Exploration of the Temperature Sensing Ability of La₂MgTiO₆:Er³⁺ Double Perovskites Using Thermally Coupled and Uncoupled Energy Levels

Abstract

This work aimed to explore the temperature-sensing performance of La₂MgTiO₆:Er³⁺ double perovskites based on thermally coupled and uncoupled energy levels. Furthermore, the crystal structure, chemical composition, and morphology of the samples were investigated by powder X-ray diffraction, energy-dispersive X-ray spectroscopy, and scanning electron microscopy, respectively. The most intense luminescence was observed for the sample doped with 5% Er³⁺. The temperature-dependent emission spectra of La₂MgTiO₆:5% Er³⁺ were investigated in the wide range of 77–398 K. The highest sensitivity of the sample was equal to 2.98%/K corresponding to the thermally coupled energy level ²H_11/2 → ⁴I_15/2 and ⁴S_3/2 → ⁴I_15/2 as compared to 1.9%/K, obtained for the uncoupled energy level ²H_11/2 → ⁴I_15/2 and ²H_9/2 → ⁴I_15/2. Furthermore, the 300 K luminescent decay profiles were analyzed using the Inokuti–Hirayama model. The energy transfer among Er³⁺ ions was mainly regulated by the dipole–dipole mechanism. The critical transfer distance R₀, critical concentration C₀, energy transfer parameter C_da, and energy transfer probability W_da were 9.81 Å, $2.53\times {10}^{20}$ ions·cm⁻³, $5.38\times {10}^{-39}$cm⁶·s⁻¹, and 6020 s⁻¹, respectively.

1. Introduction

Double perovskite compounds (DP) are among the most intensely studied materials because of their interesting chemical and physical properties, as well as their diverse applications stemming from the compositional flexibility of their structure. La₂MgTiO₆ (LMT), a representative of the double perovskite family, has recently been extensively investigated as a host of many lanthanide ions [1,2,3]. The energy transfer process from TiO₆ groups to lanthanides ions takes place very efficiently [3]. Erbium ions have been widely applied in eye-safe lasers, optical communications, or lighting owing to their broad spectral range spans in the ultraviolet, visible, and near-infrared regions [4,5,6]. The most universal approach for LMT is a white-light conversion material related to emission from Sm³⁺ and Eu³⁺ [7], Mn⁴⁺ and Yb³⁺ [8], Bi³⁺ [9], Eu³⁺ [10], Eu²⁺ [11], Mn⁴⁺ [12,13,14,15], and Gd³⁺, Bi³⁺, Sm³⁺, and Eu³⁺ ions [16]. Furthermore, an ample potential for optical thermal sensing has recently been demonstrated through these studies including LMT:Pr³⁺ [17], LMT:Eu³⁺ [3], and LMT:Nd³⁺ [2].

Temperature is one of the most important physical parameters which is present in many fields of science and life. In the last few decades, there has been an explosion of research on such optical thermometry [17,18,19,20,21,22,23] to fulfil the requirements of fast growth in a myriad of fields including chemistry, physics, biomedicine, and industry. Indeed, noncontact thermometers possess numerous advantages, such as remote, handy, and precise application, high spatial resolution, and a broad operating temperature range as compared to the conventional thermometers [24]. What is more, they can operate in harsh conditions, e.g., high pressure, corrosive, and very low or high temperature, where the traditional techniques are infeasible [22]. To design luminescent thermometry, taking into account the reliance of peak position, emission intensity, and lifetime when elevating temperature, the sensitivity of thermometers should be estimated. The ratio of emission intensity between two distinct transitions is preferable since it is an external interference-independent factor [24]. It is worth noting that there has only been one investigation into LMT:Er³⁺ published recently with regard to temperature readout application. However, it was synthesized using the conventional solid-state method, the working temperature range was quite narrow, and it was only focused on thermally coupled levels [25].

Therefore, a comprehensive investigation of the temperature-sensing ability of LMT:Er³⁺ synthesized via the coprecipitation method was conducted by exploring both thermally coupled and uncoupled energy levels. The well-known thermally coupled levels correspond to the transitions ²H_11/2 → ⁴I_15/2 and ⁴S_3/2 → ⁴I_15/2, which are separated from each other by 592 cm⁻¹. The energy gap between these levels should be neither too close to overlap nor too far to be easily populated by the other; moreover, it should be in the range from 200 cm⁻¹ to 2000 cm⁻¹ [26]. Nonetheless, uncoupled levels, which are related to the phonon-assisted process, have also gained significant attention for temperature sensing [18,27,28]. This is due to the fact that the phonon-assisted process enhanced by elevating temperature is also related to absorption, emission, and energy transfer. Thus, the exploration of all possibilities including thermally coupled and uncoupled levels is crucial to choose the highest sensitivity with the lowest uncertainty.

