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Damped spin waves in the intermediate ordered phases in Ni3V2O8
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 J. Phys.: Condens. Matter 27 256003 (http://iopscience.iop.org/0953-8984/27/25/256003) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 128.111.121.42 This content was downloaded on 09/09/2015 at 06:32
Please note that terms and conditions apply.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 27 (2015) 256003 (6pp)
doi:10.1088/0953-8984/27/25/256003
Damped spin waves in the intermediate ordered phases in Ni3V2O8 G Ehlers1 A A Podlesnyak1, M D Frontzek2, A V Pushkarev3, S V Shiryaev3 and S Barilo3 1
Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6475, USA 2 Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institute, CH-5232 Villigen, Switzerland 3 Institute of Solid State and Semiconductor Physics, Minsk 220 072, Belarus E-mail: [email protected] Received 2 April 2015, revised 4 May 2015 Accepted for publication 18 May 2015 Published 9 June 2015 Abstract
Spin dynamics in the intermediate ordered phases (between 4 and 9 K) in Ni3V2O8 have been studied with inelastic neutron scattering. It is found that the spin waves are very diffuse, indicative of short lived correlations and the coexistence of paramagnetic moments with the long-range ordered state. Keywords: neutron scattering, spin waves, multiferroic materials (Some figures may appear in colour only in the online journal)
1. Introduction Magnetic ferroelectric (‘multiferroic’) materials are the subject of intense research—both fundamental and applied—as they may form a basis for new technological applications. The coexistence of magnetic and electric order parameters and their coupling allow one to manipulate the magnetic properties of the material with an external electric field and vice versa [1–5]. Ni3V2O8 is a multiferroic material that has received particular attention, mainly because (1) it has a very complex phase diagram, and (2) large crystals can be grown enabling the use of various experimental probes such as neutron and magnetic x-ray scattering, μSR, NMR, magnetization, electric polarization, optical spectroscopy and specific heat [6–16, 17]. Measurements were complemented by first-principles calculations which identified the phonon modes that can cause electric dipole moments to form [18]. Band calculations show that the material is an intermediate-gap insulator at all temperatures and that the Ni moment is fully localized with 2 μB per site as expected for Ni2 +, S = 1, ions [19]. The dynamics of a spin system directly reveals the fundamental underlying interactions, because the dispersion, energy, and neutron scattering intensity of the spin waves can be calculated, starting from the spin Hamiltonian, in straightforward ways [20–24]. 0953-8984/15/256003+6$33.00
Inelastic neutron scattering has traditionally been regarded as the strongest experimental probe to access the spin dynamics because the neutron energy matches well the typical energies of magnetic excitations, ≲ 0.1 eV, and because scattering methods (as opposed to local probes) access space and time dimensions simultaneously. However, there has also been tremendous progress recently in the development of inelastic x-ray scattering methods [25]. During the last decade new neutron sources have emerged that host a new generation of significantly advanced instruments [26–28]. Modern time-of-flight (TOF) neutron spectrometers allow one to map out the full four-dimensional excitation spectrum of a correlated crystalline material in reciprocal space (three momentum transfer coordinates and one energy transfer coordinate) [29–33]. These instruments provide high count rate, homogeneous resolution, and, crucially, access to all three spatial dimensions, that is, one is not confined to a single plane in reciprocal space. These new capabilities meet the modern demand to study and understand more complex materials, and again Ni3V2O8 is a perfect case in point. On cooling in zero field, this material has four distinct ordered phases, which are referred to (in order of decreasing temperature) as HTI, LTI, C and C’. This paper complements two studies on the spin dynamics in Ni3V2O8 published earlier [10, 34]. A first study confirmed the presence of spin waves in the C’ phase but could not 1 Not subject to copyright in the USA. Contribution of US Dept. of Energy. Printed in the UK
G Ehlers et al
J. Phys.: Condens. Matter 27 (2015) 256003
detect inelastic scattering of significant intensity in the LTI or HTI phases [10]. The latter study focused exclusively on the low-temperature C and C’ phases, as these are very different from the LTI and HTI phases at higher temperature, and were thought to be less well understood at the time. The study presented here fills the gap and and presents new results on spin dynamics measurements in the LTI and HTI phases of Ni3V2O8. 2. Experimental methods Details about the preparation of flux-grown samples and their characterization with x-ray diffraction were given elsewhere [34]. Measurements reported in this paper were conducted at the cold neutron chopper spectrometer (CNCS) at the spallation neutron source (SNS) at Oak Ridge National Laboratory (ORNL) [35, 36]. The incident energy was Ei = 3.3 meV, and the energy resolution at the elastic line was ∼60 μeV fwhm (full width at half max). The sample was oriented with the HK 0 plane in the horizontal scattering plane, giving one access to the magnetic Bragg reflections in the LTI and HTI phases at Q points of (H ± τ , K , 0) r. l. u. (relative lattice units) where H odd, K odd, and τ ∼ 0.28 [7]. The sample was mounted in an Orange cryostat and measured at three temperatures (∼15 h each, with SNS operating at ∼1 MW at the time), at T = 5.0 K (LTI phase), T = 7.7 K (HTI phase) and at T = 50 K (paramagnetic phase, for reference). During the measurement the sample was continuously rotated around the axis that was vertical in the laboratory frame. The instrument counted scattered neutrons in event mode which allowed one to back-calculate—during the data reduction process—the motor position (i.e. sample orientation) at the time the neutron was scattered. Data reduction followed a standard protocol using the MANTID software package [37]. Calibration for detector tube efficiency was performed using a white beam vanadium measurement.
