NEUTRON SCATTERING STUDY ON THE SPIN-FLOP SYSTEM CsMnBr3.2D2O

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NEUTRON SCATTERING STUDY ON THE

SPIN-FLOP SYSTEM CsMnBr3.2D2O

J. Basten, E. Frikkee, W. de Jonge

To cite this version:

JOURNAL DE PHYSIQUE

Colloque C6, supplément au n° 8, Tome 39, août 1978, page C6-819

NEUTRON SCATTERING STUDY ON THE SPIN-FLOP SYSTEM Cs.MnBr3.2D20

J . A . J . Basten, E. Frikkee and W.J.M. De Jonge

Netherlands Energy Research Foundation (ECN), Westerduinweg Z, 17SS LE Petten (NH) The Netherlands

Department of Physios, Eindhoven University of Technology, Eindhoven, The Netherlands

Résumé.- La variation de l'aimantation alternée avec la température et le champ magnétique dans le système "spin-fiop" CsMnBr3.2D2Û a été étudiée par diffraction neutronique. Le diagramme de phase magnétique a été obtenu. Les valeurs des exposants critiques & || et B_j_ sont respectivement 0.321(6) et 0.326(7).

Abstract.- The dependence of the staggered magnetization on temperature and magnetic field in the

spin-flop system CsMnBr3.2D20 was studied by means of neutron scattering. The magnetic phase diagram

is reported. The critical exponents B|| and B[_are found to be g|| = 0.321(6) and gj_= 0.326(7)

Neutron scattering experiments on weakly a n i -sotropic antiferromagnets exhibiting a spin-flop transition, can provide several tests of the theory of bicritical behaviour, which w a s developed recent-l y / 1 , 2 / . Particurecent-larrecent-ly, the order parameters both in the antiferromagnetic (AF) and the spin-flop (SF) p h a s e , i.e. the components of the staggered m a g n e t i -zation, M ' ' along and M 4/ perpendicular to the easy axis, can b e observed b y neutron scattering. CsMnBr3 2D2O was chosen because of the convenient location of the spin-flop bicritical point (H, -26 k O e , T, = 5.3 K ) , and because o f its orthorombic structure

(space group P c c a ) . Its pseudoonedimensional H e i -senberg properties are an additional interesting feature. Below T 6 . 3 K the AFordering can b e d e s -cribed/3/ by the magnetic spacegroup Pc'c'a' (see figure 1 a ) .

^ i ^S N^ 0 T T 6

O-•Gic— > » 4 — ' 3v i V r v -V 9

9-\ ] ^J l—I—I—I—U,

(a) (b)

Fig. 1 : (a) the array of magnetic moments in CsMnBrs.2D20. (b) T h e a c -plane of the reciprocal lattice. Magnetic and nuclear reflections have b e e n indicated by filled and^open circles, respectively. <(> is the angle between K and the intermediate ( c ) -axis.

The b-axis and the c-axis a r e the easy and interme-diate direction, respectively / 4 / . In this

experi-ment the scattering vector K was confined to the a c -plane. In this plane magnetic and nuclear scat-tering occurs at different reciprocal lattice points (see figure lb) both in the AF-and in the SF-phase.

The experiments were performed on a diffrac-tometer at the HFR-reactor at Petten. The disk-like

crystal of 15x15x4 mm3 was fixed in a

superconduc-ting magnet (field homogeneity 1%0) with H parallel

to the easy (b)-axis. After mounting the crystal no final adjustments could be made. From the required canting angle of the cryomagnetic system (+ sample) out of the vertical position, the mismatch between

->• o

H and the b-axis was estimated as 0.3 ± 0.3 . Near T, the temperature stability was better than 1 mK with a maximum drift of 5 mK over a day.

The variation with H and T in the peak inten-sities" of three magnetic Bragg reflections, viz.