The aim of this work was to explore the temperature sensing performance of a novel double perovskite LMT:Er³⁺ as a function of the ratio of emission intensity of thermally coupled and uncoupled energy levels of Er³⁺ ions. Additionally, the structural, morphological, and spectroscopic properties including absorption and emission spectra were investigated. The energy transfer mechanism among Er³⁺ ions and the characteristics of luminescent decay kinetics were clarified using the Inokuti–Hirayama model.

2. Experimental

2.1. Synthesis

La₂MgTiO₆:x Er³⁺ (where x = 0%, 0.1%, 0.5%, 1%, 3%, 5%, or 7%) was successfully obtained via the coprecipitation method. The procedure was calculated for 0.5 g of sample. The erbium ions were incorporated into the lanthanum site in the structure. All precursors used for the syntheses were purchased from the Alfa Aesar company (Kandel, Germany), including lanthanum acetate (La(CH₃COO)₃∙1.5H₂O, 99.9%), magnesium nitrate (Mg(NO₃)₂∙6H₂O, 99.97%), titanium isopropoxide (Ti(C₃H₇O)₄, 95%), erbium oxide (Er₂O₃, 99.99%), nitric acid (HNO₃, 65%, POCH), and ammonium hydroxide (NH₄OH, 25%, CHEMPUR). The synthesis method, annealing time, and sintering temperature were described in previous publications [2,3]. Firstly, the proper amounts of erbium oxide and titanium isopropoxide were separately diluted in nitric acid solution. Afterward, the prepared solution of titanium isopropoxide was added into the mixture of the aqueous solution containing lanthanum, magnesium, and erbium ions (for doped samples). However, it should be emphasized that a 10% excess amount of magnesium ions was applied due to the likelihood of the sublimation of magnesium ions during the high-temperature sintering process. To obtain the precipitate, a solution of ammonium hydroxide (1 mL) was added. The obtained precipitate was dried at 80 °C for 24 h on a heater. Then, it was sintered at 600 °C for 12 h in a porcelain crucible. The second annealing was conducted at 1300 °C for 8 h in a corundum crucible in air. Grinding for a few minutes was necessary after each step of annealing.

2.2. Characterization

The powder X-ray diffractions of all samples were measured on an X’Pert ProPANalytical (PANalytical, Almelo, The Netherlands) using an X-ray diffractometer with Cu K_α radiation (λ = 1.54056 Å) in a 2$\mathsf{\theta }$ range from 10° to 90° with a step size of Δ2θ = 0.02°. The morphology and chemical composition of LMT:5% Er³⁺ were investigated using a scanning electron microscope FEI NOVA NanoSEM230 (FEI, Hillsboro, OR, USA). To determine the absorption spectrum of LMT:7% Er³⁺, a Varian Cary 5E UV/Vis–NIR spectrophotometer (Varian Incorporation, Palo Alto, CA, USA) was used. The 300 K emission spectra of all samples were obtained using a Hamamatsu Photonic multichannel analyzer PMA-12 (Hamamatsu Photonics K.K, Shizuoka, Japan) along with a BT-CCD linear image sensor. Furthermore, a McPherson spectrometer linear PIXcel detector (McPherson Incorporation, Chelmsford, MA, USA) equipped with an 808 diode laser was used for infrared emission measurement. The 300 K emission decay profiles were recorded with a Lecroy digital oscilloscope (Teledyne Technologies, New York, NY, USA) using an excitation source of Nd:YAG. The thermal quenching measurements were measured using the Hamamatsu Photonic multichannel analyzer PMA-12 equipped with the BT-CCD linear image sensor. The temperature of the samples was controlled by a Linkam THMS 600 Heating/Freezing Stage (The McCRONE Group, Westmont, IL, USA).

