Photorefractive and domain gratings in barium titanate

Abstract

We present concrete evidence for the formation of ferroelectric domain gratings induced by photorefractive space‐charge electric fields in top‐seeded solution‐grown barium titanate crystals. These domain gratings are not destroyed by light and, by applying a field, can be reconverted into photorefractive gratings that diffract much more light than the photorefractive gratings that create them, as much as 67% of an incident beam.

Full text

Photorefractive and domain gratings in barium titanate
f?. S. Cudney, J. Fousek,a) M. Zgonik, and P. GUnter
NQ~ Linear Optics Lnboratory, Institute of Quantum Hectronics, Suri.sv Federal Institute of Technology,
ET&H&ggwberg, (711-8093 Ziirich, Switzerland
M. H. Garrett and D. Rytz
S~ndoz Huningue, S. A., Centre de Recherche en Opto&Iectronique, Brit. 195/‘04, Av. de BZle,
F&330 Huningue, Frunce
(Received 25 June 1993; accepted for publication 15 October 1993)
We present concrete evidence for the formation of ferroelectric domain gratings induced by
photorefractive space-charge electric fields in top-seeded solution-grown barium titanate
crystals. These domain gratings are not destroyed by light and, by applying a field, can be
reconverted into photorefractive gratings that diffract much more light than the photorefractive
gratings that create them, as much as 67% of an incident beam.
For two decades after the discovery of its ferroelectric
properties, barium titanate was intensively studied as a rep-
resentative of compounds with a first-order ferroelectric
phase transition’ and also for its polarization reversal prop-
erties which made it a candidate for memory devices.’
Most of these measurements were performed on flux-
grown3 “butterfly wing” crystals. Later on, it was discov-
ered that photorefractive gratings could be induced in bar-
ium titanate by exposing it to an interference pattern.‘Js
Subsequent studies showed that these gratings can be made
permanent at room temperature if a field along the c axis
opposing the direction of the spontaneous polarization is
applied while two laser beams overlap in the crystal.6’7 This
phenomenon WBS explained in the following way: the light
interference pattern created by the beams produces a
space-charge field, which together with the biasing, exter-
nally applied field, reverses the polarization by 180” wher-
ever the total field exceeds the coercive field. By adjusting
the magnitude of the applied field to be slightly lower than
the coercive field, a spatially oscillating pattern of head-to-
head 180” domains is Formed, which somehow creates an
index grating.
The exact mechanism of this “hologram fixing” proce-
dure is not well understood. In the simplest model, one
might think that the spontaneous polarization 9, is re-
vers& in slab-shaped domains wherever the sum of the
applied and the internally developed fields exceeds the co-
ercive field. However, the discontinuity of the polarization
between these head-to-head slabs is quite large,’ namely
2,,- 52 @/cm” at room temperature, whereas the typical
value of the space-charge density of a photorefractive grat-
ing, integrated over half a period ( 1 ,um), is only around
5 x lo-’ ,4Ycm”. The slabs would largely overcompensate
the space charge, making this model highly improbable. In
addition, this arrangement by itself would not produce a
refractive index grating, since the linear optical properties
are the same for both orientations of
P,.
An externally
applied field would be needed to reveal the domain grating,
or a strong change of t.he index of refraction at the domain
walls.
BaPermanent address: Institute of Physics, Academy of Sciences of the
C+eh Republic, Na Slovance 2, 1X0 40 Prague 8.
In this letter we present strong evidence that charge
compensated domain gratings actually can be formed in
BaTiO,. Unlike photorefractive gratings, these do not de-
cay under illumination. By applying a field these gratings
can be reconvert.ed into enhanced replicas of the origitral
photorefractive (space-charge field induced) gratings,
which diffract light very efficiently, up to 7 times more
than an ordinary photorefractive grating.
The experiments were performed on a nominally un-
doped top-seeded solution grown a~ h~c= 2.3 ~3.5 ~2.5
mn? BaTi03 sample which was grown and initially cut and
poled at Sandoz8 It has a long photorefractive dark stor-
age time [hours-days). Electrodes were evaporated onto
the c faces of the crystal; these were used to apply electric
fields and to monitor the current produced by polarization
reversal. Hysteresis loop experiments showed that P,=2S
PC/cm’ and that, at very low frequencies, there is a well-
defined critical field &=480 V/cm at, which the switching
process begins. Two A=488 nm laser beams of equal in-
tensity were incident on the sample. The diffraction effi-
ciencies of the gratings produced by them were monitored
by a weak He-Ne laser. The polarization of the beams are
indicated in Fig. 1.
In all experiments described below we monitor the
Bragg-matched diffracted 633 nm signal and the current
while the following steps are performed.
(I) Poling. First the crystal is poled by applying a field
defined as positive, of about 4000 V/cm for 1 min or so.
Monitoring the current helps determine when the crystal is
well poled. Once the crystal is poled, the field is removed
+I
, Voltage
6
, supply
I
z
_-----
dt:tector5
--I I
I
I
I
I
I
I
FIG. 1. Experimental setup.
3399
Appl. Phys. Lett. 63 (25), 20 December 1993 0003-6951/93/63(25)/3399/3/$6.00 @ 1993 American Institute of Physics 3399
Downloaded 24 Jul 2001 to 129.132.214.119. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/aplo/aplcr.jsp

