Magnetization and thermal expansion measurements on the Ising magnet ${\mathrm{SmPt}}_2{\mathrm{Si}}_2$: Potential coexistence of spin glass and antiferromagnetic states

The Ising magnet $\mathrm{Sm}{\mathrm{Pt}}_2{\mathrm{Si}}_2$ undergoes an antiferromagnetic (AFM) transition at $T_{\mathrm{N}1}$ = 5.6 K, but the magnetic moments of some Sm ions remain disordered even below $T_{\mathrm{N}1}$. Here, we report the results of measurements of thermal expansion, magnetostriction, and dc magnetization of $\mathrm{Sm}{\mathrm{Pt}}_2{\mathrm{Si}}_2$ in the temperature range from 0.26 to 7 K. The magnetization and thermal expansion results show clear irreversible phenomena at temperatures below $T_{\mathrm{g}}\approx$ 2.4 K. These results suggest that the partially disordered state of the Sm ions becomes a cluster spin glass below $T_{\mathrm{g}}$ and coexists with the AFM long-range order. However, unlike the conventional coexistence of spin glass and antiferromagnetism, the isothermal magnetization process at 0.26 K shows a hysteresis curve with almost no remanent magnetization. This observation suggests that the cluster spin glass state is an unusual state with a short relaxation time at zero field.

Figure 1

Temperature dependence of the transverse linear thermal expansion $\mathrm{\Delta }{L}_{\mathrm{a}}\left(T\right)/L_{\mathrm{a}}$ (a) and longitudinal linear thermal expansion $\mathrm{\Delta }{L}_{\mathrm{c}}\left(T\right)/L_{\mathrm{c}}$ (b) measured in a fixed magnetic field between 0 and 5 T when the magnetic field is applied along the $c$ axis in $\mathrm{Sm}{\mathrm{Pt}}_2{\mathrm{Si}}_2$. Each data was taken with increasing temperature after ZFC, and then with decreasing temperature. The green arrow indicates the AFM transition temperature $T_{\mathrm{N}1}$, the blue arrow indicates the magnetic structure transition temperature $T_{\mathrm{N}2}$, and the red arrow indicates the temperature $T_{\mathrm{g}}$ (see text). Note that the two panels are on the same scale.

Figure 2

Temperature dependence of the transverse linear thermal expansion coefficient ${\alpha }_{\mathrm{a}}$ measured at magnetic fields of 0, 1, and 1.5 T in $\mathrm{Sm}{\mathrm{Pt}}_2{\mathrm{Si}}_2$. The red arrow indicates the onset temperature of the broad peak, $T_{\mathrm{g}}$. The black dashed line is a straight line fitting through the origin for data below $T_{\mathrm{g}}$. The green dashed line indicates $T_{\mathrm{N}1}$.

Figure 3

Temperature dependence of volume thermal expansion determined from experimental results of linear thermal expansion of $\mathrm{Sm}{\mathrm{Pt}}_2{\mathrm{Si}}_2$. The green arrow indicates $T_{\mathrm{N}1}$, the blue arrow indicates $T_{\mathrm{N}2}$, and the red arrow indicates $T_{\mathrm{g}}$.

Figure 4

Magnetic field dependence of the longitudinal (a) and transverse (b) magnetostrictions of $\mathrm{Sm}{\mathrm{Pt}}_2{\mathrm{Si}}_2$ measured at selected temperatures between 0.26 K and 6 K. The blue arrow shows the transition field from phase II when the magnetic field is reduced (see text). Note that the two panels are on the same scale.

Figure 5

Magnetic field dependence of the volume magnetostriction $\mathrm{\Delta }V\left(H\right)/V$ obtained from linear magnetostriction in $\mathrm{Sm}{\mathrm{Pt}}_2{\mathrm{Si}}_2$.