3. Results and Discussion

3.1. Structural and Morphological Characterization

The XRD patterns of all prepared samples and the standard pattern of La₂MgTiO₆ (ICSD no. 86852) are shown in Figure 1. All samples crystallized in an orthorhombic structure with space group Pbnm (62) with the following lattice parameters: a = 5.5609 (1), b = 5.5738 (1), c = 7.8623 (2), V = 243.69 ų, and Z = 4 [2,3]. No impurity traces were found. The main diffraction lines of the samples observed at 2θ values of 22.72°, 32.33°, 39.87°, 46.30°, 52.16°, 57.59°, 67.52°, and 76.82° were assigned to the lattice planes (hkl) of (110), (112), (202), (220), (310), (132), (400), and (116), respectively [29].

Due to the similarity of charge and ionic radius (121.6 pm for La³⁺ and 106.2 pm for Er³⁺ with the same coordination number, CN = 9 [30]), it can be assumed that Er³⁺ ions most likely substituted for La³⁺ ions located in the C_s symmetry site. Therefore, the replacement of smaller Er³⁺ ions with larger La³⁺ ions resulted in the contraction of the crystal structure at higher dopant concentration. In order to prove our hypothesis, the XRD of all samples was measured again with a pure powder of potassium bromide (KBr, ICSD no. 53826), and the position of diffraction lines (2$\mathsf{\theta }$ = 32.3°) of La₂MgTiO₆ was corrected (Figure 1b). The observed right-shifting of the diffraction peaks (Figure 1b) and the shrinkage of the unit cell volume with an increase in Er³⁺ concentration (Figure 1c) confirmed the above assumption. The concentration-dependent lattice parameters are shown in Figure S1 (Supplementary Materials).

The morphology and the energy-dispersive spectroscopy (EDS) X-ray microanalysis of LMT:5% Er³⁺ are presented in Figure 2 and Figure 3, respectively. From the SEM images, no individual grains were observed, and the grain size ranged from 0.5 to 1.0 mm, much smaller than that (5 μm) obtained via the conventional solid-state method [25]. It is clearly shown that small grains were strongly aggerated to form bigger objects. From the EDS measurements, all elemental compositions of LMT:5% Er³⁺ were identified and quantified including La (59.32 wt.%), Er (3.97 wt.%), Mg (6.18 wt.%), Ti (11.8 wt.%), and O (18.73 wt.%). These values are consistent with the general chemical formula: La (58.8 wt.%), Er (3.73 wt.%), Mg (5.41 wt.%), Ti (10.67 wt.%), and O (21.39 wt.%).

3.2. Absorption Spectrum

The absorption spectrum of LMT:7% Er³⁺ in the range of 200–2000 nm, shown in Figure 4, exhibited typical transitions for Er³⁺ ions. Intense absorption bands starting from 200 nm up to 350 nm were attributed to the absorption of the host. In accordance with previous studies [6,31,32,33], the obtained absorption lines were well assigned to the typical f–f transitions of Er³⁺ ions from ground state ⁴I_15/2 to the successive excited states including ⁴G_7/2, ⁴G_9/2, ⁴G_11/2, ²H_9/2, ⁴F_5/2, ⁴F_7/2, ²H_11/2, ⁴S_3/2, ⁴F_9/2, ⁴I_9/2, ⁴I_11/2, and ⁴I_13/2, among which, ⁴I_15/2 → ⁴G_11/2 was the dominant one (see the inset in Figure 4).

To determine the energy of the forbidden bandgap of the host and the sample doped with 7% Er³⁺, the modified Kubelka–Munk function (also known as the Tauc method) [34] was applied to the 300 K absorption spectra. The energy gap between the top of the valence band and the bottom of the conduction band of the host and LMT:7% Er³⁺ were found to be 4.06 eV and 4.07 eV, respectively (Figure 5). The insignificant difference between them could have resulted from a measurement error. This value was slightly higher than that (3.98 eV) obtained for the same Pr³⁺-doped host [17].

3.3. Luminescence Studies

A wide spectral range from visible to the near-infrared of LMT doped with different concentrations of Er³⁺ ions, observed for 266 nm wavelength direct excitation of TiO₆ groups, is shown in Figure 6. As can be seen, there was no difference in the shape of the emission spectrum across the samples. According to the absorption spectrum (Figure 4) and the emission spectra (Figure 6), the assignment of all energy levels of Er³⁺ ions was tabulated in Table S1.

