First-order nature of the ferromagnetic phase transition in $\left(\mathrm{La}\text{‐}\mathrm{Ca}\right)\mathrm{Mn}{\mathrm{O}}_3$ near optimal doping

Neutron scattering has been used to study the nature of the ferromagnetic transition in single crystals of ${\mathrm{La}}_{0.7}{\mathrm{Ca}}_{0.3}\mathrm{Mn}{\mathrm{O}}_3$ and ${\mathrm{La}}_{0.8}{\mathrm{Ca}}_{0.2}\mathrm{Mn}{\mathrm{O}}_3$, and polycrystalline samples of ${\mathrm{La}}_{0.67}{\mathrm{Ca}}_{0.33}\mathrm{Mn}{\mathrm{O}}_3$ and ${\mathrm{La}}_{5∕8}{\mathrm{Ca}}_{3∕8}\mathrm{Mn}{\mathrm{O}}_3$ where the naturally occurring ${}^{16}\mathrm{O}$ can be replaced with the ${}^{18}\mathrm{O}$ isotope. Small angle neutron scattering on the $x=0.3$ single crystal reveals a discontinuous change in the scattering at the Curie temperature for wave vectors below $\approx 0.065{\mathrm{\AA }}^{-1}$. Strong relaxation effects are observed for this domain scattering, for the magnetic order parameter, and for the quasielastic scattering, demonstrating that the transition is not continuous in nature, in good agreement with the temperature dependence of the central component of the magnetic fluctuation spectrum, the polaron correlations, and the spin stiffness reported previously. This behavior contrasts with the continuous behavior observed for the $x=0.2$ crystal, which is well away from optimal doping. There is a large oxygen isotope effect observed for the $T_C$ in the polycrystalline samples, and the Curie temperature is decreased by $7\mathrm{K}$ by substituting 50% ${}^{18}\mathrm{O}$ in the $x=0.33$ sample. For the optimally doped $x=3∕8$ sample we observed $T_C\left({}^{16}\mathrm{O}\right)=266.5\mathrm{K}$ and $T_C\left({}^{18}\mathrm{O}\right)=261.5\mathrm{K}$ at 90% ${}^{18}\mathrm{O}$ substitution. Although $T_C$ is decreased by $5\mathrm{K}$ for the $x=3∕8$ sample the temperature dependence of the spin-wave stiffness is found to be identical for the two samples. These results indicate that $T_C$ is not solely determined by the magnetic subsystem, but instead the ferromagnetic phase is truncated by the formation of polarons which cause an abrupt transition to the paramagnetic, insulating state. The application of uniaxial stress in the $x=0.3$ single crystal sharply enhances the polaron scattering at room temperature. Measurements of the phonon density-of-states show only modest differences above and below $T_C$ and between the two different isotopic samples.

Figure 1

(a) Measurement of the ferromagnetic order parameter at the (110) peak for a single crystal of ${\mathrm{La}}_{0.8}{\mathrm{Ca}}_{0.2}\mathrm{Mn}{\mathrm{O}}_3$ near $T_C$. Data are well described by a power law with an exponent that agrees with a three-dimensional Heisenberg model. (b) Spin wave stiffness for the same sample. $D$ renormalizes to zero as $T\to T_C$, as expected for a conventional ferromagnetic transition that is continuous in nature.

Figure 2

(a) The $q$ dependence of the small angle neutron scattering intensity above and below $T_C$ for a single crystal of ${\mathrm{La}}_{0.7}{\mathrm{Ca}}_{0.3}\mathrm{Mn}{\mathrm{O}}_3$. Below $T_C$ there is a significant increase in scattering concentrated in the forward direction with a slope of $-5$ on a log-log scale. (b) Integrated intensity as a function of temperature showing the abrupt change at $T_C=251\mathrm{K}$.

Figure 3

Time dependence of the observed SANS scattering for three different wave vectors at $250\mathrm{K}$. Data are scaled at $t=0$ and shifted vertically to the same asymptotic value, and are fit to a decaying exponential with a time constant $\tau =6.6\pm 0.3\text{minutes}$.

Figure 4

(a) Thermal irreversibility of the (100) magnetic Bragg peak on warming and cooling. The data were obtained by changing the temperature in $1\mathrm{K}$ steps every $2.5\min$. (b) Time dependence of the intensity of the (100) Bragg peak, both warming to the set point of $250\mathrm{K}$, and cooling to the same set point. Data are fit to an exponential relaxation. Note that the time constants are roughly identical and the asymptotic values are identical within experimental uncertainties, so there is no genuine hysteresis observable.

