^aResearch Center for Development of Far Infrared Region, University of Fukui, Bunkyou, Fukui 910-8507, Japan

^bNational Institute for Materials Science (NIMS), Sengen, Tsukuba 305-0047 Japan

Available online 7 November 2006.

Abstract

The coexistence of a nearly spin-singlet state and antiferromagnetic long-range order (AFLRO) were found in Cu₂CdB₂O₆. The high frequency ESR measurements have been performed by using a millimeter wave vector network analyzer (MVNA; ABmm) with a small cavity in the frequency of 35–100 GHz. The external magnetic field was applied by using a superconducting magnet. Below the temperature of , ESR absorptions were observed. The frequency–field diagram of ESR absorption lines was obtained by the multiple frequency ESR measurements at the temperature of 1.5 K. We analysed these frequency–field relations based on antiferromagnetic resonance (AFMR) of the two-sublattice antiferromagnet with uniaxial type anisotropy. The AFMR mode at zero magnetic field has a finite antiferromagnetic gap of about 38 GHz. The spin-flop magnetic field was estimated. These results are consistent with the coexistence model of a nearly spin-singlet state and AFLRO in Cu₂CdB₂O₆.

Keywords: Antiferromagnetic resonance; Quantum spin system; Millimeter-wave; Effective field

PACS classification codes: 75.10.Hk; 75.10.Jm; 75.50.Ee; 76.50.+g

Article Outline

1. Introduction

2. Experimental technique

3. Results and discussion

References

1. Introduction

Coexistence or competition of plural different states has attracted much attention for both application and theory in condensed matter researches. Hase et al. found the coexistence of a nearly spin-singlet state and antiferromagnetic long-range order (AFLRO) in Cu₂CdB₂O₆ [1]. Cu₂CdB₂O₆ has two crystallographic Cu sites [Cu(1) and Cu(2)]. Cu(1) sites are in a nearly spin-singlet state, and those on the Cu (2) sites form AFLRO, although interactions between the Cu(1) and Cu(2) spins cannot be ignored. The susceptibility of Cu₂CdB₂O₆ has a maximum around 11 K and it seems to reach a finite value even at 0 K. The specific heat has a peak at 9.8 K. AFLRO probably appears at . The magnetization measurements was performed by a SQUID magnetometer up to 5 T and by an extraction-type magnetometer in hybrid magnet up to 30 T. The magnetization shows a spin-flop transition around and a magnetization plateau above 23 T. A susceptibility and magnetization were calculated by quantum Monte Carlo (QMC) technique. From the QMC simulation, they obtained the antiferromagnetic exchange interactions between Cu sites as follows; (Cu(1)–Cu(1)), (Cu(1)–Cu(2)), (Cu(2)–Cu(2)).

2. Experimental technique

Polycrystalline specimens were prepared by a direct solid-state reaction. A powder X-ray diffraction pattern confirms the formation of Cu₂CdB₂O₆ and the absence of other materials.

The high frequency ESR measurements were performed by using a millimeter wave vector network analyzer (MVNA; ABmm) with a small cavity in the frequency of 35–100 GHz and temperature region was from 1.5 to 200 K. The external magnetic field was applied by using a superconducting magnet. The magnetic field values were calibrated by a g-marker of 1,1-diphenyl-2-picrylhydrazyl(DPPH) in all measurements.

3. Results and discussion

Fig. 1 shows the temperature dependence of ESR absorption lines observed at 70.7 GHz. Below T_N, ESR absorption lines were observed. Sharp absorptions at 2.5 T are EPR absorption lines of DPPH. As the temperature is decreased, the intensity of Cu₂CdB₂O₆ ESR absorption is increased. ESR spectra with the structure were observed at low temperature. This result suggests that observed ESR absorption lines arise from AFLRO in Cu₂CdB₂O₆. In order to obtain the magnetic properties of AFLRO state, a frequency–field diagram of antiferromagnetic resonance (AFMR) absorption lines was obtained at 1.5 K as shown in Fig. 2. In order to be easily done, a modified magnetic field H=(g/2)H_exp is introduced, where H_exp and g are experimental resonance field and g=2.1 which was obtained by X-band EPR measurement at room temperature, respectively [1]. This result suggests that AFLRO in Cu₂CdB₂O₆ has uniaxial anisotropy. AFMR modes are analyzed by the simple two-sublattice model with isotropic exchange interaction [2]. The calculated ESR modes can be expressed as follows:

where γ, H, H_E and H_A are the gyromagnetic ratio, the external field, the antiferromagnetic exchange field and the uniaxial anisotropy field, respectively. Using our experimental data, the frequency–field relations, Eqs. (1) and (2), are determined and Eqs. (1)–(4) are shown by the solid lines in Fig. 2. The antiferromagnetic zero field gap frequency and the spin-flop field are found to be 38 GHz and 1.38 T, respectively. Take into account that the Cu(2) sites are almost polarized in the plateau region, a saturation field H_S=2H_E–H_A of AFLRO state is 23 T. Therefore, the effective fields are found to be and . A value of obtained exchange interaction is . The value of which was estimated by QMC simulation, is in good agreement with our experimental value . However the frequency–field relation of AFMR on Cu₂CdB₂O₆ is not asymptotic line of paramagnetic line (dash-dot line) in high field side as shown in Fig. 2. These discrepancies had been found in antiferromagnets which have anisotropic exchange interaction [3]. Dotted lines in Fig. 2 show the best fitted curve that take into account anisotropic exchange interaction. However, in order to determine anisotropic exchange interaction value, more experiments by using a single crystal are necessary.

We observed AFMR of AFLRO state in Cu₂CdB₂O₆. A frequency–field diagram shows the relation of uniaxial antiferromagnet. The zero field gap and spin-flop magnetic field are found to be 38 GHz and 1.38 T, respectively. From the analysis on simple two-sublattice model with isotropic exchange interaction, the exchange field and the anisotropy field are obtained. Furthermore, a value of antiferromagnetic exchange interaction is estimated in Cu₂CdB₂O₆. As we are dealing with the powder sample, whose absorption lines are broad, the AFMR modes for the field applied to easy axis (Eqs. (3) and (4)) are not observed clearly. In order to observe these AFMR modes and determine the anisotropic exchange interaction tensor, the ESR measurements using single crystals are required.

Corresponding author. Tel.: +81 776 27 8654; fax: +81 776 27 8770.