Magneto-optical properties of Cr 3+ in β-Ga 2 O 3

b -Ga 2 O 3 is a wide bandgap semiconductor that is attractive for various applications, including power electronics and transparent conductive electrodes. Its properties can be strongly affected by transition metal impurities commonly present during the growth such as Cr. In this Letter, we determine the electronic structure of Cr 3 þ by performing a correlative study of magneto-photoluminescence (magneto-PL) and electron paramagnetic resonance. We unambiguously prove that the so-called R 1 and R 2 PL lines at around 1.79eV originate from an internal transition between the ﬁrst excited state ( 2 E) and the 4 A 2 ground state of Cr 3 þ . The center is concluded to have monoclinic local symmetry and exhibits a large zero-ﬁeld splitting ( (cid:2) 147 l eV) of the ground state, which can be directly measured from the ﬁne structure of the R1 transition. Furthermore, g-values of the ﬁrst excited state are accurately determined as g a ¼ 1.7, g b ¼ 1.5, and g

b-Ga 2 O 3 is a newly emerging wide bandgap semiconductor with a bandgap energy of 4.7 eV at room temperature (RT), which has a higher figure of merit for power electronics than the commonly used GaN and SiC materials due to a higher breakdown field. 1,2urthermore, it has attracted considerable attention for applications such as transparent conductive electrodes, solar-blind UV photodetectors, 3,4 gas sensors, 5,6 and photoelectrochemical water splitting. 7,8arge b-Ga 2 O 3 bulk crystals can be manufactured with a high quality and a reasonable price by melt growth techniques, which is a prerequisite for the fabrication of industrial scale high-performance power devices and other applications.For all device applications, it is a necessity to have a reliable control over electrical and optical properties of the material.Though this can be achieved by controlled doping during the growth, doping efficiency is often strongly affected by unintentional doping caused by contaminants in the starting material.][11][12][13][14][15] Moreover, these transition-metal impurities can be used as intentional dopants required to compensate for intrinsic n-type doping and achieve a semi-insulating material.Under proper doping conditions, they may also induce ferromagnetism in b-Ga 2 O 3 , 16 promising for spintronic applications.Therefore, it is of crucial importance to identify the electronic structure of these impurities that can lead to a better understanding and prediction of their effects on electrical and optical properties of the material.It is also useful to obtain a reliable and straightforward spectroscopic signature of a specific transition-metal impurity that can be used for its easy identification using standard characterization techniques, e.g., photoluminescence (PL) spectroscopy.
One of the common transition-metal impurities in b-Ga 2 O 3 is Cr. 17,18Previous electron paramagnetic resonance (EPR) studies [19][20][21] have provided spin-Hamiltonian parameters of the ground state of Cr in the 3þ charge state (Cr 3þ ), though the sign of the zero-fieldsplitting (ZFS) parameters is still uncertain and differs between the reports.Early studies were also conducted to obtain the optical signature of Cr 3þ .2][33] They were further supported by the analysis of higher-lying excited states detected in absorption 19,28 and emission 18,22,[24][25][26][27][28] spectra of Cr-doped b-Ga 2 O 3 , as well as photoluminescence excitation spectra of the R lines 24,26,28 using the Tanabe-Sugano diagrams. 34Very slow time decay of this emission [of the order of several ms at T < 50 K (Refs.19, 24-26, and 28)] indicated that it is a result of spin and parity-forbidden optical transitions.Another argument for the assignment of the R-lines to Cr was based on the observed increase in the R-lines intensity in Cr doped Ga 2 O 3 . 19,22,24,28,29Though reasonable, the later argument alone could not be considered as an unambiguous proof of the emission origin, since a change in the dopant concentration is well known to affect the Fermi level position in the sample and can also facilitate charge transfer between dopants and residual contaminants.For example, the same emission was also attributed to the 4 T 1 ! 6A 1 intracenter transition of Fe 3þ , since the dramatic enhancement of the emission intensity was observed upon Fe doping. 35o determine the exact electronic states and thereby definitely identify the chemical origin of the transition-metal impurity responsible for the R-line emissions in b-Ga 2 O 3 , it is essential to resolve and determine the spin degeneracy of both excited and ground states.In this work, we carry out a detailed study by combining EPR spectroscopy, which can determine the spin states of the ground state, with magneto-PL that is sensitive to both excited and ground states.Based on the observed splitting of the R1 emission in an applied magnetic field, we unambiguously show that the R-lines originate from the internal 2 E ! 4 A 2 transitions of the Cr 3þ center that has a monoclinic local symmetry.We obtain accurate spin-Hamiltonian parameters of its ground state ( 4 A 2 ) as well as previously unknown g-values of the first excited state ( 2 E).
