Synthesis, Optical, Magnetic and Thermodynamic Properties of Rocksalt Li1.3Nb0.3Mn0.4O2 Cathode Material for Li-Ion Batteries

Since the discovery of the reversible intercalation of lithium-ion materials associated with promising electrochemical properties, lithium-containing materials have attracted attention in the research and development of effective cathode materials for lithium-ion batteries. Despite various studies on synthesis, and electrochemical properties of lithium-based materials, fairly little fundamental optical and thermodynamic studies are available in the literature. Here, we report on the structure, optical, magnetic, and thermodynamic properties of Li-excess disordered rocksalt, Li1.3Nb0.3Mn0.4O2 (LNMO) which was comprehensively studied using powder X-ray diffraction, transient absorption spectroscopy, magnetic susceptibility, and low-temperature heat capacity measurements. Charge carrier dynamics and electron–phonon coupling in LNMO were studied using ultra-fast laser spectroscopy. Magnetic susceptibility and specific heat data are consistent with the onset of long-range antiferromagnetic order at the Néel temperatures of 6.5 (1.5) K. The effective magnetic moment of LNMO is found to be 3.60 μB. The temperature dependence of the inverse magnetic susceptibility follows the Curie–Weiss law in the high-temperature region and shows negative values of the Weiss temperature 52 K (3), confirming the strong AFM interactions.


Introduction
Lithium-ion batteries (LIBs) are one of the most auspicious energy storage technologies for smartphones, laptops, electric hybrid vehicles, and renewable energy systems [1][2][3]. LIBs consist of two electrodes called the anode (negative) and the cathode (positive) separated by an electrolyte that can be a liquid or a solid [4,5]. Various alternative anode and The powder was dried in the oven then mixed with KCl flux in a molar ratio of 2.5-5 between the flux and (TM) precursors. The resultant mixture was then heated at 950 • C for 12 h in an argon atmosphere [20]. A ramp rate of 4 • C/min was used for both heating and cooling steps. Figure 1a illustrates a schematic description of the heating and annealing process of the synthesis for LNMO. The annealing process of the sample has an important impact on the structure of the produced sample [21]. After the compilation of the process, KCl was dissolved in deionized water, and the final product was obtained via filtration and comprehensive washing with water, then it was dried in the vacuum oven [22].
Crystals 2021, 11, x FOR PEER REVIEW 3 of 12 milled together with ethanol as a solvent at 200 rpm for 12 h in a planetary ball mill (RETSCH PM100) using a zirconia jar with zirconia balls. An extra amount of Li2CO3 of about 10-15 mol% was added to overcome the loss of Li during high-temperature sintering. The powder was dried in the oven then mixed with KCl flux in a molar ratio of 2.5-5 between the flux and (TM) precursors. The resultant mixture was then heated at 950 °C for 12 h in an argon atmosphere [20]. A ramp rate of 4 °C/min was used for both heating and cooling steps. Figure 1a illustrates a schematic description of the heating and annealing process of the synthesis for LNMO. The annealing process of the sample has an important impact on the structure of the produced sample [21]. After the compilation of the process, KCl was dissolved in deionized water, and the final product was obtained via filtration and comprehensive washing with water, then it was dried in the vacuum oven [22].

