Neutron Scattering from Magnetic Materials part 12 ppt

Magnetic excitations 327 Table 1 Ordering temperatures T C , spin wave stiffness D, zone-boundary magnon energy E ZB and criteria for itinerancy D/(kT C ) and E ZB /(kT C ) of the infinite layer and bilayer manganites along with those of other known itinerant and localized magnetic materials [52,87] Sample T C (K)D(meV Å 2 ) E ZB (meV) D kT C (Å 2 ) E Z kT C La 0.95 Ca 0.05 MnO 3 123.0 (3) 4.5 (1) 1.6 [001] 0.42 0.15 La 0.92 Ca 0.08 MnO 3 26.0 (3) 7.3 (1) 1.6 [001] 0.67 0.15 La 0.67 Ca 0.33 MnO 3 250 170 7.9 La 0.85 Sr 0.15 MnO 3 235 95 (2) 56 [010] 4.62.76 La 0.7 Sr 0.3 MnO 3 355 La 0.7 Ba 0.3 MnO 3 350 152 (3) 32 [100] 5.04 1.06 La 0.7 Pb 0.3 MnO 3 355 133.7 35 [100] 4.37 1.14 La 1.2 Sr 1.8 Mn 2 O 7 128 169 37 [100] 15.33.35 [100] Ni 631 550 350 10.16.43 Fe 1021 281 800 3.19 9.1 MnSi 40 52 15.8 Ni 3 Al 41 85 24 Fe 3 Pt 504 80 1.84 Pd 2 MnSn 190 100 30 6.10 1.83 Pt 3 Mn 453 215 80 5.51 2.05 EuO 69 12 6 2.01 1.02 EuS 10.62.62.31.82 1.61 been investigated by inelastic neutron scattering. The neutron scattering investigation of the spin dynamics of the doped ferromagnetic manganites has made considerable progress. We have attempted to summarize the data obtained by neutron scattering in hole-doped manganites along with those of classical metallic itinerant ferromagnets. Mook [52] has suggested the ratios D/(kT C ) and E ZB /(kT C ) as criteria for the itinerancy of the magnetic electrons. Here E ZB is the energy of the zone boundary magnon. These two ratios have high values for itinerant electron systems like Fe and Ni and are small for localized sys- tems like EuO and EuS. Table 1 gives the ordering temperature T C , spin wave stiffness D, zone-boundary magnon energy E ZB and criteria for itinerancy D/(kT C ) and E ZB /(kT C ) of the infinite-layer and bilayer manganites along with those of other known itinerant and lo- calized magnetic materials. Comparing the ratios D kT C and E ZB kT C of different materials from Table 1 we see that the doped ferromagnetic manganites, which are close to the compo- sition at which CMR effects are maximum, are of rather itinerant character. Especially the bilayer manganite is more itinerant that the infinite-layer manganites. In fact, the ratio D/kT C for La 1.2 Sr 1.8 Mn 2 O 7 is as high as 15.3 compared to 10.1 of Ni. The ratio E ZB /kT C for La 1.2 Sr 1.8 Mn 2 O 7 is 3.35, which is lower than that for Ni (6.43), is higher than that of Pd 2 MnSn (1.83) and Pt 3 Mn (2.05). 6. Concluding remarks We have covered only a part of the huge field of magnetic excitations investigated by inelastic neutron scattering during the past half a century. The research on magnetic ex- 328 T. Chatterji citations is still very much alive and is contributing enormously to our understanding of the properties of magnetic materials in general and the recently discovered high temper- ature superconducting and colossal magnetoresistive materials in particular. Because of space limitations we have considered only some typical examples of magnetic excitations studied by inelastic neutron scattering. We have considered as introductory examples the insulating magnetic systems that can be understood by a localized Heisenberg model, viz. the so-called Heisenberg ferro-, antiferro- and ferrimagnets. Then we considered more dif- ficult itinerant metallic systems such as transition metallic elements Fe and Ni. A complete understanding of these itinerant ferromagnets is still to be achieved. Finally we consid- ered ferromagnetic strongly correlated transition metal oxide CMR manganites which are also metallic and itinerant. However to understand these materials one has to consider also the orbital and lattice degrees of freedom interacting with the spin system. The the- ory of CMR manganites has progressed enormously but still is far from being completely satisfactory. We have left out the interesting topic of low dimensional quantum spin sys- tems. Also left out is the topic of strongly correlated high temperature and heavy fermion superconductors in which magnetic fluctuations are considered to be crucial for the su- perconducting Cooper-pair formation. We have also completely left out the huge field of crystal-field excitations in rare earth and actinide magnetic systems. However there exist some good review articles covering these topics and the interested readers should consult those. For magnetic excitations in low-dimensional magnetic systems the excellent book edited by De Jong [93] is recommended. The magnetic excitations in cuprate supercon- ducting materials the book edited by Furrer [94] can be consulted. The book by Jensen and Mackintosh [95] discusses the magnetic excitations in rare earth metals in great depth. The article by Stirling and McEwen [96] is a good introduction to magnetic excitations in general and also for magnetic excitations in rare earth and actinide compounds not treated in the present chapter. Acknowledgments I wish to thank M. Böhm and P. Thalmeier for reading the manuscript and their critical comments and discussions. I also thank L.P. Regnault for collaboration over the years. References [1] B.N. Brockhouse, Inelastic Scattering of Neutrons in Solids and Liquids, p. 113, International Atomic En- ergy Agency, Vienna (1961). [2] G. Shirane, S.M. Shapiro and J.M. Tranquada, Neutron Scattering with a Triple-Axis Spectrometer Basic Techniques, Cambridge University Press (2002). [3] R. Currat, in: X-Ray and Neutron Spectroscopy, ed. F. Hippert, Grenoble Sciences and Springer (2005). [4] B. Dorner, Acta Crystallogr. Sect. A 28 319 (1972). [5] M.J. Cooper and R. Nathans, Acta Crystallogr. 23 357 (1967). [6] M. Popovici, Acta Crystallogr. Sect. A 31 507 (1975). [7] M. Popovici, A.D. Stoica and I. Ionita, J. Appl. Cryst. 20 90 (1987). [8] J. Saroun and J. Kulda, Physica B 234–236 1102 (1997). [9] A.D. Stoica, Acta Crystallogr. Sect. A 31 189 (1975). Magnetic excitations 329 [10] K. Lefmann, K. Nielsen, A. Tennant and B. Lake, Physica B 276–278 152 (2000). [11] F. Demmel, A. Fleischmann and W. Gläser, Nucl. Instrum. Methods Phys. Res. A 416 115 (1998). [12] J. Kulda, private communication. [13] B. Frick and B. Farago, in: Scattering, R. Pike and P. Sabatier (eds.), Academic Press, London (2002). [14] T. Holstein and H. Primakov, Phys. Rev. 58 1098 (1940). [15] H.G. Bohn, W. Zinn, B. Dorner and A. Kollmar, Phys. Rev. B 22 5447 (1980). [16] B.I. Halperin and P.C. Hohenberg, Rev. Mod. Phys. 49 435 (1977). [17] F.J. Dyson, Phys. Rev. 102 1217 (1956). [18] F.J. Dyson, Phys. Rev. 102 1230 (1956). [19] H.G. Bohn, A. Kollmar and W. Zinn, Phys. Rev. B 30 6504 (1984). [20] A.B. Harris, Phys. Rev. B 175 674 (1968); A.B.Harris,Phys.Rev.B184 606 (1969). [21] P. Böni, G. Shirane, H.G. Bohn and W. Zinn, J. Appl. Phys. 61 3397 (1987). [22] P. Böni and G. Shirane, Phys. Rev. B 33 3012 (1986). [23] P. Böni, M.E. Chen and G. Shirane, Phys. Rev. B 35 8449 (1987). [24] A. Okazaki, K.C. Tubberfield and R.W.H. Stevenson, Phys. Lett. 8 9 (1964). [25] W. Marshall and S.W. Lovesey, Theory of Thermal Neutron Scattering, Oxford University Press, Oxford (1971). [26] G.G. Low, in: Proc. Symposium on Inelastic Scattering of Neutrons in Solids and Liquids, 1964, IAEA (1965). [27] L. Néel, Ann. Phys. 3 139 (1948). [28] C.G. Shull, E.O. Wollan and W.C. Koehler, Phys. Rev. 84 912 (1951). [29] H. Watanabe and B.N. Brockhouse, Phys. Lett. 1 189 (1962). [30] B.N. Brockhouse and H. Watanabe, in: Symposium on Inelastic Scattering of Neutrons in Solids and Liq- uids, p. 297, IAEA (1962). [31] J.S. Kouvel, Technical Report 210, Cruft Laboratory, Harvard University, February 1 (1955). [32] T.A. Kaplan, Phys. Rev. 109 782 (1958). [33] T.A. Kaplan, Bull. American Phys. Soc. 4 178 (1959). [34] M.L. Glasser and F.J. Milford, Phys. Rev. 130 1783 (1963). [35] J. Kübler, Theory of Intinerant Electron Magnetism, Oxford University Press (2000). [36] J. Hubbard, Proc. Roy. Soc. A 276 238 (1963). [37] J. Hubbard, Proc. Roy. Soc. A 281 238 (1964). [38] M.F. Collins, V.J. Minkiewicz, R. Nathans, L. Passell and G. Shirane, Phys. Rev. 179 417 (1969). [39] H.A. Mook and R.M. Nicklow, Phys. Rev. B 7 336 (1973). [40] J.W. Lynn, Phys. Rev. B 11 2624 (1975). [41] C K. Loong, J.M. Carpenter, J.W. Lynn, R.A. Robinson and H.A. Mook, J. Appl. Phys. 55 1895 (1984). [42] J.A. Blackman, T. Morgan and J.F. Cooke, Phys. Rev. Lett. 55 2814 (1985). [43] T.G. Perring, A.T. Boothroyd, D.McK. Paul, A.D. Taylor, R. Osborn, R.J. Newport, J.A. Blackman and H.A. Mook, J. Appl. Phys. 69 6219 (1991). [44] D.McK. Paul, P.W. Mitchell, H.A. Mook and U. Steigenberger, Phys. Rev. B 38 580 (1988). [45] R.D. Lowde and C.G. Windsor, Adv. Phys. 19 813 (1970). [46] V.J. Minkiewicz, M.F. Collins, R. Nathans and G. Shirane, Phys. Rev. 182 624 (1969). [47] H.A. Mook, J.W. Lynn and R.M. Nicklow, Phys. Rev. Lett. 30 556 (1973). [48] J.W. Lynn and H.A. Mook, Phys. Rev. B 23 198 (1981). [49] J.F. Cooke, J.W. Lynn and H.L. Davis, Phys. Rev. B 21 4118 (1980). [50] J.F. Cooke, J.A. Blackman and T. Morgan, Phys. Rev. Lett. 54 718 (1985). [51] H.A. Mook and D.McK. Paul, Phys. Rev. Lett. 54 227 (1985). [52] H.A. Mook, in: Spin Waves and MagneticExcitationsI, eds. A.S. Borovik-Romanov and S.K. Sinha, p. 425, Elsevier, Amsterdam (1988). [53] Y. Ishikawa, G. Shirane, J.A. Tarvin and M. Kohgi, Phys. Rev. B 16 4956 (1977). [54] G.H. Jonker and J.H.V. Santen, Physica 16 337 (1950). [55] E.O. Wollan and W.C. Koehler, Phys. Rev. 100 545 (1955). [56] F. Moussa, M. Hennion, J. Rodriguez-Carvajal, H. Moudden, L. Pinsard and A. Revcolevschi, Phys. Rev. B 54 15149 (1996). 