PARAMAGNETIC TO ANTIFERROMAGNETIC PHASE BOUNDARY OF CoF2 FROM ULTRASONIC MEASUREMENTS

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PARAMAGNETIC TO ANTIFERROMAGNETIC PHASE BOUNDARY OF CoF2 FROM ULTRASONIC

MEASUREMENTS

Y. Shapira

To cite this version:

Y. Shapira. PARAMAGNETIC TO ANTIFERROMAGNETIC PHASE BOUNDARY OF CoF2

FROM ULTRASONIC MEASUREMENTS. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-

410-C1-411. �10.1051/jphyscol:19711144�. �jpa-00213963�

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PHENOMENES MAGNETOELASTIQUES.

PARAMAGNETIC TO ANTIFERROMAGNETIC PHASE BOUNDARY OF CoF

²

FROM ULTRASONIC MEASUREMENTS

Y. SHAPIRA

Francis Bitter National Magnet Laboratory (*)

Massachusetts Institute of Technology Cambridge, Massachusetts 02139

Resume. — On a mesure l'attenuation ultrasonique dans un monocristal de C0F2 avec 0,20 % Fe. La temperature de transition entre la phase paramagnetique et la phase antiferromagnetique etait determine dans des champs magnetiques, avec une intensite maximale de 140 kOe, appliques suivant Faxe tetragonal. Cette temperature T est bien decrite par la formule T

N

— T = AH

2

; 7V = 39,0 ± 0,3 °K etant la temperature de Neel et A = (1,76 ± 0,1) x 10-io °K.Oe"

2

. Abstract. — Ultrasonic attenuation measurements were performed on a C0F2 single crystal containing 0.20 % Fe.

The boundary between the paramagnetic and antiferromagnetic phases was determined in magnetic fields up to 140 kOe directed along the tetragonal axis. This phase boundary is well described by 7N — T = AH

2

, where TV = 39.0 ± 0.3 °K is the Neel temperature and A = (1.76 ± 0.1) x lO"

1

" °K.Oe-

2

.

Résumé. — On a mesuré l'atténuation ultrasonique dans un monocristal de C0F2 avec 0,20 % Fe. La température de transition entre la phase paramagnétique et la phase antiferromagnétique était déterminé dans des champs magnétiques, avec une intensité maximale de 140 kOe, appliqués suivant Taxe tétragonal. Cette température T est bien décrite par la formule Tn—T=AH

2

; 7V = 39,0 ± 0,3 °K étant la température de Néel et A = (1,76 ± 0,1) x 10-io °K.Oe"

2

. Abstract. — Ultrasonic attenuation measurements were performed on a C0F2 single crystal containing 0.20 % Fe.

The boundary between the paramagnetic and antiferromagnetic phases was determined in magnetic fields up to 140 kOe directed along the tetragonal axis. This phase boundary is well described by 7N — T = AH

2

, where I N = 39.0 ± 0.3 °K is the Neel temperature and A = (1.76 ± 0.1) x lO"

1

" °K.Oe-

2

.

Cobaltous fluoride CoF

2

has a rutile structure with the cations on a body-centered tetragonal lattice. At low temperatures CoF

2

is a simple two-sublattice antiferromagnet in which the sublattice magnetizations point along the c-axis (tetragonal axis). Both the crystallographic structure of CoF

2

and its magnetic order at low temperatures are similar to those of MnF

2

and FeF

2

. In the present work the dependence of the temperature at the paramagnetic-antiferroma- gnetic (P-AF) transition on applied magnetic field was determined from ultrasonic measurements. The techniques employed were similar to those used earlier with MnF

²

[1] and FeF

²

[2].

Ultrasonic attenuation measurements were carried out on a CoF

2

single crystal which contained 0.20 % iron and ~ 0.1 % nickel (by weight), and other impurities with lower concentrations. The measure- ments were performed with the sample mounted on a copper block which was inside an evacuated copper can. The copper can was surrounded by liquid helium.

The temperature T, which was regulated with a heater, was measured with a calibrated platinum resistance thermometer whose magnetoresistance had been deter- mined previously by Neuringer et al. [3]. The accuracy in T was better than 0.3 °K. Magnetic fields up to 140 kOe were produced by Bitter-type solenoids. No corrections were made for the demagnetizing field because it was estimated to be less than ~ 1 % of the applied magnetic field.

