Longitudinal Dynamical Susceptibility of the Heisenberg Ferromagnet at Short Wavelengths and Low Temperatures

The longitudinal dynamical susceptibility of the Heisenberg ferromagnet is studied at short wavelengths and low temperatures. It is shown that identical results to order 1/S are obtained using (a) a spin decoupling technique, (b) a diagrammatic method using the Holstein-Primakoff transformation, and (c) a diagrammatic method using the Dyson-Maleev transformation. We thus conclude that there are no significant kinematic effects at low temperatures. Using the random-phase approximation, we find that the Dyson-Maleev interactions between magnons are too weak to support the existence of a zero-sound mode. Both these conclusions disagree with the recent results of other authors. Disciplines Physics | Quantum Physics This journal article is available at ScholarlyCommons: http://repository.upenn.edu/physics_papers/418 27A. J. Heeger, in Ref. 26. ~8A.. A. Abrikosov, Physics (N. &. ) 2, 61 (1965). G. G. Low and Y. M. HoMen, Proc. Phys. Soc. (London) 89 119 (19ee). 3 Am analysis of the detailed magnetoresistance of the Pd 0. 1-at. % Co alloy over a wide range of magnetic fields and temperatures (which will be the subject of a further publication) yields values ofg=2. 9 +0. 1 and S=4.7+0.2. Using this value of S in'the present ana, lysis yields J~~g(5 K) = 0.053 eV, n~ (Ey) =2. 5jeV atom, and J=O. 14 eV. S~C. Herring, in Magnetism, edited by G. T. Rado and H. Suhl (Academic, New York, 1966), Vol. IV. ~2J. R. Schrieffer and P. A. %olff, Phys, Rev. 149, 491 (19ee). 33In the Anderson model fP. W. Anderson, Phys. Rev. 124, 41 (1961)j, the total polarization has two contributions, a positive polarization resulting from the admixture effect (which can be exchange enhanced to give a "giant" moment) and a negative contribution from the energy-shift term. %'bile the total polarization may be positive under certain cirdumstances (in exchange-enhanced matrices), the Kondo effect results from the energy-shift term alone, and the relevent exchange interaction froxn this source is always antiferromagnetic. K. Fischer, phys. Rev, 158, 618 (1967). 35A. B)andin, J. Appl. Phys. 39, 1285 (1968). 366. S. Knapp, Phys. Letters 25A, 114 (1967), The decx'e88e in +)~g~ is approximately 40% ovex' this texnperature range if s is take to be 4. 7, as determined from magnetoresistance measurements. This would still suggust a Kondo temperature below 1 K. SP. Lederer and D. L. Mills, Phys. Rev. 165, 837 (1968). SA. B. Kaiser and 8. Doniach, Intern. J. Magnetism 1, 11 (1970), 40M. Levine and H. SuM, Phys. Rev. 171, 567 (1968). 4~D. R. Hamann, Phys. Bev, Letters ~23 95 (1969). PHYSICAL REVIEW 8 VOLUME 3, NUMBER 9 L~ngit~dinal Dynamical Susceptibility of the Heisenberg Ferromagnet at Short Wavelengths and Lovv Temperatures A. Brooks Harris Dept tment of I'hysics, University of Pennsylvani+, Philude/pksa, I'ennsylvanie 19104 (Received 13 January 1971) The longitudinal dynamical susceptibility of the Heisenberg ferroinagnet is studied at short wavelengths and low temperatures. It is shown that identical xesults to order 1/S are obtained using (a) a spin decoupling technique, (b) a diagrammatic method using the Holstein-Primakoff transformation, and (c) a diagrammatic method using the Byson-Maleev transformation. %e thus conclude that there are no significant kinematic effects at low temperatures. Using the random-phase approximation, we find that the Dyson-Maleev interactions between magnons are too weak to support the existence of a zero-sound mode. Both' these conclusions disagree with the recent results of other authors.