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Optical properties of some magnetic materials for coherent magnetic vibrations
Volume
7, number
4
April 1973
OPTICS COMMUNICATIONS
OPTICAL
PROPERTIES
OF SOME MAGNETIC
FOR COHERENT
MAGNETIC
MATERIALS
VIBRATIONS
Alfred0 OLIVE1 Laboratorio Circuiti e Memorie, Olivetti S.p.A., Received Revised manuscript
10015-Ivrea,
14 January 1973 received 22 February
Italy
1973
In this communication we report experimental results concerning optical properties of magnetic crystals such as rare-earth iron garnets and orthoferrites doped with semimetals such as bismuth and tin. The components of the dielectric tensor of the doped magnetic material exhibit favourable magnetic properties. Such kinds of materials are employed for generating coherent magnetic vibrations having amplitudes sufficiently large for detection.
1. Introduction Recently we have presented a method for generating and processing highly coherent magnetic vibrations by reflection of laser radiation on a 180” mag netic domain wall separating regions with opposite spin orientation when the magnetization in the domains is perpendicular to the plane of incidence of the laser beam [I]. In this communication we report experimental results about optical properties of some magnetic materials, based on rare-earth iron garnets and orthoferrites, which can produce coherent magnetic vibrations of detectable amplitude. We will proceed in three well defined stages. The first is to start with optical properties of rare-earth iron garnets and orthoferrites. The second is to examine the optical properties of solid state plasmas in some semimetals. The third stage is to study the optical behaviour of doped magnetic materials by relating the optical properties of pure magnetic materials to the solid state plasma properties of the doping agents. In this way a step-by-step theoretical interpretation of the experimental results reported in this communication is made possible.
2. Remarks on the microscopic interaction radiation with a magnetooptic material
of laser
The form of the dielectric tensor appropriate for a medium which has uniaxial anisotropy with respect to the z axis or for a medium which is optically isotropic except for magnetization, is E
/
-iea
0
\
(1) where the magnetization is taken parallel to the z axis. In our case the laser radiation beam travels along the y axis in a medium magnetized along the z axis [I]. In order to make feasible the detection of coherent magnetic vibrations a magnetic material with a ratio E/E, as low as possible is needed in transparent regions [ 11. (The most desirable situation should be ea SE. An acceptable situation could be e/e, x 5-7.) Now the structures of materials such as rare-earth iron garnets and orthoferrites, usually, show E/E, ratios (e 1000) which in transparent regions are too high to allow the desired effect to take place with an appreciable amplitude.
357
Volume
I, number
OPTICS COMMUNICATIONS
4
A firm understanding of the optical properties exhibited by a magnetic material during interaction with laser radiation is only reached when the components of the dielectric tensor (1) are related to the general atomic parameters characteristic of energy levels such as level separation, linewidth, transition probabilities, etc. For the assumed geometry, one may write the components E and E, of (1) in the form [2]: f
= I
fab
+612aqPa
(2)
azb --u2tF~b+2iwFab’
- tib - 6%)
(W - ‘I‘,,) 0, b Wab ~2
ab
- o2 t l’ib + 2iWF
ab
’
(3)
with R2 = 4nNe2/m and fa+b = mm,b i&b 12/he2. The summation in eqs. (2) and (3) is extended to all kinds of ions which give transitions of significant contribution. Expressions (2) and (3) have been derived by supposing that the incoming laser radiation of frequency w induces an electron attached to an ion in the magnetic material to make a transition from an eigenstate labeled la) to another eigenstate labeled lb). I’,, is the linewidth of the transition ab. The term fl, denotes the probability that an electron is in the eigenstate la). The eigenstates la) and lb) are assumed to be the correct states in the presence of the dc magnetization of the sample. hWab is the energy level separation. The P& are the electric dipole matrix elements for right (+) or left (() circularly polarized radiation and depend upon the wavefunctions corresponding to the eigenstatcs la) and lb). fabis the oscillator strength for the ab transition for unpolarized radiation; fibis the oscillator strength for right (+) or left (() circularly polarized radiation. N is the number of ions of a given kind per cm3 and m is the mass of ions of a given kind. Now let us consider the physical mechanisms which can yield the inequality lE,I s Iel f
(4)
With reference to eqs. (2) and (3) we point out that there are basically four distinct mechanisms by which one can try to satisfy inequality (4). In the first mechanism there is a spin polarisation so that “time conjugate states” are unequally populated. This un358
April 1973
equal weighting might yield such a result that inequality (4) is satisfied. The second mechanism does not change the ground state population (i.e., 0,) but through variations in Wab with an external magnetic field, terms that previously cancelled will no longer do so and again inequality (4) might be satisfied. In the third mechanism both 0, and Wab are approximately constant and inequality (4) might be verified from the field dependence of the electric dipole tnatrix elements pab. The fourth mechanism is the result of doping the magnetic material with semime tals such as bismuth and tin. If the doping level is high enough to establish bulk electrical conductivity in the doped magnetic material, collective excitation phenomena take place and the dielectric tensor of the solid state plasma may play the main role, so that expressions (2) and (3) are no longer valid. Among the four aforementioned mechanisms for altering the ratio E/E,, we will consider in detail the fourth one since large changes in the ratio e/e, should be feasible.