We used commercially available undoped b-Ga 2 O 3 bulk crystals from Tamura and undoped b-Ga 2 O 3 bulk crystals grown by the Czochralski method. 36,37Crystallographic axes of the samples were determined by x-ray diffraction analysis.For magneto-PL experiments, the samples were placed inside a cryostat equipped with a superconducting magnet, operating between 0 and 5 T. The sample temperature could be varied between 7 K and RT.The measurements were performed in the backscattering geometry, so that the magnetic field was parallel to the light excitation and collection axis.A solidstate 532-nm laser was used as an excitation source.The laser light was focused on the sample surface using a 50Â (NA ¼ 0.5) objective lens, which was also used to collect PL.The PL was dispersed through a single-grating monochromator and detected using a Si charge coupled device.EPR experiments were performed in the dark using a Bruker E500 EPR spectrometer equipped with an X-band resonator and a He-gas flow cryostat for measurements with adjustable temperatures ranging between 5 and 300 K.
To evaluate unintentional doping of the investigated samples, we first performed EPR measurements.Figures 1(a) and 1(d) depict EPR spectra measured at 6 K with an applied magnetic field B parallel to the crystallographic b-axis, when the sample was mounted with the rotation axis perpendicular to the (ab) and (bc Ã ) planes, respectively.EPR spectra obtained under B k a and B k c Ã are shown in Figs.1(c) and 1(f), respectively.c Ã denotes a complementary axis that is orthogonal to the a and b axes.In addition to the previously observed signals from Co 2þ with a 3d 7 ground state and an effective electron spin S eff ¼ 1/2 13 and a shallow donor (SD), [38][39][40] all spectra contain a highly anisotropic signal consisting of two lines located at 130 and 1315 mT when B k b.Spin-Hamiltonian parameters of this signal can be obtained from angular dependent EPR measurements.Results of these measurements are summarized in Figs.1(b) and 1(e), where the measured peak positions (the open symbols) are shown as a function of the angle h between B and the a-axis for rotations in the (ab) plane and the c Ã -axis for rotations in the (bc Ã ) plane as indicated in the inset.We analyze these data using the following spin-Hamiltonian: Here, the first term is the electron Zeeman term with g being the electron g-tensor and l B being the Bohr magneton.To describe ZFS in the monoclinic crystal structure in an easier manner, we use the extended Stevens operators in the form of O q k with the ZFS parameters B q k : 41 The ZFS is then described by the sum of an orthorhombic component ) and a monoclinic component (B   spin Hamiltonian to the experimental data using the Easyspin software package, 42 we extract the full set of spin-Hamiltonian parameters given in Table I.The simulated angular dependencies are shown by the solid lines in Figs.1(b) and 1(e) and are in excellent agreement with the experimental data.The extracted parameters are typical [19][20][21]41 for a Cr 3þ ion with the 3d 3 electron configuration (S ¼ 3/2) that substitutes for a Ga 3þ ion likely at an octahedral Ga II site with a trigonal distortion. We ote that in the literature, the ZFS sign is uncertain and differs among reports.We accurately determine the sign from magneto-PL measurements, as will be described below.The simultaneous presence of the SD and Cr 3þ EPR signals in the dark indicates that Cr is present in the 3þ charge state even in n-type Ga 2 O 3 .The EPR experiments clearly prove trace contamination by Cr of the investigated samples with a concentration of approximately 10 17 cm À3 .Due to the low concentration, we could not detect any sign of the ferromagnetic interaction by EPR as predicted by Ichihashi et al. 16 Popa et al. 43 observe visible signs of the ferromagnetic interaction by EPR only with a Cr concentration of at least 3%.Another transition-metal impurity, which could also be detected by EPR in some of our samples, is Fe 3þ in the 3d 5 configuration with S ¼ 5/2 (not present in the sample shown in Fig. 1).
We now analyze optical properties of the investigated samples.Under the 532-nm excitation, all of them show bright R-line emissions commonly observed in b-Ga 2 O 3 18,19,22-30 -see Fig. 2(a).Both the R 1 and R 2 lines are observed at 300 K, whereas only the R 1 transition can be detected at 5 K.This suggests that the R 2 transition stems from a higher-lying excited state of a transition metal, consistent with previous studies. 