Figure 6

Temperature dependence of dc magnetization $M\left(T\right)/{\mu }_{0}H$ (a) and linear transverse thermal expansion coefficient $\alpha \left(T\right)$ (b) of $\mathrm{Sm}{\mathrm{Pt}}_2{\mathrm{Si}}_2$ when a magnetic field of 1 T is applied along the $c$ axis. $T_{\mathrm{g}}$ is the temperature at which irreversibility develops. The dashed lines are guides for the eyes.

Figure 7

Temperature dependence of the magnetization $M_{(}T)/H$ of $\mathrm{Sm}{\mathrm{Pt}}_2{\mathrm{Si}}_2$ measured at several fixed magnetic fields between 1 T and 5 T. The green arrow indicates $T_{\mathrm{N}1}$, the blue arrow indicates $T_{\mathrm{N}2}$, and the red arrow indicates $T_{\mathrm{g}}$.

Figure 8

Isothermal magnetization curve $M\left(H\right)$ of $\mathrm{Sm}{\mathrm{Pt}}_2{\mathrm{Si}}_2$ measured at selected temperatures between 0.26 and 6 K. All results were taken after ZFC. The blue arrow shows the transition field from phase II when the magnetic field is reduced. Inset: temperature dependence of the remanent magnetization $M_{\mathrm{r}}\left(T\right)$ obtained from the measurement of the $M\left(H\right)$ process (black circles). The red circle indicates the remanent magnetization when the $M\left(H\right)$ process is measured through phase II. See the text for details. The dashed lines are guides for the eyes.

Figure 9

$H$–$T$ phase diagram of $\mathrm{Sm}{\mathrm{Pt}}_2{\mathrm{Si}}_2$ for $H\parallel c$ as determined from the present measurements. The green closed ($T_{\mathrm{N}1}$), blue open ($T_{\mathrm{N}2}$) circles and red squares ($T_{\mathrm{g}}$) are the transition point obtained from Figs. 1, 2, and 7. The cross symbols are the one obtained from Figs. 4 and 8. Phase P is the paramagnetic phase. Phase I is an AFM phase with a partially disordered state. Phase II is an AFM phase with no partially disordered state. Phase III is a coexisting phase of spin glass and antiferromagnetism. Below 0.5 K (light gray region), the II-III phase transition disappears.

Figure 10

Isothermal magnetization process of $\mathrm{Sm}{\mathrm{Pt}}_2{\mathrm{Si}}_2$ at 0.26 K. The black line is the result of measurement in the normal procedure. The red line is the result obtained by the following procedure; we started with the state in phase II above 2 K at 5 T, and then lowered the temperature to 0.26 K. The data was then taken with decreasing the field from 5 T to 0 T.

Figure 11

Time variation of the remanent magnetostriction ratio $\mathrm{\Delta }{L}_{\mathrm{a}}\left(t\right)/\mathrm{\Delta }{L}_{\mathrm{a}}\left(0\right)$ in zero field immediately after magnetostriction measurement at 0.26 K after going through phase II. The red line is the result of fitting the data with the stretched exponential relaxation function $exp(-{(t/\tau )}^{\beta })$. The relaxation time $\tau =2500$ s and the stretching exponent $\beta =0.63$ are obtained.

Figure 12

(a) Calculated results of magnetic susceptibility $\chi$ of $\mathrm{Sm}{\mathrm{Pt}}_2{\mathrm{Si}}_2$. The green and blue lines are the results calculated with the two- and one sublattice models, respectively. The red line is their average. (b) Calculated result of zero-field specific heat $C/T$. Note that the model does not include contributions from partially disordered states and phonons. The black dots in both (a) and (b) are experimental results from Ref. [2]. Inset: temperature dependence of the Grüneisen parameter in $\mathrm{Sm}{\mathrm{Pt}}_2{\mathrm{Si}}_2$ in zero magnetic field. The specific heat data are taken from Ref. [2]. The bulk modulus $B_{\mathrm{T}}$ used in the evaluation is 100 GPa and the molar volume $V_{\mathrm{m}}$ is $5.21\times$10${}^{-5}{\mathrm{m}}^3$/mol. The filled and open circles are the result on heating and cooling, respectively.