Features of optical anisotropy of europium and terbium iron garnets

Optical Materials xxx (2013) xxx–xxx

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Features of optical anisotropy of europium and terbium iron garnets N.I. Tsidaeva, V.V. Abaeva ⇑, E.V. Enaldieva, T.T. Magkoev, A.G. Ramonova, T.G. Butkhuzi, V.I. Kesaev, A.M. Turiev North-Ossetian State University Natural Sciences Research and Education Centre, 44-46 Vatutina Str., Vladikavkaz 362025, RussiaNorth-Ossetian State University Natural Sciences Research and Education Centre44-46 Vatutina Str.Vladikavkaz362025Russia

a r t i c l e

i n f o

Article history: Available online xxxx Keywords: Magnetic linear birefringence Magnetooptical transducers

a b s t r a c t The results of investigation of magnetic linear birefringence (MLB) and magnetic linear dichroism of Tb3Fe5O12 (TbIG) iron garnet (IG) on 7 F6 –7 F0 and 7 F6 –7 F1 optical transitions and Eu3Fe5O12 (EuIG) iron garnet on 7 F0 –7 F6 at the variation of the directions of the magnetization vector I relative to the electric vector E linearly polarized light that propagates through single crystal iron garnets are presented. The measurements were made on Tb3Fe5O12 and Eu3Fe5O12 single-crystal samples in the form of plates 100 lm thick cut in the (1 1 0) and (1 0 0) plane a temperature of T = 82 K and in a magnetic field H = 22 kOe. The absorption spectra of the linearly polarized light were studied. It is shown that MLB and dichroism in the region of the 7 F6 –7 F0 and 7 F0 –7 F6 absorption bands reach values 103. The nonreciprocity of MLB spectra and dichroism with the change of the relative orientation of the magnetization vector I and the light wave vector is first experimentally discovered. This effect may be used as a base for the design of the different transducers such as a magnetooptical optical channels commutator. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction Rare earth (RE) iron garnets with narrow ferromagnetic resonance linewidths, very low hysteresis losses, and excellent dielectric properties have been widely applied in microwave devices in a wide range of frequencies (1–100 GHz), magnetooptical transducers and typically employed as magnetic recording media [1–7]. The general chemical structural formula for rare-earth iron garnets (REIGs) can be written as RE3Fe2Fe3O12, with eight of these formula units per unit cell. With the overall symmetry being cubic, the  IaðO10 Þ in which three special positions space group of REIG is Ia3d; h are occupied by magnetic ions. That is, two Fe3+ ions occupy the octahedral crystal site, expressed as 16a, three Fe3+ ions occupy tetrahedral crystal site (24d), and the RE ions occupy the dodecahedral crystal site (24c) with eightfold oxygen coordination. Therefore, the magnetization (M) of REIG originates from the contributions of these three kinds of magnetic ions magnetization of which can be described as Mc, Ma and Md, respectively. Thus, in this three-sublattice system, M can be written as the sum of Mc, Ma and Md, where c, a and d represent the dodecahedral, octahedral and tetrahedral sites, respectively. The garnet in fact does not allow distortion to lower symmetry owing to its non-efficiently packed structure, which makes the iron garnet structure unstable with increasing rare earth ionic radius.

⇑ Corresponding author. Tel.: +7 9188242578. E-mail address: [email protected] (V.V. Abaeva).

The study of magnetic linear birefringence of light, which also includes the effect of magnetic linear dichroism, in magnetically ordered crystals has been relatively recently started relatively recently both in the crystal transparency region and in the region of the absorption bands of individual ions [8–14]. The authors [8,9] have investigated magnetic circular dichroism (MCD) of Tb3+ and Eu3+ ions in the gadolinium gallium garnet. The interest of the part of the researchers was not accidental. It was primarily due to an unexpected result – the value of MLB, which quadratically depends on the magnetization, turned out to be extremely large in magnetically ordered crystals and comparable with the magnetic circular birefringence, which is linear in the magnetization and is responsible for the Faraday effect. This fact raised the possibility of investigating the magnetic structures of magnetically ordered crystals and of practical application of MLB in devices such as light modulators, magneto-optical waveguides, and others. In addition, MLB is extensively used to study the electronic structure of magnetically ordered crystals, as the anisotropy of their optical and magneto-optical properties is determined by the action of the anisotropic exchange and crystal fields on the magnetoactive ions. Different phenomenological models which explain observed MLB effects in Dy3Fe5O12 [12], Er3Fe5O12 [13], heavy-rare-earth (RE) garnets R3M5O12 (R = Tb, Dy, Ho, Er, Tm, Yb; M = Al, Ga) [14] were offered by the authors of works [7–14]. But the model offered in [12], to which the authors come back in [13], is badly applicable to the TbIG being the subject of our investigation. Furthermore, MLD measurements are carried out at one wavelength 1.15 lm – in [12–14] and 0.63 lm – in

