Forma, Vol. 32 (Special Issue II), pp. SII27–SII42, 2017


Theory of SpinWaves in Rare Earth Metals with Non-Linear c- f Exchange Interaction Effect

Keimei Kaino1* and Tadao Kasuya2

1Emeritus Professor, National Institute of Technology, Sendai College, Sendai 989-3128, Japan
2Emeritus Professor, Faculty of Science, Tohoku University, Japan
*E-mail address:

(Received April 26, 2017; Accepted July 25, 2017)

Abstract. Using a simple band model which produces a helical spin ordering, we show the magnetic phase diagram by minimizing the unperturbed energy which includes the c- f exchange interaction by replacing the f -spin operator Sn with the expectation value ⟨Sn⟩. As the c- f exchange interaction increases, the helix and the cone structures appears without any crystal fields, and then the ferromagnetic structure becomes more stable. Secondly, we obtain formulae of spin-wave dispersions and show their instabilities on the second-order transition boundaries. Near the ferro-helix boundary, the spin-wave constant of the ferromagnetic spin-wave vanishes, while in the helical phase the whole region of the wave-number 0 < qz < Q shows softening where the helical wave-number Q decreases continuously. Thirdly, by the method of the double-time Green function, we derive the spin-wave dispersion at finite temperatures. Finally, anomalous properties in magnon dispersions at finite temperatures for Gd, Ho and those for diluted Tb-Y alloys are explained by use of numerical calculations.

Keywords: c- f Exchange Interaction, Magnon Instabilities, Rare Earth Metals, Spin-Wave Dispersions

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