Magnetic dipole interactions in crystals
Abstract
The influence of magnetic dipole interactions (MDIs) on the magnetic properties of localmoment Heisenberg spin systems is investigated. A general formulation is presented for calculating the eigenvalues λ and eigenvectors μ ˆ of the MDI tensor of the magnetic dipoles in a line (one dimension, 1D), within a circle (2D) or a sphere (3D) of radius r surrounding a given moment μ ^{→}_{ i} for given magnetic propagation vectors k for collinear and coplanar noncollinear magnetic structures on both Bravais and nonBravais spin lattices. Results are calculated for collinear ordering on 1D chains, 2D square and simplehexagonal (triangular) Bravais lattices, 2D honeycomb and kagomé nonBravais lattices, and 3D cubic Bravais lattices. The λ and μ ˆ values are compared with previously reported results. Calculations for collinear ordering on 3D simple tetragonal, bodycentered tetragonal, and stacked triangular and honeycomb lattices are presented for c/a ratios from 0.5 to 3 in both graphical and tabular form to facilitate comparison of experimentally determined easy axes of ordering on these Bravais lattices with the predictions for MDIs. Comparisons with the easy axes measured for several illustrative collinear antiferromagnets (AFMs) are given. The calculations are extended to the cycloidal noncollinear 120 ° AFM ordering onmore »
 Authors:

 Iowa State Univ., Ames, IA (United States)
 Publication Date:
 Research Org.:
 Ames Laboratory (AMES), Ames, IA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1234520
 Alternate Identifier(s):
 OSTI ID: 1235754
 Report Number(s):
 ISJ 8640
Journal ID: ISSN 24699950
 Grant/Contract Number:
 AC0207CH11358
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physical Review B
 Additional Journal Information:
 Journal Volume: 93; Journal Issue: 01; Journal ID: ISSN 24699950
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 36 MATERIALS SCIENCE
Citation Formats
Johnston, David. Magnetic dipole interactions in crystals. United States: N. p., 2016.
Web. doi:10.1103/PhysRevB.93.014421.
Johnston, David. Magnetic dipole interactions in crystals. United States. doi:10.1103/PhysRevB.93.014421.
Johnston, David. Wed .
"Magnetic dipole interactions in crystals". United States. doi:10.1103/PhysRevB.93.014421. https://www.osti.gov/servlets/purl/1234520.
@article{osti_1234520,
title = {Magnetic dipole interactions in crystals},
author = {Johnston, David},
abstractNote = {The influence of magnetic dipole interactions (MDIs) on the magnetic properties of localmoment Heisenberg spin systems is investigated. A general formulation is presented for calculating the eigenvalues λ and eigenvectors μ ˆ of the MDI tensor of the magnetic dipoles in a line (one dimension, 1D), within a circle (2D) or a sphere (3D) of radius r surrounding a given moment μ → i for given magnetic propagation vectors k for collinear and coplanar noncollinear magnetic structures on both Bravais and nonBravais spin lattices. Results are calculated for collinear ordering on 1D chains, 2D square and simplehexagonal (triangular) Bravais lattices, 2D honeycomb and kagomé nonBravais lattices, and 3D cubic Bravais lattices. The λ and μ ˆ values are compared with previously reported results. Calculations for collinear ordering on 3D simple tetragonal, bodycentered tetragonal, and stacked triangular and honeycomb lattices are presented for c/a ratios from 0.5 to 3 in both graphical and tabular form to facilitate comparison of experimentally determined easy axes of ordering on these Bravais lattices with the predictions for MDIs. Comparisons with the easy axes measured for several illustrative collinear antiferromagnets (AFMs) are given. The calculations are extended to the cycloidal noncollinear 120 ° AFM ordering on the triangular lattice where λ is found to be the same as for collinear AFM ordering with the same k. The angular orientation of the ordered moments in the noncollinear coplanar AFM structure of GdB 4 with a distorted stacked 3D ShastrySutherland spinlattice geometry is calculated and found to be in disagreement with experimental observations, indicating the presence of another source of anisotropy. Similar calculations for the undistorted 2D and stacked 3D ShastrySutherland lattices are reported. The thermodynamics of dipolar magnets are calculated using the Weiss molecular field theory for quantum spins, including the magnetic transition temperature T m and the ordered moment, magnetic heat capacity, and anisotropic magnetic susceptibility χ versus temperature T . The anisotropic Weiss temperature θ p in the CurieWeiss law for T>T m is calculated. A quantitative study of the competition between FM and AFM ordering on cubic Bravais lattices versus the demagnetization factor in the absence of FM domain effects is presented. The contributions of Heisenberg exchange interactions and of the MDIs to T m and to θ p are found to be additive, which simplifies analysis of experimental data. Some properties in the magneticallyordered state versus T are presented, including the ordered moment and magnetic heat capacity and, for AFMs, the dipolar anisotropy of the free energy and the perpendicular critical field. The anisotropic χ for dipolar AFMs is calculated both above and below the Néel temperature T N and the results are illustrated for a simple tetragonal lattice with c/a>1, c/a=1 (cubic), and c/a<1 , where a change in sign of the χ anisotropy is found at c/a=1 . Finally, following the early work of Keffer [Phys. Rev. 87, 608 (1952)], the dipolar anisotropy of χ above T N =69 K of the prototype collinear Heisenbergexchangecoupled tetragonal compound MnF 2 is calculated and found to be in excellent agreement with experimental singlecrystal literature data above 130 K, where the smoothly increasing deviation of the experimental data from the theory on cooling from 130 K to T N is deduced to arise from dynamic shortrange collinear c axis AFM ordering in this temperature range driven by the exchange interactions.},
doi = {10.1103/PhysRevB.93.014421},
journal = {Physical Review B},
number = 01,
volume = 93,
place = {United States},
year = {2016},
month = {1}
}
Web of Science
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