Identification of the Dominant Precession-Damping Mechanism in Fe, Co, and Ni by First-Principles Calculations

Gilmore, Keith; Idzerda, Y. U.; Stiles, Mark D.

doi:10.1103/physrevlett.99.027204

Cited by 346 publications

(369 citation statements)

References 30 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%

“…[5][6][7][8]15,16 Other routes to the Gilbert damping employ relaxations of occupation numbers of individual Bloch electron states during quasistatic nonequilibrium processes or transition rates between different states induced by the spin-orbit (SO) interaction. [9][10][11][12]14,20 The dissipation of magnetic energy accompanying the slow magnetization dynamics, evaluated within a scattering theory or the Kubo linear response formalism, leads also to explicit expressions for the Gilbert damping tensor. 13,[17][18][19] Most of these formulations yield relations equivalent to the so-called torquecorrelation formula…”

Section: Introductionmentioning

confidence: 99%

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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%

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%

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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“…The importance of the nonadiabaticity for current-induced domain wall motion, has led to a number of theoretical [23][24][25][98][99][100][101][102][103][104][105][106] and experimental studies [94,[107][108][109][110][111][112] to determine the nonadiabatic spin torque parameter. Several mechanisms for the nonadiabatic spin transfer torque have been proposed.…”

Section: Non-local Spin Transfer Torque For a Narrow Domain Wallmentioning

confidence: 99%

“…For example, a phenomenological treatment of the scattering of itinerant electrons by spin-dependent impurities generates both damping and a nonadiabatic spin transfer torque in the presence of current [24]. Similarly, band structures with spin-orbit coupling and electron scattering give both damping [113] and nonadiabatic torques [103], both of which can be calculated from first principles [104,105].…”

Section: Non-local Spin Transfer Torque For a Narrow Domain Wallmentioning

confidence: 99%

Self-consistent calculation of spin transport and magnetization dynamics

et al. 2013

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A spin-polarized current transfers its spin-angular momentum to a local magnetization, exciting various types of current-induced magnetization dynamics. So far, most studies in this field have focused on the direct effect of spin transport on magnetization dynamics, but ignored the feedback from the magnetization dynamics to the spin transport and back to the magnetization dynamics. Although the feedback is usually weak, there are situations when it can play an important role in the dynamics. In such situations, simultaneous, self-consistent calculations of the magnetization dynamics and the spin transport can accurately describe the feedback. This review describes in detail the feedback mechanisms, and presents recent progress in self-consistent calculations of the coupled dynamics. We pay special attention to three representative examples, where the feedback generates non-local effective interactions for the magnetization after the spin accumulation has been integrated out. Possibly the most dramatic feedback example is the dynamic instability in magnetic nanopillars with a single magnetic layer. This instability does not occur without non-local feedback. We demonstrate that full self-consistent calculations generate simulation results in much better agreement with experiments than previous calculations that addressed the feedback effect approximately.The next example is for more typical spin valve nanopillars. Although the effect of feedback is less dramatic because even without feedback the current can make stationary states unstable and induce magnetization oscillation, the feedback can still have important consequences. For instance, we show that the feedback can reduce the linewidth of oscillations, in agreement with experimental observations. A key aspect of this reduction is the suppression of the excitation of short wave length spin waves by the non-local feedback.Finally, we consider nonadiabatic electron transport in narrow domain walls. The non-local feedback in these systems leads to a significant renormalization of the effective nonadiabatic 3 spin transfer torque. These examples show that the self-consistent treatment of spin transport and magnetization dynamics is important for understanding the physics of the coupled dynamics and for providing a bridge between the ongoing research fields of current-induced magnetization dynamics and the newly emerging fields of magnetization-dynamics-induced generation of charge and spin currents.

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Identification of the Dominant Precession-Damping Mechanism in Fe, Co, and Ni by First-Principles Calculations

Cited by 346 publications

References 30 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

Self-consistent calculation of spin transport and magnetization dynamics

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