Progress Report 1995-1996

DOE Grant DE-FG03-87ER45324

D. P. Belanger

Physics Department,

University of California Santa Cruz,

Santa Cruz, CA 95064.

During the past year we have finished a variety of projects and started new pro-

jects with a major focus on randomness and frustration in magnetic systems. A

major achievement has been to do critical behavior measurements on a random-field

system Feo.9lZno.o&’2. Some time ago (D. P. Belanger, A. R. King, V. Jaccarino

and R. M. Nicklow, Phys. Rev. Lett. 59, 930 (1987)) we conducted critical behavior

measurements in a more dilute system Feo.&no,54F2 with the hopes of determining

the critical behavior. The peculiar line shapes encountered in these neutron scat-

tering experiments and the severe extinction prevented us -from making significant

progress on the critical behavior, though we did learn some interesting things about

the behavior. To combat the extinction problem, we next used a thin epitaxial film

of Fe0.522n0.48F2 in a work that will appear soon in Phys. Rev. B. We were able

to show that this film was of exceptional quality capable of accurate critical behavior

1

-

DISCLAIMER

Portions of this document may be illegible in electronic image products. Images are produced from the best available original document.

measurements of the square of the staggered magnetization ms2 = mo21t12P, i.e. the

square of the order parameter in zero field. The goal was to measure this critical be-

havior with H > 0, since theorists are making the remarkable prediction that, whereas

p = 1/3 for the H = 0 transition, the exponent in the random-field case for H > 0

is very small, ,L? < 0.05. This means that the staggered magnetization should drop

almost vertically at T = Tc(H) . Such was not the case, however, as we observed a

curvature in ms2 that, if taken at face value, implied ,L? > l /2 , an implausible result.

We were able to show that this and the other scattering results implied that the anti-

ferromagnetic system breaks into two long-range interpenetrating domain structures

long before the transition is reached upon heating. This occurs because there are so

many vacancies that the cost in domain wall energy is insignificant. This led us to

consider doing the neutron scattering measurements on a much higher magnetic con-

centration sample Feo.91Zno.09F2 with the hope that there will be insufficient magnetic

vacancies to allow domain walls to form. My student, Zoran SlaniE, did birefringence

measurements on this sample and a graph of the results are shown in Fig. 1. The

results of this study, and a companion one where he studied the specific heat using

a pulsed heat technique, show that the crystal is a very high quality one and that

the critical behavior of the specific heat is quite similar to that of lower concentration

crystals. We have just finished the first round of neutron scattering experiments on

this crystal and have found that the scattering line shapes are dramatically different

from the lower magnetic concentration ones. Two transverse scans just below Tc(H)

and two just above at high resolution are shown in Fig. 2. We no longer observe

the system breaking into domains below T,(H). The line shape for T < Tc(H) con-

sists of a nearly Lorentzian component plus a Gaussian Bragg peak. There is no sign

of the peculiar resolution-limited squared-Lorentzian line shape seen in the samples

that did break into domains below Tc(H). The Bragg peak does not decrease very

much until T,(H), where it vanishes very abruptly, implying that ,f? is indeed small

as predicted by theory. Above the transition the system does form static clusters and

2

-

2.5~10~

2x105

2 1 . 5 ~ 1 0 ~ \ G Q

I'\ - 105

% l o 4

0

1 1 1 1 I I I I I I I I I l l 1 I I I I

T -

1 H=7T 4 H = 5 T .

I I I I I I I I I I I I I I I I I I I I I I I I

69.5 70 70.5 71 71.5 72

T(K)

Figure 1: d ( A n ) / d T vs. T for Feo.oslZPzo.ogF2 with applied fields H = 0, 3, 5, and 7 T. This gives

i the specific heat critical behavior including the hysteresis. The sharper curves are for ZFC and the

rounded curves are for FC. the rounding is from the slow critical dynamics and is similar to previous

results at low temperature. However, the scattering behavior is quite different at this concentration.

3

I 1 I I I l l

69.19 K

69.37 K

0 68.92 K

X 68.86 K

-0.04 -0.02 0 0.02 0.04 g (r.1.u)

Figure 2: Four line shapes for Feo.oglZno.ogF2. Two are just above and two are just below T,(H) =

69.061- The resolution limited Bragg peak disappears abruptly at the transition and the line shape

above has a squared-Lorentzian component that is missing below T,(H). The abrupt disappearance

of the Bragg intensity is in accord with theory and has not previously been observed. The Lorentzian

line shapes for T < T , ( H ) indicate that at this high magnetic concentration the antiferromagnetic

long-range order is completely stable.

