Unveiled magnetic transition in Na battery material: μ⁺SR study of P2-Na_0.5VO₂

Abstract

We have investigated the microscopic magnetic nature of a novel Na battery material, P2-Na_0.5VO₂, in which V ions form a two-dimensional triangular lattice, by means of muon-spin rotation and relaxation (μ⁺SR) measurements down to 50 mK. Although magnetization measurements indicated the presence of an antiferromagnetic transition at 13 K, the internal magnetic field due to the formation of magnetic order appears not at 13 K but at 2 K. Furthermore, the magnetic order is found to have a wide field distribution even at 50 mK. Such wide field distribution is reasonably explained by a combination of multiple muon sites and the formation of a long-range magnetic order, while the reliable spin structure is still unknown.

---

1 Introduction

Based on a Hubbard model for the two-dimensional triangular lattice (2DTL), the magnetic ground state of 2DTL is predicted to change both with U/t and n, where U is the onsite Coulomb repulsion, t is the hopping integral between the nearest-neighbor sites, and n is the electron filling. In fact, for the half-filling case (n = 1/2), a theoretical study¹ predicts that the system is a paramagnetic metal for small U, but when U/t ≥ 3.97, it becomes a metal with an incommensurate spiral spin density wave (SDW). As U increases further, a first-order metal-insulator transition occurs at U/t = 5.27, and the system enters into a commensurate, three-sublattices, 120° twist SDW state.

On the other hand, for the case with n ≠ 1/2, another theoretical study² proposed a complex magnetic phase diagram as a function of U/t and n. However, there is, to our knowledge, no experimental study to confirm such diagram. Indeed, the prediction that magnetic order appears at n = 3/4 even when U/t = 0 is questionable, because half of the sites are occupied by up & down spins for such filling.

Therefore, considering geometrical frustration on 2DTL, which often leads to the formation of short-range order, a sensitive local magnetic probe is suitable for investigating the variation of magnetism with n. Muon-spin rotation and relaxation (μ⁺SR) is an optimal technique for such purpose due to its unique spatial and time resolution.³ This is our motivation for the past μ⁺SR experiments on Li_xCoO₂,⁴ Na_xCoO₂,⁵ K_xCoO₂,^6,7 Li_xNiO₂,⁸ and other related 2DTL systems.^9–12 Furthermore, in order to change n, the Li and/or Na content is adjusted mainly by an electrochemical reaction. Thus, it is very difficult to prepare enough amount of samples for e.g. neutron scattering. This is the other reason that we use μ⁺SR for such purpose. Actually, we have previously used this technique to demonstrate eccentric magnetic phase diagrams for Li_xCoO₂ (ref. 4) and Li_xNiO₂.⁸

In addition, we want to emphasize that magnetic properties of alkali transition-metal oxides naturally depend on the distribution of elements, charges, and spins in the lattice, which also determines the electrochemical properties. Therefore, although there is no direct correlation between low-temperature magnetism and high-temperature electrochemical properties, there should be a certain interrelationship between them.^13,14

A recent discovery of novel P2- and O′3-Na_0.5VO₂,^15,16 in which V ions form a two-dimensional triangular lattice (see Fig. 1), naturally expands the research area of magnetism on 2DTL to a Na–V–O system. Particularly, magnetization measurements show the presence of a pronounced AF transition at T_N^χ ∼ 13 K for P2-Na_0.5VO₂, while neutron diffraction measurements revealed the absence of magnetic Bragg peaks down to 1.8 K.¹⁵ In addition, the temperature dependence of heat capacity lacks a peak at T_N^χ, but shows a very broad anomaly at ∼10 K,¹⁵ leading to the question on the origin of the magnetic anomaly at T_N^χ.

Fig. 1 (a) 3D structure of P2-Na_0.5VO₂ and (b) projection of the structure of P2-Na_0.5VO₂ along the direction perpendicular to the VO₂ planes. The unit cell is drawn with a black line.

We have, therefore, measured μ⁺SR spectra mainly for P2-Na_0.5VO₂ down to 50 mK in order to elucidate the magnetic ground state. This is because μ⁺SR is particularly sensitive to the local magnetic environment, because the muon mainly feels the internal magnetic field (H_int) due to its nearest neighbors and is specially sensitive to the short-range magnetic order, which sometimes appears in low dimensional systems, while both neutron scattering and magnetization measurements mainly detect long-range magnetic order. In particular, if the correlation length is very short, neutron diffraction peaks broaden and eventually disappear.