Characterization
The analysis of phase purity performed using laboratory X-ray diffraction (XRD) collected on Panalytical Empyrean X-ray diffractometer (Malvern Panalytical Ltd. Malvern, Worcestershire, UK) with (Cu, K 1 ) radiation (1.5406 Å ), operated at an acceleration voltage of 40 kV and 40 mA current in the range of 4.99-89.90 Å . The XRD pattern was refined using FULLPROF software [23,24]. For the transient absorption spectroscopy, about 200 mg of the powder sample prepared as described above was sonicated in water for 25 min. Then, a suspension was diluted to obtain a transparent solution. The morphology of the LNMO polycrystalline sample was investigated by using the field-emission scanning electron microscopy (FE-SEM) (Zeiss FE-SEM Sigma 500 VP, Oberkochen, Germany). The transient absorption spectroscopy was carried out on laser-based spectroscopy. A coherent legend Ti: Sapphire amplifier (800 nm, 100 fs pulse length, 1 kHz repetition rate) was used. The used technique can be described as a UV light laser pulse of wavelength 345 nm with pulses width around 120 fs used to excite the sample (suspension in water), and at a certain time, another white light pulse (from 350 nm to 800 nm) was used to measure the change in the absorption of the sample. The output was split to give pump and probe

Characterization
The analysis of phase purity performed using laboratory X-ray diffraction (XRD) collected on Panalytical Empyrean X-ray diffractometer (Malvern Panalytical Ltd. Malvern, Worcestershire, UK) with (Cu, K α1 ) radiation (1.5406 Å), operated at an acceleration voltage of 40 kV and 40 mA current in the range of 4.99-89.90 Å. The XRD pattern was refined using FULLPROF software [23,24]. For the transient absorption spectroscopy, about 200 mg of the powder sample prepared as described above was sonicated in water for 25 min. Then, a suspension was diluted to obtain a transparent solution. The morphology of the LNMO polycrystalline sample was investigated by using the field-emission scanning electron microscopy (FE-SEM) (Zeiss FE-SEM Sigma 500 VP, Oberkochen, Germany). The transient absorption spectroscopy was carried out on laser-based spectroscopy. A coherent legend Ti: Sapphire amplifier (800 nm, 100 fs pulse length, 1 kHz repetition rate) was used. The used technique can be described as a UV light laser pulse of wavelength 345 nm with pulses width around 120 fs used to excite the sample (suspension in water), and at a certain time, another white light pulse (from 350 nm to 800 nm) was used to measure the change in the absorption of the sample. The output was split to give pump and probe beams. An optical parametric amplifier was used as a source for excitation pulses at a wavelength of 345 nm. The pulses in CaF 2 crystal with wavelength 800 nm generate the probe pulses (a broad supercontinuum spectrum) and split to probe and reference pulses by a beam splitter. The probe and reference pulses were scattered in a spectrograph and a diode array is used to detect these pulses. The instrumental response time is approximately 100 fs, the polarization of the pump was adjusted at a magic angle of 54.7 • with respect to the probe beam [25][26][27][28]. Low temperature-specific heat and the magnetic properties of the investigated sample were measured by using the Quantum Design Physical Properties Measurement System (PPMS). The experiments were measured in a temperature range from 2.5 K to 300 K in the applied magnetic field up to 14 T. The AC susceptibility measurements were performed in a temperature range from 2 K to 20 K in applied AC magnetic fields and different frequencies.

Results and Discussion
The XRD shows that LNMO formed single phases in a disordered rocksalt structure. The Rietveld refinement was carried out using the disordered structural model with the cubic Fm3m space group reported in the literature in the range of 4.99-89.90 Å. In the crystal structure, 4b sites are occupied by oxygen atoms forming a cubic close-packed structure, and Li, Nb, and Mn atoms are randomly distributed in 4a sites. The refinement profile of LNMO is shown in Figure 1b. A summary of crystal structural data is given in Table 1. The value of χ 2 is higher than unity, but it is also accepted as reported previously [29,30]. As illustrated in Figure 1c,d, the LNMO polycrystalline has a nearly spherical shape, indicating the good crystallization process. The average particle size distribution is calculated to be approximately 8.88 µm. Table 1. Crystallographic parameters were obtained from the refinement of XRD data for LNMO compound. Listed are Wyckoff positions, unit cell parameters, volume, Bragg factor R Bragg , weighted profile R-factor R wp , structure factor R F , and goodness of fit χ 2 .

