Magnetic and magnetoelastic properties of ${\mathrm{Er}}_3{\mathrm{Al}}_2$

We report on comprehensive investigations of ${\mathrm{Er}}_3{\mathrm{Al}}_2$ exhibiting a number of magnetic states. We observe three spontaneous antiferromagnetic transitions at 10, 14, and 24 K. Furthermore, our high-field magnetization and sound-velocity measurements reveal a number of crystal-electric-field (CEF) transitions. Additionally, the velocity of transverse acoustic waves shows a pronounced softening with decreasing temperature in the paramagnetic state. A CEF model that includes quadrupolar interactions explains the observed magnetic and elastic properties and provides a CEF scheme of ${\mathrm{Er}}_3{\mathrm{Al}}_2$. However, to explain some of the observations, a refined, more sophisticated model needs to be developed.

Figure 1

Temperature dependences of (a) the magnetic susceptibility, $\chi$, (b) specific heat, $C$, and (c) relative sound velocity, $\mathrm{\Delta }v/v$, of longitudinal and transverse acoustic waves in ${\mathrm{Er}}_3{\mathrm{Al}}_2$. The ultrasound frequencies were 61.2, 102.8, and 36.3 MHz for the modes $C_{44}$, $(C_{11}-C_{12})/2$, and $(C_{11}+C_{12}+2C_{66})/2$, respectively. In (c), the curves are vertically shifted for clarity.

Figure 2

Field dependences of (a) the magnetization, $M$, and (b) relative sound velocity, $\mathrm{\Delta }v/v$, of longitudinal acoustic waves for field applied along the principal crystallographic directions of ${\mathrm{Er}}_3{\mathrm{Al}}_2$ at 2 K. The inset in (a) shows $M$ and its field derivative, $dM/dH$, for field applied along the [100] axis up to 6 T. The ultrasound frequencies were 36, 42, and 82 MHz for field applied along the [100], [110], and [001] axes, respectively. In (b), the curves are vertically shifted for clarity.

Figure 3

Field dependences of the magnetization, $M$, and relative sound velocity, $\mathrm{\Delta }v/v$, of longitudinal acoustic waves for field applied along the (a), (d) [100], (b), (e) [110], and (c), (f) [001] axes of ${\mathrm{Er}}_3{\mathrm{Al}}_2$ between 2 and 25 K. The ultrasound frequencies were 36, 42, and 82 MHz for field applied along the [100], [110], and [001] axes, respectively. In (d)–(f), the curves are vertically shifted for clarity.

Figure 4

Temperature dependences of (a) and (c) the relative sound-velocity, $\mathrm{\Delta }v/v$, for the transverse acoustic modes $(C_{11}-C_{12})/2$ and $C_{44}$, respectively, and (b) the inverse magnetic susceptibility, $1/\chi$. (d) CEF level scheme of an ${\mathrm{Er}}^{3+}$ ion in ${\mathrm{Er}}_3{\mathrm{Al}}_2$ obtained from the CEF parameters listed in Table 1. In (a)–(c), the symbols and the solid lines represent the experimental and calculated data, respectively. The dashed lines in (a) and (c) represent the background stiffness. In (d), all horizontal lines correspond to doublets.

Figure 5

Field dependences of the magnetization, $M$, at (a) 2 and (b) 25 K calculated for ${\mathrm{Er}}_3{\mathrm{Al}}_2$ using the CEF parameters listed in Table 1.