3. Interaction mas
of laser radiation
with solid state plas-
The absorption of photons or phonons by electrons or holes in solid state plasmas under the influence of a static magnetic field has been studied extensively. We recall [3] that when the thermal motion of particles is neglected, the dielectric tensor of solid state plasmas with the isotropic law of dispersion for semimetals like bismuth and tin has a form very similar to (1) provided that expressions (2) and (3) of the components of the dielectric tensor be substituted for solid state plasmas in semimetals by the appropriate expressions: e = 1 ~ C a*(,
t iv)/w[(wtiv)*
Ea-- CwIIn2/0[(o+iv)2-wi] e,, = 1 -
CR2/w(w+iv),
- ~$1;
(5)
;
(7)
R* = 4ne*n/m is the square of the Langmuir frequency, WH is the cyclotron frequency, n the number of
Volume 7, number 4
OPTICS COMMUNICATIONS
particles per unit volume and m the mass for particles of a definite kind; v the effective frequency of the particle collisions with a scatterer; the summation in eqs, (S)-(7) is carried out over all kinds of carriers. In semimetals like Bi and Sn, the effective masses of the holes, mh, and the electrons, m,, are very different: mh 9 m,. In a neutral electron-hole plasma one has t-2,= “h. In order to make some estimations, let us neglect in a first rough approximation the collision frequency u with respect to the incident laser frequency, tie, i.e., we suppose that the medium is non-absorbing at mo. In this case to have 1~~19 1~1the following simple inequality must be satisfied:
CS22/cd0(wo-cdWH)P 1.
(8)
According to Pines [4], the number of volume electrons per atom that take part in plasma oscillations is 5 for Bi, 4 for Sn and 11 for Cu. Now according to ref. [5] in a typical metal such as Cu the density of the electron gas is 1O23 cm-3 so that we can assume that the density of the electron gas for Bi is (S/l 1) X 1023 = 0.45 X 1023 and (4/l 1) X lO23 = 0.36 X 1023 for Sn. The Langmuir square frequency of electrons is 14.3 X 1031 sec.-I for Bi and 11.4 X 1031 for Sn. For external magnetic flux densities, B, varying from 1O* to 1O5G, the electron cyclotron frequency varies from 1.76 X lo9 set-l to 1.7 X 101* set-l. Then inequality (8) is easily verified for a large range of incoming frequencies, oo, contained between the far infrared and the far ultraviolet. Therefore even in the practical situation of an absorbing material, the value of the external magnetic field could be taken at sufficiently low intensities to be acceptable in several practical applications.