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N.I. Tsidaeva et al. / Optical Materials xxx (2013) xxx–xxx

[14] by the authors [12–14]. At the same time MLB reaches particularly large values in the region of the absorption bands of REIG, has a strongly anisotropic character, and reveals a strong dependence on the wavelength of the incident light. Some unusual features of crystal-optics properties of magnetically ordered crystals were observed [10,11], connected with the absence of a small parameter in the expansion of the dielectric tensor e in powers of the magnetization. We studied the crystal-optics properties of terbium and europium IG in the regions of the absorption bands of the rare-earth ion. Close attention was paid to the observation of those crystaloptics anisotropy features, which are connected with the change of the relative orientation of the magnetization vector I and the light wave vector. The investigation of the crystal-optics properties of europium IG in the region of the 7 F0 –7 F6 absorption band of the rare earth ion Eu3+ has shown [10] that when the light propagates k ?~ perpendicular to the magnetization (Voight geometry, ~ I) the crystal is optically uniaxial.

Fig. 1. Absorption spectra of TbIG and EuIG: (a) TbIG: solid curve – ~ kjj½1 1 0,  1 0, dashed – ~  1 1, ~ E ?~ Ijj½1 kjj½1 1 0, ~ E ?~ Ijj½0 0 1; (b) EuIG: solid curve – ~ kjj½1 1 0, ~ Ijj½1 ~    ~ ~ ~ Ejj½1 1 0, dashed – kjj½1 1 0, Ijj½1 1 0, Ejj½1 1 1.

2. Experiment Using the method of flux growth under 10 bar of oxygen pressure, single crystals of Tb3Fe5O12 and Eu3Fe5O12 were synthesized by B.V. Mill at Moscow State University. X-ray diffraction measure-

Fig. 2. Frequency dependences of the contribution made to the refractive index by the optical transition 7 F6 –7 F0 and 7 F6 –7 F1 of the Tb3+ ion of the TbIG and optical transition 7 F0 –7 F6 of the Eu3+ ion of the EuIG: (a) TbIG: solid curve – ~ kjj½1 1 0,  1 0; dashed – ~  1 1, ~ E ?~ Ijj½1 kjj½1 1 0, ~ E ?~ Ijj½0 0 1; (b) EuIG: solid curve – ~ kjj½1 1 0, ~ Ijj½1 ~    ~ ~ ~ Ejj½1 1 0, dashed – kjj½1 1 0, Ijj½1 1 0, Ejj½1 1 1.

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N.I. Tsidaeva et al. / Optical Materials xxx (2013) xxx–xxx

 structure. Polished ments were in agreement with the garnet Ia3d; platelets – 100–250 lm thick-oriented perpendicular to the [1 1 0] and [1 0 0] axes were obtained from the same ‘‘as grown’’ crystal. Magneto-optical measurements were performed at a temperature of 82 K and 295 K under a magnetic field of up to 20 kOe on the spectrometer facility, characterized in [2,3,6]. MLB spectra were obtained in energy regions 5100–5900 cm1 and 4900– 5100 cm1 with a high optical resolution 0.12 cm1 with the help of a modulation technique. The experimental accuracy is estimated at ±2%. It is noted that the samples are cooled at the lowest temperature in the absence of a magnetic field prior to MLB measurements. The angle of rotation of the samples was measured with 0.1° accuracy. 3. Results The dependence of the intensity I(x) of the light transmitted through the sample, as well as of the intensity I0(x) of the light without the sample, was registered with an automatic recorder. The absorption coefficient k0 was calculated on the equation

I ¼ I0 ð1  R2 Þe2ad ; 0

where a ¼ 2pk =k, R is the reflection coefficient calculated under the assumption that the refractive index of the garnet is n = 2.2. 0 Fig. 1 shows the measured absorption coefficient k ð hxÞ; in the Voight geometry, of an Tb3Fe5012 and Eu3Fe5012 plate cut in the  1 0, Fig. 2 shows the n0 ð kjj½1 1 0, ~ (1 1 0) plane, at ~ hxÞ specE ?~ Ijj½1 tra calculated on these results with the help of the Kramers–Kronig relations (n0 is the contribution made to the refractive index by the light absorption by the RE ions). Let’s remind that Kramers–Kronig relations connect optical constants n, k0 . Experimentally sample absorption is studied in a limited interval of light frequencies, instead of from 0 to 1. Taking into consideration that the studied frequencies interval of an absorption band is much less than a characteristic interval in which matrix absorption changes in e times, it is possible to approximate the matrix absorption kp (x) by the linear function of frequency. And to come from this function, having measured absorption edges of the studied interval where rare-earth ions absorption can be neglected. In this case the contribution of the rare-earth ion absorption band can be presented by the formula