Space Group Fm3m
Wyckoff position 4a (0, 0, 0) Li occupancy 0 The excited state optical properties of the LNMO are achieved using fs laser based spectroscopy, where at a time (t) equal to zero, electrons in the ground state (g) are excited by the pump pulse with the energy of 5.06 eV creating a non-equilibrium population in the excited states. At a certain delay time after the excitation, the prope pulse detects the difference in the absorption of the excited state as shown in Figure 2a. Particularly in our sample, the pump pulse can promote electrons from the VBM (valance band maximum) to the CBM (conduction band minima). The depletion of the ground state by the pump pulse leads to the decrease in the transition from a ground state to excited states; this is the so-called ground state bleach (GSB) (Figure 2a, negative absorption) [31]. For a deep understanding of the bleach recovery dynamics, time traces at 378 nm were extracted. The bleach recovery dynamics of LNMO can be fitted using four distinct characteristic decay times, 19 ps, 23 ps, 290 ps, and a very slow component (>8.0 ns) beyond our delay stage, through fitting with a triple exponential function, as shown in Figure 2b. Upon excitation of the LNMO with high energy photons, the electrons gain extra energy and become hot electrons [32]. As a result of the formation of these highly energetic hot electrons, they collide with each other as a way to dissipate their energy. These electrons refer to the ground state through carrier-carrier collisions; the additional energy is shared between the excited carriers [32]. The residual photon energy of the energy gap is dissipated as heat accompanied by lattice vibrations mediated by phonons [33]. The timescale of such a mechanism is in the femtosecond scale specifically after the photoexcitation process [34]. In phonon-assisted processes, the rates of carrier capture depend on the lattice temperature [35][36][37]. Carrier generation/relaxation channel can be triggered by intense carrier-carrier interactions. In such a channel, the excess energy associated with an electron in the conduction band does not disperse through electron-phonon scattering [33]. Instead, this excess energy is delivered to the electron allocated in the valance band crossing the energy gap. This is called a collision-like process, in which intense carrier-carrier Coulomb coupling is the moderator of this process. The initial electron (exciton) produced by a high-energy photon is thought to exist in either a real or virtual short-lived state, from which it undergoes coherent or incoherent movement into a final multiexciton state [33]. The multiexcitons are generated by a single photon, decay on a picosecond timescale. This relatively fast decay is due to the Auger recombination process [33,38]. The electron-hole pairs recombination process is initiated within few picoseconds and stays for more than 100 ps. The hole contribution to the transient absorption (TA) signal is trivial because they have a high effective mass, the nanosecond decay of the TA kinetics for LNMO (beginning from 1000 ps) refers to the delay recombination process of the photoexcited electron-hole pairs [39]. After the excitation process, the ground state is bleached instantly; the transient spectra are recorded at different delay times, as shown in Figure 2a. There are positive absorption changes on the left side of the absorption band. A negative band referring to strong negative bleach appears around 380 nm [40]. collide with each other as a way to dissipate their energy. These electrons refer to the ground state through carrier-carrier collisions; the additional energy is shared between the excited carriers [32]. The residual photon energy of the energy gap is dissipated as heat accompanied by lattice vibrations mediated by phonons [33]. The timescale of such a mechanism is in the femtosecond scale specifically after the photoexcitation process [34].
