Spin-Phonon Coupling in A₂BMnO₆ (A = La, Pr, Nd, Sm, Gd; B = Co, Ni) Double-Perovskite Thin Films: Impact of the A-Site Cation Radius

Abstract

Two series of B-site ordered, double-perovskite A₂CoMnO₆ and A₂NiMnO₆ (A = La, Pr, Nd, Sm, Gd) epitaxial films with thickness d ~ 100 nm were grown on SrTiO₃(111) substrates via metalorganic aerosol deposition. Polarization and temperature-dependent Raman spectroscopy were carried out in order to determine the spin-phonon coupling constant, λ, and the impact of the A-site cation radius on the phonon properties. The reduction of the A-site cation radius from La³⁺ down to Gd³⁺ systematically shifts the Raman modes to lower wavenumbers, and decreases the magnetization-induced softening of the Ag breathing mode, described by the spin-phonon coupling constant, λ, which changes from λ = 1.42 cm⁻¹ (La₂CoMnO₆) and λ = 1.53 cm⁻¹ (La₂NiMnO₆) down to λ = 0.58 cm⁻¹ (Gd₂CoMnO₆) and λ = 0.44 cm⁻¹ (Gd₂NiMnO₆). A similar effect of the A-cation radius was established for the c-lattice parameter and Curie temperature, TC, in this series of double-perovskite films. Our observations directly demonstrate a strong impact of the lattice structure on the ferromagnetic superexchange interaction in double perovskites. Moreover, the A₂CoMnO₆ and A₂NiMnO₆ series exhibit very similar behavior of spin-phonon coupling due to the only moderate difference of Co²⁺ and Ni²⁺ cation size.

1. Introduction

Double perovskites of the family A₂BMnO₆ (A = rare earth, B = Co, Ni), with a monoclinic P12₁/n1 structure, are promising materials for spintronic applications due to the presence of ferromagnetic ordering, magnetodielectric coupling, and multiferroic behavior [1,2,3,4,5,6,7]. Furthermore, they represent an attractive model system, in which the fundamental coupling between spin, charge, and lattice degrees of freedom—and, thus, their electromagnetic properties—strongly depend on the A-site cation radius [5,6,7], on the oxidation state of B-site cations [2,8,9] and, finally, on the degree of the B-site ordering [8,9,10,11,12,13].

In this context, Raman spectroscopy as a nondestructive tool represents a powerful way to distinguish between the monoclinic P12₁/n1 B-site ordered and the orthorhombic Pbnm B-site disordered A₂BMnO₆ variants; this is possible due to the different symmetry and selection rules of the corresponding Raman modes [1,14]. As a consequence, polarized Raman spectroscopy has been extensively applied to A₂BMnO₆ double-perovskite bulk samples [6,15,16,17] and thin films [1,10,14,15,18,19,20,21,22]. In addition, the spin-phonon coupling [1,10,14,16,17,19,20,21] and structural changes [10,15,22] of the double perovskites can be directly elucidated from the temperature development of the Raman spectra.

Here, we report the impact of the A-site cation size on the structural, magnetic, and phonon properties of A₂CoMnO₆ and A₂NiMnO₆ (A = La, Pr, Nd, Sm, Gd) epitaxial films grown on (111)-oriented SrTiO₃ (STO) substrates via a metalorganic aerosol deposition (MAD) technique [23]. The easy stoichiometry control within MAD is very useful for the growth of high-quality epitaxial films with different compositions. Polarization and temperature-dependent Raman spectroscopy carried out for temperatures T = 80–300 K allow us to relate the characteristic changes in the Raman spectra, induced by the A-cation size, to the changes in structure and magnetism. We observed the systematic reduction of the spin-phonon coupling by decreasing the A-site cation radius, and discussed it in the framework of variation of the internal chemical pressure induced by A-site cations.

