Raman scattering studies of the temperature- and field-induced melting of charge order in ${\mathrm{La}}_x{\mathrm{Pr}}_y{\mathrm{Ca}}_{1-x-y}{\mathrm{MnO}}_3$

We present Raman scattering studies of the structural and magnetic phases that accompany temperature- and field-dependent melting of charge- and orbital-order (COO) in ${\mathrm{La}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3$ and ${\mathrm{La}}_{0.25}{\mathrm{Pr}}_{0.375}{\mathrm{Ca}}_{0.375}{\mathrm{MnO}}_3$. Our results show that thermal and field-induced COO melting in ${\mathrm{La}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3$ exhibits three stages in a heterogeneous melting process: At low temperatures and fields we observe a long-range, strongly Jahn-Teller (JT) distorted-COO phase; at intermediate temperatures and/or fields, we find a coexistence regime comprising both strongly JT distorted-COO and weakly JT distorted/ferromagnetic metal (FMM) phases; and at high temperatures and/or high fields, we observe a weakly JT distorted homogeneous paramagnetic (PM) or ferromagnetic (FM) phase. In the high field-high temperature regime of ${\mathrm{La}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3$ and ${\mathrm{La}}_{0.25}{\mathrm{Pr}}_{0.375}{\mathrm{Ca}}_{0.375}{\mathrm{MnO}}_3$, we identify a clear structural change to a weakly JT distorted phase that is associated with either a Imma or Pnma structure. We are able to provide a complete structural phase diagram of ${\mathrm{La}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3$ for the temperature and field ranges $6\le T\le 170\mathrm{K}$ and $0\le H\le 9\mathrm{T}$. Significantly, we provide evidence that the field-induced melting transition of ${\mathrm{La}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3$ is first-order, and resembles a crystallization transition of an “electronic solid.” We also investigate thermal and field-induced melting in ${\mathrm{La}}_{0.25}{\mathrm{Pr}}_{0.375}{\mathrm{Ca}}_{0.375}{\mathrm{MnO}}_3$ to elucidate the role of disorder in melting of COO. We find that while thermal melting of COO in ${\mathrm{La}}_{0.25}{\mathrm{Pr}}_{0.375}{\mathrm{Ca}}_{0.375}{\mathrm{MnO}}_3$ is quite similar to that in ${\mathrm{La}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3$, field-induced melting of COO in the two systems is quite different in several respects: The field-induced transition from the COO phase to the weakly JT-distorted-FM phase in ${\mathrm{La}}_{0.25}{\mathrm{Pr}}_{0.375}{\mathrm{Ca}}_{0.375}{\mathrm{MnO}}_3$ is very abrupt, and occurs at significantly lower fields ($H\sim 2\mathrm{T}$ at $T\sim 0\mathrm{K}$) than in ${\mathrm{La}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3$ ($H\sim 30\mathrm{T}$ at $T=0\mathrm{K}$); the intermediate coexistence regime is much narrower in ${\mathrm{La}}_{0.25}{\mathrm{Pr}}_{0.375}{\mathrm{Ca}}_{0.375}{\mathrm{MnO}}_3$ than in ${\mathrm{La}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3$; and the critical field $H_c$ increases with increasing temperature in ${\mathrm{La}}_{0.25}{\mathrm{Pr}}_{0.375}{\mathrm{Ca}}_{0.375}{\mathrm{MnO}}_3$, in contrast to the decrease in $H_c$ observed with increasing temperature in ${\mathrm{La}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3$. To explain these differences, we propose that field-induced melting of COO in ${\mathrm{La}}_{0.25}{\mathrm{Pr}}_{0.375}{\mathrm{Ca}}_{0.375}{\mathrm{MnO}}_3$ is best described as the field-induced percolation of FM domains, and we suggest that Griffiths phase physics may be an appropriate theoretical model for describing the unusual temperature- and field-dependent transitions observed in ${\mathrm{La}}_{0.25}{\mathrm{Pr}}_{0.375}{\mathrm{Ca}}_{0.375}{\mathrm{MnO}}_3$.

Figure 1

(Color online) (a) Temperature dependence of the Raman spectrum of ${\mathrm{La}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3$ in the temperature range $6–170\mathrm{K}$. (Inset) Field-dependence of the 420 and $440{\mathrm{cm}}^{-1}$ “field-induced modes” for $T=160\mathrm{K}$, showing the enhancement of these modes with applied magnetic field. (b) Schematic representation of the $CE$-type AFM/charge/orbital order in ${\mathrm{La}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3$, showing the doubling of the unit cell. (c) Intensity (empty squares) and linewidth (filled circles) of the $480{\mathrm{cm}}^{-1}$ JT mode as a function of temperature. The intensity of this mode is suppressed by $\sim 85\%$ from $T=6$ to $170\mathrm{K}$. (d) Summary of the intensity (empty squares) and linewidth (filled circles) of the $400{\mathrm{cm}}^{-1}$ “folded phonon mode” as a function of temperature. The intensity of this mode is completely suppressed above $T=150\mathrm{K}$. The symbol sizes in parts (c) and (d) reflect an estimated 5% error associated with fits to the observed spectra.

