Adiabatic Dynamics of Coupled Spins and Phonons in Magnetic Insulators
In conventional ab initio methodologies, phonons are calculated by solving equations of motion involving static interatomic force constants and atomic masses. The Born-Oppenheimer approximation, where all electronic degrees of freedom are assumed to adiabatically follow the nuclear dynamics, is also...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2024-03-01
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| Series: | Physical Review X |
| Online Access: | http://doi.org/10.1103/PhysRevX.14.011041 |
| _version_ | 1797270226909265920 |
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| author | Shang Ren John Bonini Massimiliano Stengel Cyrus E. Dreyer David Vanderbilt |
| author_facet | Shang Ren John Bonini Massimiliano Stengel Cyrus E. Dreyer David Vanderbilt |
| author_sort | Shang Ren |
| collection | DOAJ |
| description | In conventional ab initio methodologies, phonons are calculated by solving equations of motion involving static interatomic force constants and atomic masses. The Born-Oppenheimer approximation, where all electronic degrees of freedom are assumed to adiabatically follow the nuclear dynamics, is also adopted. This approach does not fully account for the effects of broken time-reversal symmetry in systems with magnetic order. Recent attempts to rectify this involve the inclusion of the velocity dependence of the interatomic forces in the equations of motion, which accounts for time-reversal symmetry breaking, and can result in chiral phonon modes with nonzero angular momentum even at the zone center. However, since the energy ranges of phonons and magnons typically overlap, the spins cannot be treated as adiabatically following the lattice degrees of freedom. Instead, phonon and spins must be treated on a similar footing. Focusing on zone-center modes, we propose a method involving Hessian matrices and Berry curvature tensors in terms of both phonon and spin degrees of freedom, and describe a first-principles methodology for calculating these. We then solve Lagrange’s equations of motion to determine the energies and characters of the mixed excitations, allowing us to quantify, for example, the energy splittings between chiral pairs of phonons in some cases, and the degree of magnetically induced mixing between infrared and Raman modes in others. The approach is general and can be applied to determine the adiabatic dynamics of any mixed set of slow variables. |
| first_indexed | 2024-04-25T02:00:55Z |
| format | Article |
| id | doaj.art-abeb5a485093466c975b71adf11f359f |
| institution | Directory Open Access Journal |
| issn | 2160-3308 |
| language | English |
| last_indexed | 2024-04-25T02:00:55Z |
| publishDate | 2024-03-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review X |
| spelling | doaj.art-abeb5a485093466c975b71adf11f359f2024-03-07T15:03:26ZengAmerican Physical SocietyPhysical Review X2160-33082024-03-0114101104110.1103/PhysRevX.14.011041Adiabatic Dynamics of Coupled Spins and Phonons in Magnetic InsulatorsShang RenJohn BoniniMassimiliano StengelCyrus E. DreyerDavid VanderbiltIn conventional ab initio methodologies, phonons are calculated by solving equations of motion involving static interatomic force constants and atomic masses. The Born-Oppenheimer approximation, where all electronic degrees of freedom are assumed to adiabatically follow the nuclear dynamics, is also adopted. This approach does not fully account for the effects of broken time-reversal symmetry in systems with magnetic order. Recent attempts to rectify this involve the inclusion of the velocity dependence of the interatomic forces in the equations of motion, which accounts for time-reversal symmetry breaking, and can result in chiral phonon modes with nonzero angular momentum even at the zone center. However, since the energy ranges of phonons and magnons typically overlap, the spins cannot be treated as adiabatically following the lattice degrees of freedom. Instead, phonon and spins must be treated on a similar footing. Focusing on zone-center modes, we propose a method involving Hessian matrices and Berry curvature tensors in terms of both phonon and spin degrees of freedom, and describe a first-principles methodology for calculating these. We then solve Lagrange’s equations of motion to determine the energies and characters of the mixed excitations, allowing us to quantify, for example, the energy splittings between chiral pairs of phonons in some cases, and the degree of magnetically induced mixing between infrared and Raman modes in others. The approach is general and can be applied to determine the adiabatic dynamics of any mixed set of slow variables.http://doi.org/10.1103/PhysRevX.14.011041 |
| spellingShingle | Shang Ren John Bonini Massimiliano Stengel Cyrus E. Dreyer David Vanderbilt Adiabatic Dynamics of Coupled Spins and Phonons in Magnetic Insulators Physical Review X |
| title | Adiabatic Dynamics of Coupled Spins and Phonons in Magnetic Insulators |
| title_full | Adiabatic Dynamics of Coupled Spins and Phonons in Magnetic Insulators |
| title_fullStr | Adiabatic Dynamics of Coupled Spins and Phonons in Magnetic Insulators |
| title_full_unstemmed | Adiabatic Dynamics of Coupled Spins and Phonons in Magnetic Insulators |
| title_short | Adiabatic Dynamics of Coupled Spins and Phonons in Magnetic Insulators |
| title_sort | adiabatic dynamics of coupled spins and phonons in magnetic insulators |
| url | http://doi.org/10.1103/PhysRevX.14.011041 |
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