DYNAMIC BEHAVIOUR OF THE ALTERNATING LINEAR HEISENBERG ANTIFERROMAGNET

HAL Id: jpa-00217777

https://hal.archives-ouvertes.fr/jpa-00217777

Submitted on 1 Jan 1978

HAL is a multi-disciplinary open access

archive for the deposit and dissemination of

sci-entific research documents, whether they are

pub-lished or not. The documents may come from

teaching and research institutions in France or

abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est

destinée au dépôt et à la diffusion de documents

scientifiques de niveau recherche, publiés ou non,

émanant des établissements d’enseignement et de

recherche français ou étrangers, des laboratoires

publics ou privés.

DYNAMIC BEHAVIOUR OF THE ALTERNATING

LINEAR HEISENBERG ANTIFERROMAGNET

K. Diederix, T. Klaassen, N. Poulis

To cite this version:

JOURNAL DE PHYSIQUE _Colloque C6, supplkment au no 8, Tome 39, aott 1978, page _C6-737

DYNAMIC BEHAVIOUR OF THE ALTERNATING LINEAR HEISENBERG ANTIFERROMAGNET

K.M. Diederix, T.O. Klaassen and N.J. Poulis

k h e r l i n g h Onnes Laboratorium d e r R i j k s u n i v e r s i t e i t , Leiden, The Netherlands

RCsum6

.-

Les temps de relaxation spin-rlseau des protons dans CU(NO~) 2-2&20 sont mesurls en fonction du champ magngtique B plusieurs templratures. Lea rdsultats expgrimentaux montrent que les dspendan- ces en champ des densites spectrales @)U,(' et I( (U,,) des fonctions d1autocorr61ation des chafnes an- tiferromagngtiques alternles dans ce c8rps dif f~8ent complbtement

.

Nous en donnons une explication qua-litative.

Abstract

.-

Proton spin-lattice relaxation times (T1) in CU(NO~)~

.e20

have been measured as a func- tion of the applied magnetic field at different temperatures. The experime~tal results yield the com- pletely different field-dependences of the spectral densities

%)

a'(

and $,(U,) of theauto correlati- on functions of the alternating S = +F chains in this compound? A qualitative explanation is given.

-P

The dominant exchange interaction in Cu(N03X. ween the field direction and ro, and F accounts for 2 : ~ ~ 0 (J/k =

-

2.6 K) couples the copper spins into the small isotropic hyperfine interactions.

antiferromagnetic (AF) spinpairs. These pairs are In figures 1 and 2 the field dependence of

linked into alternating S =

:

Heisenberg AF chains T;' of proton 3 is given as a function of the applied aJ

by a second AF exchange interaction (- =

-

0.70 K) field strength for a fixed field direction at T = k

11-21. The relatively small exchange constants J 4.2 K and T = 1.35 K respectively. and ciJ provide us the possibility of studying the

thermodynamic properties over the whole interesting ----1--1-1---7:- 4 2 C i 4

field range (up to 70 kOe, i.e. h = $ L ) . m5

-

+- ?EL?

-

1

We have carried out proton spin-lattice rela-

1

6:

K

1

xation time (T ) measurements on CU(NO~)~.~:H~O,

1 I

using standard spin-echo techniques at frequencies p h

between 20 MHz end 300 MHz. Such measuremnts yield

"1

information on the electron spin fluctuations. The-

-

se spinfluctuations generate fluctuating fields at

the proton sites via the copper-proton interaction,

-;[

L

711

m

which in C~(N0~)~.2:~20 is mainly of dipolar charac- ?cl "c, "'h

0 I I

i L

11

I I I

I

ter. The results presented here, have been obtained 0 H 10 20 30 40 50 60 h o e

from T, measurements on a single protonline (proton

see :eference/l/) separated from all other

reso-

Fig. 1 : Field dependence of the relaxation rate T;' of proton 3 in CU(NO~)~ .2:H20 at 4.2 K. Drawn line

nance lines for many directions of the external serves as aid to the eye only. Dashed line indica-

field. This proton is situated near to one copper tes the contribution of n ) 1

ion(2.5 A). The dominant contribution to the pro-

ton relaxation rate T-' is therefore due to this The individual contributions @m'( ) and $+(m ) to

1 o n o n

nearest neighbour copper spin and is given by : T;' have been separated by analysing the dependence

T;' = :y :y

B

sin2eo cos2eo rg6+z(~n) of T;' on the field direction. This is possible

thanks to the completely different angular depen-

I 9

{iT(l-3 C O S ~ ~ ~ + F ) ~ +

8

sin'^^}

rg6$:(wn)7 (I) dencies of the geometrical factors of

4;

and $"(l).

l+='

where CL(^ ) = <GS~(~)GS~(O)>~ +'%ltdt, ,it-, The dashed lines in both figures indicate the con- n