2. Experimental Details

Double-perovskite A₂CoMnO₆ and A₂NiMnO₆ (A = La, Pr, Nd, Sm, Gd; B = Co, Ni)—further referred to as Co- and Ni-series, respectively—epitaxial thin films with thickness d ~ 100 nm were grown on SrTiO₃ (STO) substrates with (111) orientation by means of MAD [23], using a solution of acetylacetonates for the A- and B-site cations in dimethylformamide (DMF) under ambient oxygen partial pressure (pO₂ ~ 0.2 bar), with growth rates of r ~ 6 nm/min, substrate temperature of T_sub ~ 900–950 °C, and a heating/cooling rate of ~50 K/min before and after deposition [10,11,24]. X-ray reflection (XRR) and X-ray diffraction (XRD, Cu-K_α radiation, Bruker AXS D8 Advance) were used to determine the thickness, the quality, and the out-of-plane lattice parameters of the films. Temperature-dependent magnetization was measured using a SQUID magnetometer (MPMS 3, Quantum Design) at temperatures of T = 5–400 K and under an external magnetic field of H = 1000 Oe. Raman spectra were recorded using a LabRAM HR Evolution (HORIBA Jobin Yvon) spectrometer in the backscattered top-illumination geometry. A Linkam THMS350EV thermal vacuum stage, cooled by liquid nitrogen, was used for temperature-dependent measurements in the temperature range T = 80–400 K. The sample illumination and the collection of backscattered light was conducted using a 50× magnification long working distance objective (Olympus, NA = 0.5). The excitation was carried out using a linear polarized Nd:YAG laser (λ = 532 nm, Laser Quantum torus 532, second harmonic generation) with an effective incident power of P ~ 2 mW at the film surface and a laser spot size of ~1 µm² laterally. Polarized Raman spectra were recorded in a sample reference system with X‖$\left[11\overline{2}\right]$ parallel to the incident laser polarization, Y‖$\left[\overline{1}10\right]$ perpendicular to it, and Z‖[111] in the direction of light propagation. The scattered light polarization was filtered by an analyzer with two configurations (x and y) in front of the detector. Consequently, XX implies parallel scattering with the analyzer aligned parallel to the incident laser polarization, while XY is a cross-scattering polarization configuration with the analyzer aligned perpendicular to it. Transmission electron microscopy was performed using a FEI Titan 80–300 G2 environmental transmission electron microscope (TEM) operated at an acceleration voltage of 300 kV.

3. Results

To characterize the impact of the A-site cation size on the structure, we performed the XRD measurements on all of the grown films (see Supplementary Materials (SM), Figure S1 for details). XRD and TEM (SM, Figure S2) evidence an epitaxial growth for both series of samples, in good agreement with previously reported MAD-grown, double-perovskite films [10,11,18]. In Figure 1a we present the evaluated pseudocubic out-of-plane lattice parameters c_pc = c$\left(111\right)/\sqrt{3}$ of the Co- and Ni-series on STO(111) as a function of the A-site cation radius, taken from Ref. [25] for coordination number CN = 8. One can see that c_pc systematically deceases with the decrease in the A-site cation radius, and the data for both film series can be quite well described by linear fits. Note that the A₂CoMnO₆ series shows slightly larger lattice parameters than the A₂NiMnO₆ series, which can be attributed to the slightly larger B-site cation radius of Co²⁺ compared to the Ni²⁺ cation—i.e., 74.5 pm for high-spin (HS)-Co²⁺ vs. 69 pm for Ni²⁺; CN = 6, Ref. [26]. Related to the corresponding polycrystalline bulk samples of both double-perovskite series [5,6,7], the pseudocubic out-of-plane lattice parameters are slightly decreased due to an in-plane tensile epitaxy strain from the STO substrate, having a larger in-plane lattice parameter a_STO = 0.3905 nm [25], and resulting in a lattice compression in the out-of-plane direction. As the lattice parameter shrinks further by reducing the A-site cation size, the out-of-plane compressive strain ε = (c_pc − a_sub)/a_sub of the films systematically increases from ε = −0.77% for La₂CoMnO₆ (LCMO) and ε = −0.87% for La₂NiMnO₆ (LNMO) to ε = −3.76% for Gd₂CoMnO₆ (GCMO) and ε = −3.99% for Gd₂NiMnO₆ (GNMO).