nðx0 Þ ¼ cðx0 Þ þ

2

Z

p

xe

xb

½kðxÞ  kp ðxÞxdx ; x2  x20

where xb and xe – frequencies of the beginning and the end of a studied interval xb < x0 < xe, and

cðx0 Þ ¼ 1 þ

2

Z

xb

½kðxÞ  kp ðxÞxdx þ x2  x20

p 0 ½kðxÞ  kp ðxÞxdx  ; x2  x20

Z

1

xe

slowly changing function of frequency, which is exactly defined by the absorption matrix coefficients and a studied absorption band out of a studied interval, an error of an experimental definition of kp(x) at edges of a studied interval.

0

k ¼

3

Thanks to the narrowness of a studied interval it is possible to approximate c(x) by a linear function of frequency and to consider, having directly measured the refractive index at edges of the studied frequencies interval. In this work the values of the refractive index have not been defined directly therefore giving frequency dependences of studied transition to the refractive index, we mean only the contribution

nðx0 Þ ¼

2

p

Z

xe

xb

½kðxÞ  kp ðxÞxdx : x2  x20

Therefore the frequency dependences of the refractive index given by us has a characteristic systematic slope (n(x) decreases at increasing x), and the values of the refractive index near edges of absorption band there are only several times less than maximum values n. 0 The difference between k ð hxÞ and n0 ð hxÞ at two E orientations proves that the crystal is optically biaxial. This difference in k0 is a maximum at the frequency of 5450 and 5500 cm1. It reaches 60– 70%. As one can see in Fig. 2 Dn ¼ n01 0 0  n01 1 0 reaches the value of 1  103 and reverses sign several times in the region of the absorption band. Thus the character of the optical anisotropy of the crystal depends on the relative orientation of the vectors k and I. No such effect had been observed before for Tb3Fe5012 and for Eu3Fe5012 in such geometry of the experiment to our knowledge. Investigations of the MBL have shown that the anisotropy of the optical properties of an IG magnetized far from the absorption lines can be satisfactorily described with the aid of a dielectric tensor expanded in powers of the magnetization I. In general case a cubic crystal becomes optically biaxial upon magnetization, and the angle between the optical axes is determined by the orientation of the vector I in the crystal, namely, if I is directed along axes such as [1 1 1] and [1 0 0] the crystal is uniaxial, and in other directions of I it is in general biaxial. When analyzing the properties of light propagation in an isotropic absorbing medium, and in particular in the region of the absorption bands, an account should be taken of more complicated effects connected with magnetic linear and circular dichroism. It appears that this circumstance explains the lack of systematic studies of the anisotropy of the optical properties of absorbing crystals in the magnetized state. The crystal Tb3Fe5012 chosen by us is optically uniaxial in the transparency region. We have shown IÞ the crysk ?~ earlier that in the case of transverse magnetization ð~ tal remains uniaxial also in the absorption lines. One remark must be made here concerning the employed term ‘‘uniaxial’’. The fact that the two experimental plots of the absorption coefficient k0  1 0, ~ Ejj½1 Ijj½1 1 0 and ~ Ejj½0 0 1, kjj½0 0 1, ~ kjj½1 1 0, ~ coincide at ~ ~ Ijj½1 1 0 gives grounds for assuming that in this case the characteristic surfaces of the complex tensor ^e have axial symmetry with an axis parallel to I. The absorption coefficient of linearly polarized light, just as any true scalar, can be expanded in the direction cosines Ii and ki of the vectors I and k. In a cubic crystal (symmetry group Oh) we have accurate to terms quadratic in Ii and ki:

3 h     i X 2 2 2 2 2 2 2 2 e2i a1 ðxÞ kj I2j þ kk I2h þ a2 ðxÞki I2i þ a3 ðxÞ kj I2k þ kk I2j þ a4 ðxÞI2i ðki þ kk Þ þ a5 ðxÞki ðI2j þ I2k Þ i¼1 3 h i X 2 2 2 þ ei ej b1 ðxÞkk Ii Ij þ b2 ðxÞI2k ki kj þ b3 ðxÞIi Ij ðki þ kj Þ þ b4 ðxÞki kj ðI2i þ I2j Þ ; i;j¼1

