The intermetallic compound GdCo₂B₂ was first reported by Niihara et al. in 1973; it has a body-centered tetragonal crystalline structure (space group I4/mmm) and its lattice parameters are a = 3.573 ± 0.003 Å and c = 9.540 ± 0.005 Å.^[1] Felner reported that GdCo₂B₂ is a ferromagnetic material below the Curie temperature T_C = 26 K in a magnetic field of 0.1 T.^[2] Magnetic susceptibility measurements in a high-temperature region up to 800 K showed that Co in this compound has no magnetic moment.^[3] In 2009, Li et al. proposed that this material be ordered antiferromagnetically under the Néel temperature, T_N = 15 K, based on its magnetization in a field of 0.1 T as a function of temperature.^[4] Recently, a rather complicated magnetic phase diagram of single-crystal GdCo₂B₂ has been reported by Pospíšil et al.; this diagram shows four magnetic transitions at temperatures of 22, 18.5, 13, and 7 K, respectively.^[5] The conformal complex magnetic phase diagram strongly suggests the existence of complicated magnetic interactions in this material.

High pressure is recognized as one of the most powerful tools for realizing the intrinsic physical properties of materials; as is well known, the magnetic properties of the 4f and 5f electrons in rare-earth and uranium intermetallic compounds are very sensitive to pressure.^[6–8] For example, the unconventional superconductivity of 5f electrons in itinerant ferromagnetic UGe₂ under high pressure has been extensively studied.^[7] Previously, we have reported the DC magnetization and magnetic susceptibility each as a function of temperature in GdCo₂B₂ under high pressure.^[9] By increasing the pressure up to 1.27 GPa, T_C increased slightly from 22.2 K to 26.5 K and the antiferromagnetic (AFM) ordering was totally suppressed above 2.0 K.

As pointed out by the authors above, Ruderman–Kittel–Kasuya–Yosida (RKKY) indirect exchange interaction plays an important role in determining the magnetic properties of this material. The effective interatomic 4f magnetic interactions are transferred by the Fermi sea surrounding the conduction electrons. The application of high pressure changes the interatomic distances and can change the alignment of the magnetic moments. High pressure can also change the band structure of the conduction electrons by changing the density of states. By conducting experiments under high pressure, we can apprehend how these changes affect the magnetic ordering temperature of GdCo₂B₂.

In our previous paper, a remarkable phenomenon was observed: the zero-field-cooled (ZFC) and field-cooled (FC) magnetic susceptibility curves were separated at 9 K below T_N, where the FC curve was subjected to a magnetic field of 0.1 T. Pospíšil et al. found the same phenomenon in single crystal GdCo₂B₂ and they also found that the phenomenon became more obvious in low magnetic fields. It appeared at 8.5 K in a magnetic field of 100 mT and at 13.5 K just below T_N at 5 mT along the c axis.^[5] The separation phenomenon between the ZFC and FC curves is a common feature of spin glass (SG) with the essential ingredients of frustration and disorder. In GdCo₂B₂, this phenomenon is unexpected as no geometrical frustration exists given its crystalline symmetry. The SG behavior, however, has been found in some of the rare-earth compound families with body-centered tetragonal ThCr₂Si₂-type structures. As-grown single crystal URh₂Ge₂ was reported to be a three-dimensional (3D) Ising-like random-bond SG by Süllow et al. in 1997.^[10] The SG behavior disappeared because of annealing effects, implying that atomic disorderings of Rh and Ge are the origin of SG in URh₂Ge₂.^[11] PrAu₂Si₂ was also found by Hemberger et al. in 1999 to be a canonical SG with a freezing temperature of 3 K.^[12] In this compound, a frustration relates to the singlet ground state and the exchange coupling “avoided criticality” to the SG system.^[13] SGs have been extensively studied by many researchers since the pioneering work by Cannella and Mydosh in 1972,^[14] but still have unquestionable richness in condensed matter physics.

In the present paper, we perform precise measurements of AC susceptibility, AC heat capacity, and electrical resistivity to obtain more information about the phase transitions of GdCo₂B₂ by controlling the pressure of it. We define a detailed magnetic phase diagram based on these results. Moreover, we shed light on the SG-like behavior, namely, the separation phenomenon at low temperature. It is examined in terms of magnetization, aging effects, and frequency dependence of AC susceptibility measurements in order to clarify the nature of magnetic properties at low temperature. Finally, we discuss the relationship between magnetic phase transitions under pressure and SG-like behavior.

