REVIEW OF SCIENTIFIC INSTRUMENTS 76, 096101 共2005兲
Time relaxation of ac susceptibility on very short time scales
Ivica Živković, Ðuro Drobac, and Mladen Prester
Institut of Physics, Bijenička cesta 46, 10000 Zagreb, Croatia
共Received 17 December 2004; accepted 25 July 2005; published online 29 August 2005兲
We present an experimental method enabling measurements of time dependence of ac susceptibility
down to 1 ms after a steplike change of the applied dc magnetic field. An analog-digital converter
has been used to collect the transient of the current, signaling the change of the dc magnetic field.
The time window for investigation of magnetic time relaxation phenomena, as studied by the ac
susceptibility technique, thus has been expanded in the range of short time scales for three orders of
magnitudes. © 2005 American Institute of Physics. 关DOI: 10.1063/1.2038427兴
Time-dependent response of various magnetic materials
to a sudden change in the applied dc magnetic field, a
relaxation-type phenomenon usually referred to as a magnetic aftereffect, disaccommodations, magnetic viscosity,
etc., represents a subject of pronounced fundamental and
practical importance.1 Some examples of magnetic materials
revealing time relaxation are ferromagnetic amorphous
alloys,2 spin glasses,3 molecular magnets,4 etc. These relaxations extend in time over many decades and are modeled
with various models 共single exponential, stretched exponential, logarithmic, quasilogarithmic. etc.兲. Although magnetization is used more often, ac susceptibility can also give
valuable insight into magnetism, and particularly magnetic
dynamics, of the investigated magnetic material. To measure
ac susceptibility in time, one usually adopts the programming routine so that after the change of the dc field, points
are taken at regular intervals 共seconds, minutes, hours, etc.兲.5
Recording usually starts 1 s after the change in the magnitude of the dc field and sometimes even after a few minutes
关hereafter referred to as the first point time 共FPT兲兴. To the
best of our knowledge, there are no measurements of ac susceptibility in time that substantially cover the time window
of the first second after the change of the dc field. In this note
we show that ac susceptibility is especially suitable for studies of magnetic properties on shorter time scales and present
a simple method to achieve FPTs of the order of 1 ms, thus
extending the standard time window by three decades.
Our ac susceptibility measurements are performed using
a commercial CryoBIND system, integrating one primary
coil and two secondary coils inside the primary. The system
provides a full compensation of the residual misbalance between the secondary coils. The primary coil is driven by the
oscillator output of a lock-in amplifier 共LIA兲 共Perkin Elmer/
Ametek 7265兲. Simultaneously, LIA analyzes the induced
signal from the secondary coils and extracts the real and
imaginary part 共X channel and Y channel, respectively兲. For
the generation of the dc field we use an additional Helmholtz
coil located outside the primary, powered by an appropriate
current source 共Keithley 220 for currents smaller then
100 mA or a homemade current source otherwise兲. The measurement is monitored with a computer 共PC兲 via a general
purpose interface bus 共GPIB兲 interface.
In an ac susceptibility study of a time relaxation, one
measures the signal after a steplike change of the applied dc
0034-6748/2005/76共9兲/096101/3/$22.50
magnetic field. Here we elaborate the case of switching off
the dc field. The desired reduction of FPT well below 1 s
introduces the difficulty of knowing the exact moment of the
steplike change of the applied field 共t = 0 s兲. This event is
usually monitored by a PC via some specific instrument 共either directly through a current source or indirectly with a
digital voltmeter on a standard resistor兲. However, the resulting indeterminacy of the zero time is of the order of the time
needed for the communication between the PC and the instrument, typically in the range of 5 - 50 ms. In the case of a
targeted FPT being 1 s or longer, this error is of no practical
relevance. Obviously, in the case of FPT of the order of
1 ms, an error of this magnitude hinders the use of the very
first points in the measurement. To solve this problem we
have used the setup shown in Fig. 1. For buffering the current 共i.e., dc field兲 in the D coil 共voltage over a standard
resistor兲 in time this setup uses an analog-digital converter
共ADC兲 共National Instruments PCI-6111兲. Simultaneously, the
signals from the X and Y channels have been stored in the
internal buffer of the LIA. Two independent buffers are
needed because the two instruments operate in different operating regimes. The ADC monitors the transient, and its
sampling rate has to be high enough to record at least a few
points while the field is switching off 共50 ␮s in our case兲. At
variance, the LIA’s buffer stores a fully processed signal 共the
processing involves filtering, integration, etc.兲. The shortest
time interval between the two consecutive points, as provided by the LIA used, is 1.25 ms, which limits the time
constant to a maximum value of 640 ␮s. Lower values of a
time constant decrease the signal-to-noise ratio so the frequency of the driving field has to be increased.
With two separate buffers involved one has to properly
relate the two sets of data characterized by different time
steps. The easiest way to do this is by synchronizing the start
of the buffering processes. Thus the two instruments have
been connected to a common source of a transistor-transistor
logic 共TTL兲 signal used to trigger the data acquisition in the
two buffers simultaneously.
One could argue that this could be solved much easier if
the LIA’s FASTX output is used, eliminating the need for the
synchronization of the two instruments. In that case two
channels of the ADC would be involved, employing faster
and slower acquisition rates, for recording the transient and
the X channel, respectively. However, several disadvantages
76, 096101-1
© 2005 American Institute of Physics
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096101-2
Zivkovic, Drobac, and Prester
Rev. Sci. Instrum. 76, 096101 共2005兲
FIG. 1. Experimental setup for the measurement. The TTL signal on the left
is simultaneously triggering the start of the acquisition in the LIA and ADC
buffer.
render this approach useless for our application. The most
important disadvantage is in the reduction of the signal-tonoise ratio down to the unacceptable level 共see Fig. 2兲. The
latter reduction is a consequence of only the first stage of
low-pass filtering engaged with the FASTX output.6 共At variance, there is a full processing of the signal stored in the
LIA’s buffer兲. Further on, the fast rate of the transient acquisition would result in an enormous number of unnecessary
points stored for that channel 共only few points are of interest
for the method, which we will discuss later兲. Finally, our
method does not imply a very sophisticated ADC—only the
20 kHz, one-channel instrument is sufficient to record the
transient.
The buffers can store a limited number of points, so for
prolonