CRITICAL BEHAVIOUR OF A TWO-DIMENSIONAL ANTIFERROMAGNET : NUCLEAR MAGNETIC RESONANCE MEASUREMENTS

HAL Id: jpa-00214346

https://hal.archives-ouvertes.fr/jpa-00214346

Submitted on 1 Jan 1971

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.

CRITICAL BEHAVIOUR OF A TWO-DIMENSIONAL ANTIFERROMAGNET : NUCLEAR MAGNETIC

RESONANCE MEASUREMENTS

C. Bucci, G. Guidi

To cite this version:

C. Bucci, G. Guidi. CRITICAL BEHAVIOUR OF A TWO-DIMENSIONAL ANTIFERROMAG-

NET : NUCLEAR MAGNETIC RESONANCE MEASUREMENTS. Journal de Physique Colloques,

1971, 32 (C1), pp.C1-887-C1-889. �10.1051/jphyscol:19711314�. �jpa-00214346�

JOURNAL DE PHYSIQUE

Colloque C I, supple'ment au no 2-3, Tome 32, Fe'vrier-Mars 1971, page C 1 - 887

CRITICAL BEHAVIOUR OF A TWO-DIMENSIONAL ANTIFERROMAGNET : NUCLEAR MAGNETIC RESONANCE MEASUREMENTS

C. BUCCI and G . GUIDI

Istituto di Fisica dell'universith, Parma, Italy and Gruppo Nazionale di Struttura della Materia

RksumC. - La

R. M.

N.

du

F 1 9

dans le K2CoF4 poss&.de deux resonances, I'une associk aux

^{F l y}

qui ont un seul cobalt parmi les plus proches voisins

( F 1 )

et I'autre associke

i

ceux qui en ont deux

( F 1 l ) .

Nous avons mesure le deplacement et la largeur des raies

a

des differentes tempkratures entre 80

O K

et

300 O K .

Nous avons obtenu, pour la temperature critique, la valeur

Te =

107,

44 O K .

La largeur de la raie

F1

lorsque

T

+ T: est repre- sentke par la loi de puissance

A v a ( T - T c ) l . 5 2 h . 0 3 .

L'exposant obtenu est en accord avec la valeur calculCe pour une structure bid~mensionnelle de Ising.

Abstract.

-

Nuclear Magnetic Resonance of

F t g

in

K 2 C o F 4

exhibits two resonances one corresponding to

F

ions with a single Co ion neighbour

( F 1 )

and one corresponding to

F

ion with two neighbouring Co ions. Line-shift and line- widths of both lines have been measured at various temperatures and crystal orientations between 80

^{O K}

and

300 O K .

A

critical temperature has been found at

Tc =

107,44

^{O K .}

The

F 1

linewidth divergence when approaching

Tc

from above is described by the power law

Avcc(T- T s ) 1 . 5 2 + . 0 3 .

The exponent agrees with the calculated value for a two-dimensional Ising antiferromagnet.

1. Introduction.

-

A number of recent experiments [I-2-31 have established the two-dimensional or near two-dimensional nature of the magnetic structure of several compounds isomorphous with K2NiF4. When the magnetic anisotropy is very small one expects a two dimensional Heisenberg system. Breed [I] for K2MnF4 and RbMnF, and Birgeneau et al. [3] for K,NiF4 have demonstrated the validity of such a model

:

a small amount of anisotropy can induce the long range order at finite temperature.

Our interest here is focused on K2CoF4 which is, in turn, a highly anisotropic case. The two dimensional Ising model should therefore apply to such crystals and exact theoretical calculations are available also in the critical region [4].

Nuclear Magnetic Resonance measurements on fluorine nuclei yield a rather precise information regarding the magnetic behaviour of the crystals, because of the large indirect hyperfine interaction between F19 nuclei and the electronic spins of the neighbouring magnetic ions. The critical fluctuation of the magnetic system contributes drastically to the F19 n. m. r. linewidth

:

an example is described by P. Heller [5] for the 3-dimensional antiferromagnet MnF,.

2. Experimental Results.

-

For the nuclear magne- tic resonance measurements we have built a modified Robinson single coil spectrometer which operates at high radiofrequency levels (H, - I Oe). Such levels are imperative when the typical relaxation times of the spin system are very short (say -- 1 ps), as is the case for our crystals, particularly in the paramagnetic state. The single coil method is preferable compared to the cross-coils method sincc it allows a simpler and more reliable temperature control of the sample.

The measurements were performed in a static magnetic field, Ho, of about 3 700 Oe.

The room temperature (R. T.) data reveal that

:

1) Two fluorine resonances were present at all angles

(8)

between Ho and the c-axis of the samples

:

one originates from the axial F(F') and the other from the planar F(FII). Both F1 and F" exhibit a paramagnetic shift, with respect to the fluorine reso- nance in diamagnetic compounds (FO), whose depen- dence on

6,

is shown in figure 1.

I I

1 0 * o 3 0 4 0 5 0 0 0 7 0 S O s o

A N G L E B E T W E E N If A N D C - A X I S .

FIG. 1. -

Lineshift anisotropy

^for

axial

(F1) and planar (F")

fluorine

(@) and linewidth

anisotropy for

axial

fluorine,

Fr,

(A).

Ho

is

3 750

Oe.

2) All lineshapes contain a Lorentzian part and a Gaussian part. In some conditions, line intensity is not sufficient for a quantitative analysis.

