A comprehensive study of Heisenberg-like systems with internal spin fluctuation

Wang, Huaiyu; Wang, Shan-Ying; Wang, Chong-Yu; Duan, Wenhui; Chen, Ke‐Qiu

doi:10.1088/0953-8984/15/17/328

Cited by 11 publications

(6 citation statements)

References 30 publications

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“…This theory helps to deal with various systems described by Heisenberg Hamiltonian. [5][6][7][8] Recently, experimental works raised an interest to calculate more than one component of magnetization. For example, under an external perpendicular field, the magnetization rotates with the variation of the field.…”

Section: Introductionmentioning

confidence: 99%

Magnetization in the case of anisotropic exchange interaction

Wang

2004

Phys. Rev. B

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This paper describes a method to calculate the three components of statistical average of spin operators with Heisenberg model when the exchange interaction is anisotropic in z direction. By the use of many-body Green's function method, when external field is applied in both x and z directions, formalism for calculation of magnetization ͗S x ͘ and ͗S z ͘ are explicitly derived for spin value Sϭ1/2, 1, 3/2, 2, and 5/2. Based on the formalism, a general expression for calculation of ͗S z ͘ for any spin value is suggested. Numerical analysis is presented for both cases of isotropic and anisotropic exchange interaction. The results of both threedimensional and two-dimensional cases are discussed. Based on the numerical results, we suggest a method to test a film in experiments whether there is an ingredient of exchange anisotropy.

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Section: Introductionmentioning

confidence: 99%

Magnetization in the case of anisotropic exchange interaction

Wang

2004

Phys. Rev. B

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“…5,6 The technique is a substantial extension of the old one by Tahir-Kheli et al, [7][8][9] which dealt with only z-component magnetization when applied to treat various magnetic systems described by Heisenberg Hamiltonian. [10][11][12][13][14] The technique assumes that the three components of magnetization may all be nonzero. If two of them are zero, the results naturally go back to the z-component only case.…”

Section: Introductionmentioning

confidence: 99%

Many-body Green’s function theory of ferromagnetic films with arbitrarily arranged single-ion anisotropies

Wang

Jen

2006

Phys. Rev. B

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In the treatment of Heisenberg Hamiltonian containing single-ion anisotropy by means of many-body Green's function method, the decoupling of the anisotropy term in higher order Green's functions usually takes an Anderson-Callen ͑AC͒ form. In this paper, possible improvement schemes of AC decoupling are discussed by comparison of the results with those of quantum Monte Carlo and frame rotation methods. We choose one scheme with a factor concerning the effect of the external field. Next, we discuss a possible difficulty of the frame rotation method in treating systems with single-ion anisotropies in more than one direction. Then we extended our method ͓Phys. Rev. B 70, 134424 ͑2004͔͒ to treat magnetic films. Some magnetic properties of ultrathin ferromagnetic films with thicknesses up to 16 monolayers are studied. The properties investigated include transition point, effective anisotropy coefficient, field-induced magnetization reorientation, and hysteresis loop. Several cases are investigated for uniaxial anisotropy and external field along different directions. The transition point, the effective anisotropy coefficient, the coercivity, and the loop area increase with increasing film thickness. The coercivity decreases and the loop area reduces with increasing temperature. The hysteresis loop along field direction is different from that along easy-axis direction. The coercivity and the area of the loop obtained in the former case are larger than the latter case. The reasons are analyzed by investigation of the trajectory of magnetization in detail. The influence of dipole interaction on the magnetic properties is discussed.

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“…Usually, only the z-component of the magnetization S z was considered. Callen 3 developed a formalism which lead to a closed-form expression for the magnetization S z in ferromagnetic (FM) systems for any spin quantum number S. This theory has been helpful in studying various systems described by Heisenberg Hamiltonians 4,5,6,7 . Recently, experimental work has provided an incentive to calculate more than one component of the magnetization.…”

Section: Introductionmentioning

confidence: 99%

Many-body Green’s function theory of ferromagnetic Heisenberg systems with single-ion anisotropies in more than one direction

et al. 2004

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The behaviour of ferromagnetic systems with single-ion anisotropies and magnetic fields in more than one direction is investigated with many-body Green's function theory generalizing earlier work with uniaxial anisotropies only. It turns out to be of advantage to construct Green's functions in terms of the spin operators S x , S y and S z , instead of the commonly used S + , S − and S z operators. The exchange energy terms are decoupled by RPA and the single-ion anisotropy terms by a generalization of the Anderson-Callen decoupling. We stress that in the derivation of the formalism none of the three spatial axes is special, so that one is always able to select a reference direction along which a magnetization component is not zero. Analytical expressions are obtained for all three components of the magnetization and the expectation values (S x ) 2 , (S y ) 2 and (S z ) 2 for any spin quantum number S. The formalism considers both in-plane and out-of-plane anisotropies. Numerical calculations illustrate the behaviour of the magnetization for 3-dimensional and 2-dimensional systems for various parameters. In the 2-dimensional (monolayer) case, the magnetic dipole-dipole coupling is included, and a comparison is made between in-plane and out-of-plane anisotropies.

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A comprehensive study of Heisenberg-like systems with internal spin fluctuation

Cited by 11 publications

References 30 publications

Magnetization in the case of anisotropic exchange interaction

Magnetization in the case of anisotropic exchange interaction

Many-body Green’s function theory of ferromagnetic films with arbitrarily arranged single-ion anisotropies

Many-body Green’s function theory of ferromagnetic Heisenberg systems with single-ion anisotropies in more than one direction

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