Similarly to the LMT samples doped with Eu³⁺ [3] and Nd³⁺ [2], a broad emission band of TiO₆ groups also appeared from 400 nm to 550 nm at 77 K (Figure S2). The energy transfer from TiO₆ groups to Er³⁺ ions was perfectly exemplified by temperature and Er³⁺ concentration. A higher Er³⁺ content resulted in a lower intensity of the emission of TiO₆ groups. This process was also facilitated by elevating temperature. No TiO₆ emission was observed at room temperature (Figure 6). For visible emission including ²H_11/2, ⁴S_3/2, and ⁴F_9/2 to the ground state, ⁴I_15/2 located in the green, yellow, and red regions was centered at 531.7 nm (18,807 cm⁻¹), 549 nm (18,215 cm⁻¹), and 662 nm (15,106 cm⁻¹), respectively. In addition, infrared emission from ⁴I_11/2 and ⁴I_13/2 levels to the ground state was maximum at 988 nm (10,121 cm⁻¹) and 1524 nm (6562 cm⁻¹), respectively (Figure S3). Furthermore, the emission spectra were also contributed to by a few less intense transitions corresponding to ⁴G_11/2, ²H_9/2 → ⁴I_15/2, and ⁴S_3/2 → ⁴I_13/2 levels.

The energy difference (∆E) between ²H_11/2 and ⁴S_3/2 was 592 cm⁻¹; this value is similar to that found in LaAlO₃:Er³⁺ with 660 cm⁻¹ [6]. Due to the small energy difference, the transition from ²H_11/2 to ground state can be easily populated at room temperature by thermalization (see Figure 6).

Temperature plays an important role in the thermal population of ²H_11/2 from the ⁴S_3/2 level. It is regulated by the following Boltzmann distribution formula:

$$\frac{{\mathrm{N}}_{\mathrm{A}}}{{\mathrm{N}}_{\mathrm{B}}}=\frac{{\mathrm{g}}_{\mathrm{A}}}{{\mathrm{g}}_{\mathrm{B}}}\exp \left(\frac{-\Delta \mathrm{E}}{\mathrm{kT}}\right),$$

(1)

where N_A (N_B) is the population of level ²H_11/2 (⁴S_3/2), g_A (g_B) is the degeneration of level ²H_11/2 (⁴S_3/2), k is the Boltzmann constant, and ΔE is the energy difference between these levels. These levels were further considered in terms of temperature sensing.

Moreover, the integrated emission intensity of all samples is plotted in the inset. It can be clearly seen that the integrated intensity moderately increased with Er³⁺ concentration. The highest intensity was achieved for the sample doped with 5% Er³⁺ (Figure S4). Above this threshold value, the intensity decreased as a result of concentration quenching. This phenomenon could result from an exchange interaction or multipolar interaction depending on the critical transfer distance R_c between Er³⁺ ions. Therefore, to better understand, Blasse’s model was applied [35].

$${\mathrm{R}}_{\mathrm{C}}=2\times {\left(\frac{3\mathrm{V}}{4{\mathsf{\pi }\mathrm{x}}_{\mathrm{C}}\mathrm{N}}\right)}^{1/3},$$

(2)

where V is the unit cell volume, and x_c is the quenching concentration. For samples doped with 5% Er³⁺, V = 242.45 ų, x_c = 0.05, and N = 4. The value of ${\mathrm{R}}_{\mathrm{C}}$ was equal to 13.2 Å, indicating that the quenching mechanism which occurred in LMT:Er³⁺ samples was predominantly regulated by the electric multipolar interaction. A similar phenomenon was previously observed in LMT doped with Nd³⁺ ions [2].

The analysis of the emission spectra of LMT:Er³⁺ allowed concluding that, with the increase in the concentration of doping ions, two competing phenomena are observed. The increased amount of Er³⁺ ions initially led to an increase in the emission intensity of all bands (see Figure S5); however, the intensity of each of these bands changed differently depending on the Er³⁺ concentration. Due to thermalization at 300 K, both ²H_11/2 and ⁴S_3/2 levels could be regarded as one. It can be seen that, in the range 1–5% Er³⁺, the emission intensity of ⁴S_3/2 remained almost constant with a local maximum for 3%. On the other hand, the emission of the ⁴F_9/2 and ⁴I_11/2 levels increased from the 0.5% Er³⁺ concentration. This was mainly to the detriment of the (²H_11/2, ⁴S_3/2) level, which transferred energies to these lower levels in the process of cross-relaxation. As the dopant concentration increased, the likelihood of these processes increased as a function of the number of Er³⁺ ion pairs. If one of the ions in a pair was excited and the other was not, the first would be the donor and the second would be the acceptor, and the energy transfer processes could be described as follows:

(²H_11/2 + ⁴S_3/2, ⁴I_15/2) → (⁴I_11/2, ⁴I_11/2), ΔE = −1130 cm⁻¹,

(3)

(²H_11/2 + ⁴S_3/2, ⁴I_15/2) → (⁴I_11/2, ⁴I_13/2), ΔE = 2210 cm⁻¹,

(4)

(²H_11/2 + ⁴S_3/2, ⁴I_15/2) → (⁴I_13/2, ⁴I_9/2), ΔE = 93 cm⁻¹.

(5)

At continuous wave excitation, the ⁴I_13/2 level would be populated; therefore, it is possible to write another path of the CR process as follows:

(²H_11/2 + ⁴S_3/2, ⁴I_13/2) → (⁴I_9/2, ⁴I_11/2), ΔE = 436 cm⁻¹.

(6)

The ⁴I_11/2 level could also be fed in another cross-relaxation process from the ⁴F_9/2 level as follows:

(⁴F_9/2, ⁴I_15/2) → (⁴I_11/2, ⁴I_13/2) ΔE = −1530 cm⁻¹.

(7)

The ⁴F_9/2 level could also be drained by the following process:

(⁴F_9/2, ⁴I_15/2) → (⁴I_13/2, ⁴I_13/2) ΔE = 1500 cm⁻¹.

(8)

There was a certain probability of the following CR populating the 4F_9/2 level:

(²H_11/2 + ⁴S_3/2, ⁴I_15/2) → (⁴F_9/2, ⁴I_13/2) ΔE = −2280 cm⁻¹.

(9)

Please note that the maximum energy phonon of this host was found to be 741 cm⁻¹ [36]. In the processes described by Equations (3), (7), and (9), there is a shortage of energy, which can easily be obtained from the crystal lattice at 300 K. These are phonon-assisted processes; however, the process described by Equation (9), requiring the assistance of up to three phonons, is the least likely in this list. In the processes described by Equations (4) and (8), a small excess of energy would be easily absorbed by the crystal lattice. All processes are pictured in the inset of Figure 6.

3.4. Luminescent Decay Profiles

To better understand the quenching behavior of the green, red, and IR emission, the decay profiles of some samples at room temperature, registered at 549 nm, 662 nm, and 988 nm corresponding to ⁴S_3/2, ⁴F_9/2, and ⁴I_11/2 levels were taken into account (Figure S6). Nonexponential decay was observed for the samples doped with more than 1% Er³⁺. Due to the thermalization phenomenon, the decay of the ⁴S_3/2 level consisted of two components attributed to ⁴S_3/2 and ²H_11/2, respectively. Similarly, nonexponential luminescent decay monitored at ⁴F_9/2 was contributed by the ⁴F_9/2 and ⁴S_3/2 levels. The decay time of ⁴F_9/2 level was twofold shorter than that of the ⁴S_3/2 level observed for the samples containing less than 3% Er³⁺. Among these levels, the decay time of the ⁴I_11/2 level was the longest one, as also observed for LaAlO₃:Er³⁺ [6]. In addition, a very fast rise time was obtained for all samples as a result of cross-relaxation processes (Figure S6 and Table S2).

Figure S5 shows the integrated emission intensity of some levels, including ²H_11/2 (I₂), ⁴S_3/2 (I₃), ⁴F_9/2 (I₄), and ⁴I_11/2 (I₆) to ground state ⁴I_15/2. The observed emission of each level can be contributed by radiative emission or nonradiative relaxation (multi-phonon relaxation) and cross-relaxation phenomena.

As can be clearly seen, the 300 K decay profiles upon 266 nm excitation (except for the sample doped with 0.1% Er³⁺) exhibited a nonexponential behavior on account of the energy transfer between Er³⁺ ions (Figure 7). Thus, the Inokuti–Hirayama model was used to calculate the critical transfer distance ${\mathrm{R}}_0$ and the critical concentration ${\mathrm{C}}_0$ by the following equation [37]:

$${\mathrm{I}}_{\mathrm{t}}={\mathrm{I}}_0{\exp }^{\left[\frac{-\mathrm{t}}{\mathsf{\tau }}-\mathsf{\alpha }\mathsf{\times }{\left(\frac{\mathrm{t}}{\mathsf{\tau }}\right)}^{\frac{3}{s}}\right]}+\left(\mathrm{offset}\right),$$

