LiHo_(0.167)Y_(0.833)F_4 is a dilute dipolar-coupled Ising magnet with a spin glass transition which can be crossed with temperature T (T_g=0.13 K) or with an effective transverse field Γ(Γ_g=1 K at T=0). The nonlinear susceptibility contains a diverging component which dominates at T=98 mK, but disappears by 25 mK. At the same time, the onset of spin glass behavior in the dissipative linear susceptibility becomes sharper. We conclude that, contrary to theoretical expectations, quantum transitions can be qualitatively different from thermally driven transitions in real spin glasses

Aeppli, G.

Bitko, D.

Rosenbaum, T. F.

Wu, Wenhao

Caltech Authors - Main

English

Quenching of the nonlinear susceptibility at a T=0 spin glass transition

VOLUME 75, NUMBER 8 PHYSICAL REVIEW LETTERS 21 AvovsT 1995
Bitko, Rosenbaum, and Aeppli Reply: In the preceding
Comment [1], Mattsson claims that in two papers [2,3]
we have used "incorrect" methods for determining where
in the field-temperature plane transitions to a glassy
magnetic state occur for L i Hop 167Yp 833F4. Specifically,
he feels that our measuring frequencies are not sufficiently
low enough to determine the equilibrium behavior of
this system. In the real world of finite measuring times
and frequencies, we never can be sure that we have
achieved true equilibrium so, in this sense, Mattsson is
entirely correct, as he would be if he were discussing
experimental work on any phase transition. Of course,
in spite of this fundamental difficulty, we have good
empirical knowledge of phase transitions because there
are certain simple experimental tests of whether we are
looking at properties representative of the equilibrium
state. Mattsson points out one well-known example of
such a test, namely, to check whether the property in
question depends on the measuring frequency f. In our
paper [3], we showed that the nonlinear susceptibility
does depend on f for f ) 10 Hz. However, we also
noted that it depends very weakly on f for f ) 10 Hz.
Thus, to within the limits of our ability to control field and
temperature, our results for the nonlinear susceptibility
represent equilibrium values in the conventional sense
that they are derived from ac values in the f-independent
regime of ~3.
In order to reinforce this point, we show in Fig. 1
data on the f dependence of g3 for a transverse mag-
netic field of 8.62 kOe, which is 1% above the criti-
cal field strength marking the transition to the magnetic
glass at T = 60 mK. Our data, which traverse nearly five
decades of frequency, clearly illustrate the crossover be-
tween high-f (f-dependent) and low- f (f-independent)
behaviors. All of the measurements in [3] were collected
for f ~ 2 Hz, well within the f-independent regime,
which actually expands as the underlying magnetic Auc-
tuation rate increases with transverse field. At the same
time, our linear susceptibility measurements, reported ini-
tially in [2], consistently extended to frequencies well be-
low the measured roll-off frequencies for ~3. Thus the
linear response which we measure is also a reliable in-
dication of the state of the material. The agreement to
within experimental error of the phase boundaries deter-
mined by the linear and nonlinear susceptibilities rein-
forces this conclusion. The ac data [4] which Mattsson
reproduces for a thermally driven glass transition in an
0 9
0
0.7—
o 0,5— T=60mK
H = 8.62 kOe = 1.01 H '
0.167 0.833 4
~ ~
0.3
1O'
I
10'
I
10
f (Hz)
I
10 1O4 10'
D. Bitko and T. F. Rosenbaurn
The James Frank Institute
The University of Chicago
Chicago, Illinois 60637
G. Aeppli
AT&T Bell Laboratories
Murray Hill, New Jersey 07974
Received 22 May 1995
PACS numbers: 75.50.Lk, 05.30.—d, 75.40.Cx
[1] J. Mattsson, preceding Comment, Phys. Rev. Lett. 75,
1678 (1995).
[2] W. Wu et al. , Phys. Rev. Lett. 67, 2076 (1991).
[3] W. Wu, D. Bitko, T. F. Rosenbaum, and G. Aeppli, Phys.
Rev. Lett. 71, 1919 (1993).
[4] K. Gunnarsson et al. , Phys. Rev. B 43, 8199 (1991).
FIG. 1. The nonlinear susceptibihty
~3 vs frequency f at
a transverse field H, 1% above the transition into the spin
glass. Data in [2,3] were taken for f ( 2 Hz, well within the
frequency-independent regime.
unrelated compound Feo qMno s Ti03 are clearly in the f
dependent regime and, therefore, not relevant to a critique
of our papers.
In conclusion, we have followed [2,3] conventional
practice to measure properties of the magnetic glass phase
for Li Hoo167 Yp 833F4. By the ordinary criterion that one
should be measuring physical quantities at frequencies as
far below the crossover to frequency-dependent behavior
as possible, our results are generally reliable and indeed
become more reliable as the novel T = 0 quantum glass
regime is approached. Mattsson presents no new data on
Li Ho Y1 F4 to contradict our conclusions.
0031-9007/95/75(8)/1679(1)$06. 00 1995 The American Physical Society 1679


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Quenching of the nonlinear susceptibility at a T=0 spin glass transition

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