Figure 2

(Color) Normal modes associated with the $480{\mathrm{cm}}^{-1}$ JT peak: the $487{\mathrm{cm}}^{-1}$ $A_g$ and $473{\mathrm{cm}}^{-1}$ $B_{2g}$ asymmetric stretch modes of the oxygen atoms in the ${\mathrm{MnO}}_6$ octahedra (adapted from Refs. 29, 43).

Figure 3

(a) Doping dependence of the Raman spectrum of ${\mathrm{La}}_{1-x}{\mathrm{Ca}}_x{\mathrm{MnO}}_3$ at $x=0.5$, 0.495, 0.55, and 0.45. (b) Summary of the intensity of the $400{\mathrm{cm}}^{-1}$ “folded phonon” mode (empty squares) and the $480{\mathrm{cm}}^{-1}$ JT mode (filled circles) as a function of doping.

Figure 4

(Color online) (a) Magnetic field dependence of the Raman spectrum of ${\mathrm{La}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3$ at $6\mathrm{K}$, illustrating the absence of a significant change in the spectrum with increasing magnetic field. The solid lines illustrate the examples of Gaussian and Lorentzian fits to the actual spectra, and the thick dashed line illustrates the sum of all individual fits. (b) Magnetic field dependence of the Raman spectrum of ${\mathrm{La}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3$ at $120\mathrm{K}$, showing a significant suppression of the JT mode and the folded phonon modes, and indicating the appearance of field-induced modes near 420 and $440{\mathrm{cm}}^{-1}$ with increasing magnetic field. (c) Magnetic field dependence of the Raman spectrum of ${\mathrm{La}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3$ at $150\mathrm{K}$, showing the evolution of the 420 and $440{\mathrm{cm}}^{-1}$ field-induced modes with increasing field. (d) Summary of the intensity (empty squares) and linewidth (filled circles) of the $480{\mathrm{cm}}^{-1}$ “JT mode” as a function of magnetic field. The intensity of this mode is suppressed by $\sim 80\%$ from $H=0$ to $9\mathrm{T}$. (e) Summary of the intensity (empty squares) and linewidth (filled circles) of the $400{\mathrm{cm}}^{-1}$ “folded phonon” mode as a function of magnetic field. The intensity of this mode is completely suppressed above $H=8\mathrm{T}$. (f) Summary of the combined intensities (empty squares) of the $420∕440{\mathrm{cm}}^{-1}$ “field-induced phonon” modes as a function of magnetic field. The intensity of these modes is essentially fully developed above $H=8\mathrm{T}$. The symbol sizes in parts (d), (e), and (f) reflect an estimated 5% error associated with fits to the observed spectra.

Figure 5

(Color) (a) Contour plot of the intensity of the $400{\mathrm{cm}}^{-1}$ folded phonon mode as functions of temperature and magnetic field. The dark (purple) shades indicate the prevalence of the strongly JT distorted ($P{2}_1∕m$ space group) structural phase, which is associated with the AFM-COO phase. (b) Contour plot of the combined intensities of the 420 and $440{\mathrm{cm}}^{-1}$ field-induced modes as functions of temperature and field. The dark (green) shades indicate the prevalence of the weakly JT distorted ($Imma$ or $Pnma$ space group) structural phase, which is associated with the ferromagnetic metal (FMM) phase. (c) Temperature-magnetic field phase diagram of ${\mathrm{La}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3$ inferred from the intensity plots in (a) and (b), showing the phase boundary, $H^{*}\left(T\right)$, between the strongly JT distorted ($P{2}_1∕m$ space group) AFM-COO phase (purple) and intermediate “coexistence” phase (black) regimes, and the phase boundary, $H_c\left(T\right)$, between the intermediate “coexistence” phase (black) and weakly JT distorted ($Imma$ or $Pnma$ space group) FMM phase (green) regimes.