Figure 1. Elastic scattering map obtained at CNCS with E i = 3.3
meV. Nuclear (magnetic) Bragg peaks are highlighted blue (green), respectively.
phase in which moments on the spine sublattice are arranged very nearly along the a-direction and the amplitude vector (max. moment amplitude) has a length of ∼2 μB [7, 8]. The moments on the cross-tie site are disordered (near zero time average). Going to the LTI phase, moments on the spine site rearrange to form spirals that rotate in the ab-plane and propagate along the a-direction. This structure breaks time inversion symmetry and leads to spontaneous ferroelectric polarization in the material in the LTI phase. According to neutron diffraction, the moments on the cross-tie site do also acquire their full moment of ∼2 μB in the LTI phase [7], and order in the same spiral pattern with a phase shift relative to the spine site moments. On the other hand, according to magnetic x-ray diffraction, the moments on the cross-tie site remain largely (but not fully) disordered in the LTI phase [16]. The fundamental difference in the ordering patterns between the two phases seen by the scattering methods is evidenced by the occurrence of spontaneous electric polarization in the LTI phase and further supported by a marked change in the observed μSR relaxation line shape at the transition between the two phases [12]. However, results from 51V NMR in an applied magnetic field are not easily reconciled with this picture [15] and thus warrant further analysis. NMR works in an applied field whereas the spin structure was determined in zero field. In neutron diffraction all magnetic peaks were reported to be resolution limited [7]. In agreement with this earlier finding, no systematic changes in line shape or -width between the two phases are found in the CNCS data. The Q resolution was found to change systematically with Q—consistent with operating principles of a time-of-flight instrument [35]—between ∼ 0.015 r. l. u. and ∼ 0.045 r. l. u. in the H direction, and between ∼ 0.025 r. l. u. and ∼ 0.060 r. l. u. in the K direction (the b-axis is nearly twice as long as the a-axis). In the scattering plane the Q resolution is better than in the out-of-plane (here, L) direction because the horizontal beam divergence is lower than the vertical beam divergence.
3. Experimental results and discussion Elastic scattering as measured at T = 5.0 K is shown in figure 1. Data were integrated within ±0.07 meV energy transfer and in the band ∣L∣ ⩽ 0.07 r. l. u. which corresponds to the Q resolution out of plane. The accessible Q range contains both magnetic Bragg peaks of the (H ± τ , K , 0) type (circled green in the top right quadrant) and nuclear Bragg peaks (blue circles). Results from earlier work on the HTI and LTI phases can be summarized as follows. The crystal structure features two sub-lattices occupied by Ni2 +, S = 1, moments, termed ‘spine’ and ‘cross-tie’ sites, respectively [7]. The spine site makes linear chains that run along the crystallographic a-axis, whereas the cross-tie site is situated at the mid-points between such chains. The entire magnetic lattice has been described as a ‘buckled kagome’ lattice—four spine sites and two cross-tie sites, respectively, form one of the characteristic hexagons of the kagome lattice, and the buckling is along the b-direction [8]. The HTI phase is a longitudinally amplitude-modulated 2
G Ehlers et al
J. Phys.: Condens. Matter 27 (2015) 256003
Figure 2. Neutron scattering results at T = 5.0 K. A constant energy slice at E = 0.2 meV is shown in the top left for one quadrant of Q space. Below two (Q, E ) slices are shown along directions indicated above.