(10)

where ${\mathrm{I}}_0,{\mathrm{I}}_{\mathrm{t}}$ represent the emission intensity at t = 0 and after pulse excitation, $\mathsf{\tau }$is the radiative decay time, C is the Er³⁺ concentration, ${\mathrm{C}}_0$ is the Er³⁺ critical concentration, $\Gamma \left(1-\frac{3}{\mathrm{S}}\right)$ is the gamma function, S defines the dipole–dipole, dipole–quadrupole, and quadrupole–quadrupole interactions corresponding to S = 6, 8, and 10, respectively, and Q is the energy transfer parameter [37,38,39,40].

$$\mathsf{\alpha }=\frac{4\mathsf{\pi }}{3}\times \Gamma \left(1-\frac{3}{\mathrm{S}}\right)\times \mathrm{C}\times {\mathrm{R}}_0^3,$$

(11)

where ${\mathrm{R}}_0$ stands for the critical transfer distance at which the energy transfer efficiency achieves 50% and is equal the radiative decay rate ${\mathsf{\tau }}_0^{-1}$.

The correlation of $\mathrm{C},{\mathrm{C}}_0,{\mathrm{R}}_0$can be derived from Equations (10) and (11) to yield the following formula [37,38,39,40]:

$$\frac{\mathrm{C}}{{\mathrm{C}}_0}=\frac{4{\mathsf{\pi }\mathrm{CR}}_0^3}{3}.$$

(12)

The donor–acceptor energy transfer parameter $({\mathrm{C}}_{\mathrm{da}})$ and the energy transfer probability $({\mathrm{W}}_{\mathrm{da}})$ can be calculated using the following equations [40,41,42,43]:

$${\mathrm{C}}_{\mathrm{da}}={\mathrm{R}}_0^6\times {\mathsf{\tau }}_0^{-1},$$

(13)

$${\mathrm{W}}_{\mathrm{da}}={\mathrm{R}}_0^{-6}\times {\mathrm{C}}_{\mathrm{da}}={\mathsf{\tau }}_0^{-1}.$$

(14)

The energy transfer decay rates of the samples as a function of Er³⁺ concentration can be estimated as follows:

$${\mathrm{W}}_{\mathrm{tot}}={\mathrm{W}}_{\mathrm{rad}}+{\mathrm{W}}_{\mathrm{da}}=\frac{1}{{\mathsf{\tau }}_{\mathrm{rad}}}+{\mathrm{W}}_{\mathrm{da}},$$

(15)

where ${\mathsf{\tau }}_{\mathrm{rad}}$ is supposedly equal to the decay time of the sample doped with 0.1% Er³⁺ (${\mathsf{\tau }}_{\mathrm{rad}}$= 166 μs, Table S2).

$${\mathrm{W}}_{\mathrm{tot}}={\mathrm{aC}}^{\mathrm{n}}+\mathrm{b},$$

(16)

where n indicates the strength of the multipole interaction between dopants; a weak interaction is exhibited by n = 1, while a strong one is exhibited by n = 2 [43].

As seen in Figure 7, the dipole–dipole interaction was responsible for the energy transfer in all samples, as exemplified by the best-fitting curves for S = 6. The experimental data can be described by Equation (12) as a linear function of the density of Er³⁺ ions (Figure 7b). The value of ${\mathrm{R}}_0$ was 9.81 Å, similar to the ${\mathrm{R}}_{\mathrm{c}}$ derived from the Blasse model. However, it is worth emphasizing that the values have different physical meaning [44]. Furthermore, ${\mathrm{C}}_0$ = $2.53\times {10}^{20}$ ions/cm⁻³, whereas ${\mathrm{C}}_{\mathrm{da}}$and ${\mathrm{W}}_{\mathrm{da}}$ were estimated by considering the radiative decay time value of the sample doped with 0.1% Er³⁺ as ${\mathsf{\tau }}_{\mathrm{rad}}$ = 166 μs. Thereafter, ${\mathrm{C}}_{\mathrm{da}}$and ${\mathrm{W}}_{\mathrm{da}}$ were found to be $5.38\times {10}^{-39}$cm⁶·s⁻¹ and 6020 s⁻¹, respectively. With n = 1.8 obtained from the fitting curve (Figure S7), one can conclude that a strong interaction among Er³⁺ ions happened in LMT at 300 K.

