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Magnetic excitations of charge-ordered La2NiO4.11
ARTICLE IN PRESS
Journal of Magnetism and Magnetic Materials 310 (2007) 760–762 www.elsevier.com/locate/jmmm
Magnetic excitations of charge-ordered La2NiO4:11$ P.G. Freemana,, S.M. Haydenb, C.D. Frostc, D. Prabhakarand, A.T. Boothroydd a
Institut Laue-Langevin, BP 156, 38042 Grenoble Cedex 9, France Department of Physics, University of Bristol, Bristol, BS8 1TL, UK c ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, OX11 0QX, UK d Department of Physics, Oxford University, Oxford, OX1 3PU, UK b
Available online 7 November 2006
Abstract The incommensurate magnetic excitations of spin–charge ordered La2 NiO4:11 were studied by inelastic neutron scattering. With increasing energy up to 20 meV the maximum intensity of the spin excitations is observed to shift slightly towards the 2D antiferromagnetic wave vector ð1=2; 1=2Þ. This asymmetry in the magnon dispersion about the incommensurate wave vector is a similar effect, though less marked, to what has been observed in the layered cuprate superconductors. r 2006 Elsevier B.V. All rights reserved. PACS: 75.30.Ds; 71.45.Lr; 75.30.Et; 75.30.Fv Keywords: Spin waves; Stripes; La2 NiO4þd
1. Introduction It is now a decade since magnetic and charge ordering in the form of stripes was observed in a non-superconducting cuprate [1]. Since that discovery, a large effort has been made to understand the behaviour of the charge and spin degrees of freedom in cuprates, and to establish their possible role in high temperature superconductivity. A useful model reference system is La2x Srx NiO4 (LSNO), which exhibits stripe order without the complication of superconductivity. The static order and spin excitations have been studied in detail in the Sr-doped nickelates [2–5], but so far the comparison with the charge-ordered cuprates has been limited by the charge ordering period, which is typically a factor 2 smaller in LSNO than in the cuprates. In this paper we report a study of the magnetic excitations of La2 NiO4:11 , which has well correlated diagonal stripe order (i.e. charge stripes oriented at 45 to the Ni–O bonds) with a period of 4 lattice sites. This provides an interesting comparison with the proposed $
This work was funded in part by the Engineering and Physical Sciences Research Council of Great Britain. Corresponding author. E-mail address: [email protected] (P.G. Freeman). 0304-8853/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.10.488
stripe order model for the cuprates at 1/8 doping in which the charge stripes run parallel to the Cu–O bonds but are also spaced 4 lattice sites apart. 2. Experimental details Inelastic neutron scattering measurements where carried out on the direct geometry time-of-flight chopper spectrometer MAPS at the ISIS Facility. A single crystal sample was mounted in a closed-cycle refrigerator and aligned with the crystal c axis parallel to the incident beam direction. The scattered neutrons were detected in large banks of position sensitive detectors. The single crystal of La2 NiO4þd ðd ¼ 0:11Þ used in the experiment was grown by the floating-zone technique [7], and was a rod of dimensions 7 mm f 50 mm. Previous studies of LSNO [3,5] observed no c dependence to the magnetic excitations for energies above a few meV in charge-ordered nickelates, so we use the 2D wave vector ðh; kÞ, in reciprocal lattice units, to describe the spectrum. 3. Results The stripe order in La2 NiO4:11 is twinned with stripes running parallel to either the ½1; 1 or ½1; 1 directions of the
ARTICLE IN PRESS P.G. Freeman et al. / Journal of Magnetism and Magnetic Materials 310 (2007) 760–762
Fig. 1. Slice through the spin excitation spectrum of La2 NiO4:11 . The horizontal axis is the wave vector parallel to ðx; xÞ.