In Figure 1b, the values of Curie temperatures, T_C, for the Co- and Ni-series as a function of the A-site cation radius are presented; the corresponding magnetization M(T) curves are shown in Figures S3 and S4 in SM. T_C values were calculated from the minimum of the temperature coefficient of magnetization, TCM = (1/M) (dM/dT). In addition, a systematic and almost linear reduction (solid lines for the linear approximation) of T_C was observed here by decreasing the A-site cation size from Gd³⁺ to Gd³⁺. A similar decrease of T_C with decreasing r_A was obtained in recent studies on polycrystalline A₂CoMnO₆ and A₂NiMnO₆ bulk samples [5,6,7], and was assigned to the successive reduction of the Co²⁺-O²⁻-Mn⁴⁺ and the Ni²⁺-O²⁻-Mn⁴⁺ bond angles; this reduces the overlap of Mn(e_g) and O(2p) orbitals, and causes the apparent reduction of the ferromagnetic superexchange interaction between the two B-site cation species [5,6,7]. The higher Curie temperatures, T_C, for the A₂NiMnO₆ series compared to the A₂CoMnO₆ films with the same A-site cation also indicate a stronger orbital overlap of the bonds between the (Ni/Mn)O₆ octahedra compared to those of the (Co/Mn)O₆ octahedra [6], although the differences in T_C decrease by reducing the A-site cation size; this also displays the strong impact of the cations and the internal chemical pressure on the magnetic properties of the A₂BMnO₆ double-perovskite system. In addition to the optimally high values of T_C in films of both Co and Ni series, the saturation magnetization measured at T = 5 K was found to be close to the theoretical values of 6 μ_B/f.u and 5 μ_B/f.u for the Co- and Mn-series, respectively. All of this indicates a high degree of B-site ordering in studied samples.

The Raman spectra recorded at T = 300 K of the Co- and Ni-series of double-perovskite thin films are shown in Figure 2a,b, respectively, in the parallel XX-scattering configuration, whereas Figure 2c,d show the corresponding Raman spectra in the crossed XY-scattering configuration. All films exhibit very similar Raman spectra, with two significant features: first, a strong and sharp mode at a Raman shift of ~630–675 cm⁻¹, and second, a broader and less intensive band at around ~470–530 cm⁻¹. Theoretical lattice dynamical calculations (LDCs) for LCMO [14] assigned the sharp mode to a symmetric stretching of the (Co/Mn)O₆ and (Ni/Mn)O₆ octahedra (breathing mode), whereas the broader band relates to a mixed type of antisymmetric stretching and bending of the octahedra (mixed mode). For B-site-ordered double perovskites of A₂CoMnO₆ and A₂NiMnO₆ with a monoclinic P12₁/n1 structure, the breathing mode is predicted to have A_g symmetry, which is allowed in the parallel XX-scattering and is forbidden in the crossed XY-scattering configurations; the mixed mode shows a B_g symmetry with the opposite Raman selection rules [14,15,18,20]. From the polarized Raman spectra in Figure 2a–d, it is evident that all films follow this prediction for the monoclinic P12₁/n1 structure. The additional observed modes around ~1200–1350 cm⁻¹ represent second-order overtones of the breathing mode and a breathing/mixed mode combination [18], confirming the high crystalline quality of the grown films.

Furthermore, a clear impact of the A- and B-site cations on the Raman spectra can be seen. Namely, the position of all Raman modes of the A₂NiMnO₆ series is shifted by ~20–30 cm⁻¹ to higher wavenumbers compared to those in the corresponding A₂CoMnO₆ series, due to the larger degree of covalence of the A–O and Ni/Mn–O bonds in the A₂NiMnO₆ system [6]. Moreover, the radius of the A-site cation has a significant impact on the position of the Raman modes as well. For both film series, a systematic softening of all Raman modes when decreasing the A-site cation radius was observed, indicating an increase in the Co(Ni)/Mn–O bond length [9,27]. For the A_g breathing mode in the parallel XX-scattering spectra, the development for both series is illustrated in the insets of Figure 2a,b. A similarity of the phonon behavior with that of the c-lattice parameter (see Figure 1a) and T_C (Figure 1b) as a function of the A-site cation radius evidences a strong interconnection of the structural, magnetic, and lattice properties.

In Figure 3a,b the temperature dependences of the Raman shift ω(T) of the A_g mode in the Raman spectra for the Co- and Ni-series, with different A-site cations—A = La, Pr, Nd, Sm, and Gd—are shown. In general, the temperature dependences of the positions of the Raman modes result from the anharmonic contribution to the potential energy of the atomic vibrations. By considering cubic anharmonic constants on the potential energy, the scattering can be characterized by a three-phonon process, such that the Raman mode position as a function of the temperature can be described as [28,29]:

$${\omega }_{\mathrm{anh}.}\left(T\right)={\omega }_0+C\left(1+\frac{2}{\exp \left(\hslash {\omega }_0/2k_{B}T\right)-1}\right)$$

