International
Tables for
Crystallography
Volume D
Physical properties of crystals
Edited by A. Authier

International Tables for Crystallography (2006). Vol. D. ch. 1.5, p. 146

Section 1.5.11. Glossary

A. S. Borovik-Romanova and H. Grimmerb*

a P. L. Kapitza Institute for Physical Problems, Russian Academy of Sciences, Kosygin Street 2, 119334 Moscow, Russia, and bLabor für Neutronenstreuung, ETH Zurich, and Paul Scherrer Institute, CH-5234 Villigen PSI, Switzerland
Correspondence e-mail:  hans.grimmer@psi.ch

1.5.11. Glossary

| top | pdf |

[\alpha_{ij}] (linear) magnetoelectric tensor
[\beta_{ijk}] nonlinear magnetoelectric tensor [EHH]
[\gamma_{ijk}] nonlinear magnetoelectric tensor [HEE]
[\Delta] Weiss constant
[\Delta n] magnetic birefringence
[\varepsilon_{ij}] dielectric permittivity
[\lambda] constant describing magnetostriction
[\Lambda_{ijk}] tensor describing the piezomagnetic effect
[\Lambda_{i\alpha}] matrix describing the piezomagnetic effect
[\mu_{ij}] magnetic permeability
[\boldmu] magnetic moment
[\mu_B] Bohr magneton
[\pi_{ijk\ell}] piezomagnetoelectric tensor
[\rho({\bf r})] charge density
[\Phi] thermodynamic potential
[\chi^e_{ij}] dielectric susceptibility
[\chi_{ij}], [\chi^m_{ij}] magnetic susceptibility
[{\bf B}] magnetic induction
c speed of light
[c_{ijk\ell}] elastic stiffness
[{\rm d}\tau] volume element
e charge of the electron
[{\bf E}] electric field
g Landé g-factor
[{\bf H}] magnetic field
[{\bf j}({\bf r})] current density
[{\bf J}] total angular momentum
[{\bf k}] position vector in reciprocal space
[k_B] Boltzmann factor
[{\bf l}_i] sum of the magnetic moments in a unit cell, in which some of the moments are taken with opposite sign
[{\bf L}_i] antiferromagnetic vector
[{\bf L}] orbital angular momentum (Section 1.5.1.1[link]), antiferromagnetic vector (remainder of this chapter)
[{\bf m}({\bf r})] magnetic moment density
[{\bf m}] sum of the magnetic moments in a unit cell
[{\bf M}] magnetization (= magnetic moment per unit volume = ferromagnetic vector)
N No. of atoms per unit volume
p effective number of Bohr magnetons (Section 1.5.1[link]), pressure (remainder of this chapter)
[{\bf P}] electric polarization
[{\bf r}] position vector in space
[{\bf S}({\bf r})] spin density
[{\bf S}] spin angular momentum (of an atom or ion)
[s_{ijk\ell}] elastic compliance
[S_{ij}] strain tensor
[T_{ij}] stress tensor
T temperature
[T_c] transition temperature, in particular Curie temperature
[T_N] Néel temperature
U energy
[U_a] anisotropy energy
[U_{\rm el}] elastic energy
[U_{\rm me}] magnetoelastic energy
v velocity
Z atomic number (= number of electrons per atom)

