Weak ferromagnetism in antiferromagnets: Fe$_{2}$O$_{3}$ and La$_{2}$CuO$_{4}$

The problem of weak ferromagnetism in antiferromagnets due to canting of magnetic moments was treated using Green's function technique. At first the eigenvalues and eigenfunctions of the electronic Hamiltonian corresponding to collinear magnetic configuration are calculated which are then used to determine first and second variations of the total energy as a function of the magnetic moments canting angle. Spin-orbit coupling is taken into account via perturbation theory. The results of calculations are used to determine an effective spin Hamiltonian. This Hamiltonian can be mapped on conventional spin Hamiltonian that allows to determine parameters of isotropic and anisotropic (Dzyaloshinskii-Moriya) exchange interactions. The method was applied to the typical antiferromagnets with weak ferromagnetism Fe$_{2}$O$_{3}$ and La$_{2}$CuO$_{4}$. The obtained directions and values of the magnetic moments canting angles are in a reasonable agreement with experimental data.

[1]  W. Butler,et al.  Effect of electron correlations on the electronic and magnetic structure of Ti-doped α-hematite , 2004 .

[2]  C. Gros,et al.  Magnetic light scattering in low-dimensional quantum spin systems , 2003, cond-mat/0301413.

[3]  V. Anisimov,et al.  First principles electronic model for high-temperature superconductivity , 2002, cond-mat/0203117.

[4]  M. Katsnelson,et al.  Effect of local Coulomb interactions on the electronic structure and exchange interactions in Mn 12 magnetic molecules , 2001, cond-mat/0110488.

[5]  C. Koch,et al.  Magnetic properties of hematite nanoparticles , 2000 .

[6]  I. Dasgupta,et al.  Electronic structure and exchange interactions of the ladder vanadates CaV2O5 and MgV2O5 , 2000 .

[7]  M. Katsnelson,et al.  First-principles calculations of magnetic interactions in correlated systems , 1999, cond-mat/9904428.

[8]  M. Troyer,et al.  Exchange interactions and magnetic properties of the layered vanadates CaV2O5, MgV2O5, CaV3O7, and CaV4O9 , 1999, cond-mat/9901214.

[9]  K. Terakura,et al.  Effective single-particle potentials for MnO in light of interatomic magnetic interactions: Existing theories and perspectives , 1998 .

[10]  W. Pickett.  Impact of Structure on Magnetic Coupling in CaV4O9 , 1997 .

[11]  S. Nagler,et al.  Magnetic Excitations in the S=1/2 Alternating Chain Compound (VO)_2P_2O_7 , 1997, cond-mat/9704092.

[12]  A. Lichtenstein,et al.  First-principles calculations of electronic structure and spectra of strongly correlated systems: the LDA+U method , 1997 .

[13]  Hamada,et al.  Crucial role of the lattice distortion in the magnetism of LaMnO3. , 1996, Physical review letters.

[14]  L. Sandratskii,et al.  First-principles LSDF study of weak ferromagnetism in Fe2O3 , 1996 .

[15]  L. Sandratskii,et al.  Band theory for electronic and magnetic properties of , 1996 .

[16]  T. M. Rice,et al.  Surprises on the Way from One- to Two-Dimensional Quantum Magnets: The Ladder Materials , 1995, Science.

[17]  Stein,et al.  Weak ferromagnetism in the low-temperature tetragonal phase of the cuprates. , 1996, Physical review. B, Condensed matter.

[18]  Harris,et al.  Anisotropic spin Hamiltonians due to spin-orbit and Coulomb exchange interactions. , 1995, Physical review. B, Condensed matter.

[19]  J. Axe,et al.  Structural instabilities in lanthanum cuprate superconductors , 1994 .

[20]  A. Aharony,et al.  Moriya's anisotropic superexchange interaction, frustration, and Dzyaloshinsky's weak ferromagnetism. , 1992, Physical review letters.

[21]  V. Anisimov,et al.  Band theory and Mott insulators: Hubbard U instead of Stoner I. , 1991, Physical review. B, Condensed matter.

[22]  Thomas,et al.  Optical studies of gap, exchange, and hopping energies in the insulating cuprates. , 1990, Physical review. B, Condensed matter.

[23]  Coffey,et al.  Effective spin Hamiltonian for the CuO planes in La2CuO4 and metamagnetism. , 1990, Physical review. B, Condensed matter.

[24]  Fukuda,et al.  Neutron-scattering study of the transition from antiferromagnetic to weak ferromagnetic order in La2CuO , 1988, Physical review. B, Condensed matter.

[25]  Chen,et al.  Antisymmetric exchange and its influence on the magnetic structure and conductivity of La2CuO4. , 1988, Physical review. B, Condensed matter.

[26]  Y. Endoh,et al.  The effect of the heat treatments on the antiferromagnetism in La2CuO4-δ single crystals , 1987 .

[27]  V. A. Gubanov,et al.  Local spin density functional approach to the theory of exchange interactions in ferromagnetic metals and alloys , 1987 .

[28]  Jepsen,et al.  Illustration of the linear-muffin-tin-orbital tight-binding representation: Compact orbitals and charge density in Si. , 1986, Physical review. B, Condensed matter.

[29]  Ove Jepsen,et al.  Explicit, First-Principles Tight-Binding Theory , 1984 .

[30]  P. Hagenmuller,et al.  Anisotropie des proprietes electriques de l'oxyde de fer Fe2O3α , 1984 .

[31]  M. Methfessel,et al.  Bond analysis of heats of formation: application to some group VIII and IB hydrides , 1982 .

[32]  J. Coey,et al.  A study of hyperfine interactions in the system (Fe1-xRhx)2O3 using the Mossbauer effect (Bonding parameters) , 1971 .

[33]  G. Shirane,et al.  Inelastic neutron scattering investigation of spin waves and magnetic interactions in α‐Fe2O3 , 1970 .

[34]  R. E. Mills,et al.  Green's-Function Theory of Ferrimagnetism, with an Application to Magnetite , 1966 .

[35]  E. Krén,et al.  Neutron diffraction studies on the (1−x) Fe2O3 − xRh2O3 system , 1965 .

[36]  J. P. Remeika,et al.  Magnetic properties of hematite single crystals , 1965 .

[37]  P. Anderson.  Theory of Magnetic Exchange Interactions:Exchange in Insulators and Semiconductors , 1963 .

[38]  R. Newnham,et al.  Refinement of theαAl2O3, Ti2O3, V2O3and Cr2O3structures* , 1962 .

[39]  Ε. E. Newnham,et al.  Refinement of the a Al2O3, Ti2O3, V2O3 and Cr2O3 structures , 1962 .

[40]  T. Moriya.  Anisotropic Superexchange Interaction and Weak Ferromagnetism , 1960 .

[41]  John B. Goodenough,et al.  Direct cation- -cation interactions in several oxides , 1960 .

[42]  Philip W. Anderson,et al.  New Approach to the Theory of Superexchange Interactions , 1959 .

[43]  I. Dzyaloshinsky.  A thermodynamic theory of “weak” ferromagnetism of antiferromagnetics , 1958 .

[44]  L. Néel.  Some New Results on Antiferromagnetism and Ferromagnetism , 1953 .

[45]  C. Shull,et al.  NEUTRON DIFFRACTION BY PARAMAGNETIC AND ANTIFERROMAGNETIC SUBSTANCES , 1951 .

[46]  W. Heisenberg.  Zur Theorie des Ferromagnetismus , 1928 .

[47]  T. Smith.  The Magnetic Properties of Hematite , 1916 .