(1)

where ω₀ is the position of a Raman mode at T = 0 K, and C is an anharmonic constant, both of which were taken as adjustable parameters to fit the temperature dependence of the experimentally determined position of the A_g mode. One can see in Figure 3a,b that the anharmonic model (red curves) of the A_g mode position ω(T) fits the experimental data (black data points) for temperatures T ≥ T_C within the paramagnetic phase of the double-perovskite thin films nicely. However, for all films of the Co- and Ni-series, a distinct deviation from the anharmonic model approximation occurs for 80 K < T < T_C—namely, one can see a significant softening of the A_g breathing mode, initiated by the transition into a ferromagnetic phase at T_C and continuously increased by a subsequent cooling to lower temperatures. Comparing the position of the A_g mode at the lowest temperature T = 80 K with that given by anharmonic approximation for different films, it is evident that the extent of the softening appears to be coupled to the radius of the A-site cations—i.e., the largest A-site cation Gd³⁺ results in the strongest softening, which then decreases systematically by reducing the A-site radius to Gd³⁺. This is very similar to the above-shown effects of the A-site cation radius on the c-lattice parameter (Figure 1a), on the T_C (Figure 1b), and on the softening of the breathing mode with decreasing r_A, as shown in Figure 2a,b. Taken together, these data offer a clear indication of the connection between the mode softening, the lattice structure, and the magnetic properties.

The softening of the A_g breathing mode at T < T_C originates from a phonon renormalization induced by ferromagnetic ordering, also observed for ferromagnetic manganites [29,30] and cobaltates [31], resulting in a coupling between magnetism and lattice known as a spin-phonon coupling. Considering the nearest-neighbor interaction, the phonon renormalization $\Delta \omega \left(T\right)=\omega \left(T\right)-{\omega }_{\mathrm{anh}.}\left(T\right)$ is proportional to the spin–spin correlation function 〈$S_i·S_j$〉 of the spins at the ith and jth sites, which is proportional in a molecular mean-field approximation to the normalized average magnetization M²(T)/M²_max per magnetic ion at temperature T [14,29,30,31]. As there are four nearest B’-site cation neighbors for each B-site cation in the A₂BB’O₆ double perovskites with a rock-salt-type B-site ordering, the phonon renormalization $\Delta \omega \left(T\right)$ can be written as [30,31,32]:

$$\Delta \omega \left(T\right)=\omega \left(T\right)-{\omega }_{\mathrm{anh}.}\left(T\right)\approx -\lambda S_i·S_j\approx -4\lambda \frac{M^2\left(T\right)}{M_{\max }^2}$$

(2)

Within this model, the spin-phonon coupling is quantified by the spin-phonon coupling constant, λ, whereas M_max is the saturation magnetization at T = 0 K. In Figure 4a–e and Figure 5a–e we present the softening $\Delta \omega \left(T\right)=\omega \left(T\right)-{\omega }_{\mathrm{anh}.}\left(T\right)$ of the A_g breathing mode plotted against squared normalized magnetization M²(T)/M²_max for the Co- and Ni-film series, respectively. An excellent agreement between the $\Delta \omega \left(T\right)$ and magnetization data for all films at temperatures of T < T_C verifies that the A_g mode softening arises from the spin-phonon coupling. It is evident that the softening, starting at T_C, increases with increasing magnetization in the film by cooling; hence, a significant spin-phonon coupling is present for all of our films in their ferromagnetic phases.