References

First citation Anderson, J. C., Birss, R. R. & Scott, R. A. M. (1964). Linear magnetostriction in hematite. In Proc. Int. Conf. Magnetism, Nottingham, pp. 597–599. London: Institute of Physics and the Physical Society.Google Scholar
First citation Andratskii, V. P. & Borovik-Romanov, A. S. (1966). Piezomagnetic effect in α-Fe2O3. (In Russian.) Zh. Eksp. Teor. Fiz. 51, 1030–1036. [English translation: Sov. Phys. JETP, 24 (1967), 687–691.]Google Scholar
First citation Ascher, E., Rieder, H., Schmid, H. & Stössel, H. (1966). Some properties of ferromagnetoelectric nickel–iodine boracite, Ni3B7O13I. J. Appl. Phys. 37, 1404–1405.Google Scholar
First citation Astrov, D. N. (1961). Magnetoelectric effect in chromium oxide. (In Russian.) Zh. Eksp. Teor. Fiz. 40, 1035–1041. (English translation: Sov. Phys. JETP, 13, 729–733.) Google Scholar
First citation Bickford, L. R. Jr, Pappis, J. & Stull, J. L. (1955). Magnetostriction and permeability of magnetite and cobalt-substituted magnetite. Phys. Rev. 99, 1210–1214.Google Scholar
First citation Borovik-Romanov, A. S. (1959a). Investigation of weak ferromagnetism in the MnCO3 single crystal. (In Russian.) Zh. Eksp. Teor. Fiz. 36, 766–781. (English translation: Sov. Phys. JETP, 9, 539–549.)Google Scholar
First citation Borovik-Romanov, A. S. (1959b). Piezomagnetism in the antiferromagnetic fluorides of cobalt and manganese. (In Russian.) Zh. Eksp. Teor. Fiz. 36, 1954–1955. (English translation: Sov. Phys. JETP, 9, 1390–1391.)Google Scholar
First citation Borovik-Romanov, A. S. (1960). Piezomagnetism in the antiferromagnetic fluorides of cobalt and manganese. (In Russian.) Zh. Eksp. Teor. Fiz. 38, 1088–1098. (English translation: Sov. Phys. JETP, 11, 786–793.) Google Scholar
First citation Borovik-Romanov, A. S. & Ozhogin, V. I. (1960). Weak ferromagnetism in an antiferromagnetic CoCO3 single crystal. (In Russian.) Zh. Eksp. Teor. Fiz. 39, 27–36. (English translation: Sov. Phys. JETP, 12, 18–24.)Google Scholar
First citation Burzo, E. (1993). Magnetic properties of non-metallic inorganic compounds based on transition elements. Boron containing oxides. Landolt-Börnstein III 27 h, Berlin: Springer.Google Scholar
First citation Clark, A. E., DeSavage, B. F., Tsuya, N. & Kawakami, S. (1966). Magnetostriction of dysprosium, holmium, and erbium iron garnets. J. Appl. Phys. 37, 1324–1326.Google Scholar
First citation Cox, D. E. (1974). Spin ordering in magnetoelectrics. Int. J. Magn. 6, 67–75. [Reprinted in Freeman & Schmid (1975)[link], pp. 111–119.]Google Scholar
First citation Foner, S. (1963). Antiferromagnetic and ferrimagnetic resonance. In Magnetism, Vol. I, edited by G. T. Rado & H. Suhl, pp. 383–447. New York: Academic Press.Google Scholar
First citation Gijsman, H. M., Poulis, N. J. & Van den Handel, J. (1959). Magnetic susceptibilities and phase transitions of two antiferromagnetic manganese salts. Physica, 25, 954–968.Google Scholar
First citation Iida, S. (1967). Magnetostriction constants of rare earth iron garnets. J. Phys. Soc. Jpn, 22, 1201–1209.Google Scholar
First citation Kadomtseva, A. M., Agafonov, A. P., Lukina, M. M., Milov, V. N., Moskvin, A. S. & Semenov, V. A. (1981). Characteristic magnetoelastic properties of yttrium orthochromite. (In Russian.) Fiz. Tverd. Tela, 23, 3554–3557. (English translation: Sov. Phys. Solid State, 23, 2065–2067.)Google Scholar
First citation Kadomtseva, A. M., Agafonov, A. P., Milov, V. N., Moskvin, A. S. & Semenov, V. A. (1981). Direct observation of symmetry change induced in orthoferrite crystals by an external magnetic field. (In Russian.) Pis'ma Zh. Eksp. Teor. Fiz. 33, 400–403. (English translation: JETP Lett. 33, 383–386.)Google Scholar
First citation Lee, E. W. (1955). Magnetostriction and magnetomechanical effects. Rep. Prog. Phys. 18, 184–229.Google Scholar
First citation Levitin, R. Z. & Shchurov, V. A. (1973). In Physics and chemistry of ferrites, pp. 162–194. (In Russian.) Moscow: Izd. Mosk. Gos. Univ.Google Scholar
First citation Prokhorov, A. S. & Rudashevskii, E. G. (1969). Magnetostriction of antiferromagnetic cobalt fluoride. (In Russian.) Pis'ma Zh. Eksp. Teor. Fiz. 10, 175–179. (English translation: JETP Lett. 10, 110–113.)Google Scholar
First citation Prokhorov, A. S. & Rudashevskii, E. G. (1975). Magnetoelastic interactions and the single-domain antiferromagnetic state in cobalt fluoride. (In Russian.) Kratk. Soobshch. Fiz. 11, 3–6. (English translation: Sov. Phys. Lebedev Inst. Rep. 11, 1–4.)Google Scholar
First citation Turov, E. A. (1963). Physical properties of magnetically ordered crystals. (In Russian.) Moscow: Akad. Nauk SSSR. [English translation (1965): New York: Academic Press.]Google Scholar
First citation Zvezdin, A. K., Zorin, I. A., Kadomtseva, A. M., Krynetskii, I. B., Moskvin, A. S. & Mukhin, A. A. (1985). Linear magnetostriction and antiferromagnetic domain structure in dysprosium orthoferrite. (In Russian.) Zh. Eksp. Teor. Fiz. 88, 1098–1102. (English translation: Sov. Phys. JETP, 61, 645–647.)Google Scholar








































to end of page
to top of page