The origin of the additional scattering intensity at T = 5.0 K that can be seen in figure 2 around the (0, 1, 0) and (0, 3, 0) positions is unclear. It does not appear to be an instrumental artifact because of the background subtraction procedure that was applied (see above). Turning to the HTI phase, figure 3 shows similar cuts through data taken at T = 7.7 K. Clearly, the data is even more diffuse here, suggesting that the particular ordered structure with absent moments on the cross-tie site does not support well the propagation of spin waves. Since Bragg peaks are still observed and are resolution limited at this temperature, spatial correlations of the time-averaged moments still hold well over long distances, but the dynamic correlations over short distances and times are poor. Since there are two (largely decoupled) magnetic sub-lattices present, this finding is consistent with a picture of well developed long range order on the spin site which coexists with largely paramagnetic moments on the cross-tie site. In this context one notes that—by symmetry— the mean dipole field of the spine moments vanishes on the cross-tie site.
For further analysis the inelastic data were folded into the top right quadrant, see figure 2 for data taken at T = 5.0 K in the LTI phase. This plot shows neutron energy loss scattering at ℏω = 0.2 meV (top left panel) and cuts along two directions (marked with white lines) through the (0.725, 1, 0) position (bottom panels). To emphasize the magnetic scattering, data from a reference measurement at T = 50 K were subtracted. An energy of 0.2 meV is sufficiently far away from the elastic line such that the scattering is not contaminated by a contribution from the tail of the resolution function (the energy resolution at the elastic line was ∼ 60 μ eV full width at half max.). The inelastic scattering is evidently very diffuse, suggesting a short lifetime of the collective excitations. This diffusiveness prevents one to unambiguously establish the top of the lowest lying band of excitations, which may be around ∼ 0.8 meV. A hint for a second band that stretches between ∼ 1 and ∼ 2 meV can also be seen but the scattering intensity is clearly insufficient to make a more quantitative statement. 3
G Ehlers et al
J. Phys.: Condens. Matter 27 (2015) 256003
Figure 3. Neutron scattering results at 7.7 K. A constant energy slice at E = 0.2 meV is shown in the top left for one quadrant of Q space.
Below two (Q, E ) slices are shown along directions indicated above.
4. Conclusions
Cuts through the spin wave dispersion in the H and K directions are shown in figure 4. In a semi-classical approach it is possible to establish rough estimates of the correlation lengths and times at T = 7.7 K. This is shown in figure 4 for the (0.725, 1, 0), (0.725, 3, 0) and (1.275, 1, 0) peaks (as indicated by arrows). Fitting the E = 0.2 meV cut to an Ornstein– Zernicke type of correlation function, I (Q ) ∝ (1 + Q 2 /κ 2 )−1, that is convoluted with the known Q-resolution at these points, the parameter κ will indicate a (direction-dependent) inverse correlation length as in real space the spin-spin correlation function will be ∝ exp(−rκ ). This analysis results in κ −1 ∼ 8 ⋅ a along the a-direction and κ −1 ∼ 3 ⋅ b along the b-direction. Dynamic spatial correlations thus hold over a few unit cells only. This analysis can be extended to the energy (time) domain as well, as shown in the insert of figure 4. At T = 7.7 K the (0.725, 1, 0) peak clearly shows lorentzian broadening at its base, with quasi-elastic scattering likely originating in the cross-tie site. The corresponding correlation time is about t0 ∼ 4 ⋅ 10−12 s.
The HTI and LTI phases in Ni3V2O8 hardly support the propagation of spin waves. All dynamic features that can be observed with inelastic neutron scattering in these phases, below ≲2 meV, are very diffuse. This may be regarded as a strong indicator for the presence of paramagnetic (disordered) moments in the lattice, which coexist with long-range ordered moments, in agreement with earlier experimental results [7, 16]. The disordered moments effectively act as scattering centers and prevent the formation of long range spin waves. A direct calculation of spin waves based on a model Hamiltonian [21–24] allows one to match the inelastic neutron scattering data and to understand the nature and the strength of relevant near neighbor interactions. In the present case, such a calculation was not attempted as the observable data did not extend far enough into the inelastic range. 4
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J. Phys.: Condens. Matter 27 (2015) 256003
Figure 4. Cuts through the spin wave dispersion in both directions at various energy transfers. Full circles are for T = 5.0 K, hollow
diamonds are for T = 7.7 K. Lines are guides to the eye. The vertical separation of the traces is for clarity only. Arrows indicate which peaks were fitted to an Ornstein–Zernicke type correlation function. The inset shows the energy dependent scattering around the (0.725, 1, 0) peak.
Division, Office of Basic Energy Sciences, U.S. Department of Energy. Work at the Institute of Solid State and Semiconductor Physics in Minsk was supported in part by BRFFIRFFI grant No. F14R-094.
