Magnetic Properties of KGd(WO4)2 Single Crystal Studied by EPR Spectroscopy

Magnetic properties of magnetically concentrated KGd(WO4)2 single crystal are studied using EPR spectroscopy. The EPR spectra are broad and have a complex shape, showing contributions of a few gadolinium centers. Temperature dependence of the total intensity of the EPR spectra and the inverse of the total intensity reveal two temperatures when the behavior of the total intensity suddenly changes, first one at 66.8 ± 3.3 K and the second one at 9.9 ± 2.8 K. Detailed analysis of this dependence suggests the presence of different magnetic systems of the Gd ions. The EPR spectra were described by the spin Hamiltonian of monoclinic symmetry with electron spin S = 7/2, for which all g-matrix components and fine-structure parameters have been determined using EPR-NMR program. Raman spectra measured at low temperatures do not differ significantly from the one measured at room temperature. The analysis has given a deeper insight into different kinds of magnetic interactions between paramagnetic Gd centers in KGd(WO4)2 single crystal.

Previously Cherney et al. (Cherney, Nadolinny, & Pavlyuk, 2008) have calculated spin Hamiltonian parameters for KY(WO 4 ) 2 :Gd 3+ (10 to 10000 ppm of Gd 2 O 3 ) diluted system.They simulated experimental EPR spectra with using special programs and obtained g x = 1.99 ± 0.02, g y = 1.99 ± 0.02 and g z = 2.00 ± 0.01.EPR spectrum of diluted double tungstate doped with gadolinium reveals clear fine structure.Fine structure parameters are defined by the crystal field of the local oxygen surrounding (D = 3B 2 0 , E = B 2 2 ).They have found B 2 0 = 416 ± 6 G and B 2 2 = -180 ± 10 G (the order of the parameters is preserved also in a paper by Borowiec et al. (1998)) and the difference in the D parameter between different centres of KY(WO 4 ) 2 :Gd is defined by the difference in distances Y-O, that in this case changes from 0.2284 to 0.3877 nm.The shorter distance Gd-O when substituting yttrium by gadolinium in KY(WO 4 ) 2 implies the larger value of B 2 0 , while the wider variation of these distances favours a larger value of B 2 2 , which characterizes the rhombicity.This is a way to distinguish different types of gadolinium paramagnetic centers, characterized also by different values of exchange parameters.
In the first approximation the paramagnetic Curie temperatures depend on parameters B 2 0 and B 2 2 only, so it is easy to find exchange parameter characterizing exchange interactions between gadolinium ions.Borowiec et al. have stated that the comparison of the data obtained by magnetization measurements with those obtained in EPR measurements is justified because the diluted KY(WO 4 ) 2 crystal is isomorphic with KGd(WO 4 ) 2 , so crystal fields acting on Gd 3+ in KY(WO 4 ) 2 and in KGd(WO 4 ) 2 are expected to be similar.The supposition is true nevertheless, only for the first approximation, when one can neglect higher order terms in the spin Hamiltonian.Generally exchange and magnetic dipole-dipole interactions are comparable, so energies of all magnetic structures should be estimated to find the type of magnetic structure.
In this paper we analyze optical and magnetic properties of concentrated KGd(WO 4 ) 2 single crystal applying measurements and discussion of Raman and EPR spectra.Special attention is paid to EPR spectra analysis, as being very sensitive tool to describe magnetic properties of the investigated crystal, even it is a concentrated magnetic system.