High-quality polycrystalline GdCo₂B₂ was synthesized from high-purity Gd, Co, and B by an arc-melting method through using a tungsten electrode under an argon atmosphere. The sample was annealed at 1173 K for one week in an evacuated quartz tube. The sample was proved to be of a single phase with a body-centered tetragonal ThCr₂Si₂-type (space group I4/mmm) structure by an x-ray diffraction (XRD) experiment. Lattice parameters a and c were evaluated to be 3.577 Å and 9.536 Å, respectively. These results were consistent with those previously reported.^[1]

The effect of pressure was investigated through AC susceptibility, AC heat capacity, and DC electrical resistivity measurements with a laboratory-made CuBe–NiCrAl hybrid piston cylinder pressure cell.^[15] Daphne 7373 oil was used as a pressure-transmitting medium. Heat capacity measurement is known as an excellent method of observing the bulk properties of magnetic phase transitions, and it was performed using a typical Joule heating-type temperature-modulated method.^[16,17] When one applies an electrical current with frequency ω to the sample, the Joule heating is supplied at a frequency of 2ω; thus, the temperature of the sample is modulated with a frequency of 2ω. As to the requirements for the experiment, the size of the sample was minimized into a size of 0.2 mm × 0.4 mm × 0.05 mm, a combination of 0.020 mmϕ Au and 0.025 mmϕ AuFe (Fe: 0.07 %) wires was used as a thermocouple to measure the modulated temperature, and a 0.020 mmϕ Au wire was used as a heater. The wires were spot-welded directly onto the sample together with two other Au wires to measure the electrical resistivity. Another piece of the sample was placed inside the compensated pick-up and modulation coils for AC susceptibility measurement with Sn as a manometer. In our laboratory-made system, all measurements could be made under the same pressure conditions.

The SG-like behavior at ambient pressure was examined through a series of experiments. These experiments were performed using a superconducting quantum interference device magnetometer MPMS-7 from Quantum Design, Inc. First, FC and ZFC magnetization each as a function of temperature were determined under various fields. Second, two types of measurements examined the aging effect. The first was of the time-dependence of ZFC magnetization at a selected temperature. The system was cooled from 50 K (much higher than the Curie temperature) to the selected temperature at a rate of 30 mK/s and then maintained at this temperature for 1800 s. Subsequently, the measurement of magnetization as a function of time was undertaken in a magnetic field of 0.01 T. The second experiment was the ZFC measurement with intermittent stops at the selected temperatures. The system was cooled from 50 K to 1.8 K at a rate of 30 mK/s, and the magnetization measurements were performed with intermittent stops of 1800 s at 2, 3, and 4 K in a magnetic field of 0.01 T. AC susceptibility measurements were conducted at four selected frequencies, namely 1, 10, 100, and 1000 Hz, to investigate the behavior of the freezing temperature.

First, the magnetic properties under high pressure are discussed. Figure 10 shows the magnetic phase diagram under high pressure determined by our experimental results. It shows that the GdCo₂B₂ compound exhibits three anomalies that apparently reflect magnetic phase transitions at temperatures T_C = 20.5 K, T₁ = 18.0 K, and T_N = 11.5 K under ambient pressure. We define these three areas at temperatures between T_C and T₁ and T₁ and T_N, and below T_N as I, II, and III, respectively. It is realized that only phase II survives and expands its temperature range with increasing pressure. The triangular shape of phase I becomes narrow and disappears above 1.6 GPa. The temperature of the boundary between phases II and III decreases monotonically with increasing pressure and is invisible above 1.4 GPa.

Fig. 10.

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	Fig. 10. The magnetic phase diagram of GdCo2B2 under pressure. □ is from the DC magnetization measurements (see Ref. [9]); ◯ is from the AC susceptibility measurements; △ is from AC heat capacity measurements; and ▽ is from the electrical resistivity measurements.

Second, we discuss the SG-like behavior of GdCo₂B₂. The results in Subsection 3.2 prove the existence of SG-like behavior at low temperature and under ambient pressure.