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ð1Þ

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N.I. Tsidaeva et al. / Optical Materials xxx (2013) xxx–xxx

where ai (x) and bi (x) are certain coefficients that depend in the general case on the frequency x of the light. The foregoing expression is based on the complete rational basis of the Oh, group with account taken of in variance to time reversal. Let us consider some particular consequences of the Eq. (1). We direct the magnetization first along the twofold axis in Tb3Fe5O12:  1 0, ~ kjj½1 1 0, ~ Ijj½1 Ejj½0 0 1 (1) ~ 0

k ¼

1 1 1 a1 þ a3 ¼ ða1 þ a3 Þ 2 2 2

 1 0, ~  1 0 kjj½1 (2) ~ Ijj½0 0 1, ~ Ejj½1

1 2

a4 ¼ ð2a3 þ b1 Þ; then the crystal is uniaxial at any orientation of the vector I. By changing to a local coordinate frame connected with the vectors k and E, one can separate in the Eq. (1) the terms that are essentially anisotropic in the wave vector k. These terms, when taking into account data obtained, do not vanish and it can therefore be proposed that the anomalous crystal optics of the terbium IG, observed by us, is due to spatial dispersion, which begins to influence particularly strongly the optical properties of the crystal in the absorption-line region. Acknowledgments

1 k ¼ ða3 þ a5  b2 Þ; 2 0

0

i.e., there is no isotropy of k , as is indeed observed in experiment. Then we direct the magnetization first along the twofold axis in Eu3Fe5O12:  1 1, ~  1 0 kjj½1 1 0, ~ (1) ~ Ijj½1 Ejj½1

1 k ¼ ða1 þ a2 þ a3 þ a4 þ 2a5  b1 þ 2b3  2b4 Þ; 6

The work is executed at support of the Ministry of education and science of the Russian Federation (the Project No. 2.2527.2011). Investigations were carried out on the equipment of Natural Sciences Research and Education Centre at North-Ossetian State University. References

0

 1 0, ~  1 1 kjj½1 1 0, ~ (2) ~ Ijj½1 Ejj½1 0

k ¼

1 ð2a1 þ a2 þ a3 þ a4 þ a5 þ 2b3  2b4 Þ; 6

i.e., there is no isotropy of k0 , as is indeed observed in experiment. The Eq. (1) makes it possible thus to explain, from a unified point of view, all the observed features of the optical anisotropy of terbium IG. At the definite relations between the coefficients ai and bi the Eq. (1) are reduced to a form that determines the usual optical anisotropy of a magnetized cubic crystal, and the character of the anisotropy does not depend on the relative orientation of the vectors k and I. The relations

1 2

1 2

a1 ¼ a3 ; a2 ¼ ð2a3 þ b1 þ b2 Þ; a5 ¼ ð2a3 þ b2 Þ; b2 ¼ b4 ; b1 ¼ b3

[1] W. Wang, R. Chen, X. Qi, J. Alloy, Compd. 512 (2012) 128. [2] N. Tsidaeva, V. Abaeva, E. Enaldieva, T. Magkoev, A. Turiev, A. Ramonova, T. Butkhuzi, Key Eng. Mater. 543 (2013) 364–367. [3] N.I. Tsidaeva, V.V. Abaeva, T.T. Magkoev, Acta Phys. Polonica A. 121 (1) (2012) 74–77. [4] W. Wang, R. Chen, K. Wang, IEEE Trans. Magn. 48 (2012) 3638–3640. [5] W. Wang, X. Qi, G. Liu, J. Appl. Phys. 103 (7) (2008) 073908–073913. [6] N.I. Tsidaeva, J. Alloy, Compd. 408–412 (2006) 164–168. [7] M. Nath, C.L. Sharma, N. Bharti, Rev. Inorg. Chem. 20 (2000) 137–1866. [8] J.B. Gruber, U.V. Valiev, G.W. Burdick, S.A. Rakhimov, J. Lumin. 131 (2011) 1945–1952. [9] U.V. Valiev, J.B. Gruber, F.U. Dejun, V.O. Pelenivich, G.W. Burdick, M.E. Malysheva, J. Rare Earth 29 (8) (2011) 776–782. [10] G.S. Krinchik, V.D. Gorbunova, V.S. Gushchin, A.A. Kostyurin, Sov. Phys. JETP. 51 (1980) 435–441. [11] G.S. Krinchik, A.A. Kostyurin, V.D. Gorbunova, V.S. Gushchin, Sov. Phys. JETP. 54 (1981) 550–555. [12] M. Guillot, P. Feldmann, H. Le Gall, J. Magn. Magn. Mat. 30 (1982) 223–230. [13] M. Guillot, P. Feldmann, H. Le Gall, A. Marchand, J. Appl. Phys. 63 (1988) 3104– 3106. [14] N.P. Kolmakova, R.Z. Levitin, A.I. Popov, N.F. Vedernikov, A.K. Zvezdin, Phys. Rev. B 41 (1990) 6170–6178.

define an optically biaxial crystal, and if we introduce the additional relation

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