Experiment
KGW single crystals were grown by a low-gradient Czochralski technique (modified top-seeded solution method) in Pt crucibles using oriented seeds along the crystallographic b axis.The crystals obtained were colourless and had high optical quality.Orientation of the crystals was done by X-ray method giving a, b and c crystallographic axes (CAS) directions.a and b axes were the same for CAS axes system and experimental one (EAS), while c* experimental axis was perpendicular to ab plane (Macalik et al., 2002).
EPR spectra were recorded on a conventional X-band Bruker ELEXSYS E 500 CW-spectrometer operating at 9.5 GHz with 100 kHz magnetic field modulation.Temperature dependence of the EPR spectra in "a" crystallographic direction (bc*-plane), from 6 K up to room temperature, was recorded using an Oxford Instruments ESP nitrogen-flow cryostat.The crystal was rotated around a, b-and c * -EAS at temperatures 7.5-11 K, allowing draw angular dependences of EPR spectra.EPR-NMR program was applied to fit the dependences.
Raman spectra were measured in 4-300 K temperature range, using a Bruker RFS 100/S Raman Spectrometer with the back scattering configuration.The 1064 nm line of Nd:YAG laser was used as an excitation.Signal detection was performed with the LN-Ge (D418-T) liquid nitrogen-cooled NIR detector with an integrated preamplifier and high voltage power supply.The resolution of Raman spectra was 2 cm -1 .

Raman Spectra
Figure 1.Raman spectrum of KGd(WO 4 ) 2 single crystal measured at room temperature The spectra measured in 4-200 K range (not presented in the Figure ) do not differ significantly from the ones measured at room temperature (Figure 1).So we have not found any evidence on structure changes of the KGW crystal along the temperature range.
The Raman spectrum presented in Figure 1 consists of four strong bands in the 740-1000 cm -1 range (multiplets of the stretching (W-O) vibrations), two medium intensity bands in the 500-700 cm -1 range (stretching modes of the W O W and W O O W oxygen bonds), medium intensity bands in the 270-470 cm -1 range (banding vibrations) and group of medium bands in the 70-260 cm -1 range (translational motions of the cations and anions, as well as vibrations of the tungstate polyhedra).The assignment to the respective normal modes presented in Figure 1 was done according to the previous works (Macalik et al., 2000;Pilbrow, 1990;Macalik et al., 1998).As compare to double tungstates built of isolated tetrahedra, KGd(WO 4 ) 2 polymeric crystal does not exhibit the energy gap between the 450 and 750 cm -1 .