2 Experiment

A powder sample of P2-Na_0.5VO₂ was synthesized in ICMCB-CNRS by sodium electrochemical deintercalation from Na_0.71VO₂ using a Na|NaClO₄–propylene carbonate|P2-Na_0.71VO₂ cell. The P2-Na_0.71VO₂ powder was synthesized by a solid-state reaction between NaVO₂ and VO₂ at 850 °C for 24 h in a gold tube sealed under argon. According to powder X-ray diffraction (XRD) analysis at ambient temperature, the sample was single phase of orthorhombic symmetry with space group Pmmn. The structural, electrochemical, and physical properties of P2-Na_0.5VO₂ are reported elsewhere.¹⁵

The μ⁺SR spectra were recorded at a surface muon beam line using the GPS and LTF spectrometer of PSI in Switzerland. Approximately 120 mg of powder sample was pressed into a pellet with 10 mm diameter, and then placed in a titanium foil sealed copper cell for GPS or a silver cell with a Kapton window sealed by Apiezon-N grease for LTF. Since the sample is very unstable in air, such work was carried out in a He-filled glove box. On GPS, the cell was attached to a low-back ground sample holder in a liquid-He flow-type cryostat for measurements in the temperature range between 1.5 and 20 K. At LTF, the silver cell was set into a dilution refrigerator (DR) down to T = 20 mK. The experimental techniques are described in more detail elsewhere³ and the basic principle for data analyses is briefly given in Appendix 6.

3 Results

Fig. 2 shows the temperature dependence of the μ⁺SR spectrum obtained in a zero external magnetic field (ZF) on (a) GPS and (b) LTF. At 2 K, the ZF-spectrum exhibits a slow relaxation due to nuclear magnetic moments of ²³Na and ⁵¹V plus ⁶³Cu and ⁶⁵Cu from the muons stopped in the sample cell. A rapid relaxing component is clearly seen in the early time domain below 1 μs at 1.9 and 1.5 K, indicating the appearance of an internal magnetic field (H_int) due to 3d electrons. The spectrum at 1.5 K is almost the same as the one at 1.9 K. Even at 0.05 K, the ZF-spectrum looks very similar to 1.9 K, although the relaxation rate increases with decreasing temperature. Since we used an Ag sample holder at LTF, the background, which corresponds to the signal at t ≥ 1 μs, is less relaxing than in the ZF-spectrum obtained with a Cu sample cell on GPS.

Fig. 2 ZF-μ⁺SR spectrum for P2-Na_0.5VO₂ obtained (a) at 1.5, 1.9, and 2.0 K with a liquid-He flow-type cryostat on GPS and (b) at 0.05 and 0.6 K with a DR on LTF. Here, A₀ is the initial asymmetry, and for the present experiment, A₀ = 0.25 from the measurements of a silver reference. P_ZF(t) is the muon spin polarization function under ZF (see text and Appendix 6). Besides the spectrum at 1.5 K in (a) and 0.05 K in (b), each spectrum is shifted upward by 0.05 for clarity of display. In (a) we used a Cu sample cell, whereas an Ag sample cell in (b).

The overall feature of the ZF-spectrum suggests that the magnetic transition occurs not at 13 K, but at 1.9 K (= T_m). Furthermore, the absence of a clear oscillation at 0.05 K is likely to indicate the lack of static long-range magnetic order, namely, the magnetic order would be random like a spin-glass state. The longitudinal field (LF) measurements at 1.5 K, which is useful to judge whether the magnetic order is random or not through the change in the relaxation with LF, revealed that random order is most unlikely (see Fig. 3). Here LF means the field parallel to the initial muon spin polarization (S⃑_μ). Therefore, we fitted the ZF-spectrum by a combination of a Gaussian relaxing cosine oscillation for the static internal field, an exponentially relaxing non-oscillatory signal for the “1/3 tail” signal caused by fluctuations in the field component parallel to S⃑_μ, and a background (BG) signal from the muons stopped in the Cu or Ag cell:

where f_M (≡ ω_M/2π) is the muon Larmor frequency corresponding to the static H_int, A_M, A_tail, and A_BG are the asymmetries of the three signals, and σ_M and λ_tail are their relaxation rates. For the Cu sample cell, P_BG is represented by a dynamic Kubo–Toyabe function, G_KT(Δ, ν, t), where Δ is the field distribution width and ν is the field fluctuation rate. Since Δ and ν for Cu are known to show a complex temperature dependence,¹⁷ the ZF- and LF-spectra were also measured for the Cu sample cell alone. For the Ag sample cell, on the other hand, P_BG is given by an exponential relaxing signal, e^−λ_BGt.

Fig. 3 ZF- and longitudinal field (LF) μ⁺SR spectra for P2-Na_0.5VO₂ obtained at 1.5 K using a Cu sample cell. The applied LF was 20, 50, and 100 Oe, where LF means the filed parallel to the initial muon spin polarization. Solid lines represent the best fit using a combination of two dynamic Kubo–Toyabe functions for the Cu cell and P2-Na_0.5VO₂. The Kubo–Toyabe parameters for the Cu cell were determined by the ZF- and LF-measurements of the Cu cell alone (see text). The discrepancy between the experimental data and fitting results indicates that a Kubo–Toyabe function is not suitable for describing the internal magnetic field in P2-Na_0.5VO₂.

The fit provided that A_M = 0.117 (2), A_tail = 0.081 (2), and A_BG = 0.040 (2) at 1.5 K for the data obtained on GPS with the Cu cell. Here, A_BG was estimated from the LF measurements of the Cu cell at 1.5 K. More correctly, at first, we determined Δ = 0.361 (2) × 10⁶ s⁻¹ and ν = 0.171 (9) × 10⁶ s⁻¹ for the Cu cell at 1.5 K. Then, the ZF- and LF-spectra of the sample obtained at 1.5 K were fitted with eqn (1) using the above Δ and ν, but A_BG as a free parameter. Because of the rapid decay of the A_M signal, it is difficult to separate A_M and A_tail correctly, although A_tail should be equivalent to 1/2A_M.

Fig. 4 shows the temperature dependences of f_M, σ_M, and their ratio σ_M/ω_M = σ_M/(2πf_M). The f_M(T) curve exhibits an order-parameter like temperature dependence, as expected. The magnitude of σ_M also increases with decreasing temperature, while σ_M/ω_M is found to decrease slightly with decreasing temperature. Eventually, σ_M/ω_M (∼1) is almost temperature independent, meaning that the field distribution does not change with T below T_m. In other words, the f_M(T), σ_M(T), and σ_M/ω_M(T) curves indicate that P2-Na_0.5VO₂ undergoes a magnetic transition at T_m, but no additional transitions down to 0.05 K. Note that the magnetic order in P2-Na_0.5VO₂ looks very different from a usual long-range AF order, for which σ_AF/ω_AF ≪ 1. Besides a spin-glass like freezing, such a broad field distribution is usually explained by one the following three scenarios; namely, the formation of a short-range ordered state, the appearance of a complex order,^18–21 or the presence of multiple muon-sites in the lattice even for a simple long-range order. We will discuss the origin of the broad field distribution later.

Fig. 4 The temperature dependences of (a) the muon-spin precession frequency (f_M), (b) the Gaussian relaxation rate of the precession signal (σ_M), and (c) their ratio σ_M/ω_M = σ_M/(2πf_M) for P2-Na_0.5VO₂. The data were obtained by fitting the ZF spectrum using eqn (1). A solid line in (a) shows the power law fit [f(T)/f(0 K) = [(T_m − T)/T_m]^γ], where f_M (0 K) = 0.53 (3) MHz, T_m = 2.00 (2) K, and a critical exponent γ = 0.35 (7).

