Inelastic neutron scattering study of phonon anomalies in La1.5Sr0.5NiO4

The high-energy phonons in La1.5Sr0.5NiO4, in which the checkerboard charge ordering is formed, was investigated by the inelastic neutron scattering. We found that the longitudinal modes show strong anomalies compared with La2NiO4. We argue the similarity and difference in the phonon anomalies between the present sample and the preceding works of different compositions.

La 2−x Sr x NiO 4 is isostructural to one of the typical cupurate superconductors La 2−x Sr x CuO 4 . When x = 0, the compound is an antiferromagnetic insulator, where S = 1 spins on Ni 2+ (3d 8 ) ions order antiferromagnetically. Similarly to the cupurates, one hole per Ni ion is introduced in the NiO 2 planes by the substitution of a La 3+ ion with a Sr 2+ ion. In the course of exploring the origin of the superconductivity in the cupurates, the role of phonons have been extensively studied, and it was revealed that the hole doping induces a strong anomaly in the Cu-O bond stretching mode [1]. The phonon anomaly was regarded as a result of the electron-lattice coupling associated with charge inhomogeneity in the CuO 2 planes [2]. In the nickelates, the electronlattice coupling is considered to be larger than the cupurates, as the charge inhomogeneity appears in the more obvious form of static charge stripes along the direction diagonal to the Ni square lattice [3][4][5][6]. Then, phonons in the nickelates have been studied by inelastic neutron scattering (INS) to investigate whether the doped holes or charge stripes affect particularly the bond-stretching modes, which are the highest-energy longitudinal optical (LO) modes in this system. Pintschovius et al. reported that the LO modes in non-doped La 2 NiO 4 show only weak dispersion at ∼85 meV [7]. However, they found that the LO mode propagating along the [100] direction is susceptible to the non-stoichiometry, and observed similar softening to the cupurates in La 1.9 NiO 3.93 [7,8] shows a splitting of the same magnitude as the softening. However, the anomalies in the phonons are independent on the charge stripe wave vector in this compound, q CO = (0.31, 0.31, 0) [10].
In the present study, we performed an INS study of the high-energy phonons in a single crystal of La 1.5 Sr 0.5 NiO 4 . The wave vector of the charge stripes is proportional to x, and in this composition, the charge ordering results in a nearly checkerboard ordering of Ni 2+ and Ni 3+ sites: The checkerboard charge ordering with q CO = (1/2, 1/2, 0) is formed below ∼480 K, and it is taken over by incommensurate charge order with q CO ∼ (0.44, 0.44, 0) below ∼180 K [6,11]. We found that the dispersions of the phonon modes in x = 0.5 show anomalies similar to those observed in the x = 0.31 compound. However, we also found some difference between the two compositions.
Single crystals of La 1.5 Sr 0.5 NiO 4 were grown by the floating-zone method. The crystal structure is tetragonal with the space group I4/mmm [12]. The lattice constants determined by powder x-ray diffraction are a = 3.814Å and c = 12.74Å. Four crystal rods, each of which is ∼5 mm in diameter and ∼30 mm in length, were assembled for the present work. The INS measurement was performed on the chopper spectrometer 4SEASONS at J-PARC [13]. The incident energy was E i = 111 meV with the energy resolution being 10 meV at the elastic scattering condition. We aligned the crystals so that the [001] axis is parallel to the incident beam and the [110] axis is in the horizontal plane. Due to this crystal orientation, the observed data may include the contributions from out-of-plane phonon modes. However, they are expected to be small, because the high-energy phonon modes observed in the current experiment arise mainly from in-plane polarized oxygen vibrations [7,9]. We converted the raw data taken at ∼5 K to a histogram of the intensity proportional to the dynamical structure factor S(Q,hω), where Q and hω are momentum and energy transfers, using the software package Utsusemi [14]. In contrast to the previous INS studies using triple-axis spectrometers [7,8,10], scanning Q x = Ha * , Q y = Kb * , orhω simultaneously changes the value of Q z = Lc * in the present study using the chopper spectrometer. Actually, for example, (H, K) = (0, 0), (1, 0), (1, 1) correspond to (H, K, L) = (0, 0, 7.66), (1, 0, 8.48), (1, 1, 9.43) athω = 85 meV, respectively. However, considering the layered structure of the sample, we ignore Q z and express Q in terms of (H, K). Though this assumption is not strictly correct, it is supported by the weak Q z dependence of the highest-energy modes throughout the Brillouin zone observed in La 1.9 NiO 3.87 [8]. Since the obtained intensity decreases as a function ofhω, we further divided the intensity byhω for clarity in a highhω region. To correct thehω-dependent background, we estimated it by fitting the background of the intensity in the region of 0.9 < H < 1.1 and −0.1 < K < 0.1 to a quadratic function ofhω, then subtracted it from the data.