330 T. Chatterji [57] K. Hirota, N. Kaneko, A. Nishizawa and Y. Endoh, J. Phys. Soc. Jpn. 65 3736 (1996). [58] I. Solovyev, N. Hamada and K. Terakura, Phys. Rev. Lett. 76 4825 (1996). [59] F. Moussa and M. Hennion, in: Colossal Magnetoresistive Manganites, ed. T. Chatterji, p. 43, Kluwer Academic Publishers, Dordrecht (2004). [60] Y. Endoh and K. Hirota, J. Phys. Soc. Jpn. 66 2264 (1997). [61] C. Zener, Phys. Rev. 82 403 (1951). [62] P.W. Anderson and H. Hasegawa, Phys. Rev. 100 675 (1955). [63] P.G. de Gennes, Phys. Rev. 118 41 (1960). [64] N. Furukawa, J. Phys. Soc. Jpn. 65 1174 (1996). [65] N. Shannon, T. Chatterji, F. Ouchini, and P. Thalmeier, Eur. Phys. J. B 27 287 (2002). [66] T. Chatterji, G. Jackeli and N. Shannon, in: Colossal Magnetoresistive Manganites, ed. T. Chatterji, p. 321, Kluwer Academic Publishers, Dordrecht (2004). [67] N. Shannon and A. Chubukov, J. Phys.: Condens. Matter 14 L235 (2002). [68] N. Shannon and A. Chubukov, Phys. Rev. B 65 104418 (2002). [69] T.G. Perring, G. Aeppli, S.M. Hayden, S.A. Carter, J.P. Remeika and S W. Cheong, Phys. Rev. Lett. 77 711 (1996). [70] Y. Endoh, in: Colossal Magnetoresistive Oxides, ed. Y. Tokura, Gordon and Breach Science Publishers (2000). [71] H.Y. Hwang, P. Dai, S W. Cheong, G. Aeppli, D.A. Tennant and H.A. Mook, Phys. Rev. Lett. 80 1316 (1998). [72] J.A. Fernandez-Baca et al., Phys. Rev. Lett. 80 4012 (1998). [73] P. Dai, H.Y. Hwang, J. Zhang, J.A. Fernandez-Baca, S W. Cheong, C. Kloc, Y. Tomioka and Y. Tokura, Phys.Rev.B61 9553 (2000). [74] M.C. Martin, G. Shirane, Y. Endoh, K. Hirota, Y. Moritomo and Y. Tokura, Phys. Rev. B 53 R14285 (1996). [75] T. Chatterji, L.P. Regnault and W. Schmidt, Phys. Rev. B 66 214408 (2002). [76] R. von Helmolt, J. Wocker, B. Holzapfel, M. Schultz and K. Samwer, Phys. Rev. Lett. 71 2331 (1993). [77] N. Furukawa, J. Phys. Soc. Jpn. 68 2522 (1999). [78] G. Khaliullin and R. Kilian, Phys. Rev. B 61 3494 (2000). [79] Y. Motome and N. Furukawa, J. Phys. Soc. Jpn. 71 419 (2002). [80] L. Vasiliu-Doloc, J.W. Lynn, Y.M. Mukovski, A.A. Arsenov and D.A. Shulyarev, J. Appl. Phys. 83 7342 (1998). [81] L. Vasiliu-Doloc, J.W. Lynn, A.H. Moudden, A.M. de Leon-Guevara and A. Revcolevschi, Phys. Rev. B 58 14913 (1998). [82] J.W. Lynn, R.W. Erwin, J.A. Borchers, Q. Huang, A. Santoro, J L. Peng and Z.Y. Li, Phys. Rev. Lett. 76 4046 (1996). [83] Y. Moritomo, A. Asamitsu, H. Kuwahara and Y. Tokura, Nature 380 141 (1996). [84] Y. Tokura (ed.), Colossal Magnetoresistive Oxides, Gordon and Breach, Amsterdam (2000). [85] T. Chatterji, P. Thalmeier, G.J. McIntyre, R. van de Kamp, R. Suryanarayanan, G. Dahlenne and A. Revcolevschi, Europhys. Lett. 46 801 (1999). [86] T. Chatterji, L.P. Regnault, P. Thalmeier, R. Suryanarayanan, G. Dahlenne and A. Revcolevschi, Phys. Rev. B 60 R6965 (1999). [87] T. Chatterji, L.P. Regnault, P. Thalmeier, R. van de Kamp, W. Schmidt, A. Hiess, P. Vorderwisch, R. Suryanarayanan, G. Dahlenne and A. Revcolevschi, Journal of Alloys and Compounds 326 15 (2001). [88] H. Fujioka, M. Kubota, K. Hirota, H. Yoshizawa, Y. Moritomo and Y. Endoh, J. Phys. Chem. Solids 60 