3) F1 linewidth shows a very large anisotropy as it changes from - 3.5 Oe (Ho I c) to - 20 Oe (Ho/c).

with Ho

⁼

3 800 Oe.

4) When Ho is rotated away from the c axis, F" line splits in two. The splitting reaches its maximum value when Ho is directed along the axis a or

b.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711314

C 1

-

888 C . BUCCI AND G . GUIDI

At temperatures below RT the detection of F' with

Ha parallel to the c-axis (~11) is quite difficult because of the large width of the line. When fluctuations become important, they can be detected also by mea- suring F: line-width Av. Figure 2 shows the result of

(T-Tc)

i n "K.

FIG. 2.

-

Temperature dependence of FI, linewidth measured at 6 = 900 (F:). Curve (a) are the uncorrected points, curve (b) are the point corrected for a Gaussian part of the line, which was found to be temperature indepcndent with a width of 3.26 Oe.

such measurements. The temperature interval in which Av increases is surprisingly large

;

the measu- rements of Av closer to Tc become prohibitive because of the overlap with the F" line. After correction for the Gaussian part of the lineshape, Av is found to follow a power law as a function of T - T, with the exponent 1.52 + ^.03.

Below the NCel point the resonance frequency of F1 is shifted to very high frequency because of the large hyperfine field on these nuclei

[2]

and it was not measured in this experiment. The critical tempe- rature T, is determined by following the behaviour of F': line, whose width and shift do not exhibit a critical behaviour through T,, but the intensity drops by a factor five within 0.2 OK.

F" lines, both with H a /I and Ha I to the c-axis, are observed also at T < Tc since F" ions are midway bet- ween two cobalt ions and the effects of the two sublat- tice cancel at this site. The intensity of such lines for T < T, is much smaller than for T > Tc.

In contrast with F:, F~I' line shows a critical beha- viour below and above Tc not only in its width but also in its shift. This is shown in figure 3

:

the large uncertainty in the data is caused by the weakness of the line (whose intensity is about 1/30 of the R. T.

intensity) in this temperature range. Such an effect, which involves also ~ f : lines, can be attributed to an

FIG. 3. - Temperature dcpendence of FI1 linewidth (7) and lineshift ( 0 ) below and above Tc.

increase'of the relaxation times of the nuclear spin system, in analogy to what found Maarschall et al. [6]

in K2NiF4.

3. Discussion. - The first result one would like to interpret is the temperature dependence of the F' line- width.

Within the frame of the slowing down theory, the expression for the linewidth as a function of T, constant multiplicative factors being neglected,

where zII(K) and zl(K) are, respectively, the wavelength dependent parallel and perpendicular susceptibility.

Instead of the molecular field result for I@), we start, according to Kadanoff

[7],

with the following two dimensional correlation function

X being the inverse range of correlation. Fourier transform of (2) yields for x(K), q

⁼

K - KO

:

Since x,(q) is not divergent at Tc because of the anisotropy, one obtains from (1) and (3)

:

where

^{E =}

( T

-

Tc)/Tc

;

for two-dimensional Ising

model

v = 1, q = f

and Av,

C C E - ~ / ~ .

The agreement

between the measured F1-linewidth-T-dependence and

eq. (4) strongly suggests that K2CoF4 behaves like

a two dimensional Ising antiferromagnet.

CRITICAL BEHAVIOUR OF A TWO-DIMENSIONAL ANTIFERROMAGNET C 1

-

889

for the F; shift

around T,, the asymmetric does, since the effect of t h e two opposite magnetic increase shown in figure

3

could be explained in the sublattice cancel each other a t this lattice site.

following way : when the crystal orders antiferroma-

gnetically it distorts

[8]

with a consequent change

in Acknowledgment.

-

The

Authors a r e very grateful the indirect-hyperfine interaction constant A;/ for

F"

t o D r

L.

Reatto for very helpful suggestions a n d sites a n d therefore in the

F"

shift. Below

TN

the shift discussion a n d D r

D.-J.

Breed for having provided decreases approximately a s the parallel susceptibility some of his samples.

References

[l]

Mostly susceptibility measurements : BREED (D. J.), (R. J.), SKALYO (J.) and SHIRANE (G.) (Brookha- Physica, 1967, 37, 35. A more extensive review ven Nat. Lab. Rep. 14150).

of related data is contained in BREED (D. J.). [4] FISHER

(M.B.),

Rept. Progr. Phys., 1967, 30, 615.

Thesis University of Amsterdam. [5] HELLER (P'.), Rept. Progr. Phys., 1967, 30, 731.

[2],E. S. R. and N. M. R. measurements by FOLEN (V. J.), [6] MAARSCBALL (E. P.), BO-ITERMAN (A. C.), YEGA (S.) KRELS (J. J.) and RUBINSTEIN (M.). Solid State and 'MIEDEMA (A. R.), Physica, 1969, 41, 473.

Comm., 1968, 6, 865 and by RUBINSTEIN (M.) and [7] KADANOFF (L. P.), NUOVO Cim., 1966, 44,276.

FOLEN (V.

J.),

Phys. Letters, 1968, 28 A, 2, 108. [8] KADANOFF (L. P.) et a]., Rev. Mod. Phys., 1967, 39, [3] Neutron scattering studies reviewed by BIRGENEAU 395.