4

0.05

0.04

0.03

0.02

0.01

0

E !E

f G

4

m

m m m

m

m u H = O T

69 70 71 72 73 74

T (K)

Figure 3: The inverse correlation length for antiferromagnetic fluctuations, K , vs. T for

Feo,oglZno,ogFz with applied fields H = 0 and 7 T. The shape has changed with the application

of the field, indicating the new RFIM critical behavior. The ZFC and FC procedures give almost

identical values for n, indicating nearly equilibrium critical behavior. This sample provides the oppor-

tunity to measure equilibrium scattering critical behavior below T, (H) , which has not been possible

with the lower concentration samples previously studied.

5

this is reflected in the line shape, which now is fairly well described by a Lorentzian

plus a squared-Lorentzian term. A most important result is that the Lorentzian part

of the line shape below T,-(H) is observed independently of whether the sample is FC

or ZFC as demonstrated in Fig. 3. This indicates that the behavior is reflecting the

equilibrium critical behavior, which has not been observed previously in the scattering

measurements. The importance of these results is that we can now obtain the RFIM

critical behavior and compare it with theory for the first time.

Experimental collaborations are ongoing with the Marinelli group from Rome. We

extended earlier measurement of the dynamics near phase transitions to a Heisenberg

system RbMnF3. A copy of the manuscript, will appear soon in Phys. Rev. B. This,

combined with a similar study of an Ising system FeF2 has given us the background

to extend the studies to dilute systems. We are currently doing measurements on the

dilute Ising system Feo.69Zno.31F2. The measurements involve the groups in Rome

and at UCSC using specific heat, thermal diffusivity, and thermal conductivity.

We are collaborating with Montenegro from Recife, Brazil, on the behavior of an-

tiferromagnets near to the percolation threshold. We have just concluded neutron

scattering measurements on Mno.35Zno.65F2 to complement magnetization measure-

ments done in Recife. We still have to analyze the scattering data. This system

is interesting because its phase diagram seems to be quite different than a previous

sample we studied, Feo.3lZno.69&, which is much more anisotropic and shows a clear

spin-glass-like phase at large fields.

*

We concluded specific heat measurements at UCSC on the frustrated metallic sys-

tem UNi4B. The antiferromagnetic interactions are frustrated on a nearly triangular

magnetic sublattice. We were able to show that the critical behavior was suggestive of

Heisenberg universality. This work has just been submitted for publication.

6

1 Recent Publications and Manuscripts in Preparation

Z. SlaniE, D. P. Belanger, J. Wang and D. R. Taylor, Specific-heat critical behavior of

the structural random-field system Dy(As,%-,)04, Phys. Rev. B 53, 97-101, (1996).

D. P. Belanger, J. Wang, Z. SlaniE S-J. Han, R. M. Nicklow, M. Lui, C. A. Ramos,

and D. Lederman, Magnetic order in the random field Ising film Fe0.52Zn0.48F2, to

be published in Phys. Rev. B, 1996.

D. P. Belanger, Experiments on the random field Ising model, invited review in “Spin

Glasses and Random Fields” edited by A. P. Young, to be published in World Sci-

entific.

M. Marinelli, F. Mercuri, and D. P. Belanger, Specific heat, thermal diflusivity, and

thermal conductivity of RbMnF3 at the Nee1 temperature, to be published, Phys. Rev.

B, 1996.

D. P. Belanger, W. Kleemann and F. C. Montenegro, Comment on “X-Ray and Neut-

ron Scattering, Magnetization and Heat Capacity Study of the 30 Random Field Ising

Model”, to be published in Phys. Rev, Lett., 1996.

S. A. M. Mentink, H. Amitsuka, A. de Visser, Z. SlaniE, D. P. Belanger, J. J. Nueueier,

J. D. Thompson, A. A. Menovsky, J. A. Mydosh and T. E. Mason, Thermodynamic

study of the magnetic phase transition in UNi4B, submitted for publication, 1996. -

Z. SlaniE, D. P. Belanger and J. A. Flernandez-Baca, The critical behavior of the d = 3

random-field Ising model: neutron scattering in Feo.glZno.og F2, in preparation to be

submitted.

7

2 Students

We are now supporting one student on the DOE grant, Zoran SlaniE. Be is involved

in all aspects of the neutron scattering, specific heat and optical experiments done at

UCSC and at the reactors. I expect him to finish an excellent research thesis by the

end of 1998. His progress has been excelient so far and he has been a coauthor of

several of our publication manuscripts.

DISCLAIMER

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsi- bility for the accuracjr, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Refer- ence herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recom- mendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

8