Magnetism and optical properties of Yb3Al5O12 hosted Er3+ – experiment and theory

Article abstract of DOI:10.1016/j.jallcom.2019.151903

Using the recently developed method based on a combination of DFT plane wave code applied to extract the crystal field parameters and a local atomic like Hamiltonian involving electron-electron, spin-orbit and Zeeman terms we calculated the energy levels of ground and excited multiplets of Yb³⁺ and Er³⁺ ions hosted in ytterbium and yttrium aluminum garnet (YbAG and YAG) including their crystal and magnetic field splitting. The obtained energy levels and derived magnetic properties are compared with the experimental data from magnetometry, photoluminiscence and near-infrared spectroscopy.

Full text of DOI:10.1016/j.jallcom.2019.151903

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Journal of Alloys and Compounds 810 (2019) 151903
Contents lists available at ScienceDirect
Journal of Alloys and Compounds
journal homepage: http://www.elsevier.com/locate/jalcom
Magnetism and optical properties of Yb3Al5O12 hosted
Er3þ e experiment and theory
,
*
ꢀ a
David Sedmidubský a , Vít Jakes , Katerina Rubesova , Pavla Nekvindova ,
ꢀ
ꢀ
ꢁ a
ꢁ a
a
b
c
ꢁꢀ
ꢁ
ꢁ
Tomas Hlasek , Roman Yatskiv , Pavel Novak
Department of Inorganic Chemistry, University of Chemistry and Technology, Technicka 5, Prague6, 16628, Czech Republic
Institute of Photonics and Electronics, Czech Academy of Sciences, Chaberska 57, Prague 8, 182 51, Czech Republic
Institute of Physics, Czech Academy of Sciences, Cukrovarnicka 10, Prague 6, 162 00, Czech Republic
a
ꢁ
b
c
ꢁ
ꢁ
a r t i c l e i n f o
a b s t r a c t
Article history:
Using the recently developed method based on a combination of DFT plane wave code applied to extract
the crystal field parameters and a local atomic like Hamiltonian involving electron-electron, spin-orbit
and Zeeman terms we calculated the energy levels of ground and excited multiplets of Yb3þ and Er3þ
ions hosted in ytterbium and yttrium aluminum garnet (YbAG and YAG) including their crystal and
magnetic field splitting. The obtained energy levels and derived magnetic properties are compared with
the experimental data from magnetometry, photoluminiscence and near-infrared spectroscopy.
© 2019 Elsevier B.V. All rights reserved.
Received 30 May 2019
Received in revised form
10 August 2019
Accepted 15 August 2019
Available online 20 August 2019
Keywords:
Ytterbium-aluminium garnet
Erbium doping
Crystal field parameters
Luminiscence
Magnetism
1. Introduction
commonly, with co-dopant ions. In oxide matrices, co-doping with
Yb3þ ions is mostly used [6]; after the excitation of an Yb3þ ion
Er3þ ions with a 4 f 11 valence electron configuration and a
multiplet structure arising from electron-electron correlations,
spin-orbit coupling and crystal field effects can produce a wide
range of radiative electron transitions that are utilized in many
applications. Doped in either halide or oxide hosts, the violet, blue,
green and red up-conversions of Er3þ are employed in color dis-
plays, visible lasers and solar cell converters, as well as in bio-
imaging and sensor technologies [1e3]. The short-wavelength IR
emission (1530 nm) matches the wavelength used in the so-called
3rd telecommunication window. Thus, Er-doped oxides are used as
active elements, such as amplifiers or switchers, in optical net-
works [4]. In the case of materials highly doped with erbium (over
50%), the 2940 nm emission finds its application as a laser in
medicine or cosmetics [5].
(ð F7=2/2F5=2Þ energy transition ~980 nm), an energy transfer
2
4
occurs to the I11=2 exited level of erbium. For a successful sensi-
tization, erbium and ytterbium ions should be homogeneously
distributed at appropriate distances. Such a demand is fully met in
ytterbium-based oxide matrices; for example, in the Yb3Al5O12
garnet or YbAlO3 perovskite. Er:Yb3Al5O12, which has been mainly
studied in terms of up-conversion or optically active wave guiding
in the NIR range, can provide an orderly arranged crystal vicinity of
erbium. This is crucial for the effective fine split emission of erbium
with a narrow peak half-width and has been achieved not only in
single crystals [7], but also in samples prepared by sol-gel methods
or liquid phase epitaxy (LPE), LPE layers being moreover multi-
mode planar waveguides [8e12].