The shift $\Delta \omega \left(T\right)$ of the A_g breathing mode, plotted against the magnetization M²(T)/M²_max, can be described by a linear approximation—as shown for both film series in Figure 4f and Figure 5f—and the spin-phonon coupling strength is determined by the corresponding slope S = 4λ. [10,16,19,31] One can see a systematic decrease in the slope and, hence, in the spin-phonon coupling constant when the A-site cation radius is reduced from the largest cation Gd³⁺ to the smallest cation Gd³⁺ within the A₂CoMnO₆ and A₂NiMnO₆ film series. The corresponding values for the spin-phonon coupling strength, λ, are presented for both series as a function of the A-site cation radius [26] in Figure 6. For the A₂CoMnO₆ film series, the maximal value of λ = 1.42 cm⁻¹, obtained for LCMO, reduces systematically with the decreasing size of the A-cation, down to λ = 0.58 cm⁻¹ (GCMO). For the A₂NiMnO₆ films, the maximal value of λ = 1.53 cm⁻¹ (LNMO) reduces to λ = 0.44 cm⁻¹ (GNMO). Note that the λ values for GCMO and GNMO are likely underestimated, since these films show an enhanced saturation magnetization (see Table S1 in the SM) due to the strong contribution of the magnetic moment of Gd. Hence, a systematic and similar decrease in the spin-phonon coupling strength, λ, by reducing the A-site cation radius is observed for both series. A similar behavior was observed recently for A₂CoMnO₆/LaAlO₃(001) films (A = Pr, Nd, Sm) [19] and polycrystalline bulk samples (A = La, Pr, Nd) [16]. Remarkably, very different λ-values were determined in thin films and bulk samples: a PCMO film and a bulk sample show λ = 1.61 cm⁻¹ and λ = 0.51 cm⁻¹, respectively. As for the A₂NiMnO₆ series, no influence of the A-site cation radius on the spin-phonon coupling was detected in bulk samples for A = La, Pr, Nd, Gd, Y [17], in contradiction to our results for A₂NiMnO₆/STO(111) films (see Figure 6).

4. Discussion

To elucidate the origin of the A-site cation influence on the spin-phonon coupling in double-perovskite films, the intrinsic and extrinsic mechanisms should be considered. In general, the systematic decrease in the spin-phonon coupling strength, λ, for smaller A-site cations reflects the impact of chemical pressure on the structure–property (magnetic and phononic) relationship. Initially, the orbital overlap and the apparent ferromagnetic superexchange depend on the Co²⁺–O²⁻–Mn⁴⁺ or Ni²⁺–O²⁻–Mn⁴⁺ bond angles between the B-site cations [5,6,7]. This is shown in Figure 1b for the A₂CoMnO₆ and the A₂NiMnO₆ series, for which a reduction in the A-site cation size from Gd³⁺ to Gd³⁺ leads to a systematic decrease in T_C due to the chemical-pressure-induced decrease in the bond angle. Simultaneously, the reduction of the A-site cation radius modifies the internal bond lengths, yielding a decrease in the pseudocubic c-lattice parameter [5,6,7,33] (Figure 1a), an increase in the lattice mismatch and, finally, an enhancement of the epitaxy stress in films grown on the STO(111) substrates. As a result, the force constants of the perovskite lattice [30,32] also increase, and the lattice gets stiffer, as evidenced by the significant shift of the A_g breathing mode in the Raman spectra towards larger wavenumbers (Figure 2a,b). As a consequence, the decrease in the A-site cation radius results in a systematic reduction of both the magnetic superexchange interaction and the spin-phonon coupling, as the latter connects magnetic and phonon properties. A similar behavior was seen also for the rare earth RMnO₃ manganites [30,32].

Comparing the A₂CoMnO₆ and the A₂NiMnO₆ double-perovskite film series, the spin-phonon coupling strength, λ, for the same A-site cation exhibits only small differences, indicating a weak impact of the Co²⁺ and Ni²⁺ cations on the spin-phonon coupling. In general, the A₂CoMnO₆ film series shows slightly larger λ values (the only exception being A = La) than the A₂NiMnO₆ film series, although T_C values are significantly higher for the A₂NiMnO₆ series (Figure 1b). As the cation size of Co²⁺ and Ni²⁺ is comparable (74.5 pm for HS-Co²⁺ vs. 69 pm for Ni²⁺; CN = 6, Ref. [26]), and the lattice parameters are also similar (Figure 1a), the different spin contributions of HS–Co²⁺/Ni²⁺, and their impact on the bonds, force constants, and phonon properties (Figure 2a–d), must be involved. Obviously, the overall interplay results in a comparable spin-phonon coupling for both series. Recent studies on the A₂CoMnO₆ series showed similar values for the coupling strength, with λ = 1.61 cm⁻¹ for PCMO, λ = 1.20 cm⁻¹ for NCMO, and λ = 1.16 cm⁻¹ for SCMO for films on LAO(100) substrates [19], and λ ~ 1.4–2.1 cm⁻¹, depending on the substrate, for LCMO thin films [10], whereas for polycrystalline bulk PCMO with λ = 0.51 cm⁻¹, a significantly lower coupling was obtained [16]. For the A₂NiMnO₆ series, no comparative values are available. Recent studies on polycrystalline A₂NiMnO₆ bulk samples showed no A-site cation influence, but from the A_g breathing mode softening, the coupling strength can be estimated roughly to λ ~ 0.6–0.7 cm⁻¹ for the whole series [17], which is again significantly lower than for our A₂NiMnO₆ thin films.

