1 Introduction

High-pressure and multi-frequency electron spin resonance (ESR) measurement in the submillimeter wave region is a powerful means to study spin systems. In particular, it is indispensable for quantum spin systems, since the corresponding energy of this wavelength region matches their low-lying excitation energy levels well (for review, see [1]). Although in our previous high-pressure ESR system using the pulse magnet the frequency is available up to 700 GHz, the maximum pressure is 1 GPa at most and the sapphire which is used as one of the inner parts of the pressure cell is damaged below this pressure [2]. On the other hand, the ZrO2-based ceramic is tougher and much cheeper than the sapphire. The pressure region can be extended up to 1.5 GPa by replacing the sapphire parts with those made of the ZrO2-based ceramic [3]. Moreover, the hybrid-type pressure cell with larger sample space, which is developed for another ESR system having the superconducting magnet (see Fig. 1), can generate the pressure up to 2.5 GPa using this ZrO2-based ceramic [4]. However, one serious problem arises when the ZrO2-based ceramic is used. The frequency region is limited below 400 GHz because the absorption of the irradiated light by the ZrO2-based ceramic increases above around this frequency. In this study, we have established the method to achieve both the wide frequency region up to 700 GHz and the pressure region above 1.5 GPa by replacing some of the inner parts made of the ZrO2-based ceramic with those made of the Al2O3 ceramic for the hybrid-type pressure cell shown in Fig. 1b. We will show the transmission property of these ceramics and show an application example by this high-pressure ESR system.

2 Outline of High-Pressure and Multi-Frequency ESR System

Figure 1a shows the schematic diagram of our high-pressure and multi-frequency ESR system. We employ a simple single-pass transmission-type method in this system. The backward wave oscillator (BWO) is used as the light source. An InSb detector is set at the bottom of the light pipe and the transmitted light through the pressure cell is detected. The electromagnetic wave is chopped with the modulation frequency of several hundreds Hz and the output voltage from the detector is detected by the lock-in amplifier using the modulation frequency as the reference signal. We use a cryogen-free superconducting magnet and the maximum magnetic field is 10 T. The power supply of the BWO is controlled by a PC through the AD converter and not only the field-sweep measurement but also the frequency-sweep measurement can be done as is shown later. Figure 1b shows the cross section of the pressure cell of this high-pressure ESR system. All inner parts are made of ceramic which enables us to observe ESR under pressure.

Fig. 1
figure 1

Schematic diagram of the high-pressure and multi-frequency ESR system (a) and the piston–cylinder pressure cell (b). The inner parts 1 and 4 are top and bottom backup, respectively, and 2 and 3 are pistons. These inner parts are all made of ceramic

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The requirements for the inner parts of this pressure cell are toughness, transmission in the submillimeter waver region, easy availability, and so on. Although the ZrO2-based ceramic does not satisfy the transmission in the submillimeter wave region enough, we found that it is a better material for the toughness and the easy availability. On the other hand, the Al2O3 ceramics was found to show the best transmission among the examined ceramics but it does not have good toughness. Therefore, we tried to achieve both the transmittance and the toughness by combining the inner parts made of ZrO2-based ceramic and Al2O3 ceramic.

We use the ZrO2-based ceramic FCY20A and the Al2O3 ceramic FCA10, and these materials are easily available from Fuji Die, Co. Ltd. Table 1 shows the examined combinations for the inner parts of the pressure cell. The attainable pressures \(P_{\mathrm{max}}\) at low temperature for these combinations are also shown in Table 1. The relationship between the load at room temperature and the pressure at around 3 K for this pressure cell was already examined in [4], (T. Sakurai, unpubl.). From the maximum load at which the inner part was damaged, the maximum pressure \(P_{\mathrm{max}}\) was estimated using this relationship in this study. Figure 2 shows the transmittance of the pressure cell with these combinations. The Teflon capsule filled with the pressure-transmitting fluid (Daphne 7373) was also set. The transmittance was obtained by dividing the transmission of the pressure cell with inner parts by that without inner parts. These measurements were performed by the frequency sweep in the setup shown in Fig. 1. Although the output power of the BWO depends on the frequency much, its dependency is reproduced well. Therefore, the reliable transmittance can be obtained if the optical alignment is maintained. As shown in Fig. 2, large difference in the transmittance is clearly seen. Although the maximum pressure reaches 2.5 GPa when only ZrO2-based ceramic FCY20A was used (combination (d) in Table 1), the lowest transmittance was observed especially in the higher frequency region. On the other hand, the highest transmittance was observed when only Al2O3 ceramic FCA10 was used [combination (a)]. However, the toughness of FCA10 is very low and the combination (a) is not practical. To supply the toughness, we replaced the inner part 2 shown in Fig. 1b, which is directly pushed by the pushing rod and the most damaged part among four inner parts, with that made of the tougher ZrO2-based ceramic FCY20A (combination (b) in Table 1). As a result, we obtained the pressure of 1 GPa successfully with holding the reduction of the transmittance to the extent of a half as compared with that by the combination (a) as shown in Fig. 2b. Moreover, when the next damaged part 4 was replaced by that made of FCY20A [combination (c)], we obtained the pressure of 1.5 GPa. The transmittance of this combination (c) is greater than that of the combination (d), especially in the higher frequency region as shown in Fig. 2. This combination is still practical for the high-pressure ESR measurement as is mentioned in the next section.

