Appl Magn Reson DOI 10.1007/s00723-015-0655-6

Applied Magnetic Resonance

High-Field Multi-Frequency ESR in the Quasi-1D S 5 1/2 Ising-Like Antiferromagnet BaCo2V2O8 in a Transverse Field A. Okutani • S. Kimura • T. Takeuchi • M. Hagiwara

Received: 30 November 2014 / Revised: 12 February 2015 Ó Springer-Verlag Wien 2015

Abstract We have performed high-field multi-frequency electron spin resonance (ESR) measurements of a single crystal of the S = 1/2 quasi one-dimensional (1D) Ising-like antiferromagnet BaCo2V2O8 at 1.5 K in magnetic fields of up to 14 T applied along [110] and [100] directions. Two main ESR branches, which are ascending and descending with increasing magnetic fields, are observed from 400 GHz at zero magnetic field in both cases. The low ESR mode shows a softening near 10 T for H || [100], while no softening was observed below 14 T for H || [110]. This difference in the magnetic excitations may explain the distinct phase diagrams for these two directions.

1 Introduction The Co2?(3d7) spin system BaCo2V2O8 has a quasi-one-dimensional (1D) structure (space group I41/acd) at room temperature, in which edge-sharing CoO6 octahedra form a screw-chain structure along the c-axis and the chains are separated by nonmagnetic V5? and Ba2? ions [1]. The temperature dependence of the magnetic susceptibility of BaCo2V2O8 shows a broad maximum near 30 K for H || c, which is a characteristic of a low-dimensional antiferromagnet, and a large magnetic anisotropy between H || c and H \ c. At zero magnetic field, this compound exhibits an antiferromagnetic long-range ordering at TN = 5.4 K due to finite A. Okutani  M. Hagiwara (&) Center for Advanced High Magnetic Field Science, Graduate School of Science, Osaka University, Osaka 560-0043, Japan e-mail: [email protected] S. Kimura Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan T. Takeuchi Low Temperature Center, Osaka University, Osaka 560-0043, Japan

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interchain couplings [2]. On applying the magnetic field along the c-axis, which is the easy axis of BaCo2V2O8, a magnetic field-induced phase transition from a Ne´elordered phase to a quantum spin-liquid one takes place [2, 3]. This is an intriguing field-induced order-to-disorder transition. The high-field magnetization curve of BaCo2V2O8 along the c-axis at 1.3 K shows a gradual linear increase below Hc = 3.9 T, and then a steep increase above Hc, followed by saturation at Hs = 22.7 T [4]. High-field electron spin resonance (ESR) measurements of BaCo2V2O8 for H || c were also performed. It was reported that two ESR branches appear from the frequency-intercept at 400 GHz, and the low branch shows a softening at around 4 T [4]. These results are well-explained by the spin Hamiltonian for the S = 1/2 XXZ model expressed as ( ) X X  x x y y  z z H¼J Si Siþ1 þ e Si Siþ1 þ Si Siþ1  lB Si g~H : i

i

Here, J [ 0 is the antiferromagnetic exchange constant, e is an anisotropic parameter, lB is the Bohr magneton, g~ is the g-tensor, and H is the external magnetic field. The parameters obtained from the previous study are J/kB & 65 K, gc & 6.2, and e & 0.5 [4, 5]. Hence, BaCo2V2O8 is a good realization of the quasi1D S = 1/2 antiferromagnet with Ising-like anisotropy. In the Ising-like system in a transverse field, it was suggested theoretically that the Ne´el order remains up to the field where the field derivative of magnetization shows the maximum [6]. In fact, for the external field applied perpendicular to the caxis, the transition temperature obtained from the specific measurement hardly changes with increasing the magnetic field [7]. Later, an anomaly in the thermal conductivity at approximately 10 T for H \ [001] was observed [8]. The magnetostriction and the thermal expansion also indicated anomalies near 10 T and below 2 K [9]. Magnetization curves up to 55 T were found to be completely different when the field was applied along the [100] and [110] directions [10]. In addition to this finding in the magnetization curves, an anomaly was observed around 10 T for H || [100], and such an anomaly was not observed for H || [110]. The large differences in the experimental results between the field directions of H || [100] and H || [110] are quite unusual for a tetragonal system. To clarify the origin of the differences from the viewpoint of the low energy excitations, we have performed the high-field multi-frequency ESR measurements on a single crystal sample of BaCo2V2O8 in a transverse field, i.e. perpendicular to the chain direction.