An explanation for this discrepancy can be given by the sample characteristics; whereas the epitaxial thin films exhibit a high crystalline quality and are in-plane strained due to the lattice misfit [10,12,19,24], the strain effects are absent for the polycrystalline bulk samples, but problems concerning the oxygen stoichiometry can occur and play a crucial role [8,9,16]. Furthermore, the degree of the B-site ordering of the double-perovskites must be included for a complete discussion [10,12,20,21]. Beginning with the strain, it is argued that for the case of A₂CoMnO₆ films on LAO(100), the compressive biaxial strain has a significant influence on the magnetic interaction and the spin-phonon coupling, due to a reduction in oxygen vacancies and a higher degree of B-site ordering compared to bulk samples [16,19]. Our recent study on the B-site-ordered LCMO thin films with a (111) out-of-plane-orientation on various substrates also reveals a strong strain impact [10]. In this context, the largest spin-phonon coupling strength of λ ~ 2.1 cm⁻¹ was observed for LCMO(111) films on Al₂O₃(0001) and on (LaAlO₃)_0.3(Sr₂TaAlO₆)_0.7(111)(LSAT) substrates, actuating a small, compressive, in-plane strain. This coupling constant is significantly larger than λ ~ 1.4–1.5 cm⁻¹ (see Ref. [10] and the present study), obtained on LCMO(111) films grown on substrates with a larger lattice mismatch, such as LAO(111) and STO(111).

On the other hand, the spin-phonon coupling of the double-perovskite A₂BMnO₆ is affected by the degree of the B-site ordering, as it directly depends on structural and magnetic properties [8,9,10,11,12]. For B-site-ordered LCMO and LNMO films, this is reflected by a significant increase in the softening of the A_g breathing mode in the ferromagnetic phase, and by the corresponding spin-phonon coupling for the B-site-ordered films compared to partially or fully disordered systems [10,20,21]. For LCMO thin films on c-orientated Al₂O₃(0001), this results in a spin-phonon coupling strength of λ ~ 2.1 cm⁻¹ in the case of B-site ordering, and a decrease to λ ~ 1.7 cm⁻¹ for a partially B-site-disordered film [10]. Additionally, the B-site ordering in the double-perovskite films can be stimulated and improved by a compressive in-plane strain, due to a different distortion of the B/B’O₆ octahedra [12]. In combination with the higher crystalline quality of the epitaxial thin films, a higher degree of B-site ordering—and, hence, a stronger mode softening and spin-phonon coupling compared to polycrystalline, double-perovskite bulk samples—is achieved. For partially B-site-disordered or polycrystalline bulk double perovskites, this also results in a decreased impact of the A-site cation on the coupling strength, as the crystal quality, ordering, and strain have a significantly stronger influence [10,16,17,19,20,21]. Conversely, the spin-phonon coupling strength as an indicator of the crystal quality depicts a direct way to characterize and improve the suitability of a double-perovskite material for technological applications.

5. Conclusions

Epitaxial films of the B-site-ordered A₂CoMnO₆ and A₂NiMnO₆ (A = La, Pr, Nd, Sm, Gd) double-perovskite series with a monoclinic P12₁/n1 structure were grown on SrTiO₃(111) substrates using the MAD technique, in order to determine the impact of the A-site cation size on the structural, magnetic, and phonon properties. By carrying out polarization and temperature-dependent Raman measurements, the anomalous softening of the breathing mode in the ferromagnetic phase, and its dependence on the size of A-site cations, were revealed in both film series. The results were discussed within the influence of the A-site-induced variation of internal chemical pressure on the spin–lattice interaction, quantified by the corresponding spin-phonon coupling strength, λ. We observed a systematic reduction in λ by decreasing the size of the A-cation, which is very similar to the changes in the c-lattice parameters and Curie temperatures actuated by the A-cation size. Thus, the spin-phonon coupling constant—correlating structural, magnetic, and phonon properties together—displays the strong impact of the A-site cation size in the A₂CoMnO₆ and A₂NiMnO₆ double perovskites, and depicts a promising way to improve the material suitability of various double-perovskite systems for technological applications.