The family of rare-earth perovskite scandates RScO₃ (R = rare earth) have attracted continued attention due to great variety of physical properties and potential applications. For example, the Ising-like antiferromagnet,^[1] the giant magnetocaloric effect,^[2,3] and the promising candidate materials for the replacement of SiO₂ in silicon MOSFETs because of the large optical band gaps, high dielectric constants, andq chemical stabilities.^[4–9] In addition, the RScO₃ compounds with different lattice parameters have also been exploited to serve as substrates for engineering of highly strained ferroelectric and multiferroic thin films. The biaxial strain due to lattice mismatch between substrates and thin films can dramatically alter the properties of epitaxial films.^[10] For instance, the SrTiO₃ thin film exhibits a strain-induced ferroelectricity at room temperature when it is grown on DyScO₃ substrate, compared with the paraelectric behavior of bulk unstrained SrTiO₃.^[11] The compressively strained BaTiO₃ thin films grown on DyScO₃ and GdScO₃ substrates can also produce larger ferroelectric (FE) polarization and higher FE transition temperature.^[12]

Apart from the effect of strain, the intrinsic properties of RScO₃ substrates may also play important effect on the properties of thin films. For example, the magnetic properties of RScO₃ should be took into account when they are used as substrates for magnetic oxide thin films.^[13] However, due to the low magnetic ordering temperatures of RScO₃, normally only a few Kelvin degrees,^[13–15] the magnetic effects from the substrates to the magnetic thin films are usually neglected and have not been the subject of detailed investigation. However, some of this series compounds still exist strong magnetic correlation well above the magnetic transition temperature, which cannot be ignored even at dozens of Kelvin degrees, such as the short range magnetic order discovered in DyScO₃ at 30 K.^[1] Actually, it was argued that these strong fluctuations are enhanced by the one dimensionality of the rare earth magnetic spin chains. Indeed, the quantum critical Tomonaga–Luttinger liquid behavior has been reported in YbAlO₃,^[16] and the strong orbital couplings and crystal field effects was claimed to be crucial for the unexpected low dimensionality behaviors.^[1,16,17]

On the other side, for GdScO₃, with the electron configuration of Gd³⁺ is 4f⁷ and L = 0, no spin–orbit coupling is expected. Thus following the arguments in previous studies,^[1,16,17] the low-temperature magnetism of GdScO₃ should behave very different, comparing with DyScO₃ and YbAlO₃. Despite that GdScO₃ has been reported as a giant magnetocaloric system with an antiferromagnetic (AFM) transition, T_N = 2.6 K,^[3] the details of the magnetic phase diagram and Gd–Gd interactions still remained poorly understood. Moreover, the studying of the Gd–Gd interactions in GdScO₃ may also be very helpful to understand the complex magnetism in GdFeO₃ and GdMnO₃.^[18,19]

High-quality single crystals of GdScO₃ used here are commercially available.^[12,20] Magnetization measurements were performed using two magnetometers for different temperature ranges: (i) commercial vibration sample magnetometer Quantum Design Magnetic Property Measurement System (MPMS-VSM) for the high-temperature measurements T = 1.8 K–300 K; (ii) MPMS-3 with ³He insert for the temperatures T = 0.5 K–1.5 K. Heat capacity measurements were performed on the Physical Property Measurement System (PPMS) in the temperature range 1.8 K–300 K.

