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Temperature and pressure dependences of EPR spectra of Gd3+ ion doped in the EuAl3(BO3)4 monocrystal
Journal of Magnetism and Magnetic Materials 323 (2011) 1546–1550
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Temperature and pressure dependences of EPR spectra of Gd3 + ion doped in the EuAl3(BO3)4 monocrystal A.D. Prokhorov a, A.A. Prokhorov a, L.F. Chernysh a, V.P. Dyakonov a,b,n, H. Szymczak b a b
A.A. Galkin Donetsk Physico-Technical Institute, NANU, 83114 Donetsk, R. Luxembourg Str. 72, Ukraine ´w 32/46, Poland Institute of Physics, PAS, 02-668 Warsaw, Al. Lotniko
a r t i c l e i n f o
a b s t r a c t
Article history: Received 31 August 2010 Received in revised form 28 December 2010 Available online 19 January 2011
The ground state of Gd3 + ions substituting for trivalent europium in the EuAl3(BO3)4 single crystal was studied by electron paramagnetic resonance (EPR) over the temperature range of 300–4.2 K and at pressures up to 9 kbar. The EPR spectra were analysed using the spin Hamiltonian of axial symmetry. The following parameters are reported: g ¼ 1.9817 0.002, b02 ¼ 280.18 70.12, b04 ¼ 12.95 70.08 and b06 ¼ 0.61 7 0.12 (at T ¼298 K). The distortions of the nearest environment of Gd3 + ion were analysed within the framework of the superposition model of crystal field. & 2011 Published by Elsevier B.V.
Keywords: EPR spectra Gd3 + ion EuAl3(BO3)4 single crystal Pressure
1. Introduction The borates with general formula REM3(BO3)4, where RE are the rare-earth ions or yttrium and M ¼Al, Fe, Ga, Cr, attract considerable attention of researchers due to their distinctive luminescent and non-linear optical properties. The ability of borates to accommodate a high concentration of RE dopants, combined with excellent physical and chemical properties, promotes to use these crystals as a promising media for solidstate lasers. An interest to small lasers with pumping by lightemitting diodes in green-blue spectral region supports the studies of new solid-state laser systems based on non-linear crystals [1–3]. An opportunity to introduce into the borates both rare-earth ions and ions of iron group makes them attractive from the point of view of magnetism, since an interaction of two magnetic subsystems leads to a number of important features of their magnetic behaviour. An interaction between iron ions in quasione-dimensional chains of GdFe3(BO3)4 results in an antiferromagnetic ordering at 37 K, and an interaction between iron and rare-earth subsystem promotes a spin-reorientation phase transition below 10 K in such ferroborates as GdFe3(BO3)4 [4,5] and NdFe3(BO3)4 [6]. At pressure of 25 and 43 GPa two electronic phase transitions are found [7]. The magnetoelectric effect observed in some crystals allows assigning them to the category
n Corresponding author at: Institute of Physics, PAS, 02-668 Warsaw, Al. Lotniko´w 32/46, Poland. Tel.: +48 22 843 77 01; fax: + 48 22 843 09 26. E-mail address: [email protected] (V.P. Dyakonov).
0304-8853/$ - see front matter & 2011 Published by Elsevier B.V. doi:10.1016/j.jmmm.2011.01.015
of multiferroics [8]. The review of rare-earth borates properties is given in Ref. [9]. The majority of known papers in which rare-earth borates were investigated were devoted to study their properties in a magnetically ordered state. Electron paramagnetic resonance (EPR), being a powerful tool to obtain a valuable information regarding the ground state of paramagnetic impurities in the given family crystals, was rarely used for these purposes. There are number of publications on resonance properties of RE-aluminium borates. The EPR spectra of YAl3(BO3)4 doped with Cr3 + and Ti3 + ions were reported in Refs. [10–12]. The EPR spectra of RExY1 xAl3(BO3)4 crystals containing Ce3 + , Er3 + and Yb3 + ions have also been studied [13,14]. Our investigations of the EPR spectrum of Gd3 + ions introduced into the YAl3(BO3)4 crystal are presented in Ref. [15]. We present new results on the EPR spectrum and the ground state of Gd3 + ion introduced into the EuAl3(BO3)4 crystal as an impurity ion. The studies have been performed over the wide temperature and pressure range. The EPR spectrum was analysed on the basis of the superposition model of crystal field [16].
