Correlation between magnetic interactions and lattice distortions in Pr and Eu substituted NdCrO3

The study reveals the impact of rare earth (R = Pr, Eu) substitutions on the structural, optical, and magnetic properties of multiferroic NdCrO${_3}$. It has been observed recently that structural distortion in substituted NdCrO${_3}$ induces a spin-phonon coupled exchange bias [1].Here, the comparison of Nd${_{0.9}}$Pr${_{0.1}}$CrO${_3}$ and Nd${_{0.9}}$Eu${_{0.1}}$CrO${_3}$ samples where the A-site (i.e., R-site) are doped by Pr${^{3+}}$ having the larger ionic radius (1.126 A°) correspond to less chemical pressure and Eu${^{3+}}$ (1.066 A°) having the smaller ionic radius correspond to more chemical pressure exerted on the NdCrO${_3}$ with the ionic radius of Nd${^{3+}}$ ion (1.109 A°), are presented with the help of X-ray diffraction, Raman, UV- visible spectroscopy, and dc magnetization measurements. By picking such ions of different spin configuration Pr${^{3+}}$ (J = 4) and Eu${^{3+}}$ (J = 0), the alteration of the strong coupling between Nd${^{3+}}$ (J = 9/2) and Cr${^{3+}}$ (S = 3/2) spins of parent NdCrO${_3}$ compound is possible. Polycrystalline samples of Nd${_{0.9}}$Pr${_{0.1}}$CrO${_3}$ and Nd${_{0.9}}$Eu${_{0.1}}$CrO${_3}$ were prepared by standard solid-state reaction route, and the structural characterization of the samples is done by X-ray diffraction (XRD) analysis. The Rietveld refinement of XRD patterns was performed using the FULLPROF package, which shows samples are crystallized in single-phase and all observed peaks adopt the orthorhombically distorted perovskite structure (Pnma space group) similar to that of parent NdCrO${_3}$. We found that the substitution of Pr${^{3+}}$ ions gives the increment in the overall cell parameters of NdCrO${_3}$ such that the decrease in lattice parameter a, increase in b, c, and lattice volume V is observed. However, an increase in lattice parameter a and decrease in b, c, and lattice volume V is obtained for the substitution of Eu${^{3+}}$ ions in NdCrO${_3}$ showing decrement in the overall cell parameters. Similar changes are also observed for CrO${_6}$ octahedral bond lengths and angles for the two samples. The influence of the dopant on the average A-site ionic radius, ${r_{avg}}$ = $\sqrt{0.9r_{Nd}^2 +0.1r_{Eu/Pr}^2}$, could account for this variation. The distortion of cell edges from the ideal cubic perovskite is calculated using Goldschmidt’s tolerance factor, $t = (r{_R} + r{_O})/\sqrt2(r{_{Cr}} + r{_O})$ and the orthorhombic strain, $s = 2(a-c)/(a+c)$. As we decrease ${r_{avg}}$, the $t$ decreases, whereas the $s$ increases indicating the tuning of structural distortion of NdCrO${_3}$ by Pr and Eu doping. The microstructural analysis revealed the good quality of the homogenous bulk samples with considerable porosity. The phase purity of the samples is further examined by Raman spectroscopy. The modes B${_{2g}}$(2), A${_g}$(4) belonging to R-O1 vibration, B${_{1g}}$(2), B${_{2g}}$(3) related to CrO${_6}$ octahedral rotations, and A${_g}$(6) corresponds to CrO${_6}$ octahedral bending, exhibit the red shift (Pr doping) and blue shift (Eu doping) with respect to parent sample due to changes in average ionic radii and average atomic mass both, also observed from Raman investigation of RCrO${_3}$(Y, La to Lu) [2]. By combining Raman and XRD analysis, we conclude that the structural distortions are less for Nd${_{0.9}}$Pr${_{0.1}}$CrO${_3}$ and more for Nd${_{0.9}}$Eu${_{0.1}}$CrO${_3}$ system compared to parent NdCrO${_3}$. The optical behavior of the samples is investigated