No geometrical frustration exists in GdCo₂B₂, given its crystalline symmetry. Thus this behavior is unexpected. It is fascinating that the SG-like behavior appears in a non-frustrated system such as GdCo₂B₂ with the symmetry described by the space group I4/mmm. One possibility is the presence of frustration from the geometric disorders between Co and B atoms as discussed in URh₂Si₂, but this can be negated since the sample is well annealed. Recently, Motoya et al. observed a long-time variation in the magnetic structure of a non-diluted uniform magnet, CeIr₃Si₂.^[36] Similar behaviors were also studied in intermetallic compounds PrCo₂Si₂ and TbNi₂Si₂ by the same authors.^[37] The long-time variations in the magnetic structure of these materials were reported to originate from frustrating magnetic interactions.

The splitting of ZFC and FC magnetization curves and the cusp-like behavior in the ZFC magnetization are the features for spin glass or cluster glass system or the coexistence of antiferromagnetism with ferromagnetism.^[38–40]

One of the scenarios to understand the SG-like behavior of this compound is the existence of competition between complicated FM and AFM interactions distributed randomly throughout the compound. This can be understood from pervious papers, which claimed the transition at around 11.5 K as Néel ordering.^[4,5] We note that SG-like behavior starts at T₁ as discussed in Subsection 3.2.1; thus, the AFM interaction starts at T₁ and becomes larger from T_N.

In this scenario, we discuss the relationship between magnetic phase transitions under pressure and SG-like behavior. The interaction between the localized 4f spins is of RKKY type. In the case of GdCo₂B₂, Gd³⁺ ions are responsible for its magnetic orders as mentioned in the Introduction. The FM order is mainly determined by the nearest-neighbor interaction J₁ between Gd³⁺ ions, and the AFM order is mainly determined by the next-nearest-neighbor interactions J₂ between the spins of the Gd³⁺ ions. A small decrease is caused in unit cell size by increasing pressures up to 2.2 GPa. The lattice becomes shorter, which causes the FM interaction (and J₁) to be strengthened and the AFM (and J₂) weakened. As a result, T_C increases while T_N decreases and disappears with increasing pressure. The competition between FM and AFM interactions is also weakened in this process. As a response to it, the SG-like behavior of GdCo₂B₂ is apparently suppressed by pressure. As shown in Fig. 6, at t = 10⁴ s, the relative increases in the magnetization change, M(t)/M(0), are reduced by 0.14% and 0.26% under pressures of 0.7 GPa and 1.2 GPa, respectively, compared with those at ambient pressure. Also, the relaxation time is shortened under pressure. These results are identical to the above analyses and support the explanation to the SG-like behavior of GdCo₂B₂, i.e., the competition between complicated FM and AFM interactions distributed randomly throughout the compound.

Other scenarios should be considered following our new results, especially, the large magnetization below around 11.5 K (see Fig. 4) and the hysteresis loops at 2 K (see Fig. 5), which suggest the material shows ferromagnetism in bulk below around 11.5 K. Thus, this reflects that the material does show glassy magnetic behavior below around 11.5 K.^[41,42] The glassy magnetic behavior is also supported by the results of the heat capacity, aging effect and the frequency dependence of ac susceptibility at low temperature, which are shown in Figs. 2, and 6–9. In this case, on one hand, the small difference between ZFC and FC magnetizations with the decreasing of FC magnetization below around 13 K in Fig. 4 does not support the typical cluster glass state in this compound. Also, according to Fig. 9, the value of τ₀ is much shorter than that of the cluster glass state (10⁻⁵ s) but in agreement with that for a classical SG.^[43–45] On the other hand, the results in Figs. 4 and 5 suggest that this material at low temperature is not in the classical SG state, which shows small magnetization and no magnetic hysteresis. Anyway, these behaviors should be supported by the existence of mixed ordering state competition between SG and ferromagnetism at low temperature as discussed in Subsubsection 3.2.2.

In this stage, we cannot affirm the origin of the SG-like behavior in GdCo₂B₂, and have not clarified the magnetic structure in GdCo₂B₂ either. Such a clarification is required to understand both the SG-like behavior of non-geometrical frustrated compound with symmetry described by the space group I4/mmm and the pressure effects on magnetic phases. Unfortunately, it is very difficult to determine the structure by neutron scattering because of the large absorption cross-sections of Gd and B. We are planning to perform x-ray resonant magnetic scattering. It may be interesting to investigate the uniaxial pressure effect for single crystal GdCo₂B₂, because the weak-but-significant magneto-crystalline anisotropy of as-grown single crystal GdCo₂B₂ was reported by Pospíšil et al.^[5] Further investigations on single crystal GdCo₂B₂ are expected to provide more information for understanding these interesting properties on this compound.