4. Experimental results obtained for rare-earth iron garnets and orthoferrites doped with semimetals We have to point out that the choice of a doping agent is greatly conditioned by the fact that doping with semimetals should produce an immediate decrease in resistivity of the magnetic material in order that plasma collective phenomena can take place. At the same time the doped magnetic material should possess favourable magnetic properties. For example
April 1973
consider Bi ions substituted in the garnet Y3Fe5012. The Bi impurity ion, which is on a rare-earth site, appears to draw off electronic charge from the ligand oxygen orbitals in such a way as to reduce the rareearth ion exchange, but leave the iron-iron exchange unaltered. The Curie temperature, the net magnetic moment and the magnetic anisotropy constants of the pure YIG and the YlG doped with Bi (for example Y2BiFe3012) are very similar. The presence of Bi produces a change in the spin reorientation temperature of the pure YIG, due to the entirely different electronic structure of Bi ions from that of Y ions. The latter has a rare gas configuration (Kr) while the Bi ion has empty p-orbitals which may be responsible for the difference. However we were unable to produce significant changes in the resistivity of the YIG doped with Bi in order to allow plasma collective phenomena to take place. This is mainly due to the fact that Bi has no effect on the iron valence even though the spin reorientation temperature is drastically reduced. Now in order to increase the electrical conductivity, the doping agent should produce Fe2+ or Fe4+ ions. Fortunately Sn shows both a free-electron-gas like behaviour and a mechanism involving Fe*+ ion production when Sn is introduced as a doping agent in rare-earth iron garnets and orthoferrites. This is accompanied by a large dipole moment change and enlargement of the absorption edges of the absorption spectra, since absorption is proportional to the Sn concentration. The absorption in the doped material near the previous absorption edges of the pure magnetic material can be thought of as arising from a relaxation mechanism in which an electron is promoted by the photon from the minority ion to an Fe3+ ion in the vicinity. For example when Sn is added to ErFe03, a broad optical absorption occurs in the crystal. Fig. 1 shows the effects of Sn doping in ErFeO, near the absorption edge at 1.17 /J. This broad absorption is due to the effect of the Fe*+ ions. In fig. 2, the absorption coefficient 01is plotted as a function of the concentration for fixed wavelength 1.3 ~1. Below a concentration of about 0.15% Sn by weight a minimum occurs for Sn doping. In the higher concentration range (> 0.15% Sn by weight), the absorption is proportional to the Sn concentration since each impurity ion changes the valence of one Fe3+ ion. 359
Volume
7, number
April 1973
OPTICS COMMUNICATIONS
4
24 (cm-5 I4 50
t
Log,,R
ohm-cm
40
30
cl,45 20
0.2 5 ‘I. 10
~,
01
*
.
I.'
1,3
’
1,5
I,,
1p
’
’
2,l
2,3
‘*
Ay ml 2-
Fig. 1. Effect of doping with Sn4+ on optical absorption of ErFeOs. Concentrations are given in % Sn by weight. The rare-earth line absorption at 1.5 p is not shown for the doped material. (Experimental results.)
60
-
% sn 0
.“““““‘)
0,s
by weight
1
Fig. 2. Optical absorption at 1.3 p versus Sn concentrations (% Sn by weight). (Experimental results.) The resistivity of ErFe03 at 300°K decreases drastically with Sn doping as fig. 3 shows. Presumably the bulk conductivity is established when the radius of mobility of the electron on the Fe of minority valence equals half the distance between such ions. It also follows from the sign of the thermoelectric effect that the conductivity is of the thermoelectric doping level of Sn explored here (1.7% of Sn by weight). It is probable that for greater Sn concentrations, metallic properties might be observed. Now from a practical standpoint the most desirable
360
s sn
by weight 5
0
034
078
v
'9
Fig. 3. Electrical resistivity of ErFeOa + Sn4+versus Sn concentration (70 Sn by weight); n-type conduction. (Experimental results.)
situation for a given laser radiation frequency is that for which the medium exhibits reasonably low absorption at that frequency in order to have easily detectable vibrations. Then consider for ErFeO, the low absorption window in the infrared region between 1.3 and 8 /.J. In this range of frequency the bulk of the experimental data on the infrared optical constants of pure Sn can be interpreted either on the basis of free-electron theories, as we have briefly recalled in section 3, or by the use of various approximations of the anomalous skin-effect theory [6]. In fig. 4 we have reported the absorption spectrum of ErFeO, + Sn4+ (1.6% of Sn by weight). The dotted lines represent the absorption spectrum for pure Sn (optic axis) and pure ErFeO,. Fig. 5 shows the behaviour of the optical constant pz2- k2 as a function of the wavelength in the range 1-8 /J for pure Sn (optic axis), pure ErFeO, and ErFe03 + Sn4+ (1.6% of Sn by weight). The data presented in figs. 4 and 5 enable us to critically investigate the infrared optical constants of ErFeO, + Sn4+ by using an Argand diagram of the absorption (Y(= 2nkX-l) against H2 - k2. Our data for ErFeOj + Sn4+ (1.6% of Sn by weight) and for pure Sn (optic axis) are presented in this form in fig. 6. According to ref. [7] the criterion of freeelectron behaviour is a linear arrangement of the
Volume
7, number
4
OPTlCS
April
COMMUNICATIONS
6 t
1973
nz- k*
ErFe0pn4+
I
$2
I:, 1,6
I,6
2
3
4
5
6
7
6
9
10
11
12
for pure Sn (optic axis). Fig. 5. rr2 - k2 versus wavelength pure ErFeOs and ErFeOa + Sn4+(1.6% of Sn by weight). (Experimental results.)
