Rare Earth Magnetism:

    Structures and Excitations

     
 
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   by

   Jens Jensen and Allan R. Mackintosh

   Clarendon Press . Oxford   1991

Table of contents

The name is a PDF-version of the different sections or chapters.
0 PREFACE i
 
1 ELEMENTS OF RARE EARTH MAGNETISM 1
 
  1.1 A brief history 2
  1.2 Rare earth atoms 8
  1.3 The metallic state 16
  1.4 Magnetic interactions 39
  1.5 Rare earth magnetism 50
 
2 MAGNETIC STRUCTURES 68
 
  2.1 Mean-field theory of magnetic ordering 68
    2.1.1 The high-temperature susceptibility 71
    2.1.2 The mean-field approximation 74
    2.1.3 Transversely ordered phases 79
    2.1.4 Longitudinally ordered phases 83
    2.1.5 Competing interactions and structures 85
    2.1.6 Multiply periodic structures 89
  2.2 The magnetic anisotropy 94
    2.2.1 Temperature dependence of the Stevens operators 94
    2.2.2 Anisotropic contributions to the free energy 101
  2.3 Magnetic structures of the elements 111
    2.3.1 Bulk magnetic structures 112
    2.3.2 The magnetization of Holmium 125
    2.3.3 Films and superlattices 130
 
3 LINEAR RESPONSE THEORY 134
 
  3.1 The generalized susceptibility 134
  3.2 Response functions 137
  3.3 Energy absorption and the Green function 142
  3.4 Linear response of the Heisenberg ferromagnet 149
  3.5 The random-phase approximation 154
    3.5.1 The generalized susceptibility in the RPA 154
    3.5.2 MF-RPA theory of the Heisenberg ferromagnet 160
 
4 MAGNETIC SCATTERING OF NEUTRONS 163
 
  4.1 The differential cross-section in the dipole approximation 164
  4.2 Elastic and inelastic neutron scattering 173
 
5 SPIN WAVES IN THE FERROMAGNETIC HEAVY RARE EARTHS 181
 
  5.1 The ferromagnetic hcp-crystal 182
  5.2 Spin waves in the anisotropic ferromagnet 186
  5.3 The uniform mode and spin-wave theory 198
    5.3.1 The magnetic susceptibility and the energy gap 198
    5.3.2 The validity of the spin-wave theory 206
  5.4 Magnetoelastic effects 211
    5.4.1 Magnetoelastic effects on the energy gap 211
    5.4.2 The magnon-phonon interaction 219
  5.5 Two-ion anisotropy 231
    5.5.1 The dipole-dipole interaction 232
    5.5.2 General two-ion interactions 240
  5.6 Binary rare earth alloys 247
  5.7 Conduction-electron interactions 256
    5.7.1 The indirect-exchange interaction 256
    5.7.2 The mass-enhancement of the conduction electrons 270
    5.7.3 Magnetic contributions to the electrical resistivity 275
 
6 SPIN WAVES IN PERIODIC STRUCTURES 285
 
  6.1 Incommensurable periodic structures 286
    6.1.1 The helix and the cone 287
    6.1.2 The longitudinally polarized structure 300
  6.2 Commensurable periodic structures 305
 
7 CRYSTAL-FIELD EXCITATIONS IN THE LIGHT RARE EARTHS 312
 
  7.1 MF-RPA theory of simple model systems 313
  7.2 Beyond the MF-RPA Theory 322
  7.3 Perturbations of the crystal-field system 334
    7.3.1 Magnetoelastic effects and two-ion anisotropy 334
    7.3.2 Conduction-electron interactions 342
    7.3.3 Coupling to the nuclear spins 349
  7.4 Magnetic properties of Praseodymium 352
    7.4.1 Induced magnetic ordering 352
    7.4.2 The magnetic excitations 361
 
8 PERSPECTIVES FOR RARE EARTH RESEARCH 370
 
  REFERENCES 381
 
INDEX
398

A PDF-version of the whole book (with bookmarks).