As shown in Fig. 1(a), GdScO₃ crystallizes in a distorted orthorhombic perovskite structure with a = 5.4862 Å, b = 5.7499 Å, and c = 7.9345 Å in the Pbnm (No. 62) space group at room temperature.^[21] Gd³⁺ ions are located between 8 distorted ScO₆ octahedrons. Due to the distortion, the point symmetry of the Gd site is decreased from O_h in the ideal cubic structure to C_s, which is only one mirror plane normal to the c axis, in the orthorhombic structure. Figure 1(b) illustrates the T dependence of specific heat of GdScO₃ single crystal. A sharp anomaly appears near 2.6 K indicating a magnetic transition similar to GdAlO₃.^[22] The temperature evolution of the magnetic susceptibility χ(T) with an applied magnetic field of 0.3 T along the three principle crystal axis is shown in Fig. 1(c). The anomalies observed around 2.6 K confirm the AFM phase transition. The AFM order is mainly from a competition between exchange interactions and dipolar magnetic interactions for the neighbouring Gd³⁺ ions.^[23] The Néel temperature T_N = 2.6 K of GdScO₃ is lower than the isostructural GdAlO₃ (T_N = 3.98 K).^[22] This may be due to Sc³⁺ ion has larger ionic radius than Al³⁺ ion, which leads to larger distance between the neighbouring Gd³⁺ ions and produces smaller magnetic interactions. Above T_N, the susceptibilities χ(T) along the three principle crystal axis almost overlap together except the small T region near T_N, which indicates GdScO₃ only exists very weak anisotropy. This is consistent with the S = 7/2, L = 0 electron configuration of Gd³⁺ ion. Below T_N, it is seen that the susceptibility for the field parallel to axes b and c varies very little with temperature, whereas that when the field is parallel to the a axis decreases steeply (see the inset of Fig. 1(c)). Unlike the magnetic A_x structure preferred by the direct dipole–dipole interaction only, the magnetization with easy axis along a is consistent with the AF magnetic structure (G_x) as observed in GdAlO₃,^[22] where the exchange interaction between the large Gd³⁺ S = 7/2 spins in ab plane is dominant. This is very different from the cases of DyScO₃ and YbAlO₃.^[1,16,17] Figure 1(d) displays the inverse susceptibility plotted against the temperature for magnetic field applied along the c axis. Fits of 1/χ_c for the paramagnetic (PM) region (15 K < T < 300 K) to a Curie–Weiss law yield Curie temperature θ_CW of –4.85 K and effective magnetic moment μ_eff of 7.45 μ_B/Gd. The negative value in θ_CW confirms AFM interactions between the neighboring Gd³⁺ ions. The large μ_eff = 7.45 μ_B/Gd compared with the theoretical value of 7.94 μ_B assuming a spin of 7/2 for the Gd³⁺ ions.

Fig. 1.

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Fig. 1. (a) Crystal structure of GdScO3 in space group Pbnm, where a Gd3+ ion is surrounded by eight distorted ScO6 octahedrons. (b) T dependence of specific heat Cp(T). (c) T dependence of magnetic susceptibility χ(T) in an applied magnetic field of 0.3 T parallel to the a, b, and c axes, respectively. The inset: χ(T) near the AFM transition. (d) T dependence of inverse magnetic susceptibility 1/χ(T) with 0.3-T magnetic field along the c axis. The blue solid line is the fit using the Curie–Weiss law above the transition temperature.

Figure 2(a) illustrates the isothermal magnetizations of GdScO₃ as a function of applied field along the a axis ranging from 1.0 K to 5.0 K. The magnetizations closely approach to saturation around M = 6.5 μ_B/Gd above 5 T, which is consistent with the reported saturated moment of Gd³⁺ ion.^[22] An enlarged view of the low-field region of M(B) curves is shown in Fig. 2(b). All of the magnetization curves for T < T_N show an abrupt change around the field between 0.2 T and 0.45 T. This suggests the occurrence of a spin flop (SF) type transition, similar as the transition reported in GdAlO₃,^[22] where the spin direction of two sublattice Gd³⁺ ions suddenly turn perpendicular to the easy axis direction. This is due to the lower Zeeman energy of Gd³⁺ spins for the applied field along the easy axis until reaching the critical field of SF transition B_c1. In addition, the observed hysteresis loop shown in the inset of Fig. 2(a) indicates the SF transition is a subsequent field-induced first-order transition. With increasing of temperature, B_c1 also increases. This behavior is slightly different with GdAlO₃, in which the critical field is almost independent of T.^[22] Above B_c1, the magnetizations increase linearly with the field, and break off at a point which gives an AFM-to-PM critical field B_c2. The T-dependent magnetization of GdScO₃ with field applied along the a axis is shown in Fig. 2(c). Two anomalies are observed at 1.97 K and 2.55 K for B = 0.35 T, which correspond SF transition and AFM-to-PM phase transition, respectively. For the former, as the applied magnetic field increases, the phase transition T also increases, while the latter has the opposite trend (see the dash lines in Fig. 2(c)). Figure 2(d) shows the contour plot of magnetic phase diagram for applied field along the a axis. The intensity corresponds to the susceptibility χ = d M/d B. Below T_N, the critical field of SF transition divides the phase diagram into two regions. At the low-field region, GdScO₃ is an antiferrromagnet, in which the spin directions of Gd³⁺ ions are dominantly aligned in the a axis, and each Gd³⁺ ion in one sublattice might be surrounded by six nearest neighbours Gd³⁺ ions with opposite moments direction belonging to the other sublattice like GdAlO₃^[23] (the magnetic structure of GdScO₃ should be confirmed by neutron diffraction). Above B_c1, the moments turn perpendicular to the a axis due to the lower ground energy. A further increase of field rotates the spins continuously, until an AFM–PM critical field B_c2 is reached where all the moments are polarized along the applied field.