19,23,25At 5 K, the R 1 line has a very narrow linewidth with a full width at half maximum (FWHM) of around 88 leV.26]28 The narrow linewidth has enabled us to uncover that the R 1 line, in fact, contains two components split by 147 leV at zero magnetic fields, as shown in Figs.2(b)-2(d).Since no thermalization between these components is observed in PL, the detected ZFS must occur in the ground state.We note that the observation of this splitting, which was not resolved previously, allows us to accurately measure the ZFS energy of the ground state without relying on any fitting procedure.Application of an external magnetic field B causes further splitting of the R 1 doublet into eight components labeled as 1-8, on the order of increasing energy.This can be seen from Figs. 2(b)-2(d), which depict evolution of magneto-PL spectra with increasing B that were measured at 5 K with B k a (b), B k b (d), and B k c Ã (c).In order to determine whether the magnetic-field induced splitting occurs in the ground or excited state, temperature-dependent PL measurements were performed at B ¼ 5 T. The results of such measurements for B k a are shown in the inset of Fig. 2(e).We also plot the difference between the PL spectra obtained at 5 and 20 K, for more clarity.It is found that four transitions (labeled as 2, 4, 6, and 8) gain intensity at elevated temperatures, which clearly proves that they stem from the same, higher-lying spin sublevel of the excited state, which becomes thermally populated.The observation of two groups of four lines also shows that: (i) the excited state of the transition metal ion involved in the R1 transition is twofold spin degenerate with the electron spin S ¼ 1/2; and (ii) the ground state is fourfold degenerate with S ¼ 3/2.We can then extract the energy difference DE of the two spin sublevels of the excited state, i.e., the Zeeman splitting, which is plotted in Fig. 2(e) as a function of B. Linear dependencies of DE(B) are observed for all three orientations of the applied magnetic field relative to the crystallographic axes.By fitting them with the Zeeman splitting term DE ¼ l B BgS with S ¼ 1/2, the g-values of the excited state can be deduced as g a ¼ 1.  1) using the spin-Hamiltonian parameters that were obtained from the EPR experiments (see Table I).The simulation results are shown in Fig. 3 by the solid lines and are in excellent agreement with the experiment.This unambiguously proves that Cr 3þ is the origin of the R-lines commonly observed in absorption and emission spectra of b-Ga 2 O 3 .Furthermore, careful inspection of the data at high magnetic fields B > 3 T shows that the equidistant splitting between four spin sublevels of the ground state is observed only when B k a [Fig.3(a)].On the other hand, it is the largest for two lowest sublevels when B k b-see Fig. 3(b) and for the two upmost sublevels when B k c Ãsee Fig. 3(c).Such behavior can only be modeled assuming that the ZFS parameters have a positive sign.
In Fig. 4, we summarize the obtained results by using the following energy level diagram of the intracenter transitions responsible for the R lines.In a cubic lattice, substitutional Cr 3þ ions in a 3d 3 1) and the parameters obtained from the EPR measurements (given in Table I).
configuration have the fourfold degenerate ground state 4 A 2 and the fourfold degenerate first excited state 2 E. In b-Ga 2 O 3 with monoclinic symmetry, both ground and excited states exhibit zero field splittings due to combined effects of the monoclinic crystal field, spin-orbit, and spin-spin interactions.The R-lines are related to the 2 E ! 4 A 2 transitions, as suggested previously but are only proved in the present study.The 18.6 meV splitting between the R1 and R2 transitions defines the splitting between the two Kramers' doublets forming the 2 E state.The 4 A 2 state also splits into two doublets, and the related ZFS energy (d) can be directly measured from the fine structure of the R1 emission resolved at low temperatures-see Fig. 2. The d value of 147 leV measured by PL is in excellent agreement with 148 leV deduced from the EPR analysis.The suggested spin degeneracy of the involved states is directly confirmed by the magneto-PL data.Under an external magnetic field, the lower-lying doublet of the 2 E excited state splits into two spin sublevels, whereas the 4 A 2 ground state splits into four sublevels-see Fig. 4.This gives rise to eight components of the R1 emission that are labeled in Fig. 4 by the vertical red arrows according to the labeling used in the inset of Fig. 2(e).
In conclusion, by using magneto-PL spectroscopy combined with EPR measurements, we have identified the electronic structure and the spin configuration of the Cr 3þ ion in b-Ga 2 O 3 .We provided unambiguously evidence that the intracenter transitions between the 2 E excited state and the 4 A 2 ground state of Cr 3þ are responsible for the R 1 and R 2 PL lines at around 1.79 eV commonly seen in b-Ga 2 O 3 , based on the identical spin-Hamiltonian parameters of the ground state involved in the R1 emission measured by both techniques.The Cr 3þ center is concluded to have monoclinic local symmetry and exhibits a large ZFS of $147 leV in the ground state, which can be directly measured from the splitting of the R1 transition at low temperatures.Furthermore, the spin-Hamiltonian parameters of the ground state and the lowest-lying excited state are accurately determined.Our results have, therefore, contributed to a better understanding of the electronic structure of Cr in b-Ga 2 O 3 .Under an applied magnetic field (B 6 ¼ 0), both the ground and excited states further split due to the removal of their spin degeneracy.Therefore, a maximum of eight optical transitions can be observed for the R1 emission.They are labeled as 1-8 corresponding to that used in the magneto-PL data.The spin sublevels of the ground state are indicated by a magnetic quantum number m s , representing the corresponding spin state under a high-field condition for simplicity.