(1 0 3 ) , (1 0 1) and (3 0 1 ) , were recorded in the

AF-phase, where I(t) = C(ic) (Ms't)2» and in the

SF-phase where I ( K ) = C ( K ) (M-Lsin<j>)2. Here<j)is the angle between K and the intermediate (c)-axis (see figure lb). The left hand side of figure 2 shows some results of H-scans near the spin-flop transi-tion at different T. The data have been corrected for non-magnetic contributions. The proportionali-ty factors C ( K ) have been eliminated to achieve that all three curves coincide in the Af-phase. The same set of constants C ( K ) could be used for all tempe-ratures , which indicates that extinction can be ne-glected. The SF-intensities are now found to be pro-portional to the corresponding sin2<J>, showing the

c-axis to be the intermediate axis, indeed. From these curves, ( M " )2 and (M-L)2 can be obtained

se-parately, as shown in the right hand side of

figure 2.

Fig. 2 : (Left) The field dependence of the peak- intensities of three magnetic Bragg reflections for different T ; Triangles ( 1 0 3), squares ( I 0 1) and circles (3 0 1). Only a small fraction of the data in a scan is sh0.m. (Right) The resulting field de- pendences of

(~2:)

and (MA)', obtained from the three curves on the left, are indicated by open and closed circles respectively.

+-

Although the observed rotation of Mst appears to be quite rapid, it is not a first-order spin-flop transiiion. In order to observe this first-order

-+

character, the mismatch J, between H and the b-axis is not allowed to exceed J,

-

0.08' at T = 0, as can be calculated

151

from the anisotropy field (770 Oe) and the exchange field (273 kOe)/4/. For T>Q the situation is even worse as $,(TI = Qc(O).

+

(Tb-T)/Tb. For a mismatch $>>J, the rotation of Mst from an Af-like to a SF-like ordering is correctly described by the molecular-field expression 161 tan(29+2$) - = s i n ( 2 $ ) / ~ o s ( 2 J , ) - ( H / H S F ) ~ ( 1 )

-+

Here 8 is the angle between M and the easy axis st

and HSF is the spin-flop field. The lower insert of figure 3 shows a comparison between the observed and calculated variation of

(MI'

)

'

and

(M&)~

with

st

H. The calculated curves are obtained from the ob-

served M2 _st

.

2+ (MA) (dash-dotted line) and

their theoretical ratio cos29/sin28, where 8(H) is calculated form eq. (1) with J,=0.5O. The agreement is striking. HSF(T) taken as the point of intersection of these curves is shown in figure 3.

Fig. 3 : The magnetic phase diagram of CsMnBr3.2D20. The upper insert shows details near the endpoint of the spin-flop line. The lower insert shows a compa- rison between the observed and calculated (solid lines) behaviour of ('):M; and

(M&)~

with H for an arbitrarily chosen T. The value of HsF(T) is taken as the point of intersection of both curves. (See further the main text).

The location of the second-order

AF-P

boun- dary

T

:

(

H

)

and SF-P boundary

T$(H)

are obtained from best fits of the magnetic intensities to

( ~ ~ 1 ~ ' ~ ) ~ -

B(E)~'~~

'

1

.

Here E = (T/T~-I

I

and

E = (H/Hc-1

I

in temperature and field scans, respec- tively. From these fits with B,

f3

and T or Hc va- riable, we also obtained a statistical average for the critical exponents, yielding f3 = 0.321(6) and

I

I

f3

= 0.326(7). In a spin-flop system with orthorom-

1

bic anisotropy (as we have in the present case) the theoretical predictions are

f3

=B

=0.325. No change

I I

I

in

f3

along both phase boundaries was faund.

References

/ 1 / Kosterlitz,J.M., Nelson,D.R. and Fisher,M.E., Phys. Rev.

B13(1976) 412 and references therein

-

/2/ Domany,E. and Fisher,M.E., Phys. Rev. (1977) 3510 and references

131 Swiiste, C.H.W., De Jonge,W.J.M. and Van Meyel,J.A.G.W., Physica

76

(1974) 21

141

Botterman,A.C., Ph. D. Thesis (Eindhoven, 1976) (unpubli- shed)

/ 5 / Rohrer,H. and Thomas,H., J. Appl. Phys.

40

(1969) 1025