13
Fig. 4. Solid line: absorption spectrum of ErFeOs + Sn4+ (1.6% Sn by weight). Dashed lines: absorption spectrum of pure Sn (optic axis) and pure ErFeOa. (Experimental results.)
Of course the situation is much more complicated for ErFeO, t Sn4+. Fig. 6 shows that although there is a tendency toward linear arrangements at the longer wavelengths (3-8 cl), it seems questionable to discuss these results in terms of one of the three basic extreme interpretations: the free-electron theories; the anomalous skin effect with diffuse reflection 01‘ electrons; the anomalous skin effect with specular I-Uflection of electrons [6,7]. A careful evaluation of the transport theory to be used in the optical constants of ErFe03 + Sn4+. 1s essential in order to interpret also the influence of an external magnetic field. Since both the temperature and the applied magnttic
points parallel to a line passing through the origin of the Argand diagram. Let us examine in the first place the diagram for pure Sn. Even if there is a tendency toward linear arrangements at the shorter wavelengths it appears that the data cannot be discussed in terms of a simple free-electron theory. There is some evidence that the experimental curve for Sn represents the summation of the interband and intraband absorption, also at longer wavelengths. However it is not easy to separate the intraband and interband components. A
~nk);‘(cni’l
A(ym)=
Sn
t&k* I -1000
Fig. 6. Argand
diagram
for ErFeOa
-500
0
,I
1'2
+ Sn4+ (1.6% Sn by weight)
I, 3
4
5
I
ac
6
7
and pure Sn. (Experimental
results.)
Volume
7, number
0,06
4
OPTICS COMMUNICATIONS
.’ ’
z-
A-x-
p.0,004
t ,I
-
,‘<’ ,P’ 0,
0,02
-
E;
=m
q
= x
:I
I
m 10
2
103
,04 Gauss
Fig. 7. Influence of an external magnetic field on the offdiagonal elements of the dielectric tensor at a fixed wavelength of 10 ~1 for ErFe03 + Sn4+ (1.6% Sn by weight). (Experimental results.)
field can change the degree of magnetization, they both have strong effects on transport processes. The influence of an applied magnetic field on the off-diagonal elements of the dielectric tensor at a fixed wavelength of 10 1-1is shown in fig. 7 for ErFeO, + Sn4+ (1.6% Sn by weight). No change in the diagonal elements in the whole range of applied external magnetic field values has been detected at room temperature. Apparently the dependence of the offdiagonal terms E, on the external magnetic field might be partly caused by a collective electron effect due to the linear dependence of Ed, for solid state plasmas, on the cyclotron frequency “H, as shown by
362
April 1973
eq. (6). However due to the multitude of transitions allowed or partially allowed, as discussed in section 2, no further assignments would be realistic at this time. From a practical standpoint for laser radiation of 10 ~1and for a magnetic field of 1000 G, ErFe03 + Sn4+ (1.6% Sn by weight) exhibits a ratio E/E, of about 40. It is possible that analysis extended to the far infrared will yield substantially lower ratios. Further lowering of the ratio E/E, should be obtained by doping ErFeO, with Sn and Bi at the same time. In conclusion the experimental results reported in this communication provide an important check of the fabrication strategy, also with a view of further carrying out research on larger classes of suitable materials.
References [ 1] A. Olivei, Opt. Commun. 4 (1972) 368. [2] M.J. Freiser, IEEE Trans. Magnetics MAG-5 (1968) 152. [ 31 V.L. Ginzburg, Propagation of electromagnetic waves in plasma (Gordon and Breach, New York, 1961) pp. 94, 95, 153. [4] D. Pines, Rev. Mod. Phys. 28 (1956) 184. [5] D. Pines and D. Bohm, Phys. Rev. 85 (1952) 338. [6] I.M. Shkliarevskii and V.G. Padalka, Opt. Spectry. 6 (1959) 505. [7] J.R. Beatty and G.K.T. Conn, Phil. Mag. 46 (1955) 989.
