Ferromagnetism and lattice distortions in the perovskite ${\text{YTiO}}_3$

The thermodynamic properties of the ferromagnetic perovskite ${\text{YTiO}}_3$ are investigated by thermal expansion, magnetostriction, specific-heat, and magnetization measurements. The low-temperature spin-wave contribution to the specific heat, as well as an Arrott plot of the magnetization in the vicinity of the Curie temperature $T_C\simeq 27\text{K}$, is consistent with a three-dimensional Heisenberg model of ferromagnetism. However, a magnetic contribution to the thermal expansion persists well above $T_C$, which contrasts with typical three-dimensional Heisenberg ferromagnets, as shown by a comparison with the corresponding model system EuS. The pressure dependences of $T_C$ and of the spontaneous moment $M_s$ are extracted using thermodynamic relationships. They indicate that ferromagnetism is strengthened by uniaxial pressures $\mathbf{p}\parallel \mathbf{a}$ and is weakened by uniaxial pressures $\mathbf{p}\parallel \mathbf{b},\mathbf{c}$ and hydrostatic pressure. Our results show that the distortion along the $a$ and $b$ axes is further increased by the magnetic transition, confirming that ferromagnetism is favored by a large ${\text{GdFeO}}_3$-type distortion. The $c$-axis results, however, do not fit into this simple picture, which may be explained by an additional magnetoelastic effect, possibly related to a Jahn-Teller distortion.

Figure 1

(Color online) Variation with $T$ of the specific heat $C_p$ of ${\text{YTiO}}_3$.

Figure 2

(Color online) Variation with $T$ (a) of the relative lengths $\Delta L_i/L_i$ for $i=a$, $b$, and $c$ and of the relative volume $\Delta V/V$ and (b) of the thermal expansion coefficients ${\alpha }_i$ for $i=a$, $b$, $c$, and $V$.

Figure 3

(Color online) Field dependence of the magnetization $M$, on a log-log scale, at $T=1.8\text{K}$ and $T=26.5\text{K}\simeq T_C$.

Figure 4

(Color online) Field dependence of the magnetostriction ${\lambda }_i$, on a log-log scale, for $i=a$, $b$, and $c$ at $T=2.5\text{K}$ and $T_C=26.7\text{K}$ (${\lambda }_a$ is plotted with a minus sign).

Figure 5

(Color online) (a) Specific heat and (b) thermal expansion of ${\text{YTiO}}_3$ in $C_p/T$ and $\left|{\alpha }_i\right|$ versus $T$ on log-log scales, respectively.

Figure 6

(Color online) Best Arrott plot of the data, with $\beta =0.392$, $\gamma =1.475$, and $T_C=26.44\text{K}$. The dotted line indicates the critical regime at $T_C$ associated with the exponent $\delta =4.76$.

Figure 7

(Color online) Temperature dependence (a) of $\left(\Delta \alpha ={\alpha }_a-{\alpha }_c\right)$ for ${\text{YTiO}}_3$ and (b) of $\alpha$ for EuS. In both plots, the dashed line is a guide to the eyes indicating the nonmagnetic background; the shaded (colored) area is the magnetic contribution deduced from the raw data after subtraction of this background and the vertical dotted line indicates the ferromagnetic transition temperature. (c) Magnetic contribution to the thermal expansion estimated for ${\text{YTiO}}_3$ (red line) and for EuS (blue line) in a normalized ${\alpha }^{\text{mag}}/{\alpha }_{\text{max}}^{\text{mag}}$ vs $T/T_C$ plot.

Figure 8

(Color online) Temperature dependence of the magnetic contribution $C_p^{\text{mag}}$ to the specific heat in a $C_p^{\text{mag}}/T$ versus $T$ plot. The inset shows the scaling of $C_p\left(T\right)$ (red line) and ${\alpha }_V\left(T\right)$ (green line), which permitted us to estimate the nonmagnetic contribution (blue line).

Figure 9

(Color online) Ferromagnetic ordering anomaly (a) in the specific heat and (b)–(d) in the thermal expansivity coefficients along $a$, $b$, and $c$. In these curves, the jumps $\Delta C_p$, $\Delta {\alpha }_a$, $\Delta {\alpha }_b$, and $\Delta {\alpha }_c$ at the ferromagnetic ordering are indicated by arrows.

Figure 10

(Color online) Schematic magnetic phase diagram of ${\text{Y}}_{1-x}{\text{La}}_x{\text{TiO}}_3$ ($\text{AF}=\text{antiferromagnetic}$ and $\text{FM}=\text{ferromagnetic}$). The arrows indicate the effects of increasing the ${\text{GdFeO}}_3$-type distortion and of applying uniaxial pressures $\mathbf{p}\parallel \mathbf{a},\mathbf{b}$.

Figure 11

(Color online) Schematics of the lattice structure of ${\text{YTiO}}_3$. The ${\text{Ti}}^{3+}$ ions are represented by gray spheres, the ${\text{Y}}^{3+}$ ions by green spheres, and the ${\text{O}}^{2-}$ ions by red spheres. The ${\text{TiO}}_6$ octahedra are colored in yellow, and blue arrows show their elongated direction, possibly due to the Jahn-Teller distortion.

Figure 12

(Color online) Variations for the $A{\text{TiO}}_3$ and $A{\text{FeO}}_3$ systems of (a) the unit-cell volume $V$ and (b) the lattice parameters $a$, $b$, and $c/\sqrt{2}$, as a function of the ionic radius of $A^{3+}$. In (c) and (d), the volume and the lattice parameters of $A{\text{TiO}}_3$ and $A{\text{FeO}}_3$ are scaled together using the empirical factor $f=1.01$.

Figure 13

(Color online) High-temperature linear extrapolation of the lattice parameters $a$, $b$, and $c/\sqrt{2}$ of ${\text{YTiO}}_3$.