2. Crystal structure and experiment details The EuAl3(BO3)4 (EuAB) crystals crystallise in the huntite structure of CaMg3(BO3)4 with the spatial group R32. The lattice parameters of the trigonal cell of EuAB are equal to ˚ c¼7.273(3) A˚ [17]. The unit cell of EuAB cona¼b¼ 9.319(3) A, tains Z¼ 3 formula units. Trigonal prisms, octahedrons and triangles formed by oxygen ions are coordination polyhedrons of Y3 + , Al3 + and B3 + ions, respectively. The Eu3 + ions are located
A.D. Prokhorov et al. / Journal of Magnetism and Magnetic Materials 323 (2011) 1546–1550
on the rotary C3 axis in slightly deformed prisms in which the top and bottom triangles are slightly turned from each other. The Al3 + ions replace the positions in oxygen octahedrons, which being coupled by edges form the twisted columns elongated along the C3 axis. The B1 and B2 atoms are located in oxygen triangles of two types: the B1 atoms are in triangles which are perpendicular to the triple axes and alternate with Y-prisms, and the B2 atoms are in the triangles, which couple the twisted columns from Al-octahedrons between themselves. The images of structure in both the x–y projection and the axonometry are presented in Refs. [17–20]. The EuAl3(BO3)4 crystals with the impurity of 0.2% Gd3 + have been obtained from a solution in a melt as a result of spontaneous crystallisation. The potassium molybdate K2Mo3O10 was used as the solvent. Preliminary synthesised aluminium borate Eu2O3 + Al2O3 +H3BO3 (or B2O3)-EuAl3(BO3)4 in quantity of 30% was added to the solvent. Moreover, an excess quantity of 10% B2O3 and corresponding quantity of Gd2O3 were added to the mixture. Growth of crystal was realized by cooling of the solution from 1150 down to 900 1C at a speed of 21/h, followed by a slow cooling of furnace down to the room temperature. The transparent, well faceted crystals with the sizes of 2–3 mm were obtained. The EPR spectra measurements have been carried out with an X-band Bruker spectrometer with high-frequency modulation using the special resonator from sapphire, which has allowed to perform the studies over the wide temperature interval (4.2–300 K) and at high hydrostatic pressure (up to 9 kbar). The sample was placed in the resonator, which in turn was located in a high pressure chamber. The high hydrostatic pressure was produced in the chamber made from non-magnetic material— beryl bronze. A mixture of mineral oil and kerosene was used as the pressure transmitting medium.
3. Fine structure of EPR spectrum The gadolinium trivalent ion has a half filled electronic shell with a 4f7 configuration. The ground 8S7/2 multiplet is characterised by an absence of orbital moment (L¼0) and value of spin moment S ¼7/2. The eightfold degenerated level of trivalent gadolinium ion being placed in trigonal crystal field of europium– aluminium borate is split into four Kramers doublets. The EPR spectrum consists of seven absorption lines resulting from both intradoublet and interdoublet transitions. The general view of Gd3 + spectra for two isomorphic compounds, namely, EuAl3(BO3)4 and earlier investigated YAl3(BO3)4 [15], in an external magnetic field oriented parallel to the C3 axis is shown in Fig. 1. It is seen that the splitting of spectrum in EuAl3(BO3)4 crystal is essentially less than in YAl3(BO3)4. In the crystal investigated the Gd3 + ion substitutes for Eu3 + ion being in the site with the D3 symmetry. To describe the EPR spectrum the spin Hamiltonian of trigonal symmetry was used: ! 1 1 0 0 1 ðb O þ b34 O34 Þ þ ðb0 O0 þ b36 O36 þ b66 O66 Þ H ¼ b B g S^ þ b02 O02 þ 3 60 4 4 1260 6 6 ð1Þ where b is the Bohr magneton, B the magnetic induction vector, S the operator of electron spin, Om n Stevens’s spin operators [21] and bm n the crystal field parameters. As a result of both the experimental data processing and calculations using expression (1), the following spin Hamiltonian parameters were obtained: gz ¼ gx ¼ gy ¼ 1:981 7 0:002; b04
¼ 12:95 70:08; The
bm n
b06
b02 ¼ 280:18 7 0:12;
¼ 0:61 70:12
parameters are specified in units of 10 4 cm 1.
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EuAl3(BO3)4
YAl3(BO3)4
1000
2000
3000
4000
5000
B, Gs Fig. 1. EPR spectra of Gd3 + ion in the EuAl3(BO3)4 and YAl3(BO3)4 crystals (at T¼293 K).
These calculations show that the g-factor is practically isotropic and the spectrum is very close to the axial one. Since taking into account the b34, b36 and b66 parameters of spin Hamiltonian do not significantly improve the calculation results, to describe the EPR spectrum one can be limited only by three axial b02, b04 and b06 parameters of spin Hamiltonian. The sign of b02 parameter determined by the relation between the low field and high field intensities of spectra obtained at low temperatures is positive. Thus, the low-lying state is the doublet 71/2, and further the energy levels with quantum numbers 73/2, 75/2 and 77/2 are located. The energy distances between doublets obtained are the following: D1( 71/2273/2) ¼413.5 10 4 cm 1, D2( 73/227 5/2)¼928.710 4 cm 1 and D3(75/2277/2)¼1425.710 4 cm 1. The absorption linewidths related to the transitions between the energy levels with various quantum numbers are established to differ insignificantly, namely, for ( 75/2277/2), ( 73/22 75/2) and ( 71/2273/2) transitions they are equal to 41, 34 and 22 Gs, respectively. The ( +1/22 1/2) transition has the minimal (15 Gs) linewidth. The absorption linewidth is defined by several factors, namely, spin–spin interaction between gadolinium ions, electron-nuclear interaction of Gd3 + ions with the nuclear moments of surrounding their neighbours and heterogeneity of crystal field. Spin–spin interaction between nearest gadolinium ions can lead to occurrence of additional lines, as it is observed in the experimental spectrum. The interaction with next-nearest neighbours can lead to broadening of absorption lines only. Electron-nuclear interaction of Gd3 + ions with the nuclear moments of surrounding their neighbours is the main reason of broadening of the ( + 1/22 1/2) transition. The nuclei of boron (nuclear spins of 3/2, magnetic moment of 2.688 nuclear Bohr magneton and relative abundance of 80.39%) as well as the nuclei of aluminium (nuclear spin of 5/2, magnetic moment of 3.64 and relative abundance of 100%) are in the nearest environment of Gd3 + ion. It is known that in the Al2O3 crystal with minimal concentration of chromium the width of ( +1/22 1/2) transition is equal to 12 Gs [22]. This value is close to our data and shows that an environment of the paramagnetic ion in the studied crystal and in Al2O3 is similar.
