enhanced nonlinear optical response of composite materials,” Phys. Rev. Lett. 74, 1871–1874 (1995).

Zeks, B.

M. G. Cottam, D. R. Tilley, and B. Zeks, “Theory of surface modes in ferroelectrics,” J. Phys. C 17, 1793–1823 (1984).

D. R. Tilley and B. Zeks, “Landau theory of phase transitions in thick films,” Solid State Commun. 49, 823–827 (1984).

Zhang, P. L.

W. L. Zhong, Y. G. Wang, and P. L. Zhang, “Phase transitions in finite-size ferroelectrics,” Ferroelectr. Rev. 1, 131–193 (1998).

Zhong, W. L.

W. L. Zhong, Y. G. Wang, and P. L. Zhang, “Phase transitions in finite-size ferroelectrics,” Ferroelectr. Rev. 1, 131–193 (1998).

Appl. Phys. Lett. (2)

Ph. Ghosez and K. M. Rabe, “Microscopic model of ferroelectricity in stress-free PbTiO3 ultrathin films,” Appl. Phys. Lett. 76, 2767–2769 (2000).

T. Tybell, C. H. Ahn, and J.-M. Triscone, “Ferroelectricity in thin perovskite films,” Appl. Phys. Lett. 75, 856–858 (1999).

Ferroelectr. Rev. (1)

W. L. Zhong, Y. G. Wang, and P. L. Zhang, “Phase transitions in finite-size ferroelectrics,” Ferroelectr. Rev. 1, 131–193 (1998).

Ferroelectrics (2)

K. H. Chew, S. Alwi, D. R. Tilley, J. Osman, and J. F. Webb, “Optical transmission through ferroelectric thin films as a probe of surface terms,” Ferroelectrics 230, 209–214 (1999).

Y. Ishibashi, “Structure and physical properties of domain walls,” Ferroelectrics 104, 299–310 (1990).

Infrared Phys. Technol. (1)

K. Abraha and D. R. Tilley, “Theory of far-infrared reflectivity and surface magnetic polaritons of rare-earth magnets,” Infrared Phys. Technol. 35, 681–699 (1994).

Integr. Ferroelectr. (1)

K. H. Chew, J. Osman, R. L. Stamps, D. R. Tilley, and J. F. Webb, “Theory of far infrared spectroscopy for ferroelectric size effects,” Integr. Ferroelectr. 23, 161–186 (1999).

J. Appl. Phys. (1)

M. Lui, C. A. Ramos, A. R. King, and V. Jaccarino, “Antiferromagnetic standing-spin-wave resonance in epitaxial films of MnF2,” J. Appl. Phys. 67, 5518–5520 (1990).

J. Opt. Soc. Am. B (1)

J. Phys. C (1)

M. G. Cottam, D. R. Tilley, and B. Zeks, “Theory of surface modes in ferroelectrics,” J. Phys. C 17, 1793–1823 (1984).

J. Phys. Condens. Matter (1)

S. C. Lim, J. Osman, and D. R. Tilley, “The gyromagnetic Fabry–Pérot resonator. II. dipole–exchange effects,” J. Phys. Condens. Matter 10, 1891–1907 (1998).

Jpn. J. Appl. Phys. (1)

J. Osman, Y. Ishibashi, and D. R. Tilley, “Calculation of nonlinear susceptibility tensor components in ferroelectrics,” Jpn. J. Appl. Phys. 37, 4887–4893 (1998).

Phys. Rev. B (2)

L. H. Ong, J. Osman, and D. R. Tilley, “Landau theory of second-order phase transitions in ferroelectric films,” Phys. Rev. B 63, 144109, 1–10 (2001).

R. N. Philp and D. R. Tilley, “Exciton polaritons in thin films,” Phys. Rev. B 44, 8170–8180 (1991).

Phys. Rev. Lett. (1)

G. L. Fischer, R. W. Boyd, R. J. Gehr, S. A. Jenekhe, J. A. Osaheni, J. E. Sipe, and L. R. Weller-Brophy, “Enhanced nonlinear optical response of composite materials,” Phys. Rev. Lett. 74, 1871–1874 (1995).

Physica B (1)

J. F. Scott, H. M. Duiker, P. D. Beale, B. Pouligny, K. Dimmler, M. Parris, D. Butler, and S. Eaton, “Properties of ceramic KNO3 thin-film memories,” Physica B 150, 160–167 (1988).

Solid State Commun. (2)

E. K. Tan, J. Osman, and D. R. Tilley, “First-order phase transitions in ferroelectric films,” Solid State Commun. 116, 61–65 (2000).

D. R. Tilley and B. Zeks, “Landau theory of phase transitions in thick films,” Solid State Commun. 49, 823–827 (1984).

Other (3)

M. G. Cottam and D. R. Tilley, Introduction to Surface and Superlattice Excitations (Cambridge University, Cambridge, UK, 1986).

S. A. Feiven and T. J. Parker, Department of Physics, University of Essex, Colchester, UK (private communication, 1994).

W. H. Press, B. P. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipes: The Art of Scientific Computing (Cambridge University, Cambridge, UK, 1989).

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