In phonon-assisted processes, the rates of carrier capture depend on the lattice temperature [35][36][37]. Carrier generation/relaxation channel can be triggered by intense carrier-carrier interactions. In such a channel, the excess energy associated with an electron in the conduction band does not disperse through electron-phonon scattering [33]. Instead, this excess energy is delivered to the electron allocated in the valance band crossing the energy gap. This is called a collision-like process, in which intense carriercarrier Coulomb coupling is the moderator of this process. The initial electron (exciton) produced by a high-energy photon is thought to exist in either a real or virtual short-lived state, from which it undergoes coherent or incoherent movement into a final multiexciton state [33]. The multiexcitons are generated by a single photon, decay on a picosecond timescale. This relatively fast decay is due to the Auger recombination process [33,38]. The electron-hole pairs recombination process is initiated within few picoseconds and stays for more than 100 ps. The hole contribution to the transient absorption (TA) signal is trivial because they have a high effective mass, the nanosecond decay of the TA kinetics for LNMO (beginning from 1000 ps) refers to the delay recombination process of the photoexcited electron-hole pairs [39]. After the excitation process, the ground state is bleached instantly; the transient spectra are recorded at different delay times, as shown in Figure 2a. There are positive absorption changes on the left side of the absorption band. A negative band referring to strong negative bleach appears around 380 nm [40]. In order to further study the quality of the investigated system, as well as to obtain insights into its fundamental properties, magnetic properties up to 14 T were measured. In particular, the magnetic order is frequently a disturbance in battery materials associated with defects, structural disorder, and defeated magnetic interactions [41]. The molar susceptibility versus the temperature ( Figure S1a) shows an anomaly which is clear in the plot of the inverse of molar susceptibility (1/ ) versus the temperature ( Figure S1b). Above the transition temperature of 6.5 K, Curie-Weiss behavior is verified as: where , are the Curie constant and the Weiss temperature, respectively. As shown in Table 2, the Weiss temperature obtained from fitting in the temperature range 50-300 K shows a negative sign, reflecting dominant antiferromagnetic (AFM) interactions. This In order to further study the quality of the investigated system, as well as to obtain insights into its fundamental properties, magnetic properties up to 14 T were measured. In particular, the magnetic order is frequently a disturbance in battery materials associated with defects, structural disorder, and defeated magnetic interactions [41]. The molar susceptibility χ m versus the temperature ( Figure S1a) shows an anomaly which is clear in the plot of the inverse of molar susceptibility (1/χ m ) versus the temperature ( Figure S1b). Above the transition temperature of 6.5 K, Curie-Weiss behavior is verified as: where C M , Θ are the Curie constant and the Weiss temperature, respectively. As shown in Table 2, the Weiss temperature obtained from fitting in the temperature range 50-300 K shows a negative sign, reflecting dominant antiferromagnetic (AFM) interactions. This is due to the high numbers of cation-anion-cation (Mn-O-Mn) interactions that the octahedralsite cations are set on the opposite sides of a common anion, in case that they have a half-filled e g orbital, they interact antiferromagnetically [42,43]. Upon applying a magnetic field up to 1T, the AFM ordering temperature T N is suppressed and no anomaly indicating long-range order is observed down to 1.8 K.   [47]. This distortion is required to decrease both repulsion energy between electrons and the degeneracy of the orbital [45,47].
The magnetization of LNMO as a function of the applied magnetic field at different temperatures up to a magnetic field of 14 T is shown in Figure 3 and is associated with a small hysteresis at low magnetic fields. Upon increasing the applied field, the magnetization keeps rising slowly with no saturation. The existence of hysteresis is strong at a low temperature of 2.2 K (the inset of Figure 3). The detected hysteresis in Fig. 3 at low magnetic fields and temperatures is indicative of the existence of a weak ferromagnetic (FM) phase. This FM phase can be created by the mixture valence of Mn-ions, for instance, Mn 2+ , Mn 3+ , and Mn 4+ . Consequently, the presence of these Mn-ions results in FM and AFM coupling in addition to some of canted AFM phases and impurity such as LiMnO 2 [19].
is due to the high numbers of cation-anion-cation (Mn-O-Mn) interactions that the octahedral-site cations are set on the opposite sides of a common anion, in case that they have a half-filled orbital, they interact antiferromagnetically [42,43]. Upon applying a magnetic field up to 1T, the AFM ordering temperature is suppressed and no anomaly indicating long-range order is observed down to 1.8 K.  [47]. This distortion is required to decrease both repulsion energy between electrons and the degeneracy of the orbital [45,47].
