INELASTIC NEUTRON SCATTERING FROM MnF2 IN THE CRITICAL REGION

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INELASTIC NEUTRON SCATTERING FROM MnF2 IN THE CRITICAL REGION

M. Schulhof, R. Nathans, P. Heller, A. Linz

To cite this version:

M. Schulhof, R. Nathans, P. Heller, A. Linz. INELASTIC NEUTRON SCATTERING FROM MnF2 IN THE CRITICAL REGION. Journal de Physique Colloques, 1971, 32 (C1), pp.C1-521-C1-522.

�10.1051/jphyscol:19711174�. �jpa-00213996�

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JOURNAL D E PHYSIQUE Colloque C 1, supplément au na 2-3, Tome 32, Février-Mars 1971, page C l - 521

INELASTIC NEUTRON SCATTERING FROM MnF² IN THE CRITICAL REGION

M. P. SCHULHOF (*) and R. NATHANS (*) Brookhaven National Laboratory, Upton, New York 11973 and State University of New York, Stony Brook, New York 11790 P. HELLER (**), Brandeis University, Waltham, Massachusetts 02154

A. LINZ (***)

Center for Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

Résumé. — Les mesures de la diffusion des neutrons ont donné en détail la forme de la fonction de diffusion pour les fluctuations des spins transverses dans la région critique du composé antiferromagnétique uniaxial MnFj. La sus- ceptibilité statique et les temps de la relaxation sont présentés pour les températures au-dessus et au-dessous de la tran- sition de phase. Au-dessous de TN l'intervalle d'énergie varie avec la température comme l'aimantation dans la région critique.

Abstract. — Detailed neutron scattering measurements have yielded the behavior of the scattering function for transverse spin fluctuations in the critical region of the uniaxial antiferromagnet MnF2. The static wavevector dependent sus- ceptibility and relaxation rates are presented for temperatures above and below the phase transition. Below TN the spin- wave energy gap is found to vary with temperature like the magnetization in the critical region.

We have made a complete measurement of the magnetic scattering of neutrons in the critical region of the uniaxial antiferromagnet MnF². The transverse and longitudinal static susceptibilities and the corresponding correlation lengths have been measured in a quasielastic experiment [1]. In the present measurement of the inelastic scattering, we have obtained values for the transverse and longitudinal relaxation rates FL{q, T) and F^{q, T) over a 16 °K region cente- red on T^N = 67.46 °K and for wavevectors q from q = 0 to q ^ 0.26 A- 1. The behavior of the longitudinal spin correlations has already been reported [2].

In this paper, we discuss the nature of the transverse spin fluctuations SJjj, co) = S^x\q, co) = S^yy(q, co) throughout the critical region.

The cross section for the magnetic scattering of unpolarized neutrons is given by [3]

-i!^ =

^N

(4)

²

^|i,(x)|>x

dQ dco W²/ Kj ' '

x ^ ^ - i g S ^ o ) , (1)

where co and K = Kx — K{ are the energy and momen- tum loss of the neutron, and q = K — 2 nx, with 2 7tt a magnetic reciprocal lattice vector [4]. The static cross section is taken to be of the Ornstein-Zernike form while the frequency dependence of SL{q, co) is assumed to consist of the sum of two Lorentzians displaced symmetrically about co = 0 by an amount co⁰(q, T).

The cross section for the (001) magnetic reflection thus takes the form

(*) Work performed under the auspices of the U. S. Atomic Energy Commission.

(**) Work supported by the U. S. Air Force Office of Scien- tific Research, Grant No. AF 68-1480.

(***) Work supported by Advanced Research Projects Agency Contract No. SD-90.

- ^ L =^JB(o),T)^-4^22L^-^x

dQdco K{ Kl+q2 2

x \^F± +^Fx ]¹ (2)

irl + (a) - co0)2 rl + (co + co0)2i ' where B(co, T) = hco\l - e x p ( - hco/kp T)]"1. The cross section is folded with an analytic form for the instrumental resolution [5] and compared with the experimental data. In this way we determine A00l(T),

KL(X), r^x(q, T) and co⁰(q, T) by the method of least squares. All error limits quoted below for these quan- tities correspond to one standard deviation (67 % confidence level).