The garnet structure generally belongs to the most utilized ox-
ide materials in optics. It possesses a cubic structure (space group
Ia3d) in which three crystallographic sites are available [13]. When
erbium is doped into this structure it enters a dodecahedral crystal
site originally occupied by a trivalent ion with a large ionic radius
(e.g. Y in Y3Al5O12 (YAG), Yb in Yb3Al5O12 (YbAG) or Gd in
Gd3Ga5O12 (GGG)), whereas smaller cations (i.e. Al3þ, Ga3þ, Fe3þ
etc.) occupy tetrahedral and octahedral sites. The Stark fine
However, the low absorption cross-section of erbium ions can
limit its applicability in many cases. This problem can be overcome
by sensitization with induced oxygen vacancies or, more
* Corresponding author.
E-mail address: sedmidub@vscht.cz (D. Sedmidubský).
https://doi.org/10.1016/j.jallcom.2019.151903
0925-8388/© 2019 Elsevier B.V. All rights reserved.

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D. Sedmidubský et al. / Journal of Alloys and Compounds 810 (2019) 151903
splitting of Er3þ in the crystal field of a garnet lattice has been
described for several garnet compositions. Gruber et al. [14] re-
ported on Er3þ energy levels in Er:YAG as well as on the influence of
the substitution of Al3þ ions by Sc3þ or Ga3þ. Kazskan et al. [7]
compared Er:YAG splitting with that of Er:YbAG. However, both
articles are mainly focused on experiments in the visible region
utilizing the up-conversion mechanism of photoluminescence.
To enlarge the applicability of Er3þ doped garnet structures in
magneto-optical devices or in tunable optical elements, it is
important to study the electronic state changes of paramagnetic
Er3þ in the presence of an external magnetic field. Magnetically
induced Zeeman splitting can influence the emission wavelength as
well as the life time, the latter through the remaining population in
the excited states. While the Zeeman splitting of Er3þ has been
examined in several halide and oxide systems [15e17], for the
erbium ion doped in a garnet structure, only one study has been
published, describing Er3þ/Yb3þ behavior in a gadolinium gallium
iron garnet [18].
temperature with Bruker-AXS D2 Phaser powder diffractometer
with parafocusing Bragg-Brentano geometry using CoKa radiation
in the range 10e100+
2Q
with a step size of 0.02+. The phase
analysis was performed in the HighScore Plus program (PAN-
alytical) using the PDF-4 database confirming the pure garnet
phase (space group Ia3d) without any impurities. The lattice pa-
rameters were refined after the XRD pattern (see Fig. S1 in the
Supporting Information, SI) was fitted using the Pawley profile
function. Due to a slightly larger ionic radius of Er3þ compared to
Yb3þ resulting from lanthanide contraction the lattice parameter of
the Er-doped sample was 11.938(0) Å in contrast to the cell
parameter of the un-doped host Yb3Al5O12 which was 11.9310 Å.
The emission and up-conversion photoluminescence (PL)
spectra were measured with the set-up comprising a 980 nm
infrared diode laser (MDLeIIIe980L) or Ar laser (514 nm) as an
excitation source, grating monochromator Jobin Yvon THR 1000, a
closed cycle He optical cryostat, and a GaAs photomultiplier (R943-
02, Hamamatsu) or liquid nitrogen cooled high-purity Ge photo-
diode (EI-L, Edinburg Instruments) detection system. Calibrated
neutral-density filters were used to tune the excitation power
density.
The magnetic properties were measured with the Physical
Property Measurement System (PPMS) EverCool-II (Quantum
Design, USA) using the Vibrating Sample Magnetometry (VSM)
option. They comprised the measurement of the isothermal
magnetization curve up to H ¼ 70 kOe at T ¼ 5 K and the tempera-
ture dependence of magnetic susceptibility under the applied field
H ¼ 1 kOe.
In this study, we focused on the Er3þ substituted ytterbium
aluminium garnet. We use a newly developed method that allows
to calculate the crystal field parameters (CFP) and magnetism of the
rare-earth (RE) ions in crystals. This method has been applied to
many insulating compounds [19e23] and, recently also to RE in-
termetallics [24,25]. In the present paper we apply it to Yb3þ and
Er3þ ions in YbAG as a hosting material and we also report new
calculation for these ions in YAG. In order to confront our calcula-
tions with experiment, a polycrystalline sample was prepared by a
sol-gel method. Erbium was substituted in a concentration of 2 mol
% referred to a single Yb site e a concentration that was previously
optimized [8,9]. Photoluminescence properties were measured af-
ter excitation by 514 and 980 nm lasers e both NIR emission and
also up-conversion were collected. Low-temperature photo-
luminescence (down to 4 K) in a range of 1440e1650 nm was
measured to identify the “pure electron”and phonon-based tran-
2.3. DFT and atomic Hamiltonian calculations
The band structure calculations were performed using an all-
electron full potential code for periodic solids as implemented in
the WIEN2k package [26]. The augmented plane waves þ local
orbital basis set (~7700 basis functions corresponding to RKmax
parameter 6.5) and the generalized gradient approximation for
exchange correlation functional [27] were applied. Since our main
concern was to extract the crystal field parameters, the calculations
were performed in the first step as non-spin polarized with RE- 4f
states included in the core. The unit cell in our calculations con-
sisted of 80 atoms with the atomic (muffin tin) radii of RE and Y, Al
and O 2.3, 1.7 and 1.55, respectively. The eigenvalue problem was
solved self-consistently at five points of the irreducible Brillouin
zone until the charge convergence 0.0001 e was reached.