EPR Measurements
Figure 2 shows several EPR spectra (first derivative of the absorption) of KGW single crystal recorded at different temperatures.All the spectra were recorded at the same angle, when magnetic filed (B) lied in the bc-crystallographic plane.The temperature varied from 244 K (top line) down to 6 K (bottom line).One can notice that the EPR lines are very broad and have a complex shape.We have fitted them applying decomposition to at least three lines.This may suggest that the broad EPR signal registered for the KGW single crystal is a superposition of several signals from the same paramagnetic center but in a slightly different orientation in the crystal.So, the EPR spectra seem to be a superposition of a few signals originating from differently oriented Gd 3+ centers.Changes in the shape, width and height of the EPR resonance lines are clearly visible when temperature decreases.
As one can see from Figure 2 the EPR spectra are typical rather for powders than for isolated Gd 3+ centers.The total intensity of EPR spectrum is calculated by integration of the EPR absorption spectrum or as a double integral of the EPR spectrum (EPR susceptibility, χ EPR ) (Pilbrow, 1990).Temperature dependence of the total intensity of the EPR spectra is presented in Figure 3  As one can see from Figure 3, the total intensity increases when temperature decreases.Curie-Weiss temperature, T c , equals to -118.34 K, what indicates strong antiferromagnetic interactions between gadolinium ions.It is a typical behavior.But the total intensity changes considerably at a temperature about 70 K, giving Curie-Weiss temperature T c = -21.39K. Very close behavior we reported previously for not oriented KGW single crystal (Fuks et al., 2010).It means impairment of gadolinium antiferromagnetic interactions.Next, the total intensity continues to increase until the temperature of 9.9 K is reached, when it starts to drop rapidly.The inverse of the total intensity behaves similarly.In this case we can recognize three ranges of linear change: first one up to 9.9 K, the second one from 9.9 to 70 K, and the third one from 70 K to 250 K (see Figure 3).We have got two temperatures, when the behavior of the total intensity considerably changes, first one at 66.8 ± 3.3 K and the second one at 9.9 ± 2.8 K.The following spin Hamiltonian was used to generate angular dependence (roadmap) of the KGW crystal: where the first term is the electronic Zeeman term, the second one reflects pair interaction and third one contains the higher order (l = 2,4,6) Stevens parameters (crystal field).The symbols have got their usual meaning.
The roadmap was generated using EPR-NMR program (Mombourquette, Weil, & McGavin, 1999).The results of the fitting are presented in Figures 5 as thin and bold lines, solid, dashed and dotted.The bold (solid, dashed and dotted) lines represent lines fitted to the experimental data, obtained using the Hamiltonian (1), while the thin lines (solid, dashed and dotted) have been generated for this match and represent invisible, but possible transitions attributed to gadolinium ions in host lattice.To extract Hamiltonian parameters, there were taken into account three diffident paramagnetic centers: isolated gadolinium ions (solid lines), gadolinium pairs with a weak interaction (dashed lines) and gadolinium pairs with a strong interaction (dotted lines).The number of the centers results from EPR line decomposition (at least three lines) and from fitting procedure.The EPR signal originated from the isolated gadolinium ions is well resolved between 50-500 mT of magnetic field (solid lines).But itis not enough to explain all of our results.Since the EPR signal in the above range is also broad one, we assigned the signal to weakly interacting pairs of gadolinium ions (dashed lines).Very similar signal is observed also for high magnetic fields, which we assigned to strongly interacting pairs of gadolinium ions (dotted lines).
As can be seen from Figures 5, simulated lines describe experimental data well enough.At least two of the lines in each of planes were obtained for the same Hamiltonian parameters.Superposition of an EPR signal originating from many of the same paramagnetic ions but slightly shifted in the crystal lattice seem to be a reason why do some transitions are not observed.Hamiltonian parameters, obtained from the fitting procedure, are comparable to those, previously known in the literature (Table 1), (Fuks et al., 2010;Cherney et al., 2008).Nevertheless, some of them slightly differ from the standard values.One of possible explanation is coexistence of several kinds of gadolinium centers.The values of spin Hamiltonian parameters are gathered in Table 1a, b. -135(10)•10 -4 cm -1 Gd-Gd -dashed lines in -100(10)•10 -4 cm -1 275(8)•10 -4 cm -1 -100(10)•10 -4 cm -1 2.0(2)•10 -4 cm -1 J diag = -70(10)•10 -4 cm -1 J diag = -590(10)•10 -4 cm -1 Elements of g and matrices calculated using EPR-NMR program for KGd(WO 4 ) 2 single crystal: a) for isolated gadolinium centers and b) for two kinds of pairs of gadolinium ions; Stevens parameters are given in Gauss units, J-exchange constant.1b) and a shape of Raman spectrum (Figure 1), in which, between 450 and 750 cm -1 specific lines assigned to stretching modes of the W O W and W O O W oxygen bonds are observed.In KGd(WO 4 ) 2 tungstates, crystallizing in the monoclinic structure, the tungstate units built the WO 6 octahedra joined through the single and double oxygen bridges, so KGd(WO 4 ) 2 has got polymeric structure, which is a source of complex magnetic behavior between gadolinium ions.EPR spectra of KGd(WO 4 ) 2 single crystal and elements of its g matrix presented in Table 1a, a little bit differ from similar ones calculated for diluted medium e.g. in (Cherney et al., 2008).Nevertheless, two main spin Hamilitonian parameters, B 2 0 and B 2 2 (see Table 1), describing in the first approximation magnetic properties of KGd(WO 4 ) 2 single crystal, stay with good enough agreement with these calculated in (Cherney et al., 2008;Borowiec et al., 1998).Also exchange parameters, J, do not significantly differ from these calculated in (Borowiec et al., 2010).Regularity in a change of B 2 0 and B 2 2 spin Hamiltonian parameters described in (Cherney et al., 2008) and discussed by us in Introduction, is not fully preserved (see Table 1b, c).It may be an effect of magnetically concentrated medium and strong dipole-dipole interactions.What does result from the observed differences?First of all there is not clearly visible the fine-structure in the EPR spectrum of concentrated medium, whose parameters are defined by the crystal field of local oxygen surrounding.It was observed previously by Leniec et al. in (Leniec, Macalik, Kaczmarek, Skibiński, & Hanuza, 2012).So, EPR spectra of concentrated and diluted media could not be compared immediately.In magnetically concentrated medium, moreover, like KGd(WO 4 ) 2 , KGd(WO 4 ) 2 :Nd or KGd(WO 4 ) 2 :Er different Gd 3+ centers may arise because there exist different Y-O distances.For concentrated medium one can expect full representation of Gd-O distances as compare to diluted one.So, paired centers could be more often represented in the concentrated lattice than in diluted one.The above mentioned discrepancy in values of g matrix between the two media may be also due to strong dipole-dipole interactions.
Moreover, gadolinium ions in the crystal may interact with each other by two ways: a) through space or b) through bonds (Bencini & Gatteschi, 1990).The structure of the KGW unit cell indicates that both ways of Gd 3+ ions interaction are possible.The distance between two nearest Gd 3+ ions is equal to 4.0701(19) Å (Pujol et al., 2001).There are four Gd 3+ ions in such distances forming a chain.The ions within a chain may easily interact.Similarly, Gd 3+ ions interacting via O 2-oxygen bridges may form magnetically inequivalent structures, from pairs of Gd 3+ -Gd 3+ ions to various clusters of Gd 3+ ions.One can apply a law-dimensional Ising chain modelto describe the behaviour of the total intensity of the EPR spectra (Borowiec et al., 2010).