The magnetization of LNMO as a function of the applied magnetic field at different temperatures up to a magnetic field of 14 T is shown in Figure 3 and is associated with a small hysteresis at low magnetic fields. Upon increasing the applied field, the magnetization keeps rising slowly with no saturation. The existence of hysteresis is strong at a low temperature of 2.2 K (the inset of Figure 3). The detected hysteresis in Fig. 3 at low magnetic fields and temperatures is indicative of the existence of a weak ferromagnetic (FM) phase. This FM phase can be created by the mixture valence of Mn-ions, for instance, Mn 2+ , Mn 3+ , and Mn 4+ . Consequently, the presence of these Mn-ions results in FM and AFM coupling in addition to some of canted AFM phases and impurity such as LiMnO2 [19].  To further understand the above-mentioned magnetic observations, AC susceptibility χ AC experiments were performed. The χ AC is composed of a real component χ that is related to the reversible magnetization process, remains in phase with the oscillating field, and an imaginary component χ that is associated with the losses due to the irreversible magnetization process as well as the absorbed energy from the field. The field dependence of the real part of χ AC as a function of the temperature is shown in Figure 4a. The measurements were taken at a frequency of 1 kHz and zero DC magnetic field; the phase transition confirms that at low temperatures the compound has AFM behavior. The temperature Crystals 2021, 11, 825 7 of 12 was calculated from the differential (∂(χ T)/∂T) as a function of the temperature curve; T N = 5.3 K, at zero AC magnetic field, is field dependent. With an increase in the applied magnetic field, there is a shift of the peak and T N tends to decrease.
To further understand the above-mentioned magnetic observations, AC susceptibility experiments were performed. The is composed of a real component ′ that is related to the reversible magnetization process, remains in phase with the oscillating field, and an imaginary component ′′ that is associated with the losses due to the irreversible magnetization process as well as the absorbed energy from the field. The field dependence of the real part of as a function of the temperature is shown in Figure 4a. The measurements were taken at a frequency of 1 kHz and zero DC magnetic field; the phase transition confirms that at low temperatures the compound has AFM behavior. The temperature was calculated from the differential ( ( ′ )/ ) as a function of the temperature curve; = 5.3 K, at zero AC magnetic field, is field dependent. With an increase in the applied magnetic field, there is a shift of the peak and tends to decrease. Figure 4. (a) The field dependence of the real part of AC susceptibility as a function of the temperature at different applied AC magnetic fields for LNMO, all data were taken at zero DC magnetic field; (b) the field dependence of the imaginary part of AC susceptibility as a function of the temperature at different applied AC magnetic fields for LNMO, all data were taken at zero DC magnetic field.
The frequency dependence of ′ as a function of temperature is shown in Figure 5a, the measurements were taken at AC magnetic field amplitude of 1 kOe and zero DC magnetic field. The obtained Néel temperature is 5.0 K in the case of a frequency dependent measurement at a frequency of 3 kHz. From the upper panel of Figure 5, one can notice that the ′ is frequency-independent.
The field and frequency dependence of the real part of the AC susceptibility are consistent with the DC measurements and show that there is AFM order at low temperatures and paramagnetic behavior at higher temperatures. The imaginary part of the AC susceptibility, ′′ describes the losses associated with the irreversible magnetization process Figure 4. (a) The field dependence of the real part of AC susceptibility as a function of the temperature at different applied AC magnetic fields for LNMO, all data were taken at zero DC magnetic field; (b) the field dependence of the imaginary part of AC susceptibility as a function of the temperature at different applied AC magnetic fields for LNMO, all data were taken at zero DC magnetic field.
The frequency dependence of χ as a function of temperature is shown in Figure 5a, the measurements were taken at AC magnetic field amplitude of 1 kOe and zero DC magnetic field. The obtained Néel temperature is 5.0 K in the case of a frequency dependent measurement at a frequency of 3 kHz. From the upper panel of Figure 5, one can notice that the χ is frequency-independent. due to the existence of a small hysteresis loop; measuring this parameter at different AC magnetic fields and different frequencies indicates that ′′ is a field-and frequency-dependent, as illustrated in Figures 4b and 5b, respectively. Figure 5. (a) The frequency dependence of the real part of AC susceptibility as a function of the temperature at different frequencies for LNMO, all data were taken at zero DC magnetic field; (b) the frequency dependence of the imaginary part of AC susceptibility as a function of the temperature at different applied frequencies for LNMO; all data were taken at zero DC magnetic field.
