First-order nature of the spin-reorientation phase transition in $\mathrm{SmCr}{\mathrm{O}}_3$

The ever expected canted antiferromagnetic (CAFM) $Pb\prime n\prime m:{\mathrm{\Gamma }}_4({\mathit{G}}_{\mathit{x}},A_y,F_Z;F_Z^R)$ to $Pbn\prime m\prime :{\mathrm{\Gamma }}_2(F_x,C_y,{\mathit{G}}_{\mathit{Z}};F_x^R, {\mathit{C}}_{\mathit{y}}^{\mathit{R}})$ spin reorientation phase transition (SRPT) has only recently been confirmed through high-resolution time-of-flight neutron scattering studies by Sau et al. [Phys. Rev. B 103, 144418 (2021)]. Despite several studies on $\mathrm{SmCr}{\mathrm{O}}_3$, the nature of its SRPT still remains debatable. In the present study, we revisit the issue through dc $M\left(T\right)$ and ac-susceptibility, ${\chi }_{\mathrm{ac}}\left(T\right)$, measurements. Repeated cycle field-cooled-cooling and field-cooled-warming dc $M\left(T\right)$ measurements clearly expose a temperature point differentiating the regimes of continuous and discontinuous parts of the SRPT. The discontinuous part has a tiny but clear hysteresis in $M\left(T\right)$, confirming the first-order nature of the SRPT with supercooling $\left(T^{*}\right)$ and superheating $\left(T^{**}\right)$ temperatures to be $\sim 33$ and $\sim 36\mathrm{K}$, respectively. The hysteresis in the $M\left(T\right)$ is strongly supported by the occurrence of hysteresis in the nondispersing peaks in ${\chi }_{\mathrm{ac}}\left(T\right)$, measured using a 3 Oe ac signal amplitude during cooling and heating under zero dc-bias. Below SRPT, the complete reversibility of $M\left(T\right)$ and ${\chi }_{\mathrm{ac}}\left(T\right)$ confirms the second-order nature of the ${\mathrm{Sm}}^{3+}$ ordering at $T_{\mathrm{N}2}$, which arises due to independent ${\mathrm{Sm}}^{3+}\text{−}{\mathrm{Sm}}^{3+}$ interaction. Similarly, the absence of hysteresis in $M\left(T\right)$ as well as in ${\chi }_{\mathrm{ac}}\left(T\right)$, across the paramagnetic to CAFM ${\mathrm{\Gamma }}_4$ phase transition, proves the second-order nature of this phase transition.

Figure 1

Magnetic struture of (a) ${\mathrm{\Gamma }}_4$ phase at 55 K and (b) ${\mathrm{\Gamma }}_2$ phase at 25 K. It may be noted that in ${\mathrm{\Gamma }}_4$ phase the magnetic structure of Cr moments is $G_X$-type AFM with Cr moments oriented mostly along the $x$-axis and that of Sm is $F_Z$-type, with Sm moments aligned along the $z$-axis. After SRPT, i.e., in ${\mathrm{\Gamma }}_2$ phase, the magnetic structure of Cr moments still remains $G$-type AFM but now the Cr moments get flipped along the $Z$-axis and that of Sm is $C$-type AFM with moments aligned along the $Y$-axis.

Figure 2

(a) ZFC, FCC, and FCW dc $M\left(T\right)$ data of $\mathrm{SmCr}{\mathrm{O}}_3$ measured under 500 Oe, showing the occurrence of a weak-FM transition at 192 K arising due to CAFM ordering. The sharp drops in magnetization at ∼34 K and ∼19 K are due to SRPT and commencement of AFM ordering due to Sm-Sm direct interaction. The insets show the corresponding CW-fit and variation of ZFC magnetization.

Figure 3

Enlarged view of the FCC and FCW dc-magnetization variations across SRPT in $\mathrm{SmCr}{\mathrm{O}}_3$ measured under (a) 500 Oe and (b) 1500 Oe. This highlights the presence of hysteresis in the dc $M\left(T\right)$ confirming to the first-order nature of the SRPT. The superheating $\left(T^{**}\right)$/supercooling $\left(T^{*}\right)$ temperatures have been indicated.

Figure 4

The ZFC, FCC, and FCW M(T)s measured at (a) 500 Oe and (c) 1500 Oe fields. The corresponding first-derivative ($\mathit{dM}/\mathit{dT}$) curves (b) 500 Oe and (d) 1500 Oe bring out the fine features across the SRPT.

Figure 5

A sequence of FCC and FCW $M\left(T\right)$ curves, all measured under 500 Oe field, while turning back for FCW at decreasingly lower temperatures of 85, 60, 36, 31, and 25 K. It depicts complete reversibility until 36 K, but below that, e.g., at ∼31 K, it becomes irreversible. The inset shows the first derivatives ($\mathit{dM}/\mathit{dT}$) of the $M\left(T\right)$ curves measured until 25 K. The splitting of the FCC curve across SRPT is quite evident from the first-derivatives curves.

Figure 6

Isothermal magnetization curves, $M\left(H\right)$, measured for $\mathrm{SmCr}{\mathrm{O}}_3$ at (a) 60, 45, 35, and 25 K; and (b) 250 and 5 K. (c) The temperature variation of the coercive-field $\left(H_C\right)$ and the remanent-magnetization $\left(M_R\right)$ as derived form the $M\left(H\right)$ loops.

Figure 7

${\chi }_{\mathrm{ac}}\left(T\right)$ of $\mathrm{SmCr}{\mathrm{O}}_3$ measured at 331 Hz during a heating-cooling cycle in the range of 4–260 K. Inset (i) highlights the occurrence of ∼1.3-K-wide hysteresis in ${\chi }_{\mathrm{ac}}\left(T\right)$ across the SRPT. Inset (ii) shows that the transition from paramagnetic to CAFM and back to paramagnetic phase both exactly match at $T_{\mathrm{N}1}=192\mathrm{K}$. This asserts the second-order nature of the CAFM transition. Inset (iii) shows a complete absence of frequency dispersion of the ${\chi }_{\mathrm{ac}}\left(T\right)$ peak corresponding to SRPT, confirming its thermodynamic nature.

Figure 8

$M\left(T\right)$ variations of $\mathrm{SmCr}{\mathrm{O}}_3$ measured at different fields. It is clearly shown that at higher measuring fields, the hysteresis-II feature keeps slowly diminishing.