7, number
4
April 1973
OPTICS COMMUNICATIONS
OPTICAL
PROPERTIES
OF SOME MAGNETIC
FOR COHERENT
MAGNETIC
MATERIALS
VIBRATIONS
Alfred0 OLIVE1 Laboratorio Circuiti e Memorie, Olivetti S.p.A., Received Revised manuscript
10015-Ivrea,
14 January 1973 received 22 February
Italy
1973
In this communication we report experimental results concerning optical properties of magnetic crystals such as rare-earth iron garnets and orthoferrites doped with semimetals such as bismuth and tin. The components of the dielectric tensor of the doped magnetic material exhibit favourable magnetic properties. Such kinds of materials are employed for generating coherent magnetic vibrations having amplitudes sufficiently large for detection.
1. Introduction Recently we have presented a method for generating and processing highly coherent magnetic vibrations by reflection of laser radiation on a 180” mag netic domain wall separating regions with opposite spin orientation when the magnetization in the domains is perpendicular to the plane of incidence of the laser beam [I]. In this communication we report experimental results about optical properties of some magnetic materials, based on rare-earth iron garnets and orthoferrites, which can produce coherent magnetic vibrations of detectable amplitude. We will proceed in three well defined stages. The first is to start with optical properties of rare-earth iron garnets and orthoferrites. The second is to examine the optical properties of solid state plasmas in some semimetals. The third stage is to study the optical behaviour of doped magnetic materials by relating the optical properties of pure magnetic materials to the solid state plasma properties of the doping agents. In this way a step-by-step theoretical interpretation of the experimental results reported in this communication is made possible.
2. Remarks on the microscopic interaction radiation with a magnetooptic material
of laser
The form of the dielectric tensor appropriate for a medium which has uniaxial anisotropy with respect to the z axis or for a medium which is optically isotropic except for magnetization, is E
/
-iea
0
\
(1) where the magnetization is taken parallel to the z axis. In our case the laser radiation beam travels along the y axis in a medium magnetized along the z axis [I]. In order to make feasible the detection of coherent magnetic vibrations a magnetic material with a ratio E/E, as low as possible is needed in transparent regions [ 11. (The most desirable situation should be ea SE. An acceptable situation could be e/e, x 5-7.) Now the structures of materials such as rare-earth iron garnets and orthoferrites, usually, show E/E, ratios (e 1000) which in transparent regions are too high to allow the desired effect to take place with an appreciable amplitude.
357
Volume
I, number
OPTICS COMMUNICATIONS
4
A firm understanding of the optical properties exhibited by a magnetic material during interaction with laser radiation is only reached when the components of the dielectric tensor (1) are related to the general atomic parameters characteristic of energy levels such as level separation, linewidth, transition probabilities, etc. For the assumed geometry, one may write the components E and E, of (1) in the form [2]: f
= I
fab
+612aqPa
(2)
azb --u2tF~b+2iwFab’
- tib - 6%)
(W - ‘I‘,,) 0, b Wab ~2
ab
- o2 t l’ib + 2iWF
ab
’
(3)
with R2 = 4nNe2/m and fa+b = mm,b i&b 12/he2. The summation in eqs. (2) and (3) is extended to all kinds of ions which give transitions of significant contribution. Expressions (2) and (3) have been derived by supposing that the incoming laser radiation of frequency w induces an electron attached to an ion in the magnetic material to make a transition from an eigenstate labeled la) to another eigenstate labeled lb). I’,, is the linewidth of the transition ab. The term fl, denotes the probability that an electron is in the eigenstate la). The eigenstates la) and lb) are assumed to be the correct states in the presence of the dc magnetization of the sample. hWab is the energy level separation. The P& are the electric dipole matrix elements for right (+) or left (() circularly polarized radiation and depend upon the wavefunctions corresponding to the eigenstatcs la) and lb). fabis the oscillator strength for the ab transition for unpolarized radiation; fibis the oscillator strength for right (+) or left (() circularly polarized radiation. N is the number of ions of a given kind per cm3 and m is the mass of ions of a given kind. Now let us consider the physical mechanisms which can yield the inequality lE,I s Iel f
(4)
With reference to eqs. (2) and (3) we point out that there are basically four distinct mechanisms by which one can try to satisfy inequality (4). In the first mechanism there is a spin polarisation so that “time conjugate states” are unequally populated. This un358
April 1973
equal weighting might yield such a result that inequality (4) is satisfied. The second mechanism does not change the ground state population (i.e., 0,) but through variations in Wab with an external magnetic field, terms that previously cancelled will no longer do so and again inequality (4) might be satisfied. In the third mechanism both 0, and Wab are approximately constant and inequality (4) might be verified from the field dependence of the electric dipole tnatrix elements pab. The fourth mechanism is the result of doping the magnetic material with semime tals such as bismuth and tin. If the doping level is high enough to establish bulk electrical conductivity in the doped magnetic material, collective excitation phenomena take place and the dielectric tensor of the solid state plasma may play the main role, so that expressions (2) and (3) are no longer valid. Among the four aforementioned mechanisms for altering the ratio E/E,, we will consider in detail the fourth one since large changes in the ratio e/e, should be feasible.