3.5. Temperature-Sensing Ability

Furthermore, the temperature dependence of the emission intensity of LMT 5% Er³⁺ is presented in Figure 8 for the 77–398 K range, and the temperature-dependent integrated emission intensity of some levels is also shown in the inset. It is shown that the most intense emission came from ⁴S_3/2 → ⁴I_15/2 (I₃). In general, I₃ and some other levels, including ²H_9/2 → ⁴I_15/2 (I₁), ⁴S_3/2 → ⁴I_13/2 (I₅), and ⁴F_3/2 → ⁴I_15/2 (I₄), are strongly depopulated by elevating temperature, especially I₃ since it acts as an energy pump for the ²H_11/2 x2192; ⁴I_15/2 transition (I₂) via the thermalization process. The emission of I₂ reached its maximum at 248 K, before being quenched very quickly at a higher temperature. On the other hand, the ⁴I_11/2 → ⁴I_15/2 transition (I₆) was quite stable, remaining mostly unchanged until 248 K, at which point it then exhibited a significant decrease.

To verify the potential applicability of using LMT:Er³⁺ as a noncontact thermometer, all possible combinations of Er³⁺ emission bands were taken into account in the temperature range of 77–398 K (Figure 9). The first was devoted to the most frequently used, thermally coupled levels of Er³⁺, including ²H_11/2 → ⁴I_15/2 and ⁴S_3/2 → ⁴I_15/2 (abbreviated as I₂/I₃) and a combination which also started from the same level ⁴S_3/2, i.e., ²H_11/2 → ⁴I_15/2 and ⁴S_3/2 → ⁴I_13/2 (I₂/I₅). The second was constructed on the basis of uncoupled levels; due to the different thermal behaviors through radiative emission, it is highly probable that these combinations would also be sensitive to temperature fluctuations.

The temperature-sensing performance of a thermometer can be evaluated through the absolute S_a and relative sensitivity S_r parameters. However, S_a depends on the sample characteristics and experimental setup, whereas S_r can be used for a comparison among distinct materials [24].

$$\mathsf{\Delta }=\frac{{\mathrm{I}}_{\mathrm{i}}}{{\mathrm{I}}_{\mathrm{j}}},$$

(17)

$${\mathrm{S}}_{\mathrm{a}}=\frac{\partial \mathsf{\Delta }}{\mathsf{\Delta }\mathrm{T}},$$

(18)

$${\mathrm{S}}_{\mathrm{r}}=\frac{1}{\mathsf{\Delta }}\left|\frac{\partial \mathsf{\Delta }}{\mathsf{\Delta }\mathrm{T}}\right|,$$

(19)

where thermometric parameter Δ is denoted as the ratio between two different emission levels I_i, I_j.

For thermally coupled levels, the emission intensity of the ²H_11/2 → ⁴I_15/2 transition was strongly populated by thermalization via the ⁴S_3/2 level. As a result, the emission intensity of the transition coming from ⁴S_3/2 decreased, i.e., ⁴S_3/2 → ⁴I_15/2 (I₃) and ⁴S_3/2 → ⁴I_13/2 (I₅). However, ⁴S_3/2 → ⁴I_13/2 exhibited a steady quench with respect to ⁴S_3/2 → ⁴I_15/2, resulting in a much faster growth in the thermometric parameter and a higher absolute sensitivity (S_a) for I₂/I₅ (see Figure S8a,b). As shown in Figure 9, the relative sensitivities (S_r) of given coupled levels were identical as predicted, since both (I₃) and (I₅) originated from the same level ⁴S_3/2. The highest S_r recorded at 148 K with the values of 2.98%·K⁻¹ and 3.08%·K⁻¹ corresponded to I₂/I₃ and I₂/I₅, respectively.

Regarding the thermally uncoupled levels, the S_r values are plotted in Figure 9c. The best performance for temperature determination was obtained for the I₂/I₁ pair with 1.9%·K⁻¹ at 148 K.

It is crucial to note that higher relative sensitivity does not imply more reliable results. Therefore, temperature uncertainty (δT), which is usually intentionally ignored, was determined using the below equation [24].

$$\mathsf{\delta }\mathrm{T}=\frac{1}{{\mathrm{S}}_{\mathrm{r}}}\frac{\mathsf{\delta }\mathsf{\Delta }}{\mathsf{\Delta }}.$$

(20)

δT is known as the smallest change in temperature which can be detected by the measurement. In the range from 77–150 K, δT was found to be less than 1.3 K and 0.4 K for coupled levels and uncoupled levels, respectively. From 150–400 K, the values were found to be less than 0.1 K in both cases (Figure 9b,d).