In order to further understand the low temperature behavior in our investigated system, we have performed heat capacity studies up to 9 T. The specific heat per temperature against the temperature at various magnetic fields is shown in Figure 6. The classical Dulong-Petit limit is calculated to be = 3 ∼ 99.76 J/mol K (for equals four atoms in the unit cell), where is the gas constant equal to 8.314 J/mol.K. According to the Sommerfeld-Bethe theory of metals, the electronic specific heat is linear in temperature, while the lattice-specific heat is proportional to 3 in the low temperature limit [48,49]. The observed low value of the electronic specific heat-prefactor  reflects the good quality of the synthesised materials, see Supplementary Materials Figure S2 [50][51][52][53]. At very low temperatures, specific heat data show a linear behavior indicating that there are no Schottky-like contributions in the sample above 1.8 K. The heat capacity data enable the calculation of the entropy for LNMO. The entropy was derived by numerically integrating / between 0 and 50 K at magnetic fields of zero and 9 T. The field and frequency dependence of the real part of the AC susceptibility are consistent with the DC measurements and show that there is AFM order at low temperatures and paramagnetic behavior at higher temperatures. The imaginary part of the AC susceptibility, χ describes the losses associated with the irreversible magnetization process due to the existence of a small hysteresis loop; measuring this parameter at different AC magnetic fields and different frequencies indicates that χ is a field-and frequency-dependent, as illustrated in Figures 4b and 5b, respectively.
In order to further understand the low temperature behavior in our investigated system, we have performed heat capacity studies up to 9 T. The specific heat per temperature against the temperature at various magnetic fields is shown in Figure 6.

Conclusions
The optical, magnetic, and thermodynamic behavior of LNMO was investigated in detail. The ultra-fast dynamics of photoexcited carriers in LNMO shown for the fast multiexciton decay refers to the Auger recombination process. The sample has a significant negative bleach around a wavelength of 380nm. From the magnetic measurements, an antiferromagnetic behavior is dominant at low temperatures with the coexistence of other phases such as weak ferromagnetic or canted antiferromagnetic phase, due to the interaction of Mn ions. The appearance of a hysteresis loop beside AC magnetic susceptibility measurements confirms these phenomena. The investigation of the Li-excess rocksalt cathode material LNMO behavior in extreme conditions is very important for their application. This is indispensable for enhancing the synthesis as well as the revealing of such a group of Li-ion battery cathode materials in the proceeding studies. The results of this study should significantly improve the data basis for thermodynamic calculations and simulations of processes utilizing lithium-ion battery materials.
Supplementary Materials: The following are available online at www.mdpi.com/xxx/s1, Figure S1:  The classical Dulong-Petit limit is calculated to be C = 3nR ∼ 99.76 J/mol K (for n equals four atoms in the unit cell), where R is the gas constant equal to 8.314 J/mol.K. According to the Sommerfeld-Bethe theory of metals, the electronic specific heat is linear in temperature, while the lattice-specific heat is proportional to T 3 in the low temperature limit [48,49]. The observed low value of the electronic specific heat-prefactor γ reflects the good quality of the synthesised materials, see Supplementary Materials Figure S2 [50][51][52][53]. At very low temperatures, specific heat data show a linear behavior indicating that there are no Schottky-like contributions in the sample above 1.8 K. The heat capacity data enable the calculation of the entropy S for LNMO. The entropy was derived by numerically integrating C p /T between 0 and 50 K at magnetic fields of zero and 9 T.

Conclusions
The optical, magnetic, and thermodynamic behavior of LNMO was investigated in detail. The ultra-fast dynamics of photoexcited carriers in LNMO shown for the fast multiexciton decay refers to the Auger recombination process. The sample has a significant negative bleach around a wavelength of 380 nm. From the magnetic measurements, an antiferromagnetic behavior is dominant at low temperatures with the coexistence of other phases such as weak ferromagnetic or canted antiferromagnetic phase, due to the interaction of Mn ions. The appearance of a hysteresis loop beside AC magnetic susceptibility measurements confirms these phenomena. The investigation of the Li-excess rocksalt cathode material LNMO behavior in extreme conditions is very important for their application. This is indispensable for enhancing the synthesis as well as the revealing of such a group of Li-ion battery cathode materials in the proceeding studies. The results of this study should significantly improve the data basis for thermodynamic calculations and simulations of processes utilizing lithium-ion battery materials.