3. Interaction mas
of laser radiation
with solid state plas-
The absorption of photons or phonons by electrons or holes in solid state plasmas under the influence of a static magnetic field has been studied extensively. We recall [3] that when the thermal motion of particles is neglected, the dielectric tensor of solid state plasmas with the isotropic law of dispersion for semimetals like bismuth and tin has a form very similar to (1) provided that expressions (2) and (3) of the components of the dielectric tensor be substituted for solid state plasmas in semimetals by the appropriate expressions: e = 1 ~ C a*(,
t iv)/w[(wtiv)*
Ea-- CwIIn2/0[(o+iv)2-wi] e,, = 1 -
CR2/w(w+iv),
- ~$1;
(5)
;
(7)
R* = 4ne*n/m is the square of the Langmuir frequency, WH is the cyclotron frequency, n the number of
Volume 7, number 4
OPTICS COMMUNICATIONS
particles per unit volume and m the mass for particles of a definite kind; v the effective frequency of the particle collisions with a scatterer; the summation in eqs, (S)-(7) is carried out over all kinds of carriers. In semimetals like Bi and Sn, the effective masses of the holes, mh, and the electrons, m,, are very different: mh 9 m,. In a neutral electron-hole plasma one has t-2,= “h. In order to make some estimations, let us neglect in a first rough approximation the collision frequency u with respect to the incident laser frequency, tie, i.e., we suppose that the medium is non-absorbing at mo. In this case to have 1~~19 1~1the following simple inequality must be satisfied:
CS22/cd0(wo-cdWH)P 1.
(8)
According to Pines [4], the number of volume electrons per atom that take part in plasma oscillations is 5 for Bi, 4 for Sn and 11 for Cu. Now according to ref. [5] in a typical metal such as Cu the density of the electron gas is 1O23 cm-3 so that we can assume that the density of the electron gas for Bi is (S/l 1) X 1023 = 0.45 X 1023 and (4/l 1) X lO23 = 0.36 X 1023 for Sn. The Langmuir square frequency of electrons is 14.3 X 1031 sec.-I for Bi and 11.4 X 1031 for Sn. For external magnetic flux densities, B, varying from 1O* to 1O5G, the electron cyclotron frequency varies from 1.76 X lo9 set-l to 1.7 X 101* set-l. Then inequality (8) is easily verified for a large range of incoming frequencies, oo, contained between the far infrared and the far ultraviolet. Therefore even in the practical situation of an absorbing material, the value of the external magnetic field could be taken at sufficiently low intensities to be acceptable in several practical applications.