The coexistence of paramagnetic and long-range ordered moments is a phenomenon that has been observed before in some geometrically frustrated magnets [38–43]. Generally, it may be expected in those cases where two (or more) magnetic sub-lattices are present, as these may have different frustration indices [44]. The frustration index f , expressed as the ratio between the Curie–Weiss temperature and the ordering temperature, f =∣Θ W/TN∣, is commonly used to judge the degree of frustration in a system. In some cases, such as Gd2Ti2O7 or TbNiAl, it is the magnetic ordering with a
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( , , ) propagation vector that splits 1 1 1 2 2 2
the crystallographic site of the magnetic ion in two orbits, which then have different magnetic character in the ordered state [39, 41]. In other cases, such as Ni3V2O8, there is more than one magnetic site to begin with, and competing interactions conspire to de-couple them such that the topological frustration affects them differently. Acknowledgments The authors are grateful for the local support staff at SNS. Research at Oak Ridge National Laboratory’s Spallation Neutron Source was supported by the Scientific User Facilities 5
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[27] Bennington S M 2009 Instruments on the ISIS second target station Nucl. Instrum. Methods Phys. Res. A 600 32 [28] Mason T E et al 2006 The spallation neutron source in Oak Ridge: a powerful tool for materials research Physica B 385–6 955 [29] Nakamura M, Kajimoto R, Inamura Y, Mizuno F, Fujita M, Yokoo T and Arai M 2009 First demonstration of novel method for inelastic neutron scattering measurement utilizing multiple incident energies J. Phys. Soc. Japan 78 093002 [30] Loire M et al 2011 Parity-broken chiral spin dynamics in Ba3NbFe 3Si2O14 Phys. Rev. Lett. 106 207201 [31] Savary L, Ross K A, Gaulin B D, Ruff J P C and Balents L 2012 Order by quantum disorder in Er2Ti2O7 Phys. Rev. Lett. 109 167201 [32] Schmidiger D, Bouillot P, Guidi T, Bewley R, Kollath C, Giamarchi T and Zheludev A 2013 Spectrum of a magnetized strong-leg quantum spin ladder Phys. Rev. Lett. 111 107202 [33] Frontzek M et al 2011 Magnetic excitations in the geometric frustrated multiferroic CuCrO2 Phys. Rev. B 84 094448 [34] Ehlers G, Podlesnyak A A, Hahn S E, Fishman R S, Zaharko O, Frontzek M, Kenzelmann M, Pushkarev A V, Shiryaev S V and Barilo S 2013 Incommensurability and spin dynamics in the low-temperature phases of Ni3V2O8 Phys. Rev. B 87 214418 [35] Ehlers G, Podlesnyak A A, Niedziela J L, Iverson E B and Sokol P E 2011 The new cold neutron chopper spectrometer at the spallation neutron source: design and performance Rev. Sci. Instrum. 82 085108 [36] Stone M B et al 2014 A comparison of four direct geometry time-of-flight spectrometers at the spallation neutron source Rev. Sci. Instrum. 85 045113 [37] Arnold O et al 2014 Mantid—data analysis and visualization package for neutron scattering and μSR experiments Nucl. Instrum. Methods Phys. Res. 764 156 [38] Movshovich R, Jaime M, Mentink S, Menovsky A A and Mydosh J A 1999 Second low-temperature phase transition in frustrated UNi 4B Phys. Rev. Lett. 83 2065 [39] Ehlers G, Casalta H, Lechner R E and Maletta H 2001 Dynamics of frustrated magnetic moments in antiferromagnetically ordered TbNiAl probed by neutron time-of-flight and spin-echo spectroscopy Phys. Rev. B 63 224407 [40] Greedan J E, Wiebe C R, Wills A S and Stewart J R 2002 Neutron-scattering studies of the geometrically frustrated spinel LiMn2O4 Phys. Rev. B 65 184424 [41] Stewart J R, Ehlers G, Wills A S, Bramwell S T and Gardner J S 2004 Phase transitions, partial disorder and multi-k structures in Gd2Ti2O7 J. Phys.: Condens. Matter. 16 L321 [42] Cao G, Durairaj V, Chikara S, Parkin S and Schlottmann P 2007 Partial antiferromagnetism in spin-chain Sr5Rh 4O12, Ca5Ir3O12, and Ca 4IrO6 single crystals Phys. Rev. B 75 134402 [43] Thompson C M, Greedan J E, Garlea V O, Flacau R, Tan M, Nguyen P H T, Wrobel F and Derakhshan S 2014 Partial spin ordering and complex magnetic structure in BaYFeO4: a neutron diffraction and high temperature susceptibility study Inorg. Chem. 53 1122 [44] Ramirez A P 1994 Strongly geometrically frustrated magnets Annu. Rev. Mater. Sci. 24 453
