Magnetic field and in situ stress dependence of elastic behavior in ${\mathrm{EuTiO}}_3$ from resonant ultrasound spectroscopy

Magnetoelectric coupling phenomena in ${\mathrm{EuTiO}}_3$ are of considerable fundamental interest and are also understood to be key to reported multiferroic behavior in strained films, which exhibit distinctly different properties to the bulk. Here, the magnetoelastic coupling of ${\mathrm{EuTiO}}_3$ is investigated by resonant ultrasound spectroscopy with in situ applied magnetic field and stress as a function of temperature ranging from temperatures above the structural transition temperature $T{}_s$ to below the antiferromagnetic ordering temperature $T{}_n$. One single crystal and two polycrystalline samples are investigated and compared to each other. Both paramagnetic and diamagnetic transducer carriers are used, allowing an examination of the effect of both stress and magnetic field on the behavior of the sample. The properties are reported in constant field/variable temperature and in constant temperature/variable field mode where substantial differences between both data sets are observed. In addition, elastic and magnetic poling at high fields and stresses at low temperature has been performed in order to trace the history dependence of the elastic constants. Four different temperature regions are identified, characterized by unusual elastic responses. The low-temperature phase diagram has been explored and found to exhibit rich complexity. The data evidence a considerable relaxation of elastic constants at high temperatures, but with little effect from magnetic field alone above 20 K, in addition to the known low-temperature coupling.

Figure 1

SQUID magnetometry of (a) SC, (b) PC1, and (c) PC2 samples, with insets showing low-temperature behavior.

Figure 2

Analyzed RUS data for 0-, 5-, and 10-T $H\sigma$ runs from 1.5 to 300 K for the PC1 sample.

Figure 3

Analyzed RUS data for 0-, 5-, and 10-T and “poled” $H\sigma$ runs from 1.5 to 300 K for a “$C_{44}$” peak in the SC sample at 920 kHz at room temperature. $T{}_s$ is 284 K and is taken from Ref. [18].

Figure 4

Analyzed RUS data for 0-, 5-, and 10-T and “poled” $H\sigma$ runs from 1.5 to 300 K for a “$\left(C_{11}-C_{12}\right)$” peak in the SC sample at 1040 kHz at room temperature. $T{}_s$ is 284 K and is taken from Ref. [18].

Figure 5

Analyzed RUS data for 0- and 5-T $H$ runs from 1.5 to 300 K for a $C_{11}-C_{12}$ peak in the SC sample at 1040 kHz at room temperature. Note that $Q^{-1}$ data between 50 and 250 K for all traces except 5 T and heating were subject to significant instrumental noise and are thus unreliable.

Figure 6

Analyzed RUS data for 0-, 5-, 10-, and 14-T $H\sigma$ runs through $T{}_s$ for a $C_{44}$ peak in the SC sample at 920 kHz at room temperature. $T{}_s$ is 284 K and is taken from Ref. [18]. Note that sparse markers (1 marker per 3 data points) are used on the $f^2$ curves.

Figure 7

Analyzed RUS data for 0-, 5-, 10-, and 14-T $H\sigma$ runs through $T{}_s$ for a $C_{11}-C_{12}$ peak in the SC sample at 1040 kHz at room temperature. $T{}_s$ is 284 K and is taken from Ref. [18]. Note that sparse markers (1 marker per 3 data points) are used on the $f^2$ curves.

Figure 8

Analyzed RUS data for 0-, 5-, and 10-T and “poled” $H\sigma$ runs through $T{}_s$ for a $C_{11}-C_{12}$ peak in the SC sample at 1040 kHz at room temperature along with $H$-run heating and cooling data at 0 and 5 T. $T{}_s$ is 284 K and is taken from Ref. [18]. Note that sparse markers (1 marker per 3 data points) are used on the $f^2$ curves.

Figure 9

Analyzed RUS data for 0-, 5-, and 10-T $H\sigma$ runs through $T{}_s$ for the PC1 sample.

Figure 10

Analyzed RUS data for a 0-T run through $T{}_s$ for the PC2 sample. $T{}_s$ is 282 K and is taken from unpublished data of Bussmann-Holder.

Figure 11

Analyzed RUS data between 1.5 and 8 K in the PC1 sample.

Figure 12

Analyzed RUS data between 1.5 and 8 K in the SC sample.

Figure 13

Analyzed RUS data between 1.5 and 60 K in the SC sample in both $H\sigma$ configuration, with 5- and 10-T applied fields, and $H$ configuration, with 5-T applied field.

Figure 14

Analyzed RUS data near $T{}_s$ for 0 T and “poled” runs, along with the recovery after poling for $C_{11}-C_{12}$ in the SC sample. $T{}_s$ is 284 K and is taken from Ref. [18].

Figure 15

Analyzed RUS data for “unpoled” and “poled” runs through $T{}_s$ for a $C_{44}$ peak in the SC sample at 920 kHz at room temperature. $T{}_s$ is 284 K and is taken from Ref. [18]. Note that sparse markers (1 marker per 2 data points) are used on the $f^2$ curves.

Figure 16

Analyzed RUS data for “unpoled” and “poled” runs through $T{}_s$ for a $\left(C_{11}-C_{12}\right)$ peak in the SC sample at 1040 kHz at room temperature. $T{}_s$ is 284 K and is taken from Ref. [18]. Note that sparse markers (1 marker per 2 data points) are used on the $f^2$ curves.

Figure 17

Magnetic-field-dependent analyzed RUS data at 288 K, between 0 and 14 T for the SC sample, in $H\sigma$ configuration.

Figure 18

Magnetic-field-dependent analyzed RUS data at 245 K, between 0 and 14 T for the SC sample, in $H\sigma$ configuration.

Figure 19

Magnetic-field-dependent analyzed RUS data at 170 K, between 0 and 14 T for the SC sample, in $H\sigma$ configuration.

Figure 20

Magnetic-field-dependent analyzed RUS data at 80 K, between 0 and 14 T for the SC sample, in $H\sigma$ configuration.

Figure 21

Magnetic-field-dependent analyzed RUS data at 110, 170, and 245 K, between 0 and 14 T for the SC sample, in $H$ configuration, with the bottom axis reflecting dwell time, with the field from 0 to 14 to 0 T as time increases.

Figure 22

Magnetic-field-dependent analyzed RUS data at 20 K, between 0 and 14 T for the SC sample, in $H\sigma$ configuration.

Figure 23

Magnetic-field-dependent analyzed RUS data at 5 K, between 0 and 14 T for the SC sample, in $H\sigma$ configuration.

Figure 24

Magnetic-field-dependent raw RUS data at 15 K, between 0 and 14 T for the SC sample, in $H$ configuration.

Figure 25

PC1 and SC comparison, SC uses the contents of two data sets for better resolution at $T{}_s$. $\text{PC}1f^2$ data is scaled to match the SC data near room temperature.

Figure 26

A tentative low-temperature phase diagram for ETO showing newly detected magnetic-field/stress-dependent anomalies and their relationship to known and unknown phases. Both raw and demagnetizing-factor corrected data are shown for the lowest-field elastic anomaly. Markers with lines connecting them are from $H\sigma$ measurements, while the vertical bars indicate windows in which anomalies occurred for the $H$ experiments.