100 tributions of $'(a n ) to T;'. The difference of the

drawn curve and the dashed one consequently yields 6sa(t) = sci(t) -<S"> represents the spectral densi-

ty of the electronic auto correlationfunctions at the relative behaviour of $:(mn) at 4.2 K and 1.35K. the proton resonance frequency m-.re is the copper- The different field dependencies of $: and @: at

LL U

proton distance, while e0 indicates the angle bet- the proton resonance frequency wn is striking. The

Fig. 2 : Field dependence of the relaxation rate T1 of proton 3 at 1.35 K. Drawn line serves as aid to the eye only. Dashed line indicates the contri- bution of @:(mn) to T I 1 ,

spectral density +

'

(

a

) is of measurable magnitude o n

over the whole field range, while @;(wn) is only considerable below about 10kOe and in-between 30 kOe and 50 kOe at both temperatures. T;' of the amalgamated proton line at 5.0 kOe is measured to

-c/T

be proportional to e

,

with c = 4.81 K. At first approximation the alternating AF chains can be considered to be an assembly of non interacting AF spinpairs. The energy level scheme

of an AF spinpair consists of a singlet groundstate and an excited triplet. The latter is split up by applying an external field. Only near zero field and near H = two ener, levels with d

4

= I ap-

gB

proach each other closely (<

H

w _n ) . It can be ar- gued that therefore only near to these fields 4:

will have a considerable intensity at w

.

Interpair interactions (aJ) will broaden these field regions where

4;

contributes to T;'. The intensity of 4:

at an is due to quasi Raman processes (two spinpairs flip-flop). This

402

contribution yields T-& Z c

1 i,j ij n n ; where n. and n are the population of the

i j j

energy levels, while cij indicates the transition probability between these levels. Interpair ()'a in- teractions clearly determine the factors c

ij 'On

-sidering the field and temperature dependencies of n and n it is .seen that these and consequently

i j

+ ' (

W .) are only slightly field dependence at 4.2 K o n

and 1.35 K. A similar discussion can be given on the basis of the energy level scheme of the alter- nating AF chain resulting in the same qualitative conclusions. In both figures hcl, hlP and hc2 in- dicate respectively the fields at which the magne- tization at T = o of the alternating chains in CU(NO~)~.~:H~O starts to rise, reaches half its saturation value and is saturated ; _{hc3 .: l*.}

It is possible tc give a detailed explanation of the behaviour of @+(U ) in the field region 25

o n

kOe

-

55 kOe. In the field region, at which the lo- west two energy levels 11,-l> and (0,0> of the spin- pair cross, the AF pairs can be described by effec- tive spins S' =

:

in an effective field HE

(HE

= o at the level crossing)/l/. This description is only applicable when the population of the higher two energy levels is negligible ( T < 5 K). Under these conditions the Hamiltonian describing the effective spins including the Id interpair interactions (aJ) reads :

which is the Hamiltonian of a regular chain of ef- fective spins S' = $ with anisotropic intrachain interactions (J X = 3: = 23;). In the high tempera-

E

ture limit (kT>>J ) which may be applicable for E

T P 4.2 K, it can be shown that, when the Zeeman and

exchange terms in the Hamiltonian commute (a condi- tion satisfied for (2)), @:(wn)

+,(an)

= @,(o) is field independent and @:(wn) = +,(W,) .$I; thus re- flects the spectral density of the auto' correlation function

4

at the electronic frequency w of the effective spins. When we now consider our measure- ments at 4.2 K again one can see that @ (U ) starts

o e to diverge for we+o, as is expected for regular Heisenberg AF chains/3/. The experiments show that

the divergence is however cut off. The anisotropy in JE

(3

= 25" ) as well as interchain interactions

E

may be responsible for this cut off. $ (U ) vani- o e shes just above the saturation field

g8%-

= 3 for

4

-

2~: ) in accordance with predic- tions for isotropic chains. Although the effective spin model shows defficiencies and secondly does not satisfy the high temperature limit tely, we find that the above given discussion pro- vides an explanation of the experimental results.

This investigation is part of the research program of the "Stichting voor Fundamenteel Onder-

zoek der Materie (FOH)" which is financially sup- ported by the "Nederlandse Organisatie voor Zuiver Wetenschappeli jk Onderzoek (ZWO)

".

Ref erences

/ l / Diederix,K.M., Groen,J.P., Henkens,L.S.J.M., Klaa~en~T.0. and Poulis,N.J., Physics

-

93B

(1978) 99

/2/ Diederix,K.M., Groen,J.P., Klaassen.T.0. and Poulis,N.J., submitted to Phys. Rev. B /3/ Carboni,F. and Richards,P.M., Phys. Rev.

177