2 Experimental High-field multi-frequency ESR measurements have been performed at 1.5 K in external magnetic fields of up to 14 T along the [110] and [100] directions. The high-field multi-frequency ESR system at AHMF is comprised of a vector network analyzer (MVNA, ABmm), a superconducting magnet (Oxford Instruments), and a homemade transmission-type ESR cryostat. A single crystal of BaCo2V2O8 with a

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diameter of about 4 mm and a thickness of 0.5 mm, which was grown by the floating zone method, was used in the ESR measurements.

3 Results and Discussion Figure 1a, b show the ESR spectra observed in a single crystal of BaCo2V2O8 at 1.5 K for magnetic fields applied along the [110] and [100] directions, respectively. The splitting of the signals is caused by magnetic domains due to the structural phase transition from tetragonal to orthorhombic symmetry at TN with decreasing temperature [9]. The arrows in the figures indicate the resonance fields. Figure 1c, d display the frequency versus resonance-field plots for H || [110] and H || [100], respectively. Two main ESR branches indicated by filled circles appear from 400 GHz at zero magnetic field, which is consistent with the previous finding [4]. The upper ESR mode monotonically increases with increasing magnetic field in both cases. The behaviors of the lower ESR modes are different between the cases for H || [110] and H || [100]. For H || [110], no softening of the mode was observed in magnetic fields of up to 14 T, but the lower ESR mode decreases quickly with magnetic field and shows softening near 10 T for H || [100]. For this direction, almost linear ESR branches (filled triangles and open squares) appear above 10 T,

Fig. 1 a ESR spectra of BaCo2V2O8 at 1.5 K for H || [110], b ESR spectra of BaCo2V2O8 at 1.5 K for H || [100], c frequency-magnetic field plot of the resonance fields as shown by the arrows in a, and d frequency-magnetic field plot of the resonance fields as shown by the arrows in b. The arrows topped with marks in a and b correspond to the resonance fields indicated by the same marks in c and d, respectively. The solid and dotted lines are guides for the eyes (color on line)

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and a nearly field-independent resonance mode (filled rhombuses) is observed around 10 T and at 150–200 GHz. The resonance signals indicated by inverted open triangles in Fig. 1c, d come from the magnetic domains as mentioned above. The origin of the signals shown by filled rhombuses in the region of 150–200 GHz around 10 T is not clear at present. The softening of the low-excitation mode indicates that the magnetic phase transition occurs near 10 T for H || [100], which is compatible with the previous studies [8, 9]. The data points drawn by the open squares and the filled diamonds in Fig. 1c probably correspond to ESR modes from discrete upper levels at frequencies greater than 400 GHz as reported in Ref. [4]. Finally, we discuss the origin of the field-induced phase transition for H || [100]. In the S = 1/2 Ising-like XXZ model, the low-lying excitation is known as the spinon, that always emerges as a pair of quantum domain walls propagating through the chain [11]. For H || c, the field-induced order-to-disorder phase transition around 3.9 T is thought to be caused by the softening of the spinon excitation band [4]. The behavior of the lowest ESR branch for H || [100] is similar to that for H || c, and thus, the field-induced phase transition for H || [100] may be driven by the same mechanism. Acknowledgments This work is partly supported by Grants-in-Aid for Scientific Research (nos. 24340073, 242440590 and 25246006) from the MEXT, Japan.

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