Spin waves in dilute ferromagnets: Cluster-Bethe-lattice approach

Salzberg, J.B.; Silva, C. E. T. Gonçalves da; Falicov, L. M.

doi:10.1103/physrevb.14.1314

Cited by 32 publications

(7 citation statements)

References 12 publications

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“…Salzberg et al [71] employed a Heisenberg hamiltonian for dilute ferromagnet using the cluster-Bethe-lattice (CBL) approximation [72] to compute the Green function and the density of spin-wave states as a function of spin-wave frequency for several values of p in the range of 0.25 to 1.0 in body-centered cubic and simple-cubic lattices with clusters of various sizes. The utilized CBL method gives a plausible description of localized magnetic excitations but with δ-function type anomalies.…”

Section: Development Of Theoretical Approachesmentioning

confidence: 99%

“…The utilized CBL method gives a plausible description of localized magnetic excitations but with δ-function type anomalies. These anomalies are attributed (i) to isolated magnetic clusters, which result in localized modes comprising one zero-frequency mode, and to (ii) local excitations within the "bulk" ferromagnet which do not propagate beyond a few atoms due to fluctuations in the local configurations [71]. Salzberg et al showed that T c → 0 as p → p c .…”

Section: Development Of Theoretical Approachesmentioning

confidence: 99%

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Spin-wave theory in a randomly disordered lattice: A Heisenberg ferromagnet

Weiss,

Massih

2022

Preprint

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Starting from the hamiltonian for the Heisenberg ferromagnet which comprise randomly distributed nonmagnetic ions as impurities in a Bravais lattice, we express the spin operators by means of the Dyson-Maleev transformation in terms of the Bose operators of the second quantization. Then by using methods of quantum statistical field theory, we derive the partition function and the free energy for the system. We adopt the Matsubara thermal perturbation method to a portion of the hamiltonian which describes the interaction between magnons and the stationary field of nonmagnetic ions. Upon averaging over all possible distributions of impurities, we express the free energy of the system as a function of the mean impurity concentration. Subsequently, we set up the double-time single particle Green function at temperature T in the momentum space in terms of magnon operators and derive the equation of motion for the Green function through the Heisenberg equation of motion and then solve the resulting equation. From this, we calculate the self-energy and then the spectral density function for the system. We apply the formalism to the case of the simple cubic lattice and compute the density of states, the spectral density function and the lifetime of the magnons as a function of energy for several values of the mean concentration of nonmagnetic ions in the ferromagnetic lattice. We calculate the magnon energy spectrum as a function of the average impurity concentration fraction c, which shows that for low lying states, the excitation energy increases continuously with c in the studied range 0.1 ≤ c ≤ 0.7. We also use the spectral density function to compute some thermodynamical quantities through the magnon occupation number. We have obtained closed form expressions for the configurationally averaged physical quantities of interest in a unified fashion as functions of the mean concentration of nonmagnetic impurities c to any order of c applicable below a critical percolation concentration c p . The quantities of interest comprise the thermodynamic potential (free energy), the spin-wave self-energy and the spectral density function from which other quantities can be derived.

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Section: Development Of Theoretical Approachesmentioning

confidence: 99%

Section: Development Of Theoretical Approachesmentioning

confidence: 99%

Spin-wave theory in a randomly disordered lattice: A Heisenberg ferromagnet

Weiss,

Massih

2022

Preprint

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“…Indeed, for d → ∞ the percolation threshold n c → 1 d that does not coincide with the Bethe expression n B c = 1 2d−1 which is an asymptotic of the percolation threshold at large d. Nevertheless as we can see from the Table I the results for the percolation threshold obtained from (3.19) are better for d = 2 and d = 3 than the ones obtained within the Bethe-lattice approach. One can find some results of the latter approach for the theory of dilute ferromagnets in [10,11,12].…”

Section: Low Concentration Of Nonmagnetic Impuritiesmentioning

confidence: 99%

Magnetic Properties of Dilute Alloys: Equations for Magnetization and Its Structural Fluctuations

Vakarchuk

Tkachuk

Kuliy

1998

phys. stat. sol. (b)

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The dilute Heisenberg ferromagnet is studied taking into account fluctuations of magnetization caused by disorder. A self-consistent system of equations for magnetization and its mean quadratic fluctuations are derived within the configurationally averaged two-time temperature Green's function method. This system of equations is analyzed at low concentration of nonmagnetic impurities. Mean relative quadratic fluctuations of magnetization are revealed to be proportional to the square of concentration of impurities.

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“…The earlier applications included localization, 3,4 alloys, 5 spin waves, 6,7 and spin glasses. 8 Recently it has been used to investigate properties of the Potts model, 9 the Blume-Capel model, 10 and the Hubbard model.…”

Section: Introductionmentioning

confidence: 99%