Conclusions
The results of the investigations of the EPR spectra of KGd(WO 4 ) 2 single crystal recorded at different temperatures and crystallographic orientations can be summarized as follows: • The Raman spectra measured in the 4-200 K range do not differ significantly from the one measured at room temperature; there were not found structure changes in KGd(WO 4 ) 2 single crystal under temperature variation; • EPR measurements performed in a temperature range of 6-244 K show a broad resonance line with complex shape; EPR spectra have been fitted very well with four Gaussian shape lines; • Temperature dependence of the total intensity of the EPR spectra and the inverse of the total intensity reveal two "jumps" at temperatures: 66.8 ± 3.3 K and 9.9 ± 2.8 K; at these specific temperatures a change in a kind of dominating magnetic interactions or activity of different magnetic systems takes place; • At least two lines were registered and fitted in angular dependences for all crystallographic directions: ab, ac and bc, giving spin Hamiltonian parameters; • Detailed analysis of angular dependencies revealed the presence of magnetic systems forming centres with spin S = 7/2 in monoclinic (C 2 ) symmetry; • At least three types of gadolinium paramagnetic centres we found to be present in concentrated KGd(WO 4 ) 2 system: isolated Gd centres and two kinds of gadolinium pairs differing by a strength of exchange interaction, defined by exchange constant (70×10 -4 cm -1 and 590×10 -4 cm -1 ), very close to calculated in (Borowiec et al., 2010).
(upper panel, open squares).Solid line indicates Curie-Weiss law.The inverse of the total intensity is also shown in the same figure (lower panel, open circles).

Figure 2 .
Figure 2. EPR spectra of KGd(WO 4 ) 2 single crystal recorded at eight different temperatures

Figure 4 .Figure 5 .
Figure 4. Line-width of the EPR spectrum versus temperature; inset shows g-factor dependence versus temperature in the 6-60 K range

Table 1 .
The spin Hamiltonian parameters of KGd(WO 4 ) 2 single crystal Such conclusion confirm angular dependences of EPR spectra (see also Table