[9] Kenzelmann M et al 2006 Field dependence of magnetic ordering in Kagomé-staircase compound Ni3V2O8 Phys. Rev. B 74 014429 [10] Wilson N R, Petrenko O A, Balakrishnan G, Manuel P and Fåk B 2007 Magnetic excitations in the Kagomé staircase compounds J. Magn. Magn. Mater. 310 1334 [11] Chaudhury R P, Yen F, dela Cruz C R, Lorenz B, Wang Y Q, Sun Y Y and Chu C W 2007 Pressure-temperature phase diagram of multiferroic Ni3V2O8 Phys. Rev. B 75 012407 [12] Lancaster T, Blundell S J, Baker P J, Prabhakaran D, Hayes W and Pratt F L 2007 Kagome staircase compounds Ni3V2O8 and Co3V2O8 studied with implanted muons Phys. Rev. B 75 064427 [13] Cabrera I et al 2009 Coupled magnetic and ferroelectric domains in multiferroic Ni3V2O8 Phys. Rev. Lett. 103 087201 [14] Vergara L I, Cao J, Rogado N, Wang Y Q, Chaudhury R P, Cava R J, Lorenz B and Musfeldt J L 2009 Magnetoelastic coupling in multiferroic Ni3V2O8 Phys. Rev. B 80 052303 [15] Ogloblichev V et al 2010 51V NMR study of the kagome staircase compound Ni3V2O8 Phys. Rev. B 81 144404 [16] Fabrizi F, Walker H C, Paolasini L, de Bergevin F, Fennell T, Rogado N, Cava R J, Wolf Th, Kenzelmann M and McMorrow D F 2010 Electric field control of multiferroic domains in Ni3V2O8 imaged by x-ray polarization-enhanced topography Phys. Rev. B 82 024434 [17] Wang J, Tokunaga M, He Z Z, Yamaura J I, Matsuo A and Kindo K 2011 High magnetic field induced phases and half-magnetization plateau in the S = 1 kagome compound Ni3V2O8 Phys. Rev. B 84 220407 [18] Harris A B, Yildirim T, Aharony A and Entin-Wohlman O 2006 Towards a microscopic model of magnetoelectric interactions in Ni3V2O8 Phys. Rev. B 73 184433 [19] Rai R C, Cao J, Brown S, Musfeldt J L, Kasinathan D, Singh D J, Lawes G, Rogado N, Cava R J and Wei X 2006 Optical properties and magnetic-field-induced phase transitions in the ferroelectric state of Ni3V2O8: experiments and first-principles calculations Phys. Rev. B 74 235101 [20] Wagner W 1972 Introduction to the Theory of Magnetism (Oxford: Pergamon) [21] Haraldsen J T and Fishman R S 2009 Spin rotation technique for non-collinear magnetic systems: application to the generalized Villain model J. Phys.: Condens. Matter. 21 216001 [22] Ross K A, Savary L, Gaulin B D and Balents L 2011 Quantum excitations in quantum spin ice Phys. Rev. X 1 021002 [23] Rotter M, Le M D, Boothroyd A T and Blanco J A 2012 Dynamical matrix diagonalization for the calculation of dispersive excitations J. Phys.: Condens. Matter. 24 213201 [24] Toth S and Lake B 2015 Linear spin wave theory for single-Q incommensurate magnetic structures J. Phys.: Condens. Matter. 27 166002 [25] Ament L J P, van Veenendaal M, Devereaux T P, Hill J P, van den Brink J and van den Brink J 2011 Resonant inelastic x-ray scattering studies of elementary excitations Rev. Mod. Phys. 83 705 [26] Maekawa F et al 2010 First neutron production utilizing J-PARC pulsed spallation neutron source JSNS and neutronic performance demonstrated Nucl. Instrum. Methods Phys. Res. A 620 159
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Damped spin waves in the intermediate ordered phases in Ni3V2O8
This content has been downloaded from IOPscience. Please scroll down to see the full text. 2015 J. Phys.: Condens. Matter 27 256003 (http://iopscience.iop.org/0953-8984/27/25/256003) View the table of contents for this issue, or go to the journal homepage for more
Download details: IP Address: 128.111.121.42 This content was downloaded on 09/09/2015 at 06:32
Please note that terms and conditions apply.
