Magnetic properties of geometrically frustrated ${\mathrm{SrGd}}_2{\mathrm{O}}_4$

A study of the magnetic properties of the frustrated rare-earth oxide ${\mathrm{SrGd}}_2{\mathrm{O}}_4$ has been completed using bulk property measurements of magnetization, susceptibility, and specific heat on single-crystal samples. Two zero-field phase transitions have been identified at 2.73 and 0.48 K. For the field $H$, applied along the $a$ and $b$ axes, a single boundary is identified that delineates the transition from a low-field, low-temperature magnetically ordered regime to a high-field, high-temperature paramagnetic phase. Several field-induced transitions, however, have been observed with $H\parallel c$. The measurements have been used to map out the magnetic phase diagram of ${\mathrm{SrGd}}_2{\mathrm{O}}_4$, suggesting that it is a complex system with several competing magnetic interactions. The low-temperature magnetic behavior of ${\mathrm{SrGd}}_2{\mathrm{O}}_4$ is very different compared to the other $\mathrm{Sr}{L}_2{\mathrm{O}}_4$ ($L$ = Lanthanide) compounds studied so far, even though all of the $\mathrm{Sr}{L}_2{\mathrm{O}}_4$ compounds are isostructural, with the magnetic ions forming a low-dimensional lattice of zigzag chains that run along the $c$ axis. The differences are likely to be due to the fact that in the ground state ${\mathrm{Gd}}^{3+}$ has zero orbital angular momentum and therefore the spin-orbit interactions, which are crucial for other $\mathrm{Sr}{L}_2{\mathrm{O}}_4$ compounds, can largely be neglected. Instead, given the relatively short ${\mathrm{Gd}}^{3+}–{\mathrm{Gd}}^{3+}$ distances in ${\mathrm{SrGd}}_2{\mathrm{O}}_4$, dipolar interactions must be taken into account for this antiferromagnet alongside the Heisenberg exchange terms.

Figure 1

Positions of the magnetic ions in ${\mathrm{SrGd}}_2{\mathrm{O}}_4$, with the two crystallographically inequivalent sites of the rare-earth ions shown in different colors (red and blue). When viewed in the a-b plane, honeycombs of the ${\mathrm{Gd}}^{3+}$ ions are visible. Zigzag chains running along the $c$ axis connect the honeycomb layers and give rise to geometric frustration. The box indicates the dimensions of the crystallographic unit cell.

Figure 2

(Top) Magnetic susceptibility vs temperature in an applied field of 1 kOe in the temperature range of 6 to 400 K for the field applied along the three principal axes of a single-crystal sample of ${\mathrm{SrGd}}_2{\mathrm{O}}_4$. (Bottom) Reciprocal of the molar susceptibility vs temperature and the least-squares regression fits to the data (using the Curie-Weiss model).

Figure 3

Magnetic susceptibility obtained in the temperature range of 0.5 to 5 K for a field of 100 Oe applied along each of the three principal axes of ${\mathrm{SrGd}}_2{\mathrm{O}}_4$. Two dashed lines represent 0.48 K and 2.73 K, where $\lambda$ anomalies were observed in heat capacity data in zero field. A cusp is seen in the susceptibility at 2.73 K when the field is applied along either the $a$ or $b$ axes, while a sharp decrease occurs in $\chi \left(T\right)$ for a field applied along the $c$ axis, which is highlighted in the inset. Also, below 2.73 K, small differences between ZFC (closed symbols) and FC (open symbols) measurements become apparent for $H\parallel a$.

Figure 4

(Top) Temperature dependence of the magnetic susceptibility in different fields applied along the (left) $a$ and (right) $b$ axes of ${\mathrm{SrGd}}_2{\mathrm{O}}_4$. There seems to be very little difference in the behavior at low fields and upon increasing the applied field along these axes. (Bottom) Low-temperature magnetic susceptibility obtained in the temperature range of 0.5 to 5 K, and field range of 0.10 to 50 kOe, with the fields applied along the $c$ axis of ${\mathrm{SrGd}}_2{\mathrm{O}}_4$. The transition seen at 2.73 K is suppressed by the application of higher fields, and in fields between 20 and 30 kOe a second feature in the magnetic susceptibility is observed. In fields above 30 kOe, again, only a single cusp in the low-temperature susceptibility is visible.

Figure 5

(Top) Magnetization curves obtained with the field applied along the principal axes of ${\mathrm{SrGd}}_2{\mathrm{O}}_4$ at 0.5 K in the range of 0 to 70 kOe. (Bottom) Field derivatives of the magnetization. The field induced transitions are indicated by dashed lines at $H_{\mathrm{c}1}=20.0$ kOe, $H_{\mathrm{c}2}=23.3$ kOe, and $H_{\mathrm{c}3}=53.4$ kOe. Between $H_{\mathrm{c}1}$ and $H_{\mathrm{c}2}$, when $H\parallel c$, a narrow plateau in $dM/dH$ is observed at approximately one third of the value for the maximum moment along the $c$ axis.

Figure 6

(Top) Magnetization curves for ${\mathrm{SrGd}}_2{\mathrm{O}}_4$ obtained at several temperatures in the field range of 7.5 to 27.5 kOe, for $H\parallel c$. (Bottom) Field derivatives of the magnetization, the curves have been offset by 0.05 units along the vertical axis. The double peak in the derivative of magnetization seen in the data collected at 0.5 K becomes only a single peak at higher temperatures, and this single maximum in $dM/dH$ is initially shifted up, and then down in field as the temperature is increased.

Figure 7

Temperature dependence of the specific heat divided by temperature of ${\mathrm{SrGd}}_2{\mathrm{O}}_4$ and of the nonmagnetic isostructural compounds ${\mathrm{SrLu}}_2{\mathrm{O}}_4$ and ${\mathrm{SrY}}_2{\mathrm{O}}_4$ measured in zero field. Two $\lambda$ anomalies are observed at $T_{\mathrm{N}1}=2.73$ K and $T_{\mathrm{N}2}=0.48$ K. The entropy is calculated as the area under the $C\left(T\right)/T$ curve, which has been linearly extended to zero at $T$ = 0 K, with the scale given on the right-hand axis. By 6 K, the full magnetic contribution to the entropy expected for the ${\mathrm{Gd}}^{3+}$, $J=S=7/2$, system is recovered, as indicated by the solid line positioned at $Rln8$.

Figure 8

(Top) Temperature dependence of the specific heat divided by temperature of ${\mathrm{SrGd}}_2{\mathrm{O}}_4$ in several fields for $H\parallel c$. The two peaks associated with the transitions move closer with higher applied fields, before merging and then this single peak is shifted to lower temperatures in the highest applied fields. (Bottom) Field dependence of the specific heat divided by temperature at several temperatures for $H\parallel c$. At the lowest temperature, two peaks are observed in $C\left(H\right)$. As the temperature is raised, the peaks move closer together and eventually merge. For even higher temperatures, this single peak is suppressed and moves to lower fields.

Figure 9

Magnetic $H-T$ phase diagram for ${\mathrm{SrGd}}_2{\mathrm{O}}_4$ with the field applied along the $c$ axis constructed from the susceptibility, magnetization, and specific heat curves. (Inset) Field dependence of the upper critical temperature, $T_{\mathrm{N}1}$, as observed in magnetization $M\left(H\right)$ and $M\left(T\right)$ measurements for $H\parallel a$ and $H\parallel b$. The methods used to obtain the phase boundaries are given in Ref. [41].