Figure 5

Relaxation time $\tau$ as a function of temperature for the (100) Bragg peak. The short time constant found away from the transition is typical of the time it takes for a sample to equilibrate, but in the vicinity of $T_C$ the time constant increases dramatically, indicating that the transition is first order in nature.

Figure 6

Intensity of the (100) magnetic Bragg peak, in the long-time limit. The data reveal that there is no genuine hysteresis observable. The bottom curve shows the derivative of the data, where the minimum identifies a Curie temperature of $251\mathrm{K}$.

Figure 7

Intensity of the quasielastic magnetic scattering for a temperature of $266\mathrm{K}$ at a wave vector of $0.11{\mathrm{\AA }}^{-1}$. Note that it takes about an hour for the intensities to become equal on approaching from low versus high temperatures. In the long-time limit there is no genuine hysteresis observable.

Figure 8

Change in the intensity of the charge-order peak when uniaxial stress is applied. The intensity increases by more than a factor of two in going from $0\mathrm{kbar}\text{to}1\mathrm{kbar}$ of uniaxial stress. The intensity of the single-polaron (diffuse) scattering also increases with applied stress.

Figure 9

Measurement of the intensity of the magnetic scattering on warming for polycrystalline samples of ${\mathrm{La}}_{5∕8}{\mathrm{Ca}}_{3∕8}\mathrm{Mn}{\mathrm{O}}_3$ that have been treated with ${}^{16}\mathrm{O}$ and ${}^{18}\mathrm{O}$. The Curie temperature is reduced by $5\mathrm{K}$ for the ${}^{18}\mathrm{O}$ sample.

Figure 10

(a) An example of the spin wave dispersion relation for two typical temperatures. Data are well described by gapless quadratic dispersion with the indicated values of $D$. (b) $D$ versus temperature for the ${}^{16}\mathrm{O}$ and ${}^{18}\mathrm{O}$ samples. The observed $D$ values are identical at each temperature independent of the oxygen isotope, despite the difference in $T_C$ (as indicated by the arrows). The extrapolated temperature where $D\left(T\right)$ would renormalize to zero is $271\mathrm{K}$, but the ferromagnetic-metallic state abruptly disappears at the temperature where the polarons form, and this truncation occurs at a lower temperature for the ${}^{18}\mathrm{O}$ sample. The $D\left(T_C\right)$ value for the original data in Ref. 16 with $x=0.33$ is also indicated by the open diamond symbol. The inset shows the stiffness over a wider temperature range.

Figure 11

Constant-$q$ scans at a wave vector of $0.11{\mathrm{\AA }}^{-1}$ showing the nature of the magnetic fluctuation spectrum in the vicinity of $T_C$ for the ${}^{16}\mathrm{O}$ and ${}^{18}\mathrm{O}$ samples. (a) For the ${}^{16}\mathrm{O}$ sample there is a three peak structure at $265\mathrm{K}$, while just above $T_C$ at 268 there is a single quasielastic peak. (b) For the ${}^{18}\mathrm{O}$ sample at $258\mathrm{K}$ most of the weight of the magnetic scattering is in the spin wave excitations. At $261\mathrm{K}$ the weight in the spin wave scattering has decreased, and the spectral weight has shifted to the central component. At $262\mathrm{K}$ the scattering is completely diffusive in nature. There is no evidence of the usual collapse of the spin wave energies found in a second-order transition. Note that the count rates for the two samples are different even though the samples were approximately the same size, and this difference is due to the data being collected under different experimental conditions; ${}^{16}\mathrm{O}$ data were taken on BT-2 with a collimation of ${20}^{\prime }\text{‐}{10}^{\prime }\text{‐}{10}^{\prime }\text{‐}{20}^{\prime }$, while the ${}^{18}\mathrm{O}$ data were collected on BT-9 with a collimation of ${10}^{\prime }\text{‐}{13}^{\prime }\text{‐}{10}^{\prime }\text{‐}{16}^{\prime }$.

Figure 12

Phonon density-of-states for (a) ${}^{16}\mathrm{O}$ and (b) ${}^{18}\mathrm{O}$ samples taken above and below $T_C$. Units are those appropriate for the FANS spectrometer with a Cu(220) monochromator.

Figure 13

A comparison of the phonon density-of-states for ${}^{16}\mathrm{O}$ and ${}^{18}\mathrm{O}$ samples above $T_C$. There are some slight differences which are more easily seen at low temperature, shown in the inset.