Linear Response Theory and the Random Phase Approximation (International workshop on McPhase, Heinz Maier - Leibnitz Zentrum, Munich, 5.-7. November 2014).

Rare earth magnetism:
papers and reviews 1991-

 

Martin Rotter,
McPhase is a program package for the calculation of magnetic properties,
McPhase: A Mean field monte Carlo PHASE diagram program.
 
R. A. Cowley and J. Jensen,
Magnetic structures and interactions in erbium,
J. Phys. Condens. Mat. 4, 9673-96 (1992).
 
J. Jensen and R. A. Cowley,
Magnetic non-planar structures and trigonal couplings in erbium,
Europhys. Lett. 21, 705-10 (1993).
 
K. N. Clausen, K. A. McEwen, J. Jensen, and A. R. Mackintosh,
New mode of magnetic excitation in praseodymium,
Phys. Rev. Lett. 72, 3104-7 (1994).
 
J. Jensen,
1/z-renormalization of the mean-field behavior of the dipole-coupled singlet-singlet system HoF3,
Phys. Rev. B 49, 11833-41 (1994).
 
K. N. Clausen, S. Aagaard Sørensen, K. A. McEwen, J. Jensen, and A. R. Mackintosh,
Crystal fields and the conduction electrons in praseodymium,
J. Magn. Magn. Mater. 140-144, 735-8 (1995).
 
R. M. Nicklow and N. Wakabayashi,
Spin excitations in the longitudinally modulated magnetic phase of erbium,
Phys. Rev. B 51, 12425-32 (1995).
 
J. Jensen,
Theory of commensurable magnetic structures in holmium,
Phys. Rev. B 54, 4021-32 (1996).
 
J. Jensen,
Threefold symmetric magnetic two-ion coupling in hcp rare-earth metals,
Acta Phys. Pol. A 91, 89-103 (1997).
 
Magnetism in metals - A symposium in memory of Allan Mackintosh, Copenhagen, 26-29 August, 1996, eds.: D. F. McMorrow, J. Jensen, and H. M. Rønnow,
Mat. Fys. Medd. Dan. Vid. Selsk. 45 (1997), 443 p.
 
D. A. Tindall, M. J. Small, M. O. Steinitz, and Z. Tun,
Experimental verification of the significance of trigonal coupling for the 1/4 lock-in in holmium,
Physica B 241-243, 699-701 (1998). 
 
M. Ellerby, K. A. McEwen, and J. Jensen,
Magnetoresistance and magnetization study of thulium,
Phys. Rev. B 57, 8416-23 (1998). 
 
J. Jensen,
Magnetic structures and excitations in rare-earth metals.
In: Magnetic and Superconducting Materials, eds. M. Akhavan, J. Jensen, and K. Kitazawa (World Scientific, Singapore, 2000) Vol. B, 711-26.
 
M. Ellerby, K. A. McEwen, E. Bauer, R. Hauser, and J. Jensen,
Pressure dependent resistivity and magnetoresistivity of erbium,
Phys. Rev. B 61, 6790-97 (2000).
 
R. S. Sarthour, R. A. Cowley, R. C. C. Ward, M. R. Wells, D. F. McMorrow, and J. Jensen,
The magnetic phase diagram of HoxTm1-x alloys,
Phys. Rev. B 62, 14943-9 (2000).
 
H. Ohsumi
Magnetoelastic effect in holmium studied by x-ray diffraction,
J. Phys. Soc. Jpn 71, 1732 (2002).
 
I. D. Hughes, M. Däne, A. Ernst, W. Hergert, M. Lüders, J. Poulter, J. B. Staunton, A. Svane, Z. Szotek, and W. M. Temmerman,
Lanthanide contraction and magnetism in the heavy rare earth elements,
Nature 446, 650 (2007).
 
K. M. Döbrich, A. Bostwick, J. L. McChesney, K. Rossnagel, E. Rotenberg, and G. Kaindl,
Fermi-surface topology and helical antiferromagnetism in heavy lanthanide metals,
Phys. Rev. Lett. 104, 246401 (2010).
 

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