Using the fluctuation-dissipation theorem relative values of the static wavelength dependent susceptibility may be obtained from

Kl(T) + q2

We plot the results of the staggered susceptibility X±(<7> 7*) for c/ = 0 in figure 1. The transverse suscep-

1 I T 1 I —1 I I 1

5~ RELATIVE SUSCEPTIBILITY TRANSVERSE

<2 FLUCTUATIONS

§ 4~ X(q-O) |

1 3 - _

^s

**, — * ^ A**

I 2" V

V

I - 5- * \ _

pi I I I I ,_l I I _l I 58 60 62 64 66 ' 6 8 70 72 74 76

TEMPERATURE,°K

FIG. 1. •— Temperature dependence of the transverse staggered susceptibility above and below 7N. The critical temperature

7N = 67.46 °K.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19711174

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C 1

-

522 M. P. SCHULHOF AND R. NATHANS, P. HELLER, A. LINZ tibility is seen to remain finite through the critical

point because of the uniaxial anisotropy. The pro- nounced cusp in the vicinity of the transition was anticipated by Fisher [6] and is a consequencelof the longitudinal fluctuations.

The transverse relaxation rates I',(q, 7') are presented in figure 2. The presence of anisotropy increases

TRANSVERSE ENERGY WIDTH ( q . T )

1

TEMPERATURE. K'

FIG. 2. - Relaxation rates of the transverse spin fluctuations as a function of temperature and wavevector in the critical region. The q values are referred to the (100) direction r41.

The rates are in millielectron volts where 1 mev correspo;lds to 0.242 x ¹⁰¹²Hz.

the q = 0 relaxation rates above the corresponding longitudinal values. Thus at TN we have

in contrast with TI, (q = 0, T ) which goes to zero at TN [2]. Above TN and for large q these data are quite similar to the results for the longitudinal relaxation rates. This is quite reasonable since well into the para- magnetic regime the anisotropy plays too small a role to differentiate between separate components of the fluctuations. For g = 0 the rates approach zero asymptotically with decreasing temperature below TN. Again this result seems quite reasonable since well into the spin-wave region we observe sharp excitations.

Below TN there is an energy gap in the q = 0 frequency spectrum, while above TN we observe oo(q = 0, T ) = 0 for all temperatures. The tempera-

[I] SCHULHOF (M. P.), HELLER (P.). NATHANS (R.) and LINZ (A.), Phys. Rev., 1970, 31, 2304.

[2] SCHULHOF M. P.), HELLER (P.), NATHANS (R.) and LINZ t.4.1, Phys. Rev. Letters, 1970, 24, 1184.

[3] MARSHALL (W.) and LOWDE (R. D.), Rep. Progr.

Phys., 1968, 21, 705.

[4] We refer all wavev&tors to the a direction. Thus

S P I N W A V E E N E R G Y G A P

4

I7Ic. 3. -Temperature dependence of the spin-wave energy gap (q = 0) in the critical region below TN.

t u e dependence of the spin-wave gap (T < TN) is presented in figure 3. The solid line is a least squares fit to the data and has slope 0.37

+

^.02.If we divide each point by the gap at 4.2 OK these data are expressi- ble by the relation

T - T .37 + .02 Gap (') = (1.20 f .06) ^-^N^-

Gap (4.2)

(

^T

)

^'⁽⁴⁾

where we measure Gap (4.2) = 1.1 13 _+ .005 meV.

This should be compared with the behavior of the sublattice magnetization in the critical region [7]

as measured by NMR [7]. At large q values, the cross section fits two peaks to the data both above and below TN. It is envisioned that within each longitudinal cluster of correlated spins it is possible to pro- pagate spin-wave-like excitations. These should be observable when the neutron q is larger than K,,,

and this was the case.

In conclusion, we have made a complete study of the transverse spin fluctuations in the critical region of MnF2. From the data, we have obtained the wavevector and temperature dependence of the static and dynamic correlations both above and below the phase transition.

It is a pleasure to thank Drs. G. Shirane, P. Hohen- berg, R. Ferrell, and M. Blume for many enlighte- ning discussions during the course of this work.

with a = 4.87

a

^and^c⁼^3.31A.

151 COOPER (M. J.) and NATHANS (R.), Acta Crysta., 1967, 23, 357.

[6] FISHER (M. E.), private communication.

[7] HELLER (P.), Phys. Rev., 1966, 146, 403.