Table 1 Combinations of the inner parts made of FCA10 and FCY20A
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Fig. 2
figure 2

Frequency dependence of the transmittance in the frequency region from 330 to 530 GHz for four combinations (a)–(d) of the inner parts made of FCA10 and FCY20A. The details of these combinations (a)–(d) are shown in Table 1

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3 Application to Quantum Spin System SrCu2(BO3)2

Fig. 3
figure 3

Frequency-field diagram of SrCu2(BO3)2 for H\(\parallel\)a obtained at 1.51 GPa and 2 K. Several ESR spectra are also shown. The inset shows the schematic energy-field diagram of the spin gap system

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As an application example of this high-pressure and multi-frequency ESR system, we show the results on a single crystal of SrCu2(BO3)2. This compound is well known as the real material to realize the Shastry-Sutherland model. It has attracted much attention since its discovery and it has still showed us very interesting phenomena. For instance, the novel pressure-induced phenomenon has been reported recently [5]. SrCu2(BO3)2 has the singlet ground state and the first excited triplet states as is schematically shown in the inset of Fig. 3. The magnetic susceptibility measurements under pressure suggested that the gap energy between the singlet state and the triplet states is suppressed by applying the pressure [6] and our previous high-pressure ESR measurements up to around 1 GPa proved this suppression by the pressure directly [7]. Recently, Haravifard et al. [5] suggested the complete collapse of the gap around 2 GPa and they also suggested the existence of a new phase above this pressure. Therefore, the direct observation of the pressure dependence of the gap energy and the pressure-induced novel phase is desired.

Figure 3 shows the frequency-field diagram of SrCu2(BO3)2 for H\(\parallel\)a obtained at 2 K. The combination (c) in Table 1 was used for this ESR measurement. The pressure was estimated to be 1.51 GPa from the load at room temperature. Typical ESR spectra are also shown in Fig. 3 and the ESR signals are clearly seen. In addition to the simultaneous achievement of the pressure above 1.5 GPa and the frequency up to 700 GHz, the higher signal to noise ratio was obtained as compared with the previous study [7] because of the larger sample space and the lock-in detection for this system. These signals are identified as the ESR due to the transition from the singlet ground state to the triplet excited states, as is shown by the arrows in the inset. The lower ESR branch corresponds to the transition from the \(S = 0\) state to the \(S_{\mathrm{z}} = -1\) of the \(S = 1\) states, while the upper ESR branch corresponds to the transition to the \(S_{\mathrm{z}} = 1\) of the \(S = 1\) states. The dotted lines are the fitted results by the relation \(h\nu =\Delta \pm \sqrt{(2D)^{2}+(g\mu _{\mathrm{B}}H)^2}\), where \(\Delta\), \(h\), \(\nu\), \(D\), \(g\) and \(\mu _{\mathrm{B}}\) are the gap energy, the Planck constant, frequency, the Dzyaloshinskii–Moriya (DM) interaction, the \(g\) value, and the Bohr magneton [8]. The field dependence near zero field and the small gap between the upper and the lower branch at zero field are the characteristic points of this material unlike the simple four-level system shown in the inset of Fig. 3 [8]. The obtained data are fitted very well as shown in Fig. 3 and the gap energy and the DM interaction are obtained to be 479 and 22 GHz on average, respectively. The gap energy at ambient pressure was obtained to be 722 GHz [9] and it was reduced much by applying the pressure. However, we also found that the simple linear extrapolation to the zero gap energy from these two points exceeds 2 GPa and reaches 4.5 GPa. This fact strongly suggests that the gap energy remains open around 2 GPa. Further high-pressure ESR measurement is required and it is now under the planning to investigate more detailed pressure dependence of the gap energy and the DM interaction.

4 Summary

It was found that the ZrO2-based ceramic has lower transmission but enough toughness, while the Al2O3 ceramic has lower toughness but higher transmittance for our pressure cell. We have performed the transmission measurements in the submillimeter wave region for several combinations of the inner parts made of these two ceramics. The attainable pressures for these combinations were also examined. We found an optimum combination which achieves both the transmission in the frequency region up to 700 GHz and the pressure region above 1.5 GPa. In the high-pressure ESR measurement using this combination, we succeeded in obtaining the gap energy of the Shastry-Sutherland model compound SrCu2(BO3)2 directly at 1.5 GPa. This result also shows that our high-pressure and multi-frequency ESR system is a very powerful means to study quantum spin systems.