sitions between I13=2 and I15=2 energy of Er3þ. The temperature
dependence of magnetic susceptibility and magnetization curves
were measured, too.
4
4
2. Materials and methods
2.1. Sample synthesis
The Er-doped ytterbium-aluminium garnet with a stoichiom-
etry of Yb2.94Er0.06Al5O12 e i.e. 2% of ytterbium substituted by
erbium e was prepared starting from a precursor synthesized by a
sol-gel polyesterification process based on the Pechini patent. As a
source of cations, AlCl,36H2O (p.a., Honeywell), Yb(CH3COO)3$x
H2O (99.9%, Strem Chemicals) and Er(CH3COO)3$x H2O (99.9%,
Strem Chemicals) were used. The acetates were dehydrated by
heating at 200+C for 12 h prior their use. Aluminium trichloride was
dissolved in water to a concentration of ~10 g of Al per L (the actual
concentration was determined gravimetrically). First, citric acid
(p.a., Lach-Ner) was dissolved in the aqueous solution of Al3þ and
then ytterbium and erbium acetates were added to the solution and
stirred until complete dissolution. Ethylene glycol (p.a., Penta) was
added afterwards and the mixture was magnetically stirred for
30 min. Water was evaporated at 85+C and then the temperature of
the mixture was elevated to 130+C to start a polyesterification
process. Amorphous gel was then dried for 2 h at 240+C and
decomposed at 600+C (2 h) and 900+C (1.5 h). The precursor was
pressed into bars and sintered in air at 1000+C for 96 h.
In the second step, the eigenvalue problem was solved in a
single run using WIEN2k (LAPW1 program) with RE- 4f states
considered as valence states, all semi-core states left out and O-2s;
2p states shifted downwards by an energy parameter
D by applying
an orbital dependent potential. This single empirical parameter
controls the RE-4f e O-2p; 2s hybridization.
Next the wave functions in plane-wave representation were
transformed into Wannier functions by means of Wien2wannier
[28] and Wannier90 [29] programs and the crystal field parameters
were extracted from the Wannier transformed local Hamiltonian
k
b
b
Hloc by expanding it into a series of spherical tensor operators Cq
k
X
X
k
k
b
b
Hloc
¼
BqCq
(1)
kꢀ2;4;6 q¼ꢀk
The crystal field parameters Bkq were then transferred into a
modified Lanthanide package [30] to solve the eigenvalue problem
of the atomic Hamiltonian involving electron repulsion, spin-orbit,
crystal field and Zeeman terms. The results provide the multiplet
splitting by the crystal and magnetic field.
2.2. Characterization techniques
The X-ray diffraction (XRD) data were collected at room

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3
Table 1
2.4. Magnetic properties calculation
Crystal field parameters Bqk (in meV) of Yb3þ
(
D
¼ 5.7 eV) and for Er3þ
(
D
¼ 8.2 eV) in
YbAG and YAG. The parameters refer to dodecahedral site with the local coordinate
Magnetic properties can be calculated from the dependence of
eigenenergies εi on the external magnetic field using the quadratic
regression [21]. However, this approach runs into difficulties when
the εiðBÞ dependence is strongly nonlinear or when the eigenvalues
intersect with varying magnetic filed. We thus prefer a different
approach based on solving the eigenvalue problem for a dense
mesh of magnetic fields and calculating the free energy using the
Boltzmann statistics. The magnetic moment and the susceptibility
are then determined from the first and second derivative of the free
energy.
system axes parallel to [1e10], [1 1 0] and [0 0 1] directions.