11 E = 8 - 10 meV
10
E = 12-14 meV
9 Intensity (arb. units)
˚ Magnetic square lattice of the NiNiO2 layers ða ¼ 3:8 AÞ. Bragg peaks are located at the wave vectors ð1=2; 1=2Þ ð=2; =2Þ and ð1=2; 1=2Þ ð=2; =2Þ, where the incommensurability is inversely proportional to the stripe period. For La2 NiO4:11 we found ¼ 0:266, slightly away from the relation ¼ 2d for ideal doping but consistent with other LSNO compositions [2]. In our sample we observed an equal population of the two stripe domains. The width of the magnetic Bragg reflections indicated a magnetic correlation ˚ and the magnetic ordering length in excess of 60 A, temperature was observed to be 110 10 K. Additional Bragg reflections from the ordering of the intersitial oxygens were also observed [8], with an ordering temperature in excess of 200 K (the highest temperature studied). In Fig. 1 we show a slice of the energy variation of the excitations along the ðh; hÞ direction in reciprocal space for energies below 40 meV. Below 8 meV the excitations are observed to be centred on the magnetic zone centres at h ¼ 0:367 and 0.633, but with increasing energy the excitations appear to disperse inwards towards ð0:5; 0:5Þ, an effect not observed in LSNO with x1=3 [3–5]. This effect is illustrated in Fig. 2, which shows cuts along the ðh; hÞ direction averaged over the energy ranges 8–10 V and 12–14 meV for La2 NiO4:11 . The centres of the magnetic excitations are noticeably closer to ð0:5; 0:5Þ in the 13 1 meV cut than in the 9 1 meV cut. In the energy range 20225 meV there is additional scattering due to phonons [3,5]. This phonon scattering obscures the magnetic excitations and tends to exaggerate the shift towards ð0:5; 0:5Þ. With increasing energy from 8 meV the intensity of the scattering is observed to decrease to a minimum at 15 meV before increasing in intensity to a maximum between 20–25 meV, then finally decreasing in intensity for higher energies. The additional phonon scattering could be
761
(ξ, ξ)
8 7 6 5 4 3
0
0.2
0.4
0.6
0.8
1
ξ (r.l.u.) Fig. 2. Cuts performed parallel to ðx; xÞ averaged over E ¼ 8210 meV (circles) and E ¼ 12214 meV (triangles), the latter offset for clarity by the addition of 3 to the intensity. The data are fitted with two gaussian peaks on a sloping background. The vertical lines indicate the fitted centres of the E ¼ 8210 meV peaks.
responsible for this dip-peak structure in the intensity, but we note that a similar feature observed in LSNO for x13 was found to be magnetic in origin [3,4]. The magnetic excitations in La2 NiO4:11 were found to extend up to 75 meV, and at higher energies the modes dispersing away from ð0:5; 0:5Þ could clearly be observed. 4. Discussion and conclusions The main result of this work so far is the observation that below 30 meV the magnetic excitations in La2 NiO4:11 disperse anomalously towards ð0:5; 0:5Þ with increasing energy. This asymmetric dispersion is reminiscent of what is observed in the cuprates for energies below the ‘resonance peak’ [6]. It is possible that this effect has the same origin in the two materials. Recent linear spin wave calculations have been able to generate asymmetry in the magnetic dispersion for stripes orientated parallel (at 45 ) to the Cu–O (Ni–O) bonds. The asymmetry appeared when the strength of the exchange interaction across the charge stripe was weak compared to the exchange interactions in the antiferromagnetic regions between the charge stripes [9]. These results emphasize that efforts to understand the magnetic excitation spectrum of the cuprates could benefit from a better understanding of the charge and spin correlations in model non-superconducting charge-ordered systems, such as La2 NiO4:11 . Measurements with polarized neutrons are planned to separate the magnetic and phonon scattering in the energy range of interest. We hope these will enable us to determine more accurately the extent of the inward dispersion and the energy variation of the magnetic scattering intensity in La2 NiO4:11 .
ARTICLE IN PRESS P.G. Freeman et al. / Journal of Magnetism and Magnetic Materials 310 (2007) 760–762
762
References [1] [2] [3] [4] [5]
J.M. Tranquada, et al., Nature (London) 375 (1995) 561. H. Yoshizawa, et al., Phys. Rev. B 61 (2000) R854. A.T. Boothroyd, et al., Phys. Rev. B 67 (2003) art. 100407(R). A.T. Boothroyd, et al., Physica B 345 (2004) 1. H. Woo, et al., Phys. Rev. B 72 (2005) art. 064437.
[6] S.M. Hayden, et al., Nature (London) 429 (2004) 531; J.M. Tranquada, et al., Nature (London) 429 (2004) 534; N.B. Christensen, et al., Phys. Rev. Lett. 93 (2004) art. 147002. [7] D. Prabhakaran, P. Isla, A.T. Boothroyd, J. Cryst. Growth 237 (2002) 815. [8] J.M. Tranquada, et al., Phys. Rev. B 52 (1995) 3581. [9] D.X. Yao, E.W. Carlson, D.K. Campbell, Phys. Rev. B 73 (2006) 224525.