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A.D. Prokhorov et al. / Journal of Magnetism and Magnetic Materials 323 (2011) 1546–1550
Heterogeneity of crystal field can be the main reason of broadening of ( 73/22 75/2) and ( 75/22 77/2) transitions. The estimation shows that spread of the b02 parameter in the limit of 1% explains the observed broadening.
The spectrum splitting was observed to change with decrease in temperature. On temperature dependence of the b02 parameter shown in Fig. 2 two sections can be distinguished, one of which is practically linear above 160 K. It should be noted an absence of jump on the b02 (T) dependence observed in the YAl3(BO3)4 crystal [15]. Fig. 3 shows the temperature dependence of b04 parameter, which insignificantly increases with increase in temperature. A splitting of energy levels of ions in S-state is caused by a number of contributions. One of them is static and manifests itself at low temperature, when the lattice fluctuations do not influence practically on the position of energy levels, and the second contribution caused by the lattice fluctuations manifests itself
305
b20, 10-4 cm-1
4. Experimental temperature and pressure dependences of the spin Hamiltonian parameters
310
300 295 290 285 280 0
1
2
3
4
5
6
7
8
9
10
P, kbar Fig. 4. Spin Hamiltonian b02 parameter as a function of pressure.
12.88 12.86
Ib40I, 10-4 cm-1
288
b20 * 10-4 cm-1
286
284
12.82 12.80 12.78
282
12.76 0
280
1
2
3
4
5
6
7
8
9
10
P, kbar Fig. 5. Spin Hamiltonian b04 parameter as a function of pressure.
278 50
100
150
200
250
300
350
T, K
at higher temperatures. The contributions connected with fluctuations can be divided into two parts. One of them is connected with the thermal expansion (compression) of the lattice caused by anharmonicity of fluctuations, and the second part is a socalled the phonon contribution. Discussion and an estimation of the values of these contributions are presented below. Figs. 4 and 5 present the experimental pressure dependences of b02 and b04 parameters at T¼293 K. A compression of the crystal caused by both pressure and decrease in temperature increases a splitting of the ground state, however, the pressure effect is larger.
Fig. 2. Temperature dependence of the spin Hamiltonian b02 parameter.
12.80 12.75
Ib40 I *10-4 cm-1
12.84
12.70 12.65 12.60
5. Discussion
12.55 12.50 12.45 50
100
150
200
250
300
T. K Fig. 3. Temperature dependence of the spin Hamiltonian b04 parameter.
350
Let us discuss the obtained results from the point of view of superposition model (SM) of the crystal field [16]. The SM model is based on the assumption that a crystal field can be expressed as the sum of axial-symmetric contributions of all the nearest ligands surrounding the paramagnetic ion. As applied to the ions being in S-state, it is supposed that the spin Hamiltonian parameters describing a splitting of the ground
A.D. Prokhorov et al. / Journal of Magnetism and Magnetic Materials 323 (2011) 1546–1550
state, in our case of 8S7/2, can be presented in the following form: bm 2
¼
Sb2 ðRi ÞK2m ðWi ,
ji Þ, b2 ðRi Þ ¼ b2 ðR0 ÞðR0 =Ri Þ
t
ð2Þ
Km 2 ( i,
W ji) is the co-ordinate factor defined by angular where coordinates of ligands, t the exponent, b2(R0) the internal parameter and R0 the reference value defined as a result of the analysis of previously performed studies in which the b2(R0) parameter was determined. Unlike YAl3(BO3)4, the coordinates of atoms in the EuAl3(BO3)4 crystal are at present unknown. Assuming that a position of atoms changes proportionally to change in the lattice parameters, it is possible to calculate linear and angle coordinates of atoms in the EuAl3(BO3)4 structure. According to Ref. [16], the a lattice constant in EuAl3(BO3)4 is larger than the analogous constant in YAl3(BO3)4 by a factor of 1.0033, and the unit cell size along the c-axis is increased by a factor of 1.0065. Thus, the Eu–O distance ˚ will be equal to 2.331 A˚ (the Y–O distance is equal to 2.321 A), and a polar Y angle between the c-axis and the direction of Eu–O bond is equal to 54.011 (in the case of Y–O, Y ¼54.091). In the investigated EuAl3(BO3)4 crystal, the impurity Gd3 + ion is surrounded by six O2 ions located at equal distances in the vertex of prism. Then, the expression for b02 has the following form: b02 ¼ 3b2 ðR0 ÞðR0 =RÞt ð3cos2 Y1Þ
ð3Þ 2–
According to Ref. [23], for O ligands with coordination number of six, b2(R0)¼ (20007500) 10 4 cm 1, t ¼2.571.5 ˚ and R0 ¼2.699 A. When the Gd3 + ion substitutes for the Eu3 + ion, the distance to ligands will change. It can be estimated using the formula of R¼Rh + (ri–rh)/2 [23], where ri is the ionic radius of doped ion, rh the ionic radius of ion of the basic lattice and Rh the Eu–O distance. According to Ref. [24], the ionic radii of Eu3 + and Gd3 + ions are equal to 1.087 and 1.078, respectively, and then the Gd3 + –O2 ˚ distance is equal to 2.327 A. In order to obtain agreement between theory and experiment for the b02 parameter in the EuAl3(BO3)4 crystal doped with Gd3 + the bond Y angle should be equal to 55.391 (in the YAl3(BO3)4 crystal doped with Gd3 + , Y ¼55.651), which exceeds the angle between the c-axis and the direction of Eu–O bond equal to 54.011. From the above it follows that the basic contribution to the change in the b02 parameter contributes to the change in the bond angle. A change in bond length leads to very insignificant increase or reduction in the b02 parameter. For example, if