Broadband EPR Spectroscopy of the Ground Electron State of the Fe4+ Impurity Ion in Amethyst

Fine structure of ground electron state of Fe4+ impurity ion in a natural amethyst crystal was studied by broadband electron paramagnetic resonance spectroscopy in the frequency range of 34–500 GHz. It is established that energy levels scheme consists of ground quasi-doublet Sz = ± 2, quasi-doublet S z= ± 1 and singlet Sz=0 with zero-field energies ± 4.9 GHz, 435.2 ± 45.4 GHz and 584 GHz, respectively. Parameters of effective spin Hamiltonian describing dependences of electron spin levels on magnetic field are determined.


Introduction
Amethyst is a well-known violet colored kind of quartz (SiO 2 ). In most studies devoted to the nature of the color of amethyst, this color is attributed to the presence in crystals of Fe 4+ impurity ions. The precursor of this center is a Fe 3+ ion substituting Si 4+ in the tetrahedral position [1]. When an amethyst crystal is exposed to γ-radiation, trivalent iron ions donates an electron and turns into a tetravalent one, creating a characteristic color. It has been noted in a number of papers that absorption bands characteristic of divalent iron ions appear in the optical spectra under the X-or γ-irradiation [2][3][4][5]. The history of studying the nature of the amethyst color has more than 50 years, however, and at present, the structure of impurity centers in amethyst and the relationship between the violet color of amethyst and the valence state of iron ions are the subject of study by various methods [6][7][8][9][10][11].
Electron paramagnetic resonance (EPR) is one of the most effective methods for study paramagnetic centers formed by paramagnetic impurity ions in crystals. EPR spectroscopy have been widely used to determine the structure and magnetic 1 3 properties formed in amethyst by impurity Fe 3+ ions. The results of these studies are presented in the reviews [12,13] and in later articles [8,14,15].
The use of EPR spectroscopy for the characterization of divalent and tetravalent iron ions with spin S = 2 is not very efficient. This is due to the peculiarities of the fine structure of the electron spin levels of non-Kramers ions. Electric crystal field of SiO 2 splits the ground electron state of these ions with four unpaired electrons into five singlets. The large energy gap between these singlet levels makes it difficult to observe resonant transitions between them using widely used X-band EPR spectrometers with an operating frequency of about 10 GHz. The EPR spectra of the Fe 4+ ion were observed earlier at frequencies of 16 and 35 GHz [16]. The only resonant transition between the quasi-doublet levels Sz = ± 2 was observed. This made it possible to measure the zero-field splitting between the levels of this quasi-doublet, but other parameters of the fine structure of the ground electron state remained unknown. To determine the fine structure of the ground electron levels of the Fe 4+ ion in amethyst, we measured the EPR spectra in the wide frequency range of 34-500 GHz.

Sample and Experiment Details
The measurements were carried out at cryogenic temperatures in a wide frequency range on a frequency-tunable submillimeter spectrometer operating in the frequency range of 64-535 GHz [17] and in the Q-band on an ELEXSYS E580 spectrometer (34 GHz). The spectrometer is equipped with a commercial resonator ER5106QTW (with TE011 wave mode), which was placed in a CF935 cryostat. The temperature was controlled using an ITC 503 temperature controller (Oxford). It was used a programmable single-axis goniometer ER218PG1 (Bruker) with a resolution of 0.125° and a working range of 360°. A sample of natural amethyst originated from the Pamir deposit was studied. According to the data of X-ray fluorescence analysis, in addition to silicon and oxygen, the sample contained the following elements (as a percentage relative to 28 Si): 20 Ca, 0.04; 16 S, 0.09; 19 K, 0.03, 56 Fe, 0.02. The microwave path of the submillimeter spectrometer is built according to a quasi-optical scheme without a resonator. Microwave radiation is focused by a teflon lens on the sample and passes to a detector. Measurements on the spectrometer were carried out at a temperature of 4.2 K with the sample having dimensions of about 5 × 10x20 mm 3 . Measurements in the Q-band were carried out with a sample of 1 × 1x3 mm 3 in the temperature range 5-120 K.
The SiO 2 crystal below 537.5 °C has a trigonal structure and belongs to the space group P3 1 21 ( D3 4 2 ) or P3 2 21 ( D3 6 2 ). There is one screw threefold axis (c axis) and three twofold axes in the plane perpendicular to the threefold axis. The Fe 4+ ions substitute Si 4+ in three lattice sites, for which the projections of the principal z magnetic axes on the plane perpendicular to the c axis are rotated by 120° [16].

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Broadband EPR Spectroscopy of the Ground Electron State of…

