LT 21 Proceedings of the 21st International Conference on Low Temperature Physics Prague, August 8-14, 1996

Part $4 - LT Properties of Solids 1: Magnetism (theory)

Short-range order in Spin Density Wave antiferromagnets

Michel Avignon,, Vladimir N. Men'shovb and Victor V. Tugushevb

�9 LEPES-CNRS, BPI66, 38042 Grenoble Cedex 9, France b RRC "Kurchatov Institute", 1 Kurchatov sq., 123182, Moscow, Russia

The model of the short-range order state for itinerant antiferromagnets with SDW is developed. The thermodynamic transverse spin density fluctuations are sho~al to influence essentially on the formation of the long-range magnetic order. In the wide temperature range these occurs the short-range magnetic order regim. The properties of the low-frequency transverse excitations of the spin density are analized. The existence of a fully diffusive mode at small wave vectors is predicted 1. Introduction

In the mordem theory of itinerant magnetism it is assumed that the destruction of the long-range magnetic order with increasing temperature is mainly due to spin density fluctuations. One of the most physically illustrative method for their calculation is known as the "local band theory '' [1]. It has been used for strong (suturatcd) itinerant ferromagnets ~Sth a spin-density amplitude on each site close to the maximum. In Ref. [2] the "local band theory" was applied to investigate the thermodynamics of the itinerant antiferromagnets with spin-density wave (SDW). In this paper we analyse the dynamical susc~tibility of itinerant antiferromagnets in the short-rang order region. All concrete calculations have been made for the one- dimentional system in which the Neel point TN=0, but the principal results will remain for T>T,~,, when T ~ 0 .

2.Resul ts Let us introduce the local quantization axis e, for

each lattice site. For the case of the two alternating magnetic sublattices we assime e~ to be colinear to the local site magnetization Si and eiSi= Sexp(iQRi), where Q =G/2 (G being the reciprocal lattice vector). The direction of ei varies slighly from site to site so that for nearest neighbors [ei-ejl <<1. In the local coordinate system the model Hamiltonian H=H0+H~+H2 have the rotationally-invariant part H0 and the part related to the random vector field {ei}, where the HI(H2) corresponds to the quasiparticle scattering by the spin fluctuation with (without) spin-flip. Accordingly, we can ~xite the free energy of the system as:

F= Fo[A]+F,r[A, {el}], F,r=-Z Ji,i eiej (I) ij

Here F0[A] depends only on the SDW amplitude A=US (where U is the Hubbard potential). We can obtain spin-fluctuation part Fa in the form of the classical effective Heisenberg Hamiltonian. The detailled expression of Jij is obtainad in [2]. Thus, the calculation of the average of any physical quantity of the itinerant antiferromagnet reduces to the integration over the field {el} with the statistical weight exp[-F,r/T]. We limit ourselves to considering only the paramagnetic phase, for which (el)=0, and we assume the Gaussian approximation for the decoupling of the {el} field correlators.

The averaged Green's function we write in form

(G)-l=(GO)-I-E, E=(H,.)+(HIG~ (2)

where G O is the propagator of the Neel ground state. We consider the prefect "nesting" condition c(k+Q)=-e(k) for the electronic spectrum. It is possible to express the self-energy part Y. in term of correlation function f,j=(eiej) [2].

The poles of the function (2) determine the spectrum of single-electron excitations (one- dimensional system):

(fDk-+) 2 -- (Ek__.Fk) 2 "bCkVk,

H 1 ' 1 g-2 Fk2=_~ ~k ~-2, Vk._o~. k 8

(4)

where g =(q2fq) is the correlation length of magnetic shorl-range order.

Introducing the spin-densities correlator for each fluctuation Z~.(t,{ei}) we can define the average

Czechoslovak Journal of Physics, Vol. 46 (1996), Suppl. $4 ] 839

susceptibility x(t) with respect to all {e~} configurations:

x ~ ( t ) = '~# �9 ( X ~ ' (t, {ei})) (4)

In the simplest RPA approximation with respect to U for the Gaussian random field {el}, the transverse two-particles Green's function can be described as a set of the "ladder-type" diagrams. In the framework of our approximation, the most essential influence of the fluctuations is the rcnormalization of the self- energy part of the one particle Green's function, whereas the interaction in the transverse channel is unrenonnalized. After summing all the ladder-type diagrams with averaged one-particle Green's functions (2) we obtain Z~. (s (s is the frequency

of the external field). Let us consider only the poles of X~.(s to determine the spectrum of the

collective exitations. In the long-wave-length and low-frequency limit (fVA<<I and 8[Ql<<tu 'W<<l , where ~5=1 q-QI, W is the band width) at the lowest order with respect to the disorder (a/~ <<1) we can obtain the analytical expression for the spectrum ff~(5) for the one-dimentional system. We note that f2(5) has a very different behavoir for ~5<5r and 5>5c, where 5r is some characteristic quasi-momentum (in the weak-coupling limit (~ 8r 2= 1/2).

For 8>~5c, with an accuracy of order of (a/g.)(AIW)2, we find l2=f2R~(5) with

~Re - - " - a ( 8 2- 5r I/2 , if (5- 5r162 (5) W

[ '2Re-aS[I-(2gS) "21 if eS>>l (6) W

Hence, the slowly damped spin-wave mode exists for the situation when 5>8r and when 8~5r the magnetic oscillation are strongly relaxed.

For 5<5r t'2(5) is purely imaginary ffi=if2im(5) with

W a(SJ-52) In, (7)

and the magnetic oscillations become fully diffusive. We can determine the correlation length ~ (T) in

the one-dimentional case using s J(T)-(A2/W)In0V/A). Therefore, for ToO, the parameters g (T)ooo, 8r and we recover all the results of the mean-field theory.

3. Refe rences [1]. V.Korenman, J.Murray and R.Prangr Phys. Rcv. B 16 (1977) 4032. [2] V.Men'shov and V.Tugushcv, JETP 102 (1992) 1637.

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