1165 (1999). [89] K. Hirota, S. Ishihara, H. Fujioka, M. Kubota, H. Yoshizawa, Y. Moritomo, Y. Endoh and S. Maekawa, Phys.Rev.B65 64414 (2002). [90] G. Chaboussant, T.G. Perring, G. Aeppli and Y. Tokura, Physica B 276–278 801 (2000). [91] T.G. Perring, D.T. Androja, G. Chaboussant, G. Aeppli, T. Kimura and Y. Tokura, Phys. Rev. Lett. 87 217201 (2001). [92] S. Rosenkranz, R. Osborn, L. Vasiliu-Doloc, J.F. Mitchell, J.W. Lynn and S.K. Sinha, J. Appl. Phys. 87 5816 (2000). [93] L.J. De Jong, Magnetic Properties of Layered Transition Metal Compounds, Kluwer Academic Publishers, Dordrecht (1990). Magnetic excitations 331 [94] A. Furrer, Neutron Scattering in Layered Copper-Oxide Superconductors, Kluwer Academic Publishers, Dordrecht (1998). [95] J. Jensen and A.R. Mackintosh, Rare Earth Magnetism, Oxford University Press, Oxford (1991). [96] W.G. Stirling and K.A. McEwen, in: Neutron Scattering, eds. K. Sköld and D.L. Price, Part C, vol. 23, p. 159, Academic Press, London (1987). CHAPTER 7 Paramagnetic and Critical Scattering Tapan Chatterji Institut Laue–Langevin, B.P. 156X, 38042 Grenoble cedex, France E-mail: chatt@ill.fr Contents 1. Introduction . . . . . . . . . . . 335 2. Universal critical phenomenon and static critical exponents . . . . . . . . . . . . . . . . . . . . . . . . . 335 3.Magneticcriticalscattering 337 4. Magnetic correlations above T c 340 4.1.Magneticcorrelationsinlocalizedsystems 341 4.2. Diffuse magnetic scattering from metallic magnetic system . . . . . . . . . . . . . . . . . . . . . . 348 4.3. Paramagnetic excitations in itinerant electron systems . . . . . . . . . . . . . . . . . . . . . . . . . 350 4.4. Diffuse magnetic scattering from quasi-2D ferromagnetic La 1.2 Sr 1.8 Mn 2 O 7 355 5.Concludingremarks 359 Acknowledgments 359 References 360 NEUTRON SCATTERING FROM MAGNETIC MATERIALS Edited by Tapan Chatterji © 2006 Elsevier B.V. All rights reserved 333 [...]... energy-integrated neutron scattering cross-sections in the paramagnetic phase [46] 4.4 Diffuse magnetic scattering from quasi-2D ferromagnetic La1.2 Sr1.8 Mn2 O7 The exchange interactions in magnetic solids are determined by measuring the spin wave dispersions by inelastic neutron scattering at temperatures much lower than the ordering temperatures The quasielastic magnetic neutron scattering above... reproduced the incommensurate centering of the magnetic diffuse scattering in MnS2 4.2 Diffuse magnetic scattering from metallic magnetic system 4.2.1 Diffuse magnetic scattering from UAs The uranium monopnictides UX (X = N, P, As, Sb and Bi) crystallizes with the NaCl-type crystal structure where U atoms form an f.c.c sublattice They form a family of antiferromagnetic compounds in which the Néel temperatures... give the measured neutron cross-sections around (100) and (001), respectively Paramagnetic and critical scattering 343 Fig 4 Constant-Q scans from MnF2 at different Q around 100 at temperatures below and above TN Both the transverse and the longitudinal fluctuations contribute to the scattered neutron intensity (from Schulhof et al [17]) 4.1.3 Diffuse magnetic scattering from MnS2 The magnetic semiconductor... been performed above TN at Q