the bond angle is fixed, a change in the bond length at transition from YAl3(BO3)4 to EuAl3(BO3)4 will lead to a change in the b02 parameter by 2% only. Let us consider the linear part of temperature dependence of the b02 parameter above 160 K shown in Fig. 2. The b02 parameter decreases from 287 10 4 cm 1 (at 160 K) to 280 10 4 cm 1 (at 293 K). Knowing the coefficients of temperature expansion along the a- and c-axis equal to 2 10 6 and 9.7 10 6/K, respectively [25], it is easy to calculate a change in both the length and the angle of the bond. At cooling from 293 to 160 K, ˚ and the bond the Gd–O distance decreases from 2.327 to 2.325 A, angle increases from 55.391 to 55.421. The b02 parameter calculated using a superposition model is obtained to be equal to 290.6 10 4 cm 1. Thus, the experimental and calculated values of the b02 parameter are increased by 7 10 4 and 10.6 10 4 cm 1, respectively, over the same temperature interval (about 133 K). According to results obtained, an increase in the b02 parameter by approximately 70% is caused by change in the geometrical sizes of crystal cell while approximately 30% of the effect results from a so-called phonon contribution to the spectrum splitting (which increases with increase in
1549
temperature). Of course, these results of calculations are approximate, since, firstly, the parameters of superposition model [23] used for calculations have a wide spread, secondly, the temperature factors defined for the temperature interval of 298– 573 K [25] can differ from the values for temperatures, at which the EPR spectra measurements were carried out, thirdly, experimental parametres of the crystalline lattice of EuAl3(BO3)4 are unavailable. Therefore, approximate estimations are made with certain assumptions. Nevertheless, the obtained calculation data argue for using of superposition model for the analysis of EPR spectra. The measurements of EPR spectra performed as a function of pressure have allowed obtaining added information on the spin Hamiltonian parameters. According to Fig. 4, the b02 parameter increases with increase in pressure as well as by cooling of the crystal. From this it follows that the crystal is compressed along the c-axis stronger than that in the perpendicular direction. Note that the b04 parameter changes insignificantly with increase in pressure and slightly influences the spectrum splitting. Taking into account that the change in b02 parameter is basically caused by increase in the bond angle and using relation (3), we obtain DY/DP¼7.4 1031/kbar. More detailed analysis can be made when the compressibility coefficients of the investigated crystals will be known. Thus, the performed measurements have allowed to determine the parameters of the EPR spectrum of the Gd3 + ion replacing the trivalent europium ion in the EuAl3(BO3)4 crystal. The ratio between the spin Hamiltonian parameters testifies that the EPR spectrum is very close to the axial one. The spectrum linewidth is shown to be defined by two mechanisms, namely, by spread of the crystal field parameters and by interaction of the paramagnetic ion with the nuclear moments of boron and aluminium atoms. The change in the bond angle, which differs from this angle in the crystal-matrix is established to contribute basically to the change in the b02 parameter. The bond Y angle is increased by 1.381 in the EuAl3(BO3)4 crystal (in YAl3(BO3)4, the Y angle increases by 1.561). Anisotropy of coefficients of both compression (sJ 4 s? ) and thermal expansion (aJ 4 a? ) has similar character. Here J and ? symbols correspond to the directions along and perpendicular to the C3 axis, respectively. Changes in the b02 parameter (Db02/DP¼3 10 4 cm 1/kbar) and the bond Y angle (DY/DP¼ 7.4 10 31/kbar) as a function of pressure were determined.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16]
D. Jaque, Adv. Mater. 10 (1998) 10. P. Wang, J.M. Dawes, P. Dekker, J.A. Piper, Opt. Commun. 174 (2000) 467. P.A. Burns, J.M. Dawes, P. Dekker, J.A. Paper, Opt. Commun. 207 (2002) 315. A.D. Balaev, L.N. Bezmaternykh, I.A. Gudim, V.L. Temerov, S.G. Ovchinnikov, S.A. Kharlamova, J. Magn. Magn. Mater. 258–259 (2003) 542. S.A. Kharlamova, S.G. Ovchinnikov, A.D. Balaev, M.F. Thomas, L.S. Lyubutin, A.G. Gavriliuk, JETP 101 (2005) 1098. J.A. Campa, C. Cascales, E. Gutierrez-Puebla, M.A. Monge, I. Raines, C. Ruiz-Valero, Chem. Mater. 9 (1997) 237. A.G. Gavriliuk, S.A. Kharlamova, L.S. Lyubutin, I.A. Troyan, S.G. Ovchinnikov, A.M. Potseluiko, M.I. Eremiet, R. Boehler, JETF Lett. 80 (2004) 426. A.K. Zvezdin, S.S. Krotov, A.M. Kadomtseva, G.P. Vorob’ev, Yu.F. Popov, A.P. Pyatakov, L.N. Bezmaternykh, E.A. Popova, JTPh Lett. 81 (2005) 272–276. A.N. Vasiliev, E.A. Popova, FNT 32 (2006) 968. V.A. Atsarkin, V.B. Kravchenko, I.G. Matveeva, FTT 9 (1967) 3353–3354. J.-P.R. Wells, M. Yamaga, T.P.J. Han, M. Honda, J. Phys.:Condens. Matter 15 (2003) 539. G. Wang, H.G. Gallagher, T.P.J. Han, B. Henderson, M. Yamaga, T. Yosida, J. Phys.: Condens. Matter 9 (1649) 1997. F.A. Vorotunov, G. Petrakovskii, Ya. Shuyan, L. Bezmaternuch, V. Temerov, A. Bovina, P. Aleshkevich, FTT 49 (2007) 446. A. Waterich, P. Aleshkevych, M.T. Borowiec, T. Zayarnyuk, H. Szymczak, T. Beregi, L. Kovacs, J. Phys.: Condens. Matter 15 (2003) 3323. A.D. Prokhorov, I.M. Krygin, A.A. Prokhorov, L.F. Chernush, P. Aleshkevych, V. Dyakonov, H. Szymczak, Phys. Status Solidi A 206 (2009) 2617. D.J. Newman, Ng. Betty, Rep. Prog. Phys. 52 (1989) 699.