by the UV–Vis Diffuse Reflectance Spectroscopy technique. The samples have the direct bandgap ${E_g}$ = 3.24 eV (Pr doping), and 3.20 eV (Eu doping) lies in the visible region. From the magneto-optical study of NdCrO${_3}$, we know that the coupling between Nd${^{3+}}$ and Cr${^{3+}}$ spins are extremely strong [3], hence the substitution of different R on Nd-site can influence Cr-O overlap integral, which can also modify the structural distortion via the distortion of CrO${_6}$ octahedra, resulting in the change in the optical bandgap. The magnetization measurements confirm the antiferromagnetic ordering of Cr${^{3+}}$ spins occurring at ${T_N}$ = 226.7 K, 224.1 K and the spin reorientation transition due to reorientation of Cr${^{3+}}$ spins at ${T_{SR}}$ = 41.8 K, 39.2 K for Nd${_{0.9}}$Pr${_{0.1}}$CrO${_3}$ and Nd${_{0.9}}$Eu${_{0.1}}$CrO${_3}$ samples respectively. In addition to that, the magnetic behavior below $T{_N}$ varies significantly due to different alignment of Cr sublattice,$|Nd + Pr|$ and $|Nd + Eu|$ sublattice such that their moment alignment weakens the reorientation of Cr${^{3+}}$ spins in Nd${_{0.9}}$Pr${_{0.1}}$CrO${_3}$ but leaves the Nd${_{0.9}}$Eu${_{0.1}}$CrO${_3}$ system slightly affected. The negative exchange bias effect having the exchange bias field of ${H_{EB}}$ = -748 Oe and -1280 Oe with the coercive field ${H_C}$ = 405 Oe and 1049 Oe at 100 K (below ${T_N}$) is obtained for Nd${_{0.9}}$Pr${_{0.1}}$CrO${_3}$ and Nd${_{0.9}}$Eu${_{0.1}}$CrO${_3}$ samples. The value of both the field decreases at 5 K (below TSR) such that ${H_{EB}}$ = -258 Oe and -209 Oe with ${H_C}$ = 1528 Oe and 583 Oe is observed for Nd${_{0.9}}$Pr${_{0.1}}$CrO${_3}$ and Nd${_{0.9}}$Eu${_{0.1}}$CrO${_3}$ samples, respectively. The temperature variation of exchange bias field has the minimum ${H_{EB}}$ across ${T_{SR}}$ after that the ${H_{EB}}$ increases sharply with increasing $T$ having the maximum ${H_{EB}}$ in the $T$ window of 60–120 K and vanishes after ${T_N}$ for the Nd${_{0.9}}$Eu${_{0.1}}$CrO${_3}$ sample. In summary, the single-phase Nd${_{0.9}}$Pr${_{0.1}}$CrO${_3}$ and Nd${_{0.9}}$Eu${_{0.1}}$CrO${_3}$ samples were formed via the solid-state reaction method. The XRD and Raman analysis confirmed that the structural distortion increases from Nd${_{0.9}}$Pr${_{0.1}}$CrO${_3}$ to Nd${_{0.9}}$Eu${_{0.1}}$CrO${_3}$ samples. The change in optical band gap is observed for substituting different R on Nd-site, influencing the Cr-O overlap integral. The magnetic interactions of Nd${^{3+}}$/R${^{3+}}$ and Cr${^{3+}}$ spins were altered due to different spin configuration Pr${^{3+}}$ and Eu${^{3+}}$ ions resulting the change in ${T_N}$ and ${T_{SR}}$ values. The huge exchange bias field at 100 K for Nd${_{0.9}}$Eu${_{0.1}}$CrO${_3}$ is obtained due to high chemical pressure acting on competing antiferromagnetic interaction between the weak ferromagnetic component of canted Cr${^{3+}}$ moments and the paramagnetic moment of Nd${^{3+}}$/R${^{3+}}$ ions. The ordering of Pr${^{3+}}$ spins significantly increases the ${H_C}$ below ${T_{SR}}$ for the Nd${_{0.9}}$Pr${_{0.1}}$CrO${_3}$ sample. Our results clearly demonstrate the magnetic interaction between Nd/R and Cr moments is varying with the average A-site ionic radius ($r{_{avg}}$), due to different chemical pressure in Nd${_{0.9}}$R${_{0.1}}$CrO${_3}$ (R = Pr, Eu) system.

[1] Pragya Gupta, D Pal, J. Phys.: Condens. Matter, 33, 135806 (2021)
[2] M. C. Weber et al., Phys. Rev. B - Condens. Matter Mater. Phys., 85, 1–9 (2012)
[3] R. M. Hornreich et al., Phys. Rev. B 12, 5094 (1975)