Time !seconds)
FIG. 2. Field, current, charge, and difiaction efficiency VT, time. Step I:
Poling. The crystal is poled by applying a positive field. Step II: Fixing.
The writing beams create a grating while a negative field is appiied. The
maximum magnitude of this field is [,??,.I Step III: Shelf time. Only one
writing beam floods the crystal, erasing the grating. No diJYracted signal is
observed. Step IV: Revealing. Both writing beams are off. A positive field
is applied and the diffracted signal appears again. A = 33 pm; intensity per
beam: 2.2 W/cm’; E,= 1.1 kV/cm,
slowly in order to avoid backswitching, presumably in-
duced by the field produced by screening c.harges ascumu-
lated at the electrodes.’
(II) Fixing. We let both 488 nm beams interfere in t.he
sample while a negative field that reaches a maximum
value ( EYI, called the fixing field, is applied. This field
enhances the space-charge field as explained below and,
when exceeding the critical field Em, also produces polar-
ization reversal in the sample, the degree of which can be
evaluated by integrating the current.
(III) Shelf-time (from minutes to tens of hours). No
field is applied. The crystal is illuminated by only one 488
nm beam.
(IV> Revealing. A positive field is applied to the crys-
tal. During this step both 488 nm writing beams are off.
Figure 2 shows a typical cycle of events. During the
fixing stage II the diffracted signal increases with the ap-
plied field until polarization reversal begins, reaching a
13% diffraction efficiency, and then decays as polarization
reversal continues. During the shelf-time period no appre-
ciable diffracted signal is detected. Under homogeneous
illumination, a purely photorefractive grating would be
completely erased and could not be revived by any subse-
quent treatment. However, if the fixing field 1 E’J > E,,,
when a positive revealing field is applied while both writing
beams are blocked, 67% of the incident beam is diffracted.
We explain the phenomena the following way. During
the beginning of the fixing stage trapped charges that are
optically excited preferentially at the maxima of the inter-
ference pattern drift due to the applied field and recombine
into empty traps located elsewhere, giving rise to a space-
charge distribution
qsc(Ef) =qO(Ef)sin 2irz/A, (1)
where qa is an amplitude which depends on the trap site
concentration and on the applied field, z is the distance
along the c axis, and A is the period of the interference
pattern. This charge distribution creates a space-charge
field that changes the index of refraction through the
electm-optic effect, creating a photorefract.ive grating
which diffracts the reading beam. When the field reaches
the value EC, it triggers the formation of nuclei of domains
with negative P, at the electrodes and at the built-in nu-
cleation sites such as defects of polar character. As in a
normal switching process’” these nuclei grow in the form
of needle-shaped domains to reach the crystal surfaces.
The degree of polarization reversal will depend on 1 EfI
and on how long the field is applied. In the given situation,
however, the presence of
qssc
codetermines the domain con-
figuration reached when the partial switching comes to an
end. A number of domains are expected to temnnate
within the sample, their ends being located so that maxi-
mum compensation of the free charges takes place. Assum-
ing that the charges in a half-period of the grating can be
ascribed to a single plane- then charge compensation re-
quires that on this plane some domain walls are located
covering a fraction f of the total area, given by
Acl,
j-C--
2%+$ * (2)
Taking A=23 pm, and qo=lO’ @.Ycm” (a typicril value
for the effective charge density located in trap sites in pho-
torefractive crystals), we get f = 1.3 X lo-“. However, un-
der the conditions used to obtain the data shown in Fig. 2,
the charge switched during the fixing stage amounts to 1.4
pCs about 30% of the maximum attainable if the whole
volume were switched. Therefore, most of the swimhing
does not contribute to the fixing process.
In this state of full or almost full charge compensation
the spatially modulated fteld disappears and no diffraction
is expected. In addition, the partial reversal diminishes the
value of the e&ctive electro-optic coefficient r,, and there-
fore the diffraction efficiency, since
rcff=r(L’_--J+)/{U_CUi-). (3)
Here U- and ZJ+ are the volume of domains aligned along
the - and + directions of the axis, respectively, and r is
the relevant electro-optic coeflicient for a single domain
crystal. In particular, no diffraction can occur (and none is
observed > when LJ- = u+ since
relr= 0.
When the revealing field is applied the domains disap-
pear and the crystal is brought back to its original state,
leaving behind the previous photorefractive space-charge
distribution. This charge, which now is not compensated,
produces a space-charge field and consequently an index of
refraction grating capable of diffracting light. The whoIe
process is depicted in Fig. 3.
In short, the fixing field triggers the formation of 180”
domains whose distribution length is codetermined by the
photorefractive space-charge distribution. The domain tips
create a bound charge grating which we somewhat loosely
call a domain grating. This grating can be reconverted into
a photorefractive grating. To prove this we tried to fkx
gratings by applying fixing fields 1 .Efl slightly above and
slightly below the critical field of the crystal, .&=;480
V/cm. Figure 4 shows the results. When 1 Erj =450 V/cm
the current is zero during the fixing stage and no diffrac-
3400 Appi. Phys. Lett., Vol. 63, No. 25,20 December 1993 Cudney
et
al. 3400
Downloaded 24 Jul 2001 to 129.132.214.119. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/aplo/aplcr.jsp