Journal of Magnetism and Magnetic Materials 310 (2007) 760–762 www.elsevier.com/locate/jmmm
Magnetic excitations of charge-ordered La2NiO4:11$ P.G. Freemana,, S.M. Haydenb, C.D. Frostc, D. Prabhakarand, A.T. Boothroydd a
Institut Laue-Langevin, BP 156, 38042 Grenoble Cedex 9, France Department of Physics, University of Bristol, Bristol, BS8 1TL, UK c ISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot, OX11 0QX, UK d Department of Physics, Oxford University, Oxford, OX1 3PU, UK b
Available online 7 November 2006
Abstract The incommensurate magnetic excitations of spin–charge ordered La2 NiO4:11 were studied by inelastic neutron scattering. With increasing energy up to 20 meV the maximum intensity of the spin excitations is observed to shift slightly towards the 2D antiferromagnetic wave vector ð1=2; 1=2Þ. This asymmetry in the magnon dispersion about the incommensurate wave vector is a similar effect, though less marked, to what has been observed in the layered cuprate superconductors. r 2006 Elsevier B.V. All rights reserved. PACS: 75.30.Ds; 71.45.Lr; 75.30.Et; 75.30.Fv Keywords: Spin waves; Stripes; La2 NiO4þd
1. Introduction It is now a decade since magnetic and charge ordering in the form of stripes was observed in a non-superconducting cuprate [1]. Since that discovery, a large effort has been made to understand the behaviour of the charge and spin degrees of freedom in cuprates, and to establish their possible role in high temperature superconductivity. A useful model reference system is La2x Srx NiO4 (LSNO), which exhibits stripe order without the complication of superconductivity. The static order and spin excitations have been studied in detail in the Sr-doped nickelates [2–5], but so far the comparison with the charge-ordered cuprates has been limited by the charge ordering period, which is typically a factor 2 smaller in LSNO than in the cuprates. In this paper we report a study of the magnetic excitations of La2 NiO4:11 , which has well correlated diagonal stripe order (i.e. charge stripes oriented at 45 to the Ni–O bonds) with a period of 4 lattice sites. This provides an interesting comparison with the proposed $
This work was funded in part by the Engineering and Physical Sciences Research Council of Great Britain. Corresponding author. E-mail address: [email protected] (P.G. Freeman). 0304-8853/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2006.10.488
stripe order model for the cuprates at 1/8 doping in which the charge stripes run parallel to the Cu–O bonds but are also spaced 4 lattice sites apart. 2. Experimental details Inelastic neutron scattering measurements where carried out on the direct geometry time-of-flight chopper spectrometer MAPS at the ISIS Facility. A single crystal sample was mounted in a closed-cycle refrigerator and aligned with the crystal c axis parallel to the incident beam direction. The scattered neutrons were detected in large banks of position sensitive detectors. The single crystal of La2 NiO4þd ðd ¼ 0:11Þ used in the experiment was grown by the floating-zone technique [7], and was a rod of dimensions 7 mm f 50 mm. Previous studies of LSNO [3,5] observed no c dependence to the magnetic excitations for energies above a few meV in charge-ordered nickelates, so we use the 2D wave vector ðh; kÞ, in reciprocal lattice units, to describe the spectrum. 3. Results The stripe order in La2 NiO4:11 is twinned with stripes running parallel to either the ½1; 1 or ½1; 1 directions of the
ARTICLE IN PRESS P.G. Freeman et al. / Journal of Magnetism and Magnetic Materials 310 (2007) 760–762
Fig. 1. Slice through the spin excitation spectrum of La2 NiO4:11 . The horizontal axis is the wave vector parallel to ðx; xÞ.
