2.7 Discussion and Conclusion
3.1.1 Experiments on the Critical Behavior of Perovskite Manganites 56
Perovskite manganites (R1−xAxMnO3) (cf. Sec. 1.6.1) have been investigated ex- tensively for decades due to their exotic structural, electronic, and magnetic behav- ior and due to the existence of colossal magnetoresistance (CMR)—the dramatic reduction of resistivity in a magnetic field[234,104,148,14,197]. In these compounds, different choice of R and A have different atomic sizes and therefore produce varying stresses on the Mn-O-Mn bond. It was shown that the average R/A size in terms of ionic radii, expressed by the tolerance factor f[148,197], affects their critical behavior. To investigate the PM-FM phase transition, various experiments have been performed based on the DC magnetization, AC suceptibility, and
specific heatmeasurements followed by scaling analysis with Arrot plot, mod- ified Arrot plot (MAP)[117,92], Kouvel-Fisher (KF) formalism, and critical isotherm (CI)[155,185,52,162] analysis. These experiments clearly show that a change either in the doping level (x) or in the tolerance factor (f) lead to different critical expo- nents.
In fact, although initial experimental investigations[142,68] suggested inconclu- sive results as regards the universality classes, a number of subsequent experimen- tal studies on some samples[117,233,52,163] showed that the critical exponents were close to those of the tricritical mean-field theory (β = 14, γ = 1, and δ= 5). For instance, in a polycrystalline La0.6Ca0.4MnO3, the specific heat and magne- tization measurements with MAP and CI analysis yield α= 0.48±0.06, β = 0.25±0.03,γ= 1.03±0.05, and δ= 5.0±0.8. The magnetization data for polycrys- talline La0.1Nd0.6Sr0.3MnO3 yields two sets of results, namely, β = 0.248±0.006, γ= 1.066±0.002with MAP andβ= 0.257±0.005,γ= 1.12±0.03, andδ= 5.17±0.02 with KF method and CI analysis. In polycrystalline Nd0.67Sr0.33MnO3, the mag- netization data analysed with MAP yields β = 0.23±0.02, γ = 1.05±0.03, and δ= 5.13±0.04.
Although the above mentioned samples exhibit tricritical mean-field exponents, there are other compounds[68,92,118,162,220,176,167,185,53,69,154] whose critical expo- nents deviate from those of the tricritical mean-field values. For instance, in single crystal La0.7Sr0.3MnO3, the critical exponents obtained via Arrot plot and CI anal- ysis are β= 0.37±0.04, γ = 1.22±0.03, and δ = 4.25±0.2. In polycrystalline Pr0.5Sr0.5MnO3, the MAP analysis yieldsβ= 0.443±0.002,γ= 1.339±0.006, while the KF method as well as CI analysis giveβ= 0.448±0.009,γ= 1.334±0.010, and δ= 3.955±0.001.
In a number of studies, a change in the doping level x in the same compound
led to different critical exponents[68,92,117,162,233]. For instance, different sets of critical exponents were obtained for La1−xCaxMnO3 when x = 0.2 and x= 0.4. Similar behavior was noted for La1−xSrxMnO3 when x= 0.3 and x= 0.125. This was also observed in Ref. for a different compound, namely, Nd1−xSrxMnO3 withx= 0.33andx= 0.4.
The above mentioned experimental findings clearly indicate that different criti- cal exponents are obtained with different choices for R and/or A as well as with dif- ferent levels of doping,x. Although in some of these experimental works[68,162,52], the critical exponents were compared with those of the existing theoretical mod- els, namely, mean-field, tricritical mean-field, 3D Ising, and 3D Heisenberg, these existing models were unable to reproduce their widely varying critical exponents.
3.1.2 Studies on Microscopic Models
An essential microscopic mechanism in perovskite manganites is the coupling of spin and lattice degrees of freedom (cf. Sec.1.6.1). The electron-phonon JT cou- pling leading to lattice distortions are known to be important as indicated by a number of theoretical[151,188,148,149,6] and experimental studies[99,200,43,24,26]. A pronounced variation of electrical resistivity and a large shift of Tc after isotope exchange (18O for 16O) indicate a strong spin-lattice coupling[257,14]. The lattice distortions are shown to be directly related to the imposed strain due to pertur- bations induced via changes inR, A, andx[148,149,26,200,105]. A quantitative analy- sispredicted a dramatic sensitivity of material properties to strain, particularly the shifting ofTc with strain. Different strain modes are shown to evolve depend- ing on whether the perturbation is due to the size distribution of R/Aatoms or to the change in the doping concentration x. Elastic interactions are shown to play an essential role in the formation of superstructures[115,116] and texturing ob-
served in perovskite manganites. In addition to JT distortions, another essential microscopic mechanism is the spin-spin DE interaction[255,148,197]. The microscopic models for the magnetic (and electrical) properties of perovskite manganites are based on the framework of these two mechanisms which provide a satisfactory ex- planation for the origin of CMR and the change in resistivity as the system passes through the PM-FM transition. They also explain satisfactorily the systematic vari- ation ofTcwith doping[99,148,188]. A number of Monte Carlo (MC) simulations have been performed[32,158,157,156]on a DE model Hamiltonian
q1 +Si.Sj (3.1)
for the investigation of the static critical behavior. These simulations yield ν = 0.6949±0.0038, β = 0.3535±0.0030, γ = 1.3909±0.0030 in Ref., β ≈0.365 in Refs.[158,156], β = 0.36±0.01 in Ref., and ν = 0.686±0.010, that are close to those of the 3D Heisenberg model (with SR interaction). This suggests that the DE and 3D Heisenberg models[36,91] belong to the same universality class.
Although a few perovskite manganite samples[162,167] are found to have critical indices near to the 3D Heisenberg model predictions, a vast majority of sam- ples[142,68,92,117,220,185,233,52], as discussed above, exhibit a widely varying sets of critical indices including the tricritical mean-field exponents. Thus, although the DE is widely accepted as one of the key mechanisms for CMR in perovskite man- ganites, models involving the DE interaction can not capture their widely varying critical behavior near the PM-FM phase transition.