ibi
FIG. 3. Proposed fixing mechanism. (a) A light interference pattern
creates a spacecharge distribution. (b) ISO” domains form once iErl
>&&I The bonndarie~s of some of these domains compensate the space-
charge distribution. Other domains contribute to the switching hut not to
the fixing process. (c) light erases any remnant space charge. (d) A
positive field switches the polarirization of these domains back to its orig-
inal direction, A space-charge distribution is left behind.
tion occurs during the revealing stage. When lEfl is in-
creaed to 530 V/cm domain reversal occurs in both the
fixing and revealing stages, and an unambiguous diffracted
signal is detected during the revealing stage.
0 3 40 60 WI
iO!J
Time iseconds~
FIG. 4. Field thrt?shold for domain-grating formation. (a) Current and
diffraction efficiency vs time. 1 Kfl < &,. . No current is detected and no
diffraction occurs during step LX’. (b) Current and diffraction efficiency vs
time. 1 Efl > E;, I A diffracted signal is observed during step IV. A = 33
Pam; intensity per beam: 0.83 W/cm’.
In order to make sure that the revealed grating is a
photorefractive grating, we observed the decay as a func-
tion of the light intensity of the reading beam. Although no
quantitative measurements were made the trend was that
the weaker the reading beam, the longer the persistence of
the diffracted signal, as expected from a photorefractive
grating.
We have also performed experiments (not shown) to
compare the diffraction efficiencies of a normal, drift-
enhanced photorefractive grating and of a revealed
domain-fixed grating. In both cases we kept the experimen-
tal conditions equal, except for the sign of the field in step
II. In the case of the fixed and revealed grating we obtained
a dili?action efficiency of 52%. However, in the case of the
normal drift-enhanced grating the difFraction efficiency
during step II reached a maximum of only 7.7% almost
seven times less. Therefore, this fixing process somehow
enhances the final attainable space-charge field.
In conclusion, we have proven that in top-seeded
solut.ion-grown BaTiQs crystals it is possible to convert
photorefractive gratings into domain gratings and vice
versa. These domain gratings do not decay under illumi-
nation and can store information until they are reconverted
into a photorefractive gratings. During the domain-grating
formation the photorefractive grating is greatly amplified.
We thank V. Janovec, M. Klein, and J. Seglins for
some enlightening discussions. We also thank J. Hajfler for
expert crystal cutting and polishing. This work was
financed in part by the Swiss National Science Foundation,
Project. No. 70TP=03 1579.
hrote added in proof: Similar results have been recently
reported by Qiao et al. lt in Sro.7sBao.zsNbz06.
‘F. Jona and G. Shiwne, Fwroelectric Crymb (Pergamon, New York,
1962).
’ J. C. Burfoot and G. W. Taylor, P&r Dielectrics und Their Applications
(University of California Press, Berkeley, 1979).
‘J. P. Remeika, J. Am. Chem. Sot. 76, 940 ( 1954).
“R. L. Townsend and J. T. LaMacchia, J. A@. Phys. 41, 51% ( 1970).
‘P. Giinter and J.-P. Huignard, in Photorefmctiue Muterids and Their
Applications I, edited by P. Giinter and J.-P. Huignard (Springer, Ber-
lin, 1988).
6F. Micheron and G. Bismuth. Appl. Phys. Lett. 20, 79 ( 1972).
‘F. Micheron and G. Bismuth, Appl. Phys. Lett. 23, 71 ( 1973).
‘M. H. Garrett, J. Y. Chang, H. P. Jennsen, and C. Warde, Ferroelec-
tries 120, 167 (1991).
9R. Williams, J. Phys. Chem. Solids 26, 399 ( 1965).
to E. Fatuzzo and W. J. Mere, Ferroelectricity (North-Holland, Amster-
dam, 1967).
“Y. Qiao, S. Grlov, LX Psaltis, and R. R. Ncurgaonkar, Opt. Lott. 18,
1004 (1993).
3401 Appt. Phys. L&t., Vol. 63, No. 25, 20 December 1993 Cudney et a/. 3401
Downloaded 24 Jul 2001 to 129.132.214.119. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/aplo/aplcr.jsp