11 E = 8 - 10 meV
10
E = 12-14 meV
9 Intensity (arb. units)
˚ Magnetic square lattice of the NiNiO2 layers ða ¼ 3:8 AÞ. Bragg peaks are located at the wave vectors ð1=2; 1=2Þ ð=2; =2Þ and ð1=2; 1=2Þ ð=2; =2Þ, where the incommensurability is inversely proportional to the stripe period. For La2 NiO4:11 we found ¼ 0:266, slightly away from the relation ¼ 2d for ideal doping but consistent with other LSNO compositions [2]. In our sample we observed an equal population of the two stripe domains. The width of the magnetic Bragg reflections indicated a magnetic correlation ˚ and the magnetic ordering length in excess of 60 A, temperature was observed to be 110 10 K. Additional Bragg reflections from the ordering of the intersitial oxygens were also observed [8], with an ordering temperature in excess of 200 K (the highest temperature studied). In Fig. 1 we show a slice of the energy variation of the excitations along the ðh; hÞ direction in reciprocal space for energies below 40 meV. Below 8 meV the excitations are observed to be centred on the magnetic zone centres at h ¼ 0:367 and 0.633, but with increasing energy the excitations appear to disperse inwards towards ð0:5; 0:5Þ, an effect not observed in LSNO with x1=3 [3–5]. This effect is illustrated in Fig. 2, which shows cuts along the ðh; hÞ direction averaged over the energy ranges 8–10 V and 12–14 meV for La2 NiO4:11 . The centres of the magnetic excitations are noticeably closer to ð0:5; 0:5Þ in the 13 1 meV cut than in the 9 1 meV cut. In the energy range 20225 meV there is additional scattering due to phonons [3,5]. This phonon scattering obscures the magnetic excitations and tends to exaggerate the shift towards ð0:5; 0:5Þ. With increasing energy from 8 meV the intensity of the scattering is observed to decrease to a minimum at 15 meV before increasing in intensity to a maximum between 20–25 meV, then finally decreasing in intensity for higher energies. The additional phonon scattering could be
761
(ξ, ξ)
8 7 6 5 4 3
0
0.2
0.4
0.6
0.8
1
ξ (r.l.u.) Fig. 2. Cuts performed parallel to ðx; xÞ averaged over E ¼ 8210 meV (circles) and E ¼ 12214 meV (triangles), the latter offset for clarity by the addition of 3 to the intensity. The data are fitted with two gaussian peaks on a sloping background. The vertical lines indicate the fitted centres of the E ¼ 8210 meV peaks.
responsible for this dip-peak structure in the intensity, but we note that a similar feature observed in LSNO for x13 was found to be magnetic in origin [3,4]. The magnetic excitations in La2 NiO4:11 were found to extend up to 75 meV, and at higher energies the modes dispersing away from ð0:5; 0:5Þ could clearly be observed. 4. Discussion and conclusions The main result of this work so far is the observation that below 30 meV the magnetic excitations in La2 NiO4:11 disperse anomalously towards ð0:5; 0:5Þ with increasing energy. This asymmetric dispersion is reminiscent of what is observed in the cuprates for energies below the ‘resonance peak’ [6]. It is possible that this effect has the same origin in the two materials. Recent linear spin wave calculations have been able to generate asymmetry in the magnetic dispersion for stripes orientated parallel (at 45 ) to the Cu–O (Ni–O) bonds. The asymmetry appeared when the strength of the exchange interaction across the charge stripe was weak compared to the exchange interactions in the antiferromagnetic regions between the charge stripes [9]. These results emphasize that efforts to understand the magnetic excitation spectrum of the cuprates could benefit from a better understanding of the charge and spin correlations in model non-superconducting charge-ordered systems, such as La2 NiO4:11 . Measurements with polarized neutrons are planned to separate the magnetic and phonon scattering in the energy range of interest. We hope these will enable us to determine more accurately the extent of the inward dispersion and the energy variation of the magnetic scattering intensity in La2 NiO4:11 .
ARTICLE IN PRESS P.G. Freeman et al. / Journal of Magnetism and Magnetic Materials 310 (2007) 760–762
762
References [1] [2] [3] [4] [5]
J.M. Tranquada, et al., Nature (London) 375 (1995) 561. H. Yoshizawa, et al., Phys. Rev. B 61 (2000) R854. A.T. Boothroyd, et al., Phys. Rev. B 67 (2003) art. 100407(R). A.T. Boothroyd, et al., Physica B 345 (2004) 1. H. Woo, et al., Phys. Rev. B 72 (2005) art. 064437.
[6] S.M. Hayden, et al., Nature (London) 429 (2004) 531; J.M. Tranquada, et al., Nature (London) 429 (2004) 534; N.B. Christensen, et al., Phys. Rev. Lett. 93 (2004) art. 147002. [7] D. Prabhakaran, P. Isla, A.T. Boothroyd, J. Cryst. Growth 237 (2002) 815. [8] J.M. Tranquada, et al., Phys. Rev. B 52 (1995) 3581. [9] D.X. Yao, E.W. Carlson, D.K. Campbell, Phys. Rev. B 73 (2006) 224525.