Table 1. The maximum relative sensitivity S_m (%·K⁻¹) of some materials doped with Er³⁺ corresponding to thermally coupled level and uncoupled levels at temperature T_m (K) with temperature uncertainty δT_m (K).

Material	λexc (nm)	Temperature Range (K)	Sm (%·K−1)	Tm (K)	δTm (K)	References
Al2O3:Er3+, Y3+	978	295–973	0.35	450	0.3	[45]
Sr2CaWO6:Er3+, La3+	980	250–2000	0.5	439	-	[46]
NaNbO3:Er3+	976	293–353	0.51	355	-	[47]
NaLaMgWO6:Er3+	378	303–483	1.04	303	-	[48]
Gd2O3:Er3+, Yb3+	980	300–550	1.18	300	-	[49]
Y2O3:Er3+ Coupled levels	379	296–500	1.54	483	-	[18]
Uncoupled levels	379	303–434	0.87	434	-	[18]
LiLaMgWO6:Er3+	378	303–483	2.24	483	-	[29]
Y3Ga5O12:Er3+	488	300-850	0.64	547	-	[50]
La2MgTiO6:Er3+	380	303–483	1.107	303	-	[25]
(solid-state)
La2MgTiO6:Er3+	266	77–398	2.98	148	0.09	This work
(coprecipitation)
Coupled levels
Uncoupled levels	266	77–398	1.9	148	0.027	This work

The obtained result is also easily comparable with various dopants, such as LMT: Pr³⁺ S_r = 1.28%·K⁻¹ at 350 K [17], LMT:Eu³⁺ S_r = 3%·K⁻¹ at 77 K [3], LMT:Nd³⁺ S_r = 0.83%·K⁻¹ at 275 K [2], and LMT:V⁵⁺ and Cr³⁺ S_r = 1.96%·K⁻¹ at 165 K [1]. Such an exceptional value of S_r of 2.98%·K⁻¹ at 148 K demonstrates LMT:5% Er³⁺ as a potential candidate for temperature readout at low temperature.

presents the relative sensitivities of numerous materials doped or co-doped with Er³⁺ ions. The results in this work completely dominate in comparison with other compounds investigated in the literature. For some samples studied on both thermally coupled and uncoupled levels, it can be seen that the thermally coupled levels had higher sensitivity. However, only a few transitions can work as thermally coupled levels, while many uncoupled levels can provide more promising pairs across the different temperature ranges. Furthermore, the introduction of some co-dopants (Y³⁺, La³⁺, Yb³⁺) into the Er³⁺-doped system was not only to enhance the green up-conversion emission of Er³⁺ ions, but also to create more potential pairs to tackle the limitations of the thermally coupled level-based optical thermometer.

4. Conclusions

In this study, La₂MgTiO₆:Er³⁺ was prepared via the coprecipitation method. All samples crystallized in n orthorhombic structure with the space group Pbnm (62). The chemical composition of the representative sample was in agreement with the theoretical chemical composition. The morphology of the sample was inhomogeneous, and the grain size was distributed in the micro range, from 0.5 to 1 µm. The energy transfer among Er³⁺ ions occurred predominantly via dipole–dipole interactions. The critical transfer distance R₀, critical concentration C₀, energy transfer parameter C_da, and energy transfer probability W_da were found to be 9.81 Å, $2.53\times {10}^{20}$ ions·cm⁻³, $5.38\times {10}^{-39}$cm⁶·s⁻¹_, and 6020 s⁻¹, respectively. More importantly, the low-temperature-sensing ability of La₂MgTiO₆:5% Er³⁺ was explored using the ratio of emission intensity of the thermally coupled and uncoupled energy levels. The thermally coupled energy levels ²H_11/2 → ⁴I_15/2 and ⁴S_3/2 → ⁴I_15/2 exhibited the greatest sensitivity of around 2.98%·K⁻¹ at 148 K, and the uncertainty temperature was less than 1 K in the range of 77–398 K. The abovementioned findings indicate the huge potential of La₂MgTiO₆:Er³⁺ for temperature-sensing operating at low temperature.