Magnetovolume and magnetocaloric effects in Er${}_2$Fe${}_{17}$

Combining different experimental techniques, investigations in hexagonal $P{6}_3/mmc$ Er${}_2$Fe${}_{17}$ show remarkable magnetovolume anomalies below the Curie temperature, $T_C$. The spontaneous magnetostriction reaches $1.6\times {10}^{-2}$ at 5 K and falls to zero well above $T_C$, owing to short-range magnetic correlations. Moreover, Er${}_2$Fe${}_{17}$ exhibits direct and inverse magnetocaloric effects (MCE) with moderate isothermal magnetic entropy $\Delta S_M$, and adiabatic temperature $\Delta T_{\mathrm{ad}}$ changes [$\Delta S_M\sim -4.7$ J(kgK)${}^{-1}$ and $\Delta T_{\mathrm{ad}}\sim 2.5$ K near the $T_C$, and $\Delta S_M\sim 1.3$ J(kgK)${}^{-1}$ and $\Delta T_{\mathrm{ad}}\sim -0.6$ K at 40 K for $\Delta H=80$ kOe, respectively, determined from magnetization measurements]. The existence of an inverse MCE seems to be related to a crystalline electric field-level crossover in the Er sublattice and the ferrimagnetic arrangement between the magnetic moments of the Er and Fe sublattice. The main trends found experimentally for the temperature dependence of $\Delta S_M$ and $\Delta T_{\mathrm{ad}}$ as well as for the atomic magnetic moments are qualitatively well described considering a mean-field Hamiltonian that incorporates both crystalline electric field and exchange interactions. $\Delta S_M\left(T\right)$ and $\Delta T_{\mathrm{ad}}\left(T\right)$ curves are essentially zero at $\sim$150 K, the temperature where the transition from direct to inverse MCE occurs. A possible interplay between the MCE and the magnetovolume anomalies is also discussed.

Figure 1

Temperature dependence of the magnetization, $M\left(T\right)$ for Er${}_2$Fe${}_{17}$ under $H=1$ and 10 kOe. (Inset) $M\left(T\right)$ curve at $H=50$ Oe.

Figure 2

Applied magnetic field dependence of the magnetization in the temperature range where the $M\left(T\right)$ curve at $H=10$ kOe (see Fig. 1) increases with $T$. (Inset) $M$($H$) curves between 200 and 390 K.

Figure 3

(a) Temperature dependence of the heat capacity for Er${}_2$Fe${}_{17}$ under different applied magnetic fields. (b) $C_P/T$ vs $T$ plot in the low-temperature range. (c) Detail of the heat capacity near the Curie temperature.

Figure 4

Observed (dots) and calculated (solid line) neutron powder diffraction patterns collected on D2B at (a) $T=2$ K and (b) $T=320$ K for Er${}_2$Fe${}_{17}$. The vertical bars indicate the position of the Bragg diffraction reflections; the upper (lower) row corresponds to the nuclear (magnetic) scattering. The observed-calculated difference is depicted at the bottom of each figure.

Figure 5

Reduced temperature dependence of the magnetic moment for (a) the two nonequivalent crystallographic Er sites and the four Fe sites and (b) similary for the Fe and Er-sublattices as well as for Er${}_2$Fe${}_{17}$. Solid lines represent the calculated temperature dependence of the magnetic moment (see text for more detail).

Figure 6

Temperature dependence of (a) the cell parameters and (b) the experimental unit cell volume $V\left(T\right)$ for Er${}_2$Fe${}_{17}$. The solid line $V_{\text{NM}}$ corresponds to the nonmagnetic contribution to the unit cell volume, which is an extrapolation of $V\left(T\right)$ from the paramagnetic region down to low temperature using a Grüneisen law (see text for details).

Figure 7

Reduced temperature dependence of the volume spontaneous magnetostriction, ${\omega }_S\left(T\right)/{\omega }_S$ at 5 K, compared with that of the square of the magnetic moment over ${\left({\mu }_{\mathrm{Fe}}^{\mathrm{Total}}\right)}^2$(5 K) for the Fe sublattice. The value of ${\omega }_S$(5 K) is $\sim$$1.6\times {10}^{-2}$ and ${\mu }_{\mathrm{Fe}}^{\mathrm{Total}}$(5 K) is $\sim$14.7${\mu }_B$, respectively.

Figure 8

Observed (dots) and calculated (solid line) x-ray powder diffraction patterns for Er${}_2$Fe${}_{17}$ collected at (a) $P=0$ and (b) 15 GPa. The observed-calculated difference is depicted at the bottom of each figure. (c) Fit of the $P\left(V\right)$ curve using the Birch-Murnaghan equation of state. (Inset) Pressure dependence of the unit cell parameters normalized to the value at $P=0$ GPa ($a_0$ and $c_0$) for the ${\mathrm{Th}}_2{\mathrm{Ni}}_{17}$-type crystal structure in Er${}_2$Fe${}_{17}$ at room temperature. The dashed line is a guide for the eyes.

Figure 9

Temperature dependence of (a) the isothermal magnetic entropy and (b) the adiabatic temperature changes under $\Delta H$ up to 80 kOe for Er${}_2$Fe${}_{17}$ determined from magnetization measurements. The insets show the theoretical values of $\Delta S_M$ and $\Delta T_{\mathrm{ad}}$ using the CEF and exchange parameters quoted in Sec. 3 (see text).

Figure 10

Temperature dependence of (a) the isothermal magnetic entropy and (b) the adiabatic temperature changes under $\Delta H$ of 20, 50, and 80 kOe for Er${}_2$Fe${}_{17}$ determined from heat-capacity measurements (see text).