In order to study the change in the volume of the paramagnetic phase, Fig. 5 shows the temperature dependences of the fitted μ⁺SR parameters obtained from weak transverse field (wTF) measurements with H_TF = 50 Oe on GPS. Here, wTF means that H⃑_TF⊥S⃑_μ and usually |H_TF| ≪ |H_int|. However, based on the ZF measurements, |H_TF| ≥ |H_int| in this case. Hence, the wTF-spectra were fitted by:

where A_TF is the asymmetry for the oscillatory signal due to applied wTF and A_M is the same to that in eqn (1). Due to the effect of wTF, σ_M,TF ≠ σ_M, ω_M,TF ≠ ω_M, and ϕ_M,TF ≠ 0. We also assume that the tail component, which appears below T_m, provides the oscillatory signal by wTF, i.e. A_TF consists not only of the contributions from the paramagnetic phase in the sample but also A_BG and A_tail. This is the reason why we use a stretched exponential relaxation for the wTF oscillatory signal. In fact, β = 1 at T > 2.5 K, but β ∼ 0.5 at T ≤ 2.5 K.

Fig. 5 The temperature dependences of (a) the two normalized asymmetries, A_TF/A₀ and A_M/A₀ and (b) their relaxation rates (λ_TF and σ_M,TF), and (c) susceptibility (χ = M/H)¹⁵ for P2-Na_0.5VO₂. Since A_TF ∼ A₀ = 0.25 in the temperature range between 2.5 and 15 K, the whole volume of the sample is paramagnetic above 2.5 K.

Since A_TF = A₀ = 0.25 at 15 K, which is the maximum value for the present setup, the whole volume of the sample is found to be paramagnetic. As temperature decreases from 15 K, such behavior is observed down to 2.5 K, then, A_TF/A₀ suddenly decreases and becomes a constant (∼0.5) below 2 K. On the contrary, A_M signal appears at T = 2.5 K and levels off to A_M/A₀ ∼ 0.5, with further lowering temperature. Furthermore, λ_TF looks independent of temperature down to just above T_m. This clearly demonstrates that the magnetic transition occurs not at 13 K but at ∼2 K, from the viewpoint of the change in volume of each phase. The transition width (ΔT_m) is estimated as about 0.5 K, since the A_M levels off at T ≤ 2.0 K. The present μ⁺SR results are, thus, consistent with those of neutron and heat capacity measurements.¹⁵

4 Discussion

Here, we wish to point out a few possibilities for the spin structure below T_m. Based on magnetization and resistivity measurements,¹⁵ P2-Na_0.5VO₂ is assigned as a Curie–Weiss insulator with a negative Weiss temperature (Θ_W = −7.4 K). Considering the Na ordering pattern, both V³⁺ (d²) and V⁴⁺ (d¹) ions are thought to coexist in the lattice. This situation is slightly different from the related compound, Na_0.5CoO₂, which is a Pauli-paramagnetic metal above T_N ∼ 88 K.²² Also, both ZF-μ⁺SR and neutron diffraction clearly detect the formation of static AF order below T_N.^23–25

LF measurements below T_m reveal that the spin-glass freezing state is most unlikely a ground state for P2-Na_0.5VO₂ (Fig. 3). In fact, for the spin-glass freezing state, we usually expect that localized moments appear far above the freezing temperature (T_f) and then evolve with decreasing temperature towards T_f. As a result, λ_TF gradually increases with decreasing temperature and the A_TF(T) curve often indicates a wide transition width. Since such behavior is not observed for P2-Na_0.5VO₂, the spin-glass freezing state is excluded as a ground state.

In the P2-Na_0.5VO₂ lattice, there are six different oxygen sites,¹⁵ implying the presence of six different muon sites about 1 Å away from each O²⁻. Since electrostatic potential (E_p) calculations predict that E_p = −13.5 ± 0.7 eV for the six sites, the implanted muons are most likely to sit at each site. Then, dipole field calculations at the six muon sites provide a wide field distribution (see Appendix 7) even for the stripe-type AF order proposed for Na_0.5CoO₂ (ref. 25) and the A-type AF order proposed for Na_0.75CoO₂ (ref. 26–28) and NaNiO₂ (ref. 29 and 30). Here, in the A-type AF order, the magnetic moments align ferromagnetically in the ab plane but antiferromagnetically along the c-axis.