Results and Discussion
Measurements in the submillimeter range revealed resonance transitions with zero-field splitting at 385.1, 394.7, 475.6, and 485.3 GHz. The absolute frequency measurement accuracy in the submillimeter spectrometer is ± 0.5 GHz, and the accuracy of determining the difference between two close frequencies is no worse than ± 0.1 GHz. The frequency-field dependences of resonance transitions when the magnetic field is oriented parallel to the z-axis of the paramagnetic centers are shown in Fig. 1.
In the crystal field of amethyst, the fine structure of the ground state of the Fe 4+ impurity ion with electron spin S = 2 consist of five singlets: one singlet state 0 and two quasi-doublets S z= ± 1 and S z= ± 2. The dependence of the energy of electron spin levels on the magnetic field can be described by the effective spin Hamiltonian Fig. 1 Frequency-field dependences of resonance transitions of Fe 4+ impurity ions in amethyst. Circles are experimental data, lines are theoretical ones. Magnetic field is parallel to z-axis of paramagnetic center. The numbers denote resonance transitions according to Fig. 2 where the first term corresponds to the Zeeman energy of the electron spin in an external magnetic field, and the subsequent terms determine the fine structure of the electron spin levels in an electric crystal field.
For the theoretical description of the frequency-field dependences of the EPR spectra, the specialized software package EasySpin was used [18]. The fitting was carried out assuming that the g-factor is isotropic, and the ground state is the quasidoublet S z= ± 2 [16]. The parameters obtained by fitting g x = g y = g z = 1.9864, B 0 2 =− 48.09 GHz, B 2 2 = 15.14 GHz, B 4 4 =− 0.215 GHz with the sign of B 2 2 does not affecting the values of the zero-field splitting. Lines in Fig. 1 present theoretical dependences calculated with above parameters of spin Hamiltonian Eq. (1). The structure of the electron spin levels obtained with these parameters is shown in Fig. 2. Arrows show the observed resonant transitions. The obtained values of the g-factor and zero-field splitting between the levels of the quasi-doublet S z= ± 2 Δ = 9.7 GHz are close to the corresponding values of g = 1.9876 and Δ = 10.17 GHz obtained in [16]. The energies of electron spin levels in zero magnetic field for quasi-doublets S z= ± 2, ± 1 and singlet Sz=0 are equal to ± 4.9 GHz, 435.2 ± 45.4 GHz and 584 GHz, respectively. Transitions between the levels of the ground quasi-doublet S z= ± 2 and the singlet Sz=0 were not observed, probably because magnetic dipole transitions between these spin states are forbidden by the selection rules.
The study of the orientational dependences of the spectra under rotation of the magnetic field in planes perpendicular to the threefold and twofold symmetry axes showed the presence of three magnetically nonequivalent centers. Figure 3 shows the orientation dependences of resonance transition 1 in Fig. 2 under rotation of the magnetic field in a plane perpendicular to the c axis.
The obtained dependences are very close to the dependence of the form.
where B extr is the minimum value of the resonance magnetic field in the extremum corresponding to the maximum value of the projection of the principal magnetic axis of the impurity center on the magnetic field direction, θ is the deviation of the magnetic field from the direction corresponding to the extremum. Such an axial dependence with the only principal magnetic axis z is a characteristic feature of isolated quasi-doublet of non-Kramers paramagnetic centers under conditions when the splitting between the quasi-doublet significantly exceeds the Zeeman energy of electron spin levels [19]. In this case, the principal magnetic axes lay in a plane perpendicular to the crystallographic c axis.
(2) B = B extr ∕cos , In ref. [16], it was assumed that the ground electronic state of the Fe 4+ ion in SiO 2 is a quasi-doublet ± 2, as it is shown in Fig. 2. To verify this assumption, we measured the temperature dependence of the intensity of resonance lines for the transition 5 in Fig. 2 between the levels of this quasi-doublet. The measurements were carried out in the Q-band at a frequency of 34.34 GHz. In the Q band, EPR spectra of impurity iron ions in amethyst contain a large number of resonance lines belonging to the Fe 3+ ion. To identify the lines belonging to the Fe 4+ ion, the orientation dependence of the spectra was recorded under the rotation of the sample around the twofold symmetry axis. The orientation dependence of the lines corresponding to the Fe 4+ ions was calculated and compared with the experimental spectra. The results of comparing are presented in Fig. 4.
It can be seen that there are two resonance transitions belonging to two magnetically nonequivalent Fe 4+ centers. The splitting of the lines is due to deviation of the axis of rotation from the crystallographic twofold axis of about 4°. The principal magnetic axes of these centers are deviated by 30° from the plane of rotation of the magnetic field. The z-axis of the third center is near perpendicular to the magnetic field, so there is no signal from the third center in the spectra.
The temperature dependence of the intensity of resonance lines was recorded for the line in the field of 344 mT, corresponding to the extreme value of the orientation dependence. Results are presented in Fig. 5. The experimental and calculated data were normalized to 1 at the minimum measurement temperature T = 5 K. The solid line is the calculation for an ion with spin S = 2 with the above parameters of the spin Hamiltonian. The dashed line is the calculation for the intra-doublet transition for the center with spin S = ½, when the population Fig. 4 Orientation dependences of the EPR spectra of the Fe ions in amethyst for the magnetic field lying in the (ac) plane. B || c at 70°. The microwave frequency is 34.34 GHz, T = 20 K. The dashed lines correspond to the Fe 4+ transitions calculated using the spin Hamiltonian Eq. (1) difference decreases in accordance with the Boltzmann distribution of the level populations. It can be seen that as the temperature increases from 5 K, the intensity of the Fe 4+ line decreases faster than it is for the spin S = ½. This is due to the fact that, as the temperature increases, the spin states S z= ± 1 and Sz=0 are populated, and population of the S z= ± 2 states decreases.

Conclusion
EPR spectroscopy in wide frequency range 34-500 GHz is used to determine fine structure of electron spin levels of the ground electron state of Fe 4+ impurity ion in a natural amethyst. It is established that the fine structure consists of five singlets, that can be represented as ground quasi-doublet S z= ± 2, quasi-doublet S z= ± 1 and singlet Sz=0 with zero-field energies ± 4.9 GHz, 435.2 ± 45.4 GHz and 584 GHz, respectively. Parameters of effective spin Hamiltonian describing dependences of electron spin levels on magnetic field are determined.