4. Experimental results obtained for rare-earth iron garnets and orthoferrites doped with semimetals We have to point out that the choice of a doping agent is greatly conditioned by the fact that doping with semimetals should produce an immediate decrease in resistivity of the magnetic material in order that plasma collective phenomena can take place. At the same time the doped magnetic material should possess favourable magnetic properties. For example
April 1973
consider Bi ions substituted in the garnet Y3Fe5012. The Bi impurity ion, which is on a rare-earth site, appears to draw off electronic charge from the ligand oxygen orbitals in such a way as to reduce the rareearth ion exchange, but leave the iron-iron exchange unaltered. The Curie temperature, the net magnetic moment and the magnetic anisotropy constants of the pure YIG and the YlG doped with Bi (for example Y2BiFe3012) are very similar. The presence of Bi produces a change in the spin reorientation temperature of the pure YIG, due to the entirely different electronic structure of Bi ions from that of Y ions. The latter has a rare gas configuration (Kr) while the Bi ion has empty p-orbitals which may be responsible for the difference. However we were unable to produce significant changes in the resistivity of the YIG doped with Bi in order to allow plasma collective phenomena to take place. This is mainly due to the fact that Bi has no effect on the iron valence even though the spin reorientation temperature is drastically reduced. Now in order to increase the electrical conductivity, the doping agent should produce Fe2+ or Fe4+ ions. Fortunately Sn shows both a free-electron-gas like behaviour and a mechanism involving Fe*+ ion production when Sn is introduced as a doping agent in rare-earth iron garnets and orthoferrites. This is accompanied by a large dipole moment change and enlargement of the absorption edges of the absorption spectra, since absorption is proportional to the Sn concentration. The absorption in the doped material near the previous absorption edges of the pure magnetic material can be thought of as arising from a relaxation mechanism in which an electron is promoted by the photon from the minority ion to an Fe3+ ion in the vicinity. For example when Sn is added to ErFe03, a broad optical absorption occurs in the crystal. Fig. 1 shows the effects of Sn doping in ErFeO, near the absorption edge at 1.17 /J. This broad absorption is due to the effect of the Fe*+ ions. In fig. 2, the absorption coefficient 01is plotted as a function of the concentration for fixed wavelength 1.3 ~1. Below a concentration of about 0.15% Sn by weight a minimum occurs for Sn doping. In the higher concentration range (> 0.15% Sn by weight), the absorption is proportional to the Sn concentration since each impurity ion changes the valence of one Fe3+ ion. 359
Volume
7, number
April 1973
OPTICS COMMUNICATIONS
4
24 (cm-5 I4 50
t
Log,,R
ohm-cm
40
30
cl,45 20
0.2 5 ‘I. 10
~,
01
*
.
I.'
1,3
’
1,5
I,,
1p
’
’
2,l
2,3
‘*
Ay ml 2-
Fig. 1. Effect of doping with Sn4+ on optical absorption of ErFeOs. Concentrations are given in % Sn by weight. The rare-earth line absorption at 1.5 p is not shown for the doped material. (Experimental results.)
60
-
% sn 0
.“““““‘)
0,s
by weight
1
Fig. 2. Optical absorption at 1.3 p versus Sn concentrations (% Sn by weight). (Experimental results.) The resistivity of ErFe03 at 300°K decreases drastically with Sn doping as fig. 3 shows. Presumably the bulk conductivity is established when the radius of mobility of the electron on the Fe of minority valence equals half the distance between such ions. It also follows from the sign of the thermoelectric effect that the conductivity is of the thermoelectric doping level of Sn explored here (1.7% of Sn by weight). It is probable that for greater Sn concentrations, metallic properties might be observed. Now from a practical standpoint the most desirable
360
s sn
by weight 5
0
034
078
v
'9
Fig. 3. Electrical resistivity of ErFeOa + Sn4+versus Sn concentration (70 Sn by weight); n-type conduction. (Experimental results.)
situation for a given laser radiation frequency is that for which the medium exhibits reasonably low absorption at that frequency in order to have easily detectable vibrations. Then consider for ErFeO, the low absorption window in the infrared region between 1.3 and 8 /.J. In this range of frequency the bulk of the experimental data on the infrared optical constants of pure Sn can be interpreted either on the basis of free-electron theories, as we have briefly recalled in section 3, or by the use of various approximations of the anomalous skin-effect theory [6]. In fig. 4 we have reported the absorption spectrum of ErFeO, + Sn4+ (1.6% of Sn by weight). The dotted lines represent the absorption spectrum for pure Sn (optic axis) and pure ErFeO,. Fig. 5 shows the behaviour of the optical constant pz2- k2 as a function of the wavelength in the range 1-8 /J for pure Sn (optic axis), pure ErFeO, and ErFe03 + Sn4+ (1.6% of Sn by weight). The data presented in figs. 4 and 5 enable us to critically investigate the infrared optical constants of ErFeO, + Sn4+ by using an Argand diagram of the absorption (Y(= 2nkX-l) against H2 - k2. Our data for ErFeOj + Sn4+ (1.6% of Sn by weight) and for pure Sn (optic axis) are presented in this form in fig. 6. According to ref. [7] the criterion of freeelectron behaviour is a linear arrangement of the
Volume
7, number
4
OPTlCS
April
COMMUNICATIONS
6 t
1973
nz- k*
ErFe0pn4+
I
$2
I:, 1,6
I,6
2
3
4
5
6
7
6
9
10
11
12
for pure Sn (optic axis). Fig. 5. rr2 - k2 versus wavelength pure ErFeOs and ErFeOa + Sn4+(1.6% of Sn by weight). (Experimental results.)