If well-distinct multiple muon-spin precession frequencies are extracted from a ZF-μ⁺SR spectrum, we could conjecture the spin structure by μ⁺SR.^12,31–35 However, since there is only one f_M below T_m, it is impossible to determine the most probable AF spin structure based on the present result. Furthermore, although the wide field distribution below T_m in P2-Na_0.5VO₂ is reasonably explained using a combination of multiple muon sites and a relatively popular AF spin structure, the formation of a short-range order or a complex order is still not excluded. In order for further clarifying the spin structure, it is definitely required to perform neutron diffraction measurements well below T_m.

Back to the comparison between theory and experiment, since P2-Na_0.5VO₂ is an insulator, the distribution of d electron in the VO₂ plane should be inhomogeneous, i.e. both V³⁺ (S = 1) and V⁴⁺ (S = 1/2) coexist. Furthermore, the formation of V pseudo-trimers alters the VO₂ plane from an ideal 2DTL to isolated triangles. As a result, it is very difficult to predict the magnetic ground state of P2-Na_0.5VO₂ by a simple Hubbard model.

The fact that T_m = 2 K, however, indicates a relatively weak magnetic interaction between V ions compared with that in Na_0.5CoO₂. This would make Na⁺ ions mobile in P2-Na_0.5VO₂ at ambient temperature,¹⁵ despite its insulating nature.

Appendix

μ⁺SR

When spin-polarized muons are implanted into a magnetically ordered material in ZF, the muon-spins process around the local magnetic fields H_int in the material at the frequency, ω/2π = f = γ_μ/2π × H_int, where γ_μ (= 13.554 kHz Oe⁻¹) is the muon gyromagnetic ratio. Such oscillation in the ZF-spectrum is represented by;

Here, A₀ is the initial asymmetry, and for the present experiment, A₀ = 0.25 from the measurements of a silver reference. P_ZF(t) is the muon spin polarization function under ZF.

Both G_x(t) and G_z(t) are the relaxation function caused by inhomogeneous distribution of H_int at the muon sites. Here, G_z(t) corresponds to the relaxation of H_int parallel to the initial muon-spin direction (S_μ) and shows only dynamic depolarization, while G_x(t) corresponds to the relaxation of H_int⊥S_μ and includes both static and dynamic depolarization. The G_z(t) component is usually called as a “1/3” tail signal.

When there are multiple muon sites with different H_ints, the ZF spectrum is given by;

where n is the number of the muon sites and A_i/A₀ represents the fraction of the muon sites with H_intⁱ to the all sites.

AF spin structure

According to electrostatic potential calculations, the implanted muons are predicted to sit at the following six sites; that is, (0.4024, 0.0437, 0.1818), (0.0957, −0.0135, 0.8185), (0.1982, 0.25, 0.1684), (0.1918, 0.25, 0.3281), (0.3534, 0.25, 0.6966), and (0.3463, 0.25, 0.8203). Then, dipole field calculations provide the internal magnetic field for each muon site, if we assume a certain AF spin structure.

Fig. 6 shows the calculated distribution of H_int for the stripe-type and A-type AF ordered states together with the Fourier transform amplitude (A_Fourier) of the ZF-μ⁺SR time-spectrum at 0.05 K. The former is proposed for Na_0.5CoO₂ by neutron,²⁵ whereas the latter for Na_0.75CoO₂ (ref. 27 and 28). Both states are consistent with the present μ⁺SR result, because the Fourier transformed frequency spectrum has only one broad maximum at around 0.5 MHz. In other words, we cannot determine the AF spin structure, based only on the present μ⁺SR results.

Fig. 6 Dipole field distribution for (a) the stripe-type AF order and (b) A-type AF order, and (c) the Fourier transformed frequency spectrum of the ZF-μ⁺SR time spectrum at 0.05 K for P2-Na_0.5VO₂.

If we compare the H_int/μ_V at which with H_int at which the ordered V moment (μ_V) is evaluated as 0.11 μ_B [0.2 μ_B] at 0.05 K for a stripe-type state [an A-type state].

Acknowledgements

We thank the staff of PSI for help with the μ⁺SR experiments. DA acknowledges financial support from the Romanian UEFISCDI Project PN-II-ID-PCE-2011-3-0583 (85/2011). This work was supported by MEXT KAKENHI Grant no. 23108003 and JSPS KAKENHI Grant no. 26286084.