Journal of Physics: Condensed Matter J. Phys.: Condens. Matter 27 (2015) 256003 (6pp)
doi:10.1088/0953-8984/27/25/256003
Damped spin waves in the intermediate ordered phases in Ni3V2O8 G Ehlers1 A A Podlesnyak1, M D Frontzek2, A V Pushkarev3, S V Shiryaev3 and S Barilo3 1
Quantum Condensed Matter Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6475, USA 2 Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institute, CH-5232 Villigen, Switzerland 3 Institute of Solid State and Semiconductor Physics, Minsk 220 072, Belarus E-mail: [email protected] Received 2 April 2015, revised 4 May 2015 Accepted for publication 18 May 2015 Published 9 June 2015 Abstract
Spin dynamics in the intermediate ordered phases (between 4 and 9 K) in Ni3V2O8 have been studied with inelastic neutron scattering. It is found that the spin waves are very diffuse, indicative of short lived correlations and the coexistence of paramagnetic moments with the long-range ordered state. Keywords: neutron scattering, spin waves, multiferroic materials (Some figures may appear in colour only in the online journal)
1. Introduction Magnetic ferroelectric (‘multiferroic’) materials are the subject of intense research—both fundamental and applied—as they may form a basis for new technological applications. The coexistence of magnetic and electric order parameters and their coupling allow one to manipulate the magnetic properties of the material with an external electric field and vice versa [1–5]. Ni3V2O8 is a multiferroic material that has received particular attention, mainly because (1) it has a very complex phase diagram, and (2) large crystals can be grown enabling the use of various experimental probes such as neutron and magnetic x-ray scattering, μSR, NMR, magnetization, electric polarization, optical spectroscopy and specific heat [6–16, 17]. Measurements were complemented by first-principles calculations which identified the phonon modes that can cause electric dipole moments to form [18]. Band calculations show that the material is an intermediate-gap insulator at all temperatures and that the Ni moment is fully localized with 2 μB per site as expected for Ni2 +, S = 1, ions [19]. The dynamics of a spin system directly reveals the fundamental underlying interactions, because the dispersion, energy, and neutron scattering intensity of the spin waves can be calculated, starting from the spin Hamiltonian, in straightforward ways [20–24]. 0953-8984/15/256003+6$33.00
Inelastic neutron scattering has traditionally been regarded as the strongest experimental probe to access the spin dynamics because the neutron energy matches well the typical energies of magnetic excitations, ≲ 0.1 eV, and because scattering methods (as opposed to local probes) access space and time dimensions simultaneously. However, there has also been tremendous progress recently in the development of inelastic x-ray scattering methods [25]. During the last decade new neutron sources have emerged that host a new generation of significantly advanced instruments [26–28]. Modern time-of-flight (TOF) neutron spectrometers allow one to map out the full four-dimensional excitation spectrum of a correlated crystalline material in reciprocal space (three momentum transfer coordinates and one energy transfer coordinate) [29–33]. These instruments provide high count rate, homogeneous resolution, and, crucially, access to all three spatial dimensions, that is, one is not confined to a single plane in reciprocal space. These new capabilities meet the modern demand to study and understand more complex materials, and again Ni3V2O8 is a perfect case in point. On cooling in zero field, this material has four distinct ordered phases, which are referred to (in order of decreasing temperature) as HTI, LTI, C and C’. This paper complements two studies on the spin dynamics in Ni3V2O8 published earlier [10, 34]. A first study confirmed the presence of spin waves in the C’ phase but could not 1 Not subject to copyright in the USA. Contribution of US Dept. of Energy. Printed in the UK
G Ehlers et al
J. Phys.: Condens. Matter 27 (2015) 256003
detect inelastic scattering of significant intensity in the LTI or HTI phases [10]. The latter study focused exclusively on the low-temperature C and C’ phases, as these are very different from the LTI and HTI phases at higher temperature, and were thought to be less well understood at the time. The study presented here fills the gap and and presents new results on spin dynamics measurements in the LTI and HTI phases of Ni3V2O8. 2. Experimental methods Details about the preparation of flux-grown samples and their characterization with x-ray diffraction were given elsewhere [34]. Measurements reported in this paper were conducted at the cold neutron chopper spectrometer (CNCS) at the spallation neutron source (SNS) at Oak Ridge National Laboratory (ORNL) [35, 36]. The incident energy was Ei = 3.3 meV, and the energy resolution at the elastic line was ∼60 μeV fwhm (full width at half max). The sample was oriented with the HK 0 plane in the horizontal scattering plane, giving one access to the magnetic Bragg reflections in the LTI and HTI phases at Q points of (H ± τ , K , 0) r. l. u. (relative lattice units) where H odd, K odd, and τ ∼ 0.28 [7]. The sample was mounted in an Orange cryostat and measured at three temperatures (∼15 h each, with SNS operating at ∼1 MW at the time), at T = 5.0 K (LTI phase), T = 7.7 K (HTI phase) and at T = 50 K (paramagnetic phase, for reference). During the measurement the sample was continuously rotated around the axis that was vertical in the laboratory frame. The instrument counted scattered neutrons in event mode which allowed one to back-calculate—during the data reduction process—the motor position (i.e. sample orientation) at the time the neutron was scattered. Data reduction followed a standard protocol using the MANTID software package [37]. Calibration for detector tube efficiency was performed using a white beam vanadium measurement.