13
Fig. 4. Solid line: absorption spectrum of ErFeOs + Sn4+ (1.6% Sn by weight). Dashed lines: absorption spectrum of pure Sn (optic axis) and pure ErFeOa. (Experimental results.)
Of course the situation is much more complicated for ErFeO, t Sn4+. Fig. 6 shows that although there is a tendency toward linear arrangements at the longer wavelengths (3-8 cl), it seems questionable to discuss these results in terms of one of the three basic extreme interpretations: the free-electron theories; the anomalous skin effect with diffuse reflection 01‘ electrons; the anomalous skin effect with specular I-Uflection of electrons [6,7]. A careful evaluation of the transport theory to be used in the optical constants of ErFe03 + Sn4+. 1s essential in order to interpret also the influence of an external magnetic field. Since both the temperature and the applied magnttic
points parallel to a line passing through the origin of the Argand diagram. Let us examine in the first place the diagram for pure Sn. Even if there is a tendency toward linear arrangements at the shorter wavelengths it appears that the data cannot be discussed in terms of a simple free-electron theory. There is some evidence that the experimental curve for Sn represents the summation of the interband and intraband absorption, also at longer wavelengths. However it is not easy to separate the intraband and interband components. A
~nk);‘(cni’l
A(ym)=
Sn
t&k* I -1000
Fig. 6. Argand
diagram
for ErFeOa
-500
0
,I
1'2
+ Sn4+ (1.6% Sn by weight)
I, 3
4
5
I
ac
6
7
and pure Sn. (Experimental
results.)
Volume
7, number
0,06
4
OPTICS COMMUNICATIONS
.’ ’
z-
A-x-
p.0,004
t ,I
-
,‘<’ ,P’ 0,
0,02
-
E;
=m
q
= x
:I
I
m 10
2
103
,04 Gauss
Fig. 7. Influence of an external magnetic field on the offdiagonal elements of the dielectric tensor at a fixed wavelength of 10 ~1 for ErFe03 + Sn4+ (1.6% Sn by weight). (Experimental results.)
field can change the degree of magnetization, they both have strong effects on transport processes. The influence of an applied magnetic field on the off-diagonal elements of the dielectric tensor at a fixed wavelength of 10 1-1is shown in fig. 7 for ErFeO, + Sn4+ (1.6% Sn by weight). No change in the diagonal elements in the whole range of applied external magnetic field values has been detected at room temperature. Apparently the dependence of the offdiagonal terms E, on the external magnetic field might be partly caused by a collective electron effect due to the linear dependence of Ed, for solid state plasmas, on the cyclotron frequency “H, as shown by
362
April 1973
eq. (6). However due to the multitude of transitions allowed or partially allowed, as discussed in section 2, no further assignments would be realistic at this time. From a practical standpoint for laser radiation of 10 ~1and for a magnetic field of 1000 G, ErFe03 + Sn4+ (1.6% Sn by weight) exhibits a ratio E/E, of about 40. It is possible that analysis extended to the far infrared will yield substantially lower ratios. Further lowering of the ratio E/E, should be obtained by doping ErFeO, with Sn and Bi at the same time. In conclusion the experimental results reported in this communication provide an important check of the fabrication strategy, also with a view of further carrying out research on larger classes of suitable materials.
References [ 1] A. Olivei, Opt. Commun. 4 (1972) 368. [2] M.J. Freiser, IEEE Trans. Magnetics MAG-5 (1968) 152. [ 31 V.L. Ginzburg, Propagation of electromagnetic waves in plasma (Gordon and Breach, New York, 1961) pp. 94, 95, 153. [4] D. Pines, Rev. Mod. Phys. 28 (1956) 184. [5] D. Pines and D. Bohm, Phys. Rev. 85 (1952) 338. [6] I.M. Shkliarevskii and V.G. Padalka, Opt. Spectry. 6 (1959) 505. [7] J.R. Beatty and G.K.T. Conn, Phil. Mag. 46 (1955) 989.