Experiments with 10 to 50 MHz longitudinal ultra- sonic waves propagating along the c-axis showed that the P-AF transition at both zero and finite magnetic fields is accompanied by a 2-type peak in the ultrasonic attenuation. For a given frequency the attenuation peak was smaller than that found in either MnF

²

[1]

or FeF

2

[2]. This observation is consistent with the fact that the Neel temperature T

^N

of CoF

²

is less sensitive to pressure than that of MnF

2

[4].

The P-AF transition temperature for a magnetic field H along the c-axis was determined at several fields up to 140 kG. At each field the temperature at the peak of the X anomaly in the attenuation was taken

(*) Supported by the U. S. Air Force Office of Scientific Research.

to be the P-AF transition temperature. The P-AF phase boundary in the H-T plane, obtained from several experimental runs, is shown in figure 1.

3 6 37 38 3 9 TEMPERATURE (K)

FIG. 1. — The dependence of the paramagnetic-antiferroma- necgit transition temperature T on magnetic H applied along

the c-axis.

For a simple uniaxial antiferromagnet, molecular- field theory predicts that near T

^N

the P-AF boundary in the H-T plane has the form

r

^N

- T = AH

²

, (1)

where A is a constant which depends on the direction of H. Figure 2 shows a plot of H

2

versus r

N

— T for the three sets of data shown in figure 1. From figure 2 it appears that Eq. (1) is satisfied in CoF

2

. The best fit of the data to Eq. (1) gives

A = (1.76 + 0.1) x 1 0 -

1 0

°K.Oe~

2

.

The Neel temperature is T

^N

= 39.0 + 0.3 °K. The specific heat data of Catalano and Stout [5] on a purer crystal of CoF

²

gave T

^N

= 37.7-°K. Susceptibility measurements by Astrov et al. [4] gave T

N

= 39.0 °K,

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711144

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PARAMAGNETIC TO ANTIFERROMAGNETIC PHASE BOUNDARY C l - 4 1 1

whereas their results on the coefficient of thermal

20 -

expansion gave TN

=

40.0 OK.

Assuming that the specific heat at constant H, C,,

C O F2

diverges at the P-AF boundary, Skaylo et al. [6]

~ l l c

showed that at temperatures just below TN the P-AF

boundary obeys the relation

15

-

d2T/dH2

=

- (TICH) ( d ~ / d T ) ,

₍₂₎

where

X

is the isothermal susceptibility at H

=

0. To

-

Nc8

evaluate the right side of eq. (2) one needs accurate

,,

^{1 0}

^- ^- ^{data for}

^{C, and}

^X at temperatures very close to TN

-

51

i. e., in the critical region. Using the susceptibility data

N

I

of Prandl and Stout [7], and taking C, to be the

magnetic contribution to the specific heat as deter- mined by Catalano and Stout

[5],

we estimated that d2T/dH2

^g

- 2.7

^X

1 0 - ~ ~ o K . O e - ~ . The best fit of our data for the P-AF boundary to eq. (1) gave d2T/dH2

=

- (3.5 + ^0.2)

^X

10-l0 0K.0eC2.

The longitudinal and shear velocities for sound

I 2 3 4

waves propagating along the c-axis at 770K are

T N - T ( l 0

(6.5 + ^0.1)

^X

105cm.s-l and (2.85

$.

0.1)

^X

105cm.s-l,

respectively. These values are close to those found in

FIG. 2.

-

The dependence of TN-Ton H2 for H along the c-axis.

MnFz and FeF, [2].

References

[ l ]

SHAPIRA

(Y.)

and FONER (S.),

Phys. Rev. B, 1970, 1 , [5]

CATALANO

(E.)

and STOUT (J. W.),

J. Chem. Phys.,

3083. 1955, 23, 1803,

and

ibid. 23, 2013.

12]

^SHAplRA

v.), Pbs.

Letters, ¹⁹⁶⁹⁷ 30 A, 3887 and _[6]

SKALYO

( J .

JT),

COHEN (A. F.),

FRIEDBERG (S. A.)

Phys. Rev., 1970, 2 B , 2725.

and GRICFITHS

(R. B.), Phys. Rev., 1967,164,705.

[3]

NEURINGER (L. J.), PERLMAN (A. J.), RUBIN (L. G.)

and SHAPIRA W.),

to be

published.

^[7]

PRANDL

(W.)

and STOUT

(J.

W.), private communi-

[4]

ASTROV

(D.

N.), NOVIKOVA (S.

I.)

and

ORLOVA (M.

P.), cation.

Soviet Physics JETP, 1960, 10, 851.