FIG. 1 .
FIG. 1. EPR spectra from bulk b-Ga 2 O 3 with an applied magnetic field B parallel to the crystallographic b-axis [(a) and (d)], a-axis (c), and c Ã -axis (f).(b) and (e) depict angular dependence of the Cr 3þ EPR signal when the magnetic field is rotated in the (ab) plane and the (bc Ã ) plane, respectively.The experimental data are shown by the open circles, while the simulation results using the spin-Hamiltonian in Eq. (1) are depicted by the solid lines.All measurements were done at 6 K.The signals marked by (Ã) originate from an empty microwave cavity, unrelated to the sample.

FIG. 2 .
FIG. 2. (a) Representative PL spectra from the investigated b-Ga 2 O 3 crystals measured at 7 and 300 K. Magneto-PL spectra measured at 5 K under an applied magnetic field (varying from 0 to 5 T) parallel to the crystallographic a-axis (b), b-axis (d), and c Ã -axis (c).(e) Energy difference DE between the two spin sublevels of the first excited state, i.e., the Zeeman splitting, as a function of B. The inset in (e) shows the PL spectra measured at 5 and 20 K at 5 T with B || a.The transitions are labeled as 1-8 in the order of increasing energy.
7, g b ¼ 1.5, and g c Ã ¼ 2.1.Knowing the g-values of the excited state, fan diagrams of the ground state can be obtained.The corresponding results for B k a, B k b, and B k c Ã are shown by the open symbols in Figs.3(a), 3(b), and 3(c), respectively.The experimental data can be fitted in Eq. ( electron

FIG. 3 .
FIG. 3. Energy level splitting of the Cr 3þ ground state with an applied magnetic field along the crystallographic a-axis (a), b-axis (b), and c Ã -axis (c).The open circles are the experimental data from the magneto-PL experiments.The solid lines are simulation results using Eq.(1) and the parameters obtained from the EPR measurements (given in TableI).

FIG. 4 .
FIG. 4. Electronic structure and spin configuration of Cr 3þ in b-Ga 2 O 3 with and without an applied magnetic field B. The solid red and orange arrows labeled as R1 and R2, respectively, indicate the optical transitions from the two Kramers' doublets of the 2 E state to the 4 A 2 ground state at B ¼ 0. The 4 A 2 ground state also experiences ZFS, indicated by d, which gives rise to the fine structure of the R-lines.Under an applied magnetic field (B 6 ¼ 0), both the ground and excited states further split due to the removal of their spin degeneracy.Therefore, a maximum of eight optical transitions can be observed for the R1 emission.They are labeled as 1-8 corresponding to that used in the magneto-PL data.The spin sublevels of the ground state are indicated by a magnetic quantum number m s , representing the corresponding spin state under a high-field condition for simplicity.

TABLE I .
Summary of the spin-Hamiltonian parameters of Cr 3þ in b-Ga 2 O 3 responsible for the R 1 emission.