further away from the magnetic zone-center to check whether the excitation spectrum peaks at finite energy 346 T Chatterji Fig 7 Temperature variation of the incommensurate component of the vector at which the diffuse magnetic scattering is centered (from Chattopadhyay et al [19]) (a) (b) Fig 8 (a) Diffuse magnetic neutron scattering from MnS2 in constant-Q scans at several... the incoming neutron energy and also to the energy equivalent of the temperature at which the measurements are done Chatterji et al [58] have determined exchange interactions in La1.2 Sr1.8 Mn2 O7 above TC by measuring diffuse magnetic neutron scattering Neutron scattering experiments [58] were carried out on the flat-cone diffractometer of the Berlin Neutron Scattering Center using a neutron wavelength... to exist in the magnetic interactions This led to the detailed neutron scattering investigation [57] of magnetic correlations in UAs above the ordering temperature TN in the paramagnetic state as soon as good quality single crystals were available Below TN UAs does not show any magnetic Bragg peak at Q = (0, 0, 1) because the magnetic moments are parallel to [001] Also no critical scattering was observed... function S(Q, ω) corresponding to a constant-Q scan, showing the lineshape of the spin wave peak for T = 1.28TC (from Lynn [39]) Paramagnetic and critical scattering 355 range of temperature Polarization analysis was used to separate the magnetic part of scattering from other types of scattering They found significant structure in the “spin-density– spin-density correlation function” (SDSDCF) over... inelastic neutron scattering [19] The diffuse scattering above TN is centered at incommensurate positions like (1, ky , 0) and is temperature dependent The component ky increases continuously from ky = 0.40 at T = 115 K to ky = 0.44 at T = 48 K As the temperature is further lowered to TN = 48.2 K, a magnetic Bragg peak develops abruptly at (1, 1 , 0) corresponding 2 344 T Chatterji Fig 5 Neutron scattering. .. incommensurate component of the vector at which the diffuse magnetic scattering of MnS2 is centered This figure mimics the temperature variation of the propagation vector close to a long-range-ordered incommensurate–commensurate lock-in transition Such behavior is quite unique and has Paramagnetic and critical scattering 345 Fig 6 (a) Magnetic diffuse neutron scattering of MnS2 in Q scans parallel to the modulation... = (0, 0, 1) above TN There exists a magnetic Bragg reflection at Q = (1, 1, 0), because this reciprocal point is obtained by subtracting the propagation vector k = (0, 0, 1) from Paramagnetic and critical scattering 349 the nuclear Bragg position Q = (1, 1, 1) The deviations from the antiferromagnetic superlattice point Q = (1, 1, 0) are denoted by q and q⊥ The scattering at Q = (1, 1, 0) samples fluctuations . . . . . 335 3.Magneticcriticalscattering 337 4. Magnetic correlations above T c 340 4.1.Magneticcorrelationsinlocalizedsystems 341 4.2. Diffuse magnetic scattering from metallic magnetic system. 359 References 360 NEUTRON SCATTERING FROM MAGNETIC MATERIALS Edited by Tapan Chatterji © 2006 Elsevier B.V. All rights reserved 333