Figure 1. Elastic scattering map obtained at CNCS with E i = 3.3
meV. Nuclear (magnetic) Bragg peaks are highlighted blue (green), respectively.
phase in which moments on the spine sublattice are arranged very nearly along the a-direction and the amplitude vector (max. moment amplitude) has a length of ∼2 μB [7, 8]. The moments on the cross-tie site are disordered (near zero time average). Going to the LTI phase, moments on the spine site rearrange to form spirals that rotate in the ab-plane and propagate along the a-direction. This structure breaks time inversion symmetry and leads to spontaneous ferroelectric polarization in the material in the LTI phase. According to neutron diffraction, the moments on the cross-tie site do also acquire their full moment of ∼2 μB in the LTI phase [7], and order in the same spiral pattern with a phase shift relative to the spine site moments. On the other hand, according to magnetic x-ray diffraction, the moments on the cross-tie site remain largely (but not fully) disordered in the LTI phase [16]. The fundamental difference in the ordering patterns between the two phases seen by the scattering methods is evidenced by the occurrence of spontaneous electric polarization in the LTI phase and further supported by a marked change in the observed μSR relaxation line shape at the transition between the two phases [12]. However, results from 51V NMR in an applied magnetic field are not easily reconciled with this picture [15] and thus warrant further analysis. NMR works in an applied field whereas the spin structure was determined in zero field. In neutron diffraction all magnetic peaks were reported to be resolution limited [7]. In agreement with this earlier finding, no systematic changes in line shape or -width between the two phases are found in the CNCS data. The Q resolution was found to change systematically with Q—consistent with operating principles of a time-of-flight instrument [35]—between ∼ 0.015 r. l. u. and ∼ 0.045 r. l. u. in the H direction, and between ∼ 0.025 r. l. u. and ∼ 0.060 r. l. u. in the K direction (the b-axis is nearly twice as long as the a-axis). In the scattering plane the Q resolution is better than in the out-of-plane (here, L) direction because the horizontal beam divergence is lower than the vertical beam divergence.
3. Experimental results and discussion Elastic scattering as measured at T = 5.0 K is shown in figure 1. Data were integrated within ±0.07 meV energy transfer and in the band ∣L∣ ⩽ 0.07 r. l. u. which corresponds to the Q resolution out of plane. The accessible Q range contains both magnetic Bragg peaks of the (H ± τ , K , 0) type (circled green in the top right quadrant) and nuclear Bragg peaks (blue circles). Results from earlier work on the HTI and LTI phases can be summarized as follows. The crystal structure features two sub-lattices occupied by Ni2 +, S = 1, moments, termed ‘spine’ and ‘cross-tie’ sites, respectively [7]. The spine site makes linear chains that run along the crystallographic a-axis, whereas the cross-tie site is situated at the mid-points between such chains. The entire magnetic lattice has been described as a ‘buckled kagome’ lattice—four spine sites and two cross-tie sites, respectively, form one of the characteristic hexagons of the kagome lattice, and the buckling is along the b-direction [8]. The HTI phase is a longitudinally amplitude-modulated 2
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J. Phys.: Condens. Matter 27 (2015) 256003
Figure 2. Neutron scattering results at T = 5.0 K. A constant energy slice at E = 0.2 meV is shown in the top left for one quadrant of Q space. Below two (Q, E ) slices are shown along directions indicated above.
The origin of the additional scattering intensity at T = 5.0 K that can be seen in figure 2 around the (0, 1, 0) and (0, 3, 0) positions is unclear. It does not appear to be an instrumental artifact because of the background subtraction procedure that was applied (see above). Turning to the HTI phase, figure 3 shows similar cuts through data taken at T = 7.7 K. Clearly, the data is even more diffuse here, suggesting that the particular ordered structure with absent moments on the cross-tie site does not support well the propagation of spin waves. Since Bragg peaks are still observed and are resolution limited at this temperature, spatial correlations of the time-averaged moments still hold well over long distances, but the dynamic correlations over short distances and times are poor. Since there are two (largely decoupled) magnetic sub-lattices present, this finding is consistent with a picture of well developed long range order on the spin site which coexists with largely paramagnetic moments on the cross-tie site. In this context one notes that—by symmetry— the mean dipole field of the spine moments vanishes on the cross-tie site.