References

1. H. R. Krishnamurthy, C. Jayaprakash, S. Sarker and W. Wenzel, Phys. Rev. Lett., 1990, 64, 950–953.
2. M. Fujita, M. Ichimura and K. Nakao, J. Phys. Soc. Jpn., 1991, 60, 2831–2834.
3. G. M. Kalvius, D. R. Noakes and O. Hartmann, in Handbook on the Physics and Chemistry of Rare Earths, ed. K. A. Gschneidner, L. Eyring Jr and G. H. Lander, North-Holland, Amsterdam, 2001, vol. 32, ch. 206.
4. K. Mukai, Y. Ikedo, H. Nozaki, J. Sugiyama, K. Nishiyama, D. Andreica, A. Amato, P. L. Russo, E. J. Ansaldo, J. H. Brewer, K. H. Chow, K. Ariyoshi and T. Ohzuku, Phys. Rev. Lett., 2007, 99, 087601.
5. J. Sugiyama, J. H. Brewer, E. J. Ansaldo, H. Itahara, T. Tani, M. Mikami, Y. Mori, T. Sasaki, S. Hébert and A. Maignan, Phys. Rev. Lett., 2004, 92, 017602.
6. J. Sugiyama, H. Nozaki, Y. Ikedo, K. Mukai, J. H. Brewer, E. J. Ansaldo, G. D. Morris, D. Andreica, A. Amato, T. Fujii and A. Asamitsu, Phys. Rev. Lett., 2006, 96, 037206.
7. J. Sugiyama, Y. Ikedo, P. L. Russo, H. Nozaki, K. Mukai, D. Andreica, A. Amato, M. Blangero and C. Delmas, Phys. Rev. B: Condens. Matter Mater. Phys., 2007, 76, 104412.
8. J. Sugiyama, H. Nozaki, Y. Ikedo, P. L. Russo, K. Mukai, D. Andreica, A. Amato, T. Takami and H. Ikuta, Phys. Rev. B: Condens. Matter Mater. Phys., 2008, 77, 092409.
9. J. Sugiyama, Y. Ikedo, K. Mukai, J. H. Brewer, E. J. Ansaldo, G. D. Morris, K. H. Chow, H. Yoshida and Z. Hiroi, Phys. Rev. B: Condens. Matter Mater. Phys., 2006, 73, 224437.
10. J. Sugiyama, H. Nozaki, Y. Ikedo, K. Mukai, P. L. Russo, D. Andreica, A. Amato, H. Yoshida and Z. Hiroi, Phys. Rev. B: Condens. Matter Mater. Phys., 2008, 78, 104427.
11. J. Sugiyama, K. Mukai, Y. Ikedo, H. Nozaki, M. Månsson and I. Watanabe, Phys. Rev. Lett., 2009, 103, 147601.
12. J. Sugiyama, K. Mukai, H. Nozaki, M. Harada, M. Månsson, K. Kamazawa, D. Andreica, A. Amato and A. D. Hillier, Phys. Rev. B: Condens. Matter Mater. Phys., 2013, 87, 024409.
13. C. M. Julien, A. Ait-Salah, A. Mauger and F. Gendron, Ionics, 2006, 12, 21–32.
14. J. Sugiyama, Y. Ikedo, K. Mukai, H. Nozaki, M. Månsson, O. Ofer, M. Harada, K. Kamazawa, Y. Miyake, J. H. Brewer, E. J. Ansaldo, K. H. Chow, I. Watanabe and T. Ohzuku, Phys. Rev. B: Condens. Matter Mater. Phys., 2010, 82, 224412.
15. M. Guignard, C. Didier, J. Darriet, P. Bordet, E. Elkaïm and C. Delmas, Nat. Mater., 2013, 12, 74–80.
16. C. Didier, M. Guignard, J. Darriet and C. Delmas, Inorg. Chem., 2012, 51, 11007–11016.
17. R. Kadono, J. Imazato, T. Matsuzaki, K. Nishiyama, K. Nagamine, T. Yamazaki, D. Richter and J.-M. Welter, Phys. Rev. B: Condens. Matter Mater. Phys., 1989, 39, 23–41.
18. Y. Imai, I. Solovyev and M. Imada, Phys. Rev. Lett., 2005, 95, 176405.