Fig. 2.

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	Fig. 2. (a) Field dependence of magnetization M of GdScO3, measured at different T, with field along the a axis. (b) The magnetization discontinuity at several T corresponds the SF phase transition. (c) T dependence of magnetization M of GdScO3 measured at several fields along the a axis. (d) The contour plot of the magnetic phase diagram of GdScO3 with applied field along the a axis.

The measurement of isothermal magnetizations of GdScO₃ with applied field along the b and c axes from 1.8 K to 3.0 K is shown in Figs. 3(a) and 3(c), respectively. Both the saturation moments and critical fields along the two axes are very similar with the a axis, which is consistent with the S-state of Gd³⁺ ions. In addition, since the spins direction of Gd³⁺ ions are dominantly along the a axis, there is no SF transition occurred when the field along the two axes. Figures 3(b) and 3(d) illustrate the magnetic phase diagram for field parallel to the b and c axes, respectively. With the increasing field, the AFM arrangement of spins of two-sublattice Gd³⁺ ions are gradually polarised, forming a PM magnetic state.

Fig. 3.

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	Fig. 3. (a) and (c) Field dependence of magnetization M of GdScO3, measured at different T, with field along the b and c axes. (b) and (d) The contour plot of the magnetic phase diagram of GdScO3 with applied field along the b and c axes. The AFM to PM phase boundary is given by the red open circles.

It usually believed that the AFM phase will directly enter into trivial PM phase in GdScO₃ with the applied field increased. However, since the AFM–PM transition is of second order and the transition temperature is gradually suppressed by the applied field, it might be existed a quantum critical field B_c2 at 0 K, where the AFM state transforms into the PM state. Around the QCP, the magnetic fluctuations are quantum mechanical in nature, which can exhibit scale invariance in both space and time. Unlike classical critical points, where the critical fluctuations are limited to a narrow region around the phase transition, the influence of the QCP can be felt over a wide range of temperatures above the QCP, so the effect of quantum criticality is felt without ever reaching 0 K. Figure 4(a) illustrates the field-dependence of the magnetic susceptibilities χ = dM/dB measured below and above T_N. Around the QCP, susceptibilities with different T can be scaled as

Fig. 4.

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	Fig. 4. (a) Field dependencies of the magnetic susceptibility χ = d M/d B from 1.0 K to 4.2 K with field along a axis. (b) Critical scaling of the magnetic susceptibility in panel(a).

As previous discussed, in GdScO₃, the orbital contribution (L = 0) is absent, and the magnetic ground states of Gd³⁺ are isotropic eight-degenerated S = 7/2 states. Due to the large spin values of S = 7/2, the in plane exchange interactions of the form JS ⋅ S are greatly enhanced, and become dominant in GdScO₃ and GdAlO₃.^[23]

On the other hand, although sharing the same crystal structure, the situations in YbAlO₃ and DyScO₃ are completely different. Due to the large orbital contributions, the degenerated spin states of YbAlO₃ and DyScO₃ are lifted by the crystal field effect, and the ground states are well separated Kramer doublets. These doublet ground states could be treated as effective spin S = 1/2, which turns out to be crucial for observed unconventional one dimensional physics in YbAlO₃ and DyScO₃ and related systems.^[16,17]

In summary, we investigated the magnetism and heat capacity of single crystal GdScO₃ at low temperatures. GdScO₃ is an uniaxial antiferromagnet with the easy axis of magnetization along the a axis. The Néel temperature is found to be 2.6 K. The magnetization measurements show it exists an SF phase transition when the applied field along the a axis. The field-temperature phase diagrams for B along the three principle crystal axes are established. By scaling the magnetic susceptibilities, we demonstrate there might be a quantum critical point (QCP) at B = 3.2 T and T = 0 K corresponding to the AFM-to-PM phase transition. Compared to the one-dimensional physics observed in YbAlO₃ and DyScO₃, the magnetic structure and the critical scaling indicate that the in-plane exchange interactions are more important in GdScO₃. It is found that quantum critical like fluctuations affect the physical properties over a large temperature and field area in GdScO₃, and additional caution may need be paid at low temperatures, when it was treated as a simple PM substrates for the epitaxial growth of magnetic thin films.