For further analysis the inelastic data were folded into the top right quadrant, see figure 2 for data taken at T = 5.0 K in the LTI phase. This plot shows neutron energy loss scattering at ℏω = 0.2 meV (top left panel) and cuts along two directions (marked with white lines) through the (0.725, 1, 0) position (bottom panels). To emphasize the magnetic scattering, data from a reference measurement at T = 50 K were subtracted. An energy of 0.2 meV is sufficiently far away from the elastic line such that the scattering is not contaminated by a contribution from the tail of the resolution function (the energy resolution at the elastic line was ∼ 60 μ eV full width at half max.). The inelastic scattering is evidently very diffuse, suggesting a short lifetime of the collective excitations. This diffusiveness prevents one to unambiguously establish the top of the lowest lying band of excitations, which may be around ∼ 0.8 meV. A hint for a second band that stretches between ∼ 1 and ∼ 2 meV can also be seen but the scattering intensity is clearly insufficient to make a more quantitative statement. 3
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J. Phys.: Condens. Matter 27 (2015) 256003
Figure 3. Neutron scattering results at 7.7 K. A constant energy slice at E = 0.2 meV is shown in the top left for one quadrant of Q space.
Below two (Q, E ) slices are shown along directions indicated above.
4. Conclusions
Cuts through the spin wave dispersion in the H and K directions are shown in figure 4. In a semi-classical approach it is possible to establish rough estimates of the correlation lengths and times at T = 7.7 K. This is shown in figure 4 for the (0.725, 1, 0), (0.725, 3, 0) and (1.275, 1, 0) peaks (as indicated by arrows). Fitting the E = 0.2 meV cut to an Ornstein– Zernicke type of correlation function, I (Q ) ∝ (1 + Q 2 /κ 2 )−1, that is convoluted with the known Q-resolution at these points, the parameter κ will indicate a (direction-dependent) inverse correlation length as in real space the spin-spin correlation function will be ∝ exp(−rκ ). This analysis results in κ −1 ∼ 8 ⋅ a along the a-direction and κ −1 ∼ 3 ⋅ b along the b-direction. Dynamic spatial correlations thus hold over a few unit cells only. This analysis can be extended to the energy (time) domain as well, as shown in the insert of figure 4. At T = 7.7 K the (0.725, 1, 0) peak clearly shows lorentzian broadening at its base, with quasi-elastic scattering likely originating in the cross-tie site. The corresponding correlation time is about t0 ∼ 4 ⋅ 10−12 s.
The HTI and LTI phases in Ni3V2O8 hardly support the propagation of spin waves. All dynamic features that can be observed with inelastic neutron scattering in these phases, below ≲2 meV, are very diffuse. This may be regarded as a strong indicator for the presence of paramagnetic (disordered) moments in the lattice, which coexist with long-range ordered moments, in agreement with earlier experimental results [7, 16]. The disordered moments effectively act as scattering centers and prevent the formation of long range spin waves. A direct calculation of spin waves based on a model Hamiltonian [21–24] allows one to match the inelastic neutron scattering data and to understand the nature and the strength of relevant near neighbor interactions. In the present case, such a calculation was not attempted as the observable data did not extend far enough into the inelastic range. 4
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Figure 4. Cuts through the spin wave dispersion in both directions at various energy transfers. Full circles are for T = 5.0 K, hollow
diamonds are for T = 7.7 K. Lines are guides to the eye. The vertical separation of the traces is for clarity only. Arrows indicate which peaks were fitted to an Ornstein–Zernicke type correlation function. The inset shows the energy dependent scattering around the (0.725, 1, 0) peak.
Division, Office of Basic Energy Sciences, U.S. Department of Energy. Work at the Institute of Solid State and Semiconductor Physics in Minsk was supported in part by BRFFIRFFI grant No. F14R-094.
The coexistence of paramagnetic and long-range ordered moments is a phenomenon that has been observed before in some geometrically frustrated magnets [38–43]. Generally, it may be expected in those cases where two (or more) magnetic sub-lattices are present, as these may have different frustration indices [44]. The frustration index f , expressed as the ratio between the Curie–Weiss temperature and the ordering temperature, f =∣Θ W/TN∣, is commonly used to judge the degree of frustration in a system. In some cases, such as Gd2Ti2O7 or TbNiAl, it is the magnetic ordering with a
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( , , ) propagation vector that splits 1 1 1 2 2 2
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