Figure 6

(Color online) (a) Temperature dependence of the Raman spectrum of ${\mathrm{La}}_{0.25}{\mathrm{Pr}}_{0.375}{\mathrm{Ca}}_{0.375}{\mathrm{MnO}}_3$ in the temperature range $3.5–210\mathrm{K}$. (b) Schematic representation of the effect of Pr substitution in ${\mathrm{La}}_{0.25}{\mathrm{Pr}}_{0.375}{\mathrm{Ca}}_{0.375}{\mathrm{MnO}}_3$ on COO, where double circles represent charge (hole) defects in COO. (c) Summary of the intensity (empty squares) and linewidth (filled circles) of the $480{\mathrm{cm}}^{-1}$ “JT mode” of ${\mathrm{La}}_{0.25}{\mathrm{Pr}}_{0.375}{\mathrm{Ca}}_{0.375}{\mathrm{MnO}}_3$ as a function of temperature. The intensity of this mode is suppressed by $\sim 75\%$ from $T=3.5$ to $210\mathrm{K}$. (d) Summary of the intensity (empty squares) and linewidth (filled circles) of the $400{\mathrm{cm}}^{-1}$ “folded phonon” mode of ${\mathrm{La}}_{0.25}{\mathrm{Pr}}_{0.375}{\mathrm{Ca}}_{0.375}{\mathrm{MnO}}_3$ as a function of temperature. The intensity of this mode is completely suppressed above $T=170\mathrm{T}$. The symbol sizes in parts (c) and (d) reflect an estimated 5% error associated with fits to the observed spectra.

Figure 7

(Color online) (a) Magnetic field dependence of the Raman spectrum of ${\mathrm{La}}_{0.25}{\mathrm{Pr}}_{0.375}{\mathrm{Ca}}_{0.375}{\mathrm{MnO}}_3$ at $3.5\mathrm{K}$, showing a dramatic suppression of the $480{\mathrm{cm}}^{-1}$ JT and $400{\mathrm{cm}}^{-1}$ folded phonon modes, and the appearance of the 420 and $440{\mathrm{cm}}^{-1}$ field-induced modes at $H\sim 2\mathrm{T}$. (b) Magnetic field dependence of the Raman spectrum of ${\mathrm{La}}_{0.25}{\mathrm{Pr}}_{0.375}{\mathrm{Ca}}_{0.375}{\mathrm{MnO}}_3$ at $130\mathrm{K}$, showing an abrupt field-induced transition between strongly JT distorted and weakly JT distorted structural phases. (c) Magnetic field dependence of the Raman spectrum of ${\mathrm{La}}_{0.25}{\mathrm{Pr}}_{0.375}{\mathrm{Ca}}_{0.375}{\mathrm{MnO}}_3$ at $190\mathrm{K}$. (d) Summary of the intensity (empty squares) and linewidth (filled circles) of the $480{\mathrm{cm}}^{-1}$ “JT mode” as a function of magnetic field. The intensity of this mode is completely suppressed above $H=2\mathrm{T}$. (e) Summary of the intensity (empty squares) and linewidth (filled circles) of the $400{\mathrm{cm}}^{-1}$ “folded phonon” mode as a function of magnetic field. The intensity of this mode is completely suppressed above $H=2\mathrm{T}$. (f) Summary of the combined intensities (empty squares) of the $420∕440{\mathrm{cm}}^{-1}$ “field-induced phonon” modes as a function of magnetic field. The intensity of this mode is essentially fully developed above $H=2\mathrm{T}$. The symbol sizes in parts (d)–(f) reflect an estimated 5% error associated with fits to the observed spectra.

Figure 8

(Color) (a) Contour plot of the intensity of the $400{\mathrm{cm}}^{-1}$ folded phonon mode in ${\mathrm{La}}_{0.25}{\mathrm{Pr}}_{0.375}{\mathrm{Ca}}_{0.375}{\mathrm{MnO}}_3$ as functions of temperature and field. The dark (purple) shades indicate the prevalence of the strongly JT distorted ($P{2}_1∕m$ space group) structural phase, which is associated with the AFM-COO phase. (b) Contour plot of the combined intensities of the 420 and $440{\mathrm{cm}}^{-1}$ field-induced modes of ${\mathrm{La}}_{0.25}{\mathrm{Pr}}_{0.375}{\mathrm{Ca}}_{0.375}{\mathrm{MnO}}_3$ as functions of temperature and field. The dark (green) shades indicate the prevalence of the weakly JT distorted ($Imma$ or $Pnma$ space group) structural phase, which is associated with the ferromagnetic metal (FMM) phase. (c) Temperature-magnetic field phase diagram of ${\mathrm{La}}_{0.25}{\mathrm{Pr}}_{0.375}{\mathrm{Ca}}_{0.375}{\mathrm{MnO}}_3$, inferred from the intensity plots in (a) and (b), illustrating strongly JT distorted ($P{2}_1∕m$ space group) AFM-COO phase (purple), weakly JT distorted ($Imma$ or $Pnma$ space group) FMM phase (green), and coexistent crossover phase (black) regimes.