k q
Yb:YbAG
Er:YbAG
Yb:YAG
Er:YAG
2 0
2 2
4 0
4 2
4 4
6 0
6 2
6 4
6 6
88.7
7.7
72.7
2.9
56.9
73.4
ꢀ6.1
ꢀ2.4
ꢀ15.6
139.8
ꢀ76.0
ꢀ122.2
49.7
ꢀ18.6
175.3
ꢀ86.9
ꢀ175.0
71.4
ꢀ17.8
144.9
ꢀ72.8
ꢀ132.9
57.4
0.0
159.5
ꢀ90.8
ꢀ163.9
64.5
69.5
60.9
70.4
69.3
53.7
45.3
55.9
48.2
In polycrystals, averaging over all possible directions of mag-
netic field is necessary. This is simple for the susceptibility, which
transforms as a tensor and the average susceptibility cav is given as
reduction of
z in YAG compared to LaF3 is consistent with higher
covalency of 4f electrons in oxides than in fluorides.
cav ¼ ðca
þ
cb
þ
ccÞ=3
(2)
As shown in Fig. 1, the ground state multiplet of Yb3þ-2F7=2 is
split into four Kramers doublets and separated by spin-orbit
where the a, b and c axes are parallel with ½110ꢁ, ½110ꢁ and ½001ꢁ
directions, respectively [21]. For the magnetic moment we take use
of the fact that its principal axes coincide with the axes a; b; c and its
magnitude in a general direction ðw ; w ; w Þ is then
2
coupling energy ~1.2 eV from the first excited state F5/2 (split
into 3 Kramers doublets). The excitation spectrum of Er3þ (Fig. 2) is
more complex. The ground term 4I is split by spin-orbit interaction
into four multiplets (with 4I15=2 ground multiplet) that are further
split by the crystal field into the corresponding Kramers doublets.
In Fig. 2 energies of the Er3þ-4F15=2 multiplet in YAG and YbAG
a
c
b
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
mðw ; w ; w Þ ¼ w2m2a þ w2m2 þ w2m2
(3)
a
c
b
a
c
c
b
b
calculated for
D
¼ 8.1 eV are displayed together with the experi-
To obtain average magnetic moment we evaluated the integral
over the azimuthal and spherical angles w and 4
mental data for Er:YAG of Gruber et al. [14] and with the results of
Burdick et al. [32] obtained by the least squares analysis of the
Gruber's data. The agreement of calculation and experiment is
good, similar to that obtained by Burdick et al.. Note that the 7th
state was not detected in the experiment.
p
2
p
ð
ð
1
mav
¼
sinw mðw; 4Þdwd4
(4)
4p
0
0
The emission spectra of Yb2.94Er0.06Al5O12 in the NIR region
measured at different power and energy excitation using IR laser
(980 nm) are shown in Fig. 3a. The broad emission band in a range
of 1450e1680 nm can be attributed to the 4I13/2 / 4I15/2 transition.
Due to the splitting of RE ions Stark levels in a crystalline host, the
broadband emission is split into many components. The compari-
son of the NIR spectrum with the calculated transitions (taking into
account all possible combinations between the split levels of 4I13=2
where w ¼ cos4sinw, wb ¼ sin4sinw and w ¼ cosw.
a
c
3. Results and discussion
As mentioned in the experimental part, we used the previously
optimized composition with 2 mol% of Er3þ substituting Yb3þ in
YbAG as a material which has been synthesized and further char-
acterized. However, a higher Er3þ content of 8.3 mol% corre-
sponding to the composition Yb2.75Er0.25Al5O12 was considered in
4
and I15=2 multiplets, i.e. without considering the transition in-
tensities based on Judd-Ofelt theory) revealed a good agreement for
the bands centered at 1770 and 1530 nm but a relatively poor
congruence for 1575 and 1625 bands. The latter two bands origi-
nate from transitions to upper four Stark levels of the ground state
4I15=2 multiplet where a slightly greater difference is observed
our DFT calculatios. The solid solution was simulated by a pseu-
pffiffiffi
dotetragonal supercell (at
¼
2ac, ct ¼ ac, orthorhombic space
group F222, four formula units per primitive unit cell) with a single
position occupied by Er3þ. The same structure model was also
adopted for pure YbAG and Er:YAG. The atomic position around the
Er3þ were relaxed to minimize the forces acting on the individual
atoms.
The parameter
D controlling the hybridization with oxygen
valence states was fixed to
D
¼ 5:7 eV and
D
¼ 8:1 eV for Yb3þ and
Er3þ, respectively, by minimizing the mean square root deviation
s
of the calculated energies from experiment [14,31] (see Fig. S2 in
SI). The obtained parameters Bkq defined by Eq. (1) are plotted as a
function of
D in Fig. S3 in SI and, for the selected values of D,
compiled in Table 1 for both YbAG and YAG hosts. These were than
transferred into the modified Lanthanide code to get the multiplet
energy levels.
