Hysteresis effects in the phase diagram of multiferroic ${\mathrm{GdMnO}}_3$

We present high-resolution thermal expansion $\alpha \left(T\right)$ and magnetostriction $\mathrm{\Delta }L\left(H\right)∕L$ measurements of ${\mathrm{GdMnO}}_3$, which develops an incommensurate antiferromagnetic order (ICAFM) below $T_N\simeq 42\mathrm{K}$ and transforms into a canted A-type antiferromagnet (cAFM) below $T_c\simeq 20\mathrm{K}$. In addition, a ferroelectric polarization $\mathbf{P}\parallel a$ is observed below $T_{\mathrm{FE}}$ for finite magnetic fields applied along the $b$ direction. In zero-magnetic field, we find a strongly anisotropic thermal expansion with certain, rather broad anomalous features. In finite magnetic fields, however, very strong anomalies arise at $T_c$ for fields applied along each of the orthorhombic axes and at $T_{\mathrm{FE}}$ for fields along the $b$ axis. Both phase transitions are of first-order type and strongly hysteretic. We observe a downbending of the ICAFM-to-cAFM phase boundary $T_c\left(H\right)$ for low magnetic fields and our data give evidence for coexisting phases in the low-field low-temperature range.

Figure 1

(Color online) Thermal expansion of ${\mathrm{GdMnO}}_3$ along $a$, $b$, and $c$.

Figure 2

(Color online) Panel (a): Field-cooled thermal expansion ${\alpha }_a\left(T\right)$ for $H\parallel a$ measured with increasing $T$. Panel (b) shows the hysteresis around $T_c$ between the data obtained with increasing and decreasing $T$. Panel (c) compares two zero-field ${\alpha }_a\left(T\right)$ curves for increasing $T$. The first curve [0T-(1)] has been recorded after zero-field cooling the sample and the second [0T-(2)] after cooling the sample to $12\mathrm{K}$ and subsequently applying and removing a magnetic field of $8\mathrm{T}$. The lower panels (d) and (e) present the ZFC magnetostriction $\mathrm{\Delta }{L}_i\left(H\right)∕L_i$ recorded with increasing (solid lines) and decreasing (dashed) field.

Figure 3

(Color online) The relative length changes of the $a$, $b$, and $c$ axes as a function of $T$ at constant field ($H=6\mathrm{T}$; left) and as a function of $H$ at constant temperature ($T=15\mathrm{K}$; right). In all cases, $H$ was applied parallel to the measured direction.

Figure 4

(Color online) FC measurements of ${\alpha }_b\left(T\right)$ in fields up to $1\mathrm{T}$ (a) and between $8\mathrm{T}$ and $14\mathrm{T}$ (b). The inset of panel (a) compares ${\alpha }_b\left(T\right)$ for $H=4\mathrm{T}$ applied along $b$ (solid line) and $c$ (dashed). The upper inset of panel (b) shows ${\alpha }_b\left(T\right)$ for $H=12\mathrm{T}$ ($H\parallel b$; $dT∕dt>0$) obtained in a FC (symbols) and a ZFC run (line). The lower inset displays the hysteresis between ${\alpha }_b\left(T\right)$ for $H=6\mathrm{T}$ recorded with $dT∕dt>0$ (solid line) and $dT∕dt<0$ (dashed). Panels (c) and (d) show the ZFC magnetostriction obtained for $dH∕dt>0$.

Figure 5

(Color online) Phase diagrams of ${\mathrm{GdMnO}}_3$ based on the measurements of ${\alpha }_i$ (triangles) and $\mathrm{\Delta }{L}_i\left(H\right)∕L_i$ (squares) measured along $i=a$, $b$, and $c$ with $H\parallel i$. Filled and open symbols are obtained with increasing and decreasing $T$ or $H$, respectively. Hatched areas signal regions of strong hysteresis, where different phases coexist.