19. Y. Imai and M. Imada, J. Phys. Soc. Jpn., 2006, 75, 094713.
20. J. Sugiyama, H. Nozaki, I. Umegaki, W. Higemoto, E. J. Ansaldo, J. H. Brewer, H. Sakurai, T.-H. Kao, H.-D. Yang and M. Månsson, Phys. Rev. B: Condens. Matter Mater. Phys., 2014, 89, 020402.
21. J. Sugiyama, H. Nozaki, I. Umegaki, W. Higemoto, E. J. Ansaldo, J. H. Brewer, H. Sakurai, T.-H. Kao, H.-D. Yang and M. Månsson, J. Phys.: Conf. Ser., 2014, 551, 012011.
22. M. L. Foo, Y. Wang, S. Watauchi, H. W. Zandbergen, T. He, R. J. Cava and N. P. Ong, Phys. Rev. Lett., 2004, 92, 247001.
23. P. Mendels, D. Bono, J. Bobroff, G. Collin, D. Colson, N. Blanchard, H. Alloul, I. Mukhamedshin, F. Bert, A. Amato and A. D. Hillier, Phys. Rev. Lett., 2005, 94, 136403.
24. J. Sugiyama, Y. Ikedo, P. Russo, K. Mukai, H. Nozaki, J. Brewer, E. Ansaldo, K. Chow, D. Andreica, A. Amato, T. Fujii, A. Asamitsu, K. Ariyoshi and T. Ohzuku, J. Mater. Sci.: Mater. Electron., 2008, 19, 883–893.
25. G. Gašparović, R. A. Ott, J.-H. Cho, F. C. Chou, Y. Chu, J. W. Lynn and Y. S. Lee, Phys. Rev. Lett., 2006, 96, 046403.
26. J. Sugiyama, H. Itahara, J. H. Brewer, E. J. Ansaldo, T. Motohashi, M. Karppinen and H. Yamauchi, Phys. Rev. B: Condens. Matter Mater. Phys., 2003, 67, 214420.
27. S. Bayrakci, I. Mirebeau, P. Bourges, Y. Sidis, M. Enderle, J. Mesot, D. Chen, C. Lin and B. Keimer, Phys. Rev. Lett., 2005, 94, 157205.
28. L. Helme, A. Boothroyd, R. Coldea, D. Prabhakaran, D. Tennant, A. Hiess and J. Kulda, Phys. Rev. Lett., 2005, 94, 157206.
29. C. Darie, P. Bordet, S. de Brion, M. Holzapfel, O. Isnard, A. Lecchi, J. E. Lorenzo and E. Suard, Eur. Phys. J. B, 2005, 43, 159–162.
30. M. Lewis, B. Gaulin, L. Filion, C. Kallin, A. Berlinsky, H. Dabkowska, Y. Qiu and J. Copley, Phys. Rev. B: Condens. Matter Mater. Phys., 2005, 72, 014408.
31. H. Nozaki, M. Janoschek, B. Roessli, J. Sugiyama, L. Keller, J. H. Brewer, E. J. Ansaldo, G. D. Morris, T. Takami and H. Ikuta, Phys. Rev. B: Condens. Matter Mater. Phys., 2007, 76, 014402.
32. P. L. Russo, J. Sugiyama, J. H. Brewer, E. J. Ansaldo, S. L. Stubbs, K. H. Chow, R. Jin, H. Sha and J. Zhang, Phys. Rev. B: Condens. Matter Mater. Phys., 2009, 80, 104421.
33. O. Ofer, Y. Ikedo, T. Goko, M. Månsson, J. Sugiyama, E. J. Ansaldo, J. H. Brewer, K. H. Chow and H. Sakurai, Phys. Rev. B: Condens. Matter Mater. Phys., 2010, 82, 094410.
34. J. Sugiyama, H. Nozaki, M. Månsson, K. Prša, D. Andreica, A. Amato, M. Isobe and Y. Ueda, Phys. Rev. B: Condens. Matter Mater. Phys., 2012, 85, 214407.
35. J. Sugiyama, H. Nozaki, K. Miwa, H. Yoshida, M. Isobe, K. Prša, A. Amato, D. Andreica and M. Månsson, Phys. Rev. B: Condens. Matter Mater. Phys., 2013, 88, 184417.

---