First, to survey the overall structure of the high-energy phonons, we investigated a Q map of the neutron scattering intensity. Figure 1(a) shows the intensity map athω = 85 meV on the H-K plane. This energy is almost equal to that of the bond-stretching mode in La 2 NiO 4 [7]. A characteristic intensity modulation is observed in Fig. 1, which reflects some dispersions of the high-energy modes. There are strong spots at (H, K) = (1, 1), (±1, 0), and (0, ±1). In addition, the intensity shows streaks along the (H, ±1) and (±1, K) lines. These spots and streaks suggest that the phonon mode along these lines shows a weak dispersion, while those along the other Next, to investigate the Q dependence of the high-energy phonons in more detail, we cut the data along the lines shown in figure 1(b). We should note that this minimum energy is almost equal to that of the sub-band in the phonon DOS appearing at x > 1/3 [9], which suggests these anomalies in the LO modes are the origin of the ∼75 meV sub-band. On the other hand, for the TO modes in figures 2(c) and 2(d), the observed dispersions are almost similar to La 2 NiO 4 , though the energies are slightly higher. The hole doping and charge ordering do not affect the energies of the TO modes except for slight hardenings.
The observed anomalies in the LO modes as well as their minimum energies at ∼73 meV are apparently similar to those observed in x = 0.31 [10]. In x = 0.31, though the energy of the LO phonon along [100] continuously softens as a function of Q, that along [110] shows a splitting into two modes. Moreover, the latter anomaly is independent on q CO . Tranquada et al. interpreted the splitting of the LO mode is caused by the local breathing motion of O ions about the hole-doped Ni sites (Ni 3+ sites). The similarities between the phonon anomalies in x = 0.5 and those in x = 0.31 supports their idea that the doped holes cause local effects on the bond-stretching phonons independent on the hole concentration.
However, there is some difference between the two compounds. Contrary to x = 0.31, in x = 0.5, the dispersion of the LO mode along [110] shows a clear softening with its minimum at (0.5,0.5) [ figure 2(b)], though there is very weak Q independent intensity at ∼85 meV. In other words, the softening behavior is superior to the splitting behavior along [110] in this compound. On the other hand, the splitting behavior is more clearly observed in the data along [100] [figure 2(a)]. The difference between the present x = 0.5 sample and x = 0.31 may be related to the difference in types of the charge ordering. In the case of the checkerboard charge ordering in x = 0.5, the holes enter every two Ni sites, and Ni 2+ sites and Ni 3+ sites always share the in-plane O ions. Therefore, the vibrations of the shared in-plane O ions may become more coherent along the direction of the charge-ordering wave vector, [110], resulting in the softening of the dispersion.
In conclusion, we performed an INS study on La 1.5 Sr 0.5 NiO 4 to investigate the effects of hole doping on the high-energy phonon modes. We found that the longitudinal modes show clearly different dispersions compared with La 2 NiO 4 , though the transverse modes are quite similar to those in La 2 NiO 4 . In particular, the longitudinal mode along the direction diagonal to the Ni square lattice shows a clear softening, in contrast to x = 0.31 where the mode shows a splitting [10]. We interpret the difference in the phonon anomalies between x = 0.5 and x = 0.31 as the difference in the type of charge ordering.