<i>Ab Initio</i>Calculation of the Gilbert Damping Parameter via the Linear Response Formalism

Ebert, H.; Mankovsky, S.; Ködderitzsch, D.; Kelly, Paul J.

doi:10.1103/physrevlett.107.066603

Cited by 182 publications

(215 citation statements)

References 21 publications

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“…A large number of theoretical approaches to the Gilbert damping has been worked out during the last two decades; here we mention only schemes within the oneelectron theory of itinerant magnets, [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] where the most important effects of electron-electron interaction are captured by means of a local spin-dependent exchangecorrelation (XC) potential. These techniques can be naturally combined with existing first-principles techniques based on the density-functional theory, which leads to parameter-free calculations of the Gilbert damping tensor of pure ferromagnetic metals, their ordered and disordered alloys, diluted magnetic semiconductors, etc.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal torque operators inab initiotheory of the Gilbert damping in random ferromagnetic alloys

2015

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We present an ab initio theory of the Gilbert damping in substitutionally disordered ferromagnetic alloys. The theory rests on introduced nonlocal torques which replace traditional local torque operators in the well-known torque-correlation formula and which can be formulated within the atomic-sphere approximation. The formalism is sketched in a simple tight-binding model and worked out in detail in the relativistic tight-binding linear muffin-tin orbital (TB-LMTO) method and the coherent potential approximation (CPA). The resulting nonlocal torques are represented by nonrandom, non-site-diagonal and spin-independent matrices, which simplifies the configuration averaging. The CPA-vertex corrections play a crucial role for the internal consistency of the theory and for its exact equivalence to other first-principles approaches based on the random local torques. This equivalence is also illustrated by the calculated Gilbert damping parameters for binary NiFe and FeCo random alloys, for pure iron with a model atomic-level disorder, and for stoichiometric FePt alloys with a varying degree of L10 atomic long-range order.

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Section: Introductionmentioning

confidence: 99%

Nonlocal torque operators inab initiotheory of the Gilbert damping in random ferromagnetic alloys

2015

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“…Ebert et al 1 and Lounis et al 28 suggested that α int is proportional to n(E F ) in the breathing Fermi-surface model (that is, intraband transitions) in the cases of a minimally varying spin-orbit coupling (SOC) (as is the case for the Co x Fe 1−x system) and small electron-phonon coupling 2,29 . Alternatively, interband transitions become significant only if bands have a finite overlap due to band broadening, caused for example by coupling to the phonons.…”

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confidence: 99%

“…The uncertainties in the linewidths were obtained by means of the standard method for the determination of confidence limits on estimated parameters for nonlinear models under the assumption of Gaussian white noise. The lines are error-weighted fits to equation (1), which are used to determine both the total damping α tot and the inhomogeneous linewidth broadening for each alloy.…”

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Ultra-low magnetic damping of a metallic ferromagnet

et al. 2016

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Magnetic damping is of critical importance for devices that seek to exploit the electronic spin degree of freedom, as damping strongly a ects the energy required and speed at which a device can operate. However, theory has struggled to quantitatively predict the damping, even in common ferromagnetic materials 1-3 . This presents a challenge for a broad range of applications in spintronics 4 and spin-orbitronics that depend on materials and structures with ultra-low damping 5,6 . It is believed that achieving ultra-low damping in metallic ferromagnets is limited by the scattering of magnons by the conduction electrons. However, we report on a binary alloy of cobalt and iron that overcomes this obstacle and exhibits a damping parameter approaching 10 −4 , which is comparable to values reported only for ferrimagnetic insulators 7,8 . We explain this phenomenon by a unique feature of the band structure in this system: the density of states exhibits a sharp minimum at the Fermi level at the same alloy concentration at which the minimum in the magnetic damping is found. This discovery provides both a significant fundamental understanding of damping mechanisms and a test of the theoretical predictions proposed by Mankovsky and colleagues 3 .In recent decades, several theoretical approaches have attempted to quantitatively predict magnetic damping in metallic systems. One of the early promising theories was that of Kambersky, who introduced the so-called breathing Fermi-surface model 9-11 . More recently, Gilmore and Stiles 2 as well as Thonig et al. 12 demonstrated a generalized torque correlation model that includes both intraband (conductivity-like) and interband (resistivity-like) transitions. The use of scattering theory to describe damping was later applied by Brataas et al. 13 and Liu et al. 14 to describe damping in transition metals. A numerical realization of a linear response damping model was implemented by Mankovsky 3 for Ni-Co, Ni-Fe, Fe-V and Co-Fe alloys. For the Co-Fe alloy, these calculations predict a minimum intrinsic damping of α int ≈ 0.0005 at a Co-concentration of 10% to 20%, but was not experimentally observed 15 .Underlying this theoretical work is the goal of achieving new systems with ultra-low damping that are required in many magnonic and spin-orbitronics applications 7,8 . Ferrimagnetic insulators such as yttrium-iron-garnet (YIG) have long been the workhorse for these investigations, because YIG films as thin as 25 nm have experimental damping parameters as low as 0.9 × 10 −4 (ref. 16). Such ultra-low damping can be achieved in insulating ferrimagnets in part due to the absence of conduction electrons-and, therefore, the suppression of magnon-electron scattering. However, insulators cannot be used in most spintronic and spin-orbitronic applications, where a charge current through the magnetic material is required, nor is the requirement of growth on gadolinium gallium garnet templates compatible with spintronics and complementary metal-oxide semiconductor (CMOS) fabrication processes. One...

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“…A different CPA formula incorporating thermal displacements and u 2 (T ) has recently been implemented in SPRKKR using a Debye approximation in Refs. [32,33] but does not yet allow for the calculation of the J ρη ij . The cubic symmetry is broken by the finite displacement and subsequently restored on the exchange integrals by resymmetrizing the full J ij matrix with the original cubic symmetry operations along x, y, and z (we assume uncorrelated thermal displacements).…”

Section: Thermal-dependent Exchange Integralsmentioning

confidence: 99%

Competition of lattice and spin excitations in the temperature dependence of spin-wave properties

et al. 2018

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(2018). Competition of lattice and spin excitations in the temperature dependence of spin-wave properties. Physical Review B (PRB), 97 (21). The interplay of magnons and phonons can induce strong temperature variations in the magnetic exchange interactions, leading to changes in the magnetothermal response. This is a central mechanism in many magnetic phenomena, and in the new field of Spin Caloritronics, which focuses on the combination of heat and spin currents. Boson model systems have previously been developed to describe the magnon-phonon coupling but, until recently, studies rely on empirical parameters. In this paper, we propose a first-principles approach to describe the dependence of the magnetic exchange integrals on phonon renormalization, leading to changes in the magnon dispersion as a function of temperature. The temperature enters into the spin dynamics (by introducing fluctuations) as well as in the magnetic exchange itself. Depending on the strength of the coupling, these two temperatures may or may not be equilibrated, yielding different regimes. We test our approach in typical and well-known ferromagnetic materials: Ni, Fe, and Permalloy. We compare our results to recent experiments on the spin-wave stiffness, and discuss departures from Bloch's law and parabolic dispersion. Copyright and re-use policy

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Ab InitioCalculation of the Gilbert Damping Parameter via the Linear Response Formalism

Cited by 182 publications

References 21 publications

Nonlocal torque operators inab initiotheory of the Gilbert damping in random ferromagnetic alloys

Nonlocal torque operators inab initiotheory of the Gilbert damping in random ferromagnetic alloys

Ultra-low magnetic damping of a metallic ferromagnet

Competition of lattice and spin excitations in the temperature dependence of spin-wave properties

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