Nineteen atomic Hamiltonian parameters of Er3þ ion were taken
from the analysis of Er3þ energy levels in YAG by Burdick et al. [32].
For the Yb3þ ion only the spin-orbit coupling constant
z
is used in
local atomic Hamiltonian. Its value was assessed from the differ-
2
2
ence of the gravicentres of ground F7=2 and excited F5=2 multi-
plets. This approach yielded slightly lower value,
than the one used by Mihokova et al. [21],
mined from Yb:LaF3 optical spectra [33]. Let us note that the
z
¼ 2895.3 cm1
Fig. 1. Energy levels of Yb3þ ion in YbAG and YAG obtained for the hybridization
ꢁ
ꢁ
z
¼ 2928 cm1 as deter-
parameter
D
¼ 5.7 eV.

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D. Sedmidubský et al. / Journal of Alloys and Compounds 810 (2019) 151903
Fig. 2. Energy levels of Er3þ ion in YbAG and YAG obtained for the hybridization
parameter
D
¼ 8.1 eV. The experimental values for Er:YAG extracted from optical
spectra [14] as well as the results from their least squares fit [32] are also displayed for
a comparison.
between our ab-initio and Burdick's et al. [32] fitted data (see
Fig. 2). The origin of this discrepancy may not be just in the crystal
field parameters themselves, but also in the interplay with other
parameters of the atomic Hamiltonian such as electrostatic, spin-
orbit and many-body interaction terms adopted from Ref. [32].
The IR laser excites the 4I11=2 level of Er3þ mainly by the energy
transfer from Yb3þ and additionally by the Er3þ ground state ab-
sorption itself. The emission spectra recorded under the excitation
by green laser (540 nm) are shown for comparison in Fig. S3a in SI.
In this case Er3þ is first brought to the 2H11=2 energy level which is
quickly de-excited (radiatively or non-radiatively) reaching the
4I13=2 state. The radiative transition to the ground state generates a
broad NIR emission. The emission spectra for both excitation en-
ergies demonstrate identical structure and power dependence but
slightly higher emission intensity under the IR laser excitation.
The luminescence was measured at temperature decreasing
down to 4.4 K (see the spectrum in Fig. 3b recorded under 980 nm
and 0.4 mW). For the bands in the region 1510e1550 nm (band C)
and 1610e1690 nm (band D) only a small variation in integrated
absolute photoluminescence intensity (not exceeding 10%) was
observed. This is due to the electron transition being unaffected by
thermal vibrations [18]. On the other hand, the integrated absolute
photoluminescence intensity for bands in region 1440e1500 nm
(band A) and 1560e1590 nm (band B) shows negative thermal
quenching and is suppressed with the decreasing temperature
down to a full dissipation, as manifested on the temperature
dependence of integrated PL intensity in Fig. 3c. Transitions in these
regions probably arise from Stark levels populated by electrons
excited by lattice thermal vibrations. However, the effect may be
more complex. When we measured the thermal dependence of
luminescence intensity using a laser with a higher output (10 mW
instead of 0.4 mW), the decrease of PL intensity in the above
mentioned regions was not so strong (Fig. S3b in SI). Let us note
that the observed temperature induced suppression corresponds to
Fig. 3. NIR PL emission spectra of Yb2.94Er0.06Al5O12 under 980 nm. (a) Laser power
dependence at room temperature, calculated transitions are depicted in cyan; (b)
Temperature dependence for laser power 0.4 mW; (c) Dependence of the integrated
absolute PL intensity on the temperature. (For interpretation of the references to color
in this figure legend, the reader is referred to the Web version of this article.)
the transitions from the upper two and the lower two doublets of
4
4I13=2 into four lowest doublets of I15=2
.
The up-conversion (UC) emission spectra of Yb2.94Er0.06Al5O12
are presented in Fig. 4a and compared with Er:LiNbO3. The green
emission at 530 and 550 nm can be attributed to the 2H11=2/4I15=2
980 nm is shown in SI, Fig. S4(i). The two-photon process to
populate the green and red UC emission has been previously dis-
cussed in detail [34] and can be explained as follows: the F7=2
4
4
and S3=2/4I15=2 transition, whereas the red emissions at 660
and 820 nm refer to the 4F9=2/4I15=2 and 4I9=2/4I15=2 transition,
respectively.
manifold is populated by combined ground state (GSA) and excited
4
state absorption (ESA) via the I11=2 state. The observed emission
bands at 530, 550, 660 and 820 nm result from multi-phonon
The UC emission mechanism of Er:LiNbO3 crystals under