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[17] N.I. Leonyuk, L.I. Leonyuk, Prog. Cryst. Growth Charact. 31 (1995) 179. [18] E.L. Belokoneva, A.V. Azizov, N.I. Leonyuk, M.A. Simonov, N.V. Belov, J. Struct. Chem. 22 (1981) 196. [19] E.L. Belokoneva, L.I. Alshanska, M.A. Simonov, N.I. Leonyuk, T.I. Timchenko, N.V. Belov, J. Struct. Chem. 20 (1979) 542. [20] S.A. Klimin, D. Fausti, A. Meetsma, L.N. Bezmaternykh, P.H.M. van Loosdrecht, T.M.M. Palstra, Acta. Crystallogr. B 61 (2005) 481.
[21] S.A. Altshuler, B.M. Kozyrev, Electronic Paramagnetic Resonance, Izd. Nauka, Moskva, 1972. [22] A.A. Manenkov, V.B. Fedorov, JETF 38 (1960) 1042. [23] W.C. Zheng, S.Y. Wu, Physica B 304 (2001) 137. [24] R.D. Shennon, Acta. Crystallogr. A 32 (1976) 751. [25] N.I. Leonyuk, E.V. Kaporulina, V.V. Maltsev, J. Li, H.J. Zhang, J.X. Zhang, J.Y. Wang, J. Cryst. Growth 277 (2005) 252.
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Temperature and pressure dependences of EPR spectra of Gd3 + ion doped in the EuAl3(BO3)4 monocrystal A.D. Prokhorov a, A.A. Prokhorov a, L.F. Chernysh a, V.P. Dyakonov a,b,n, H. Szymczak b a b
A.A. Galkin Donetsk Physico-Technical Institute, NANU, 83114 Donetsk, R. Luxembourg Str. 72, Ukraine ´w 32/46, Poland Institute of Physics, PAS, 02-668 Warsaw, Al. Lotniko
a r t i c l e i n f o
a b s t r a c t
Article history: Received 31 August 2010 Received in revised form 28 December 2010 Available online 19 January 2011
The ground state of Gd3 + ions substituting for trivalent europium in the EuAl3(BO3)4 single crystal was studied by electron paramagnetic resonance (EPR) over the temperature range of 300–4.2 K and at pressures up to 9 kbar. The EPR spectra were analysed using the spin Hamiltonian of axial symmetry. The following parameters are reported: g ¼ 1.9817 0.002, b02 ¼ 280.18 70.12, b04 ¼ 12.95 70.08 and b06 ¼ 0.61 7 0.12 (at T ¼298 K). The distortions of the nearest environment of Gd3 + ion were analysed within the framework of the superposition model of crystal field. & 2011 Published by Elsevier B.V.
Keywords: EPR spectra Gd3 + ion EuAl3(BO3)4 single crystal Pressure
1. Introduction The borates with general formula REM3(BO3)4, where RE are the rare-earth ions or yttrium and M ¼Al, Fe, Ga, Cr, attract considerable attention of researchers due to their distinctive luminescent and non-linear optical properties. The ability of borates to accommodate a high concentration of RE dopants, combined with excellent physical and chemical properties, promotes to use these crystals as a promising media for solidstate lasers. An interest to small lasers with pumping by lightemitting diodes in green-blue spectral region supports the studies of new solid-state laser systems based on non-linear crystals [1–3]. An opportunity to introduce into the borates both rare-earth ions and ions of iron group makes them attractive from the point of view of magnetism, since an interaction of two magnetic subsystems leads to a number of important features of their magnetic behaviour. An interaction between iron ions in quasione-dimensional chains of GdFe3(BO3)4 results in an antiferromagnetic ordering at 37 K, and an interaction between iron and rare-earth subsystem promotes a spin-reorientation phase transition below 10 K in such ferroborates as GdFe3(BO3)4 [4,5] and NdFe3(BO3)4 [6]. At pressure of 25 and 43 GPa two electronic phase transitions are found [7]. The magnetoelectric effect observed in some crystals allows assigning them to the category
n Corresponding author at: Institute of Physics, PAS, 02-668 Warsaw, Al. Lotniko´w 32/46, Poland. Tel.: +48 22 843 77 01; fax: + 48 22 843 09 26. E-mail address: [email protected] (V.P. Dyakonov).
0304-8853/$ - see front matter & 2011 Published by Elsevier B.V. doi:10.1016/j.jmmm.2011.01.015
of multiferroics [8]. The review of rare-earth borates properties is given in Ref. [9]. The majority of known papers in which rare-earth borates were investigated were devoted to study their properties in a magnetically ordered state. Electron paramagnetic resonance (EPR), being a powerful tool to obtain a valuable information regarding the ground state of paramagnetic impurities in the given family crystals, was rarely used for these purposes. There are number of publications on resonance properties of RE-aluminium borates. The EPR spectra of YAl3(BO3)4 doped with Cr3 + and Ti3 + ions were reported in Refs. [10–12]. The EPR spectra of RExY1 xAl3(BO3)4 crystals containing Ce3 + , Er3 + and Yb3 + ions have also been studied [13,14]. Our investigations of the EPR spectrum of Gd3 + ions introduced into the YAl3(BO3)4 crystal are presented in Ref. [15]. We present new results on the EPR spectrum and the ground state of Gd3 + ion introduced into the EuAl3(BO3)4 crystal as an impurity ion. The studies have been performed over the wide temperature and pressure range. The EPR spectrum was analysed on the basis of the superposition model of crystal field [16].
2. Crystal structure and experiment details The EuAl3(BO3)4 (EuAB) crystals crystallise in the huntite structure of CaMg3(BO3)4 with the spatial group R32. The lattice parameters of the trigonal cell of EuAB are equal to ˚ c¼7.273(3) A˚ [17]. The unit cell of EuAB cona¼b¼ 9.319(3) A, tains Z¼ 3 formula units. Trigonal prisms, octahedrons and triangles formed by oxygen ions are coordination polyhedrons of Y3 + , Al3 + and B3 + ions, respectively. The Eu3 + ions are located
A.D. Prokhorov et al. / Journal of Magnetism and Magnetic Materials 323 (2011) 1546–1550
on the rotary C3 axis in slightly deformed prisms in which the top and bottom triangles are slightly turned from each other. The Al3 + ions replace the positions in oxygen octahedrons, which being coupled by edges form the twisted columns elongated along the C3 axis. The B1 and B2 atoms are located in oxygen triangles of two types: the B1 atoms are in triangles which are perpendicular to the triple axes and alternate with Y-prisms, and the B2 atoms are in the triangles, which couple the twisted columns from Al-octahedrons between themselves. The images of structure in both the x–y projection and the axonometry are presented in Refs. [17–20]. The EuAl3(BO3)4 crystals with the impurity of 0.2% Gd3 + have been obtained from a solution in a melt as a result of spontaneous crystallisation. The potassium molybdate K2Mo3O10 was used as the solvent. Preliminary synthesised aluminium borate Eu2O3 + Al2O3 +H3BO3 (or B2O3)-EuAl3(BO3)4 in quantity of 30% was added to the solvent. Moreover, an excess quantity of 10% B2O3 and corresponding quantity of Gd2O3 were added to the mixture. Growth of crystal was realized by cooling of the solution from 1150 down to 900 1C at a speed of 21/h, followed by a slow cooling of furnace down to the room temperature. The transparent, well faceted crystals with the sizes of 2–3 mm were obtained. The EPR spectra measurements have been carried out with an X-band Bruker spectrometer with high-frequency modulation using the special resonator from sapphire, which has allowed to perform the studies over the wide temperature interval (4.2–300 K) and at high hydrostatic pressure (up to 9 kbar). The sample was placed in the resonator, which in turn was located in a high pressure chamber. The high hydrostatic pressure was produced in the chamber made from non-magnetic material— beryl bronze. A mixture of mineral oil and kerosene was used as the pressure transmitting medium.
3. Fine structure of EPR spectrum The gadolinium trivalent ion has a half filled electronic shell with a 4f7 configuration. The ground 8S7/2 multiplet is characterised by an absence of orbital moment (L¼0) and value of spin moment S ¼7/2. The eightfold degenerated level of trivalent gadolinium ion being placed in trigonal crystal field of europium– aluminium borate is split into four Kramers doublets. The EPR spectrum consists of seven absorption lines resulting from both intradoublet and interdoublet transitions. The general view of Gd3 + spectra for two isomorphic compounds, namely, EuAl3(BO3)4 and earlier investigated YAl3(BO3)4 [15], in an external magnetic field oriented parallel to the C3 axis is shown in Fig. 1. It is seen that the splitting of spectrum in EuAl3(BO3)4 crystal is essentially less than in YAl3(BO3)4. In the crystal investigated the Gd3 + ion substitutes for Eu3 + ion being in the site with the D3 symmetry. To describe the EPR spectrum the spin Hamiltonian of trigonal symmetry was used: ! 1 1 0 0 1 ðb O þ b34 O34 Þ þ ðb0 O0 þ b36 O36 þ b66 O66 Þ H ¼ b B g S^ þ b02 O02 þ 3 60 4 4 1260 6 6 ð1Þ where b is the Bohr magneton, B the magnetic induction vector, S the operator of electron spin, Om n Stevens’s spin operators [21] and bm n the crystal field parameters. As a result of both the experimental data processing and calculations using expression (1), the following spin Hamiltonian parameters were obtained: gz ¼ gx ¼ gy ¼ 1:981 7 0:002; b04
¼ 12:95 70:08; The
bm n
b06
b02 ¼ 280:18 7 0:12;
¼ 0:61 70:12
parameters are specified in units of 10 4 cm 1.
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EuAl3(BO3)4
YAl3(BO3)4
1000
2000
3000
4000
5000
B, Gs Fig. 1. EPR spectra of Gd3 + ion in the EuAl3(BO3)4 and YAl3(BO3)4 crystals (at T¼293 K).
These calculations show that the g-factor is practically isotropic and the spectrum is very close to the axial one. Since taking into account the b34, b36 and b66 parameters of spin Hamiltonian do not significantly improve the calculation results, to describe the EPR spectrum one can be limited only by three axial b02, b04 and b06 parameters of spin Hamiltonian. The sign of b02 parameter determined by the relation between the low field and high field intensities of spectra obtained at low temperatures is positive. Thus, the low-lying state is the doublet 71/2, and further the energy levels with quantum numbers 73/2, 75/2 and 77/2 are located. The energy distances between doublets obtained are the following: D1( 71/2273/2) ¼413.5 10 4 cm 1, D2( 73/227 5/2)¼928.710 4 cm 1 and D3(75/2277/2)¼1425.710 4 cm 1. The absorption linewidths related to the transitions between the energy levels with various quantum numbers are established to differ insignificantly, namely, for ( 75/2277/2), ( 73/22 75/2) and ( 71/2273/2) transitions they are equal to 41, 34 and 22 Gs, respectively. The ( +1/22 1/2) transition has the minimal (15 Gs) linewidth. The absorption linewidth is defined by several factors, namely, spin–spin interaction between gadolinium ions, electron-nuclear interaction of Gd3 + ions with the nuclear moments of surrounding their neighbours and heterogeneity of crystal field. Spin–spin interaction between nearest gadolinium ions can lead to occurrence of additional lines, as it is observed in the experimental spectrum. The interaction with next-nearest neighbours can lead to broadening of absorption lines only. Electron-nuclear interaction of Gd3 + ions with the nuclear moments of surrounding their neighbours is the main reason of broadening of the ( + 1/22 1/2) transition. The nuclei of boron (nuclear spins of 3/2, magnetic moment of 2.688 nuclear Bohr magneton and relative abundance of 80.39%) as well as the nuclei of aluminium (nuclear spin of 5/2, magnetic moment of 3.64 and relative abundance of 100%) are in the nearest environment of Gd3 + ion. It is known that in the Al2O3 crystal with minimal concentration of chromium the width of ( +1/22 1/2) transition is equal to 12 Gs [22]. This value is close to our data and shows that an environment of the paramagnetic ion in the studied crystal and in Al2O3 is similar.
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Heterogeneity of crystal field can be the main reason of broadening of ( 73/22 75/2) and ( 75/22 77/2) transitions. The estimation shows that spread of the b02 parameter in the limit of 1% explains the observed broadening.
The spectrum splitting was observed to change with decrease in temperature. On temperature dependence of the b02 parameter shown in Fig. 2 two sections can be distinguished, one of which is practically linear above 160 K. It should be noted an absence of jump on the b02 (T) dependence observed in the YAl3(BO3)4 crystal [15]. Fig. 3 shows the temperature dependence of b04 parameter, which insignificantly increases with increase in temperature. A splitting of energy levels of ions in S-state is caused by a number of contributions. One of them is static and manifests itself at low temperature, when the lattice fluctuations do not influence practically on the position of energy levels, and the second contribution caused by the lattice fluctuations manifests itself
305
b20, 10-4 cm-1
4. Experimental temperature and pressure dependences of the spin Hamiltonian parameters
310
300 295 290 285 280 0
1
2
3
4
5
6
7
8
9
10
P, kbar Fig. 4. Spin Hamiltonian b02 parameter as a function of pressure.
12.88 12.86
Ib40I, 10-4 cm-1
288
b20 * 10-4 cm-1
286
284
12.82 12.80 12.78
282
12.76 0
280
1
2
3
4
5
6
7
8
9
10
P, kbar Fig. 5. Spin Hamiltonian b04 parameter as a function of pressure.
278 50
100
150
200
250
300
350
T, K
at higher temperatures. The contributions connected with fluctuations can be divided into two parts. One of them is connected with the thermal expansion (compression) of the lattice caused by anharmonicity of fluctuations, and the second part is a socalled the phonon contribution. Discussion and an estimation of the values of these contributions are presented below. Figs. 4 and 5 present the experimental pressure dependences of b02 and b04 parameters at T¼293 K. A compression of the crystal caused by both pressure and decrease in temperature increases a splitting of the ground state, however, the pressure effect is larger.
Fig. 2. Temperature dependence of the spin Hamiltonian b02 parameter.
12.80 12.75
Ib40 I *10-4 cm-1
12.84
12.70 12.65 12.60
5. Discussion
12.55 12.50 12.45 50
100
150
200
250
300
T. K Fig. 3. Temperature dependence of the spin Hamiltonian b04 parameter.
350
Let us discuss the obtained results from the point of view of superposition model (SM) of the crystal field [16]. The SM model is based on the assumption that a crystal field can be expressed as the sum of axial-symmetric contributions of all the nearest ligands surrounding the paramagnetic ion. As applied to the ions being in S-state, it is supposed that the spin Hamiltonian parameters describing a splitting of the ground
A.D. Prokhorov et al. / Journal of Magnetism and Magnetic Materials 323 (2011) 1546–1550
state, in our case of 8S7/2, can be presented in the following form: bm 2
¼
Sb2 ðRi ÞK2m ðWi ,
ji Þ, b2 ðRi Þ ¼ b2 ðR0 ÞðR0 =Ri Þ
t
ð2Þ
Km 2 ( i,
W ji) is the co-ordinate factor defined by angular where coordinates of ligands, t the exponent, b2(R0) the internal parameter and R0 the reference value defined as a result of the analysis of previously performed studies in which the b2(R0) parameter was determined. Unlike YAl3(BO3)4, the coordinates of atoms in the EuAl3(BO3)4 crystal are at present unknown. Assuming that a position of atoms changes proportionally to change in the lattice parameters, it is possible to calculate linear and angle coordinates of atoms in the EuAl3(BO3)4 structure. According to Ref. [16], the a lattice constant in EuAl3(BO3)4 is larger than the analogous constant in YAl3(BO3)4 by a factor of 1.0033, and the unit cell size along the c-axis is increased by a factor of 1.0065. Thus, the Eu–O distance ˚ will be equal to 2.331 A˚ (the Y–O distance is equal to 2.321 A), and a polar Y angle between the c-axis and the direction of Eu–O bond is equal to 54.011 (in the case of Y–O, Y ¼54.091). In the investigated EuAl3(BO3)4 crystal, the impurity Gd3 + ion is surrounded by six O2 ions located at equal distances in the vertex of prism. Then, the expression for b02 has the following form: b02 ¼ 3b2 ðR0 ÞðR0 =RÞt ð3cos2 Y1Þ
ð3Þ 2–
According to Ref. [23], for O ligands with coordination number of six, b2(R0)¼ (20007500) 10 4 cm 1, t ¼2.571.5 ˚ and R0 ¼2.699 A. When the Gd3 + ion substitutes for the Eu3 + ion, the distance to ligands will change. It can be estimated using the formula of R¼Rh + (ri–rh)/2 [23], where ri is the ionic radius of doped ion, rh the ionic radius of ion of the basic lattice and Rh the Eu–O distance. According to Ref. [24], the ionic radii of Eu3 + and Gd3 + ions are equal to 1.087 and 1.078, respectively, and then the Gd3 + –O2 ˚ distance is equal to 2.327 A. In order to obtain agreement between theory and experiment for the b02 parameter in the EuAl3(BO3)4 crystal doped with Gd3 + the bond Y angle should be equal to 55.391 (in the YAl3(BO3)4 crystal doped with Gd3 + , Y ¼55.651), which exceeds the angle between the c-axis and the direction of Eu–O bond equal to 54.011. From the above it follows that the basic contribution to the change in the b02 parameter contributes to the change in the bond angle. A change in bond length leads to very insignificant increase or reduction in the b02 parameter. For example, if the bond angle is fixed, a change in the bond length at transition from YAl3(BO3)4 to EuAl3(BO3)4 will lead to a change in the b02 parameter by 2% only. Let us consider the linear part of temperature dependence of the b02 parameter above 160 K shown in Fig. 2. The b02 parameter decreases from 287 10 4 cm 1 (at 160 K) to 280 10 4 cm 1 (at 293 K). Knowing the coefficients of temperature expansion along the a- and c-axis equal to 2 10 6 and 9.7 10 6/K, respectively [25], it is easy to calculate a change in both the length and the angle of the bond. At cooling from 293 to 160 K, ˚ and the bond the Gd–O distance decreases from 2.327 to 2.325 A, angle increases from 55.391 to 55.421. The b02 parameter calculated using a superposition model is obtained to be equal to 290.6 10 4 cm 1. Thus, the experimental and calculated values of the b02 parameter are increased by 7 10 4 and 10.6 10 4 cm 1, respectively, over the same temperature interval (about 133 K). According to results obtained, an increase in the b02 parameter by approximately 70% is caused by change in the geometrical sizes of crystal cell while approximately 30% of the effect results from a so-called phonon contribution to the spectrum splitting (which increases with increase in
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temperature). Of course, these results of calculations are approximate, since, firstly, the parameters of superposition model [23] used for calculations have a wide spread, secondly, the temperature factors defined for the temperature interval of 298– 573 K [25] can differ from the values for temperatures, at which the EPR spectra measurements were carried out, thirdly, experimental parametres of the crystalline lattice of EuAl3(BO3)4 are unavailable. Therefore, approximate estimations are made with certain assumptions. Nevertheless, the obtained calculation data argue for using of superposition model for the analysis of EPR spectra. The measurements of EPR spectra performed as a function of pressure have allowed obtaining added information on the spin Hamiltonian parameters. According to Fig. 4, the b02 parameter increases with increase in pressure as well as by cooling of the crystal. From this it follows that the crystal is compressed along the c-axis stronger than that in the perpendicular direction. Note that the b04 parameter changes insignificantly with increase in pressure and slightly influences the spectrum splitting. Taking into account that the change in b02 parameter is basically caused by increase in the bond angle and using relation (3), we obtain DY/DP¼7.4 1031/kbar. More detailed analysis can be made when the compressibility coefficients of the investigated crystals will be known. Thus, the performed measurements have allowed to determine the parameters of the EPR spectrum of the Gd3 + ion replacing the trivalent europium ion in the EuAl3(BO3)4 crystal. The ratio between the spin Hamiltonian parameters testifies that the EPR spectrum is very close to the axial one. The spectrum linewidth is shown to be defined by two mechanisms, namely, by spread of the crystal field parameters and by interaction of the paramagnetic ion with the nuclear moments of boron and aluminium atoms. The change in the bond angle, which differs from this angle in the crystal-matrix is established to contribute basically to the change in the b02 parameter. The bond Y angle is increased by 1.381 in the EuAl3(BO3)4 crystal (in YAl3(BO3)4, the Y angle increases by 1.561). Anisotropy of coefficients of both compression (sJ 4 s? ) and thermal expansion (aJ 4 a? ) has similar character. Here J and ? symbols correspond to the directions along and perpendicular to the C3 axis, respectively. Changes in the b02 parameter (Db02/DP¼3 10 4 cm 1/kbar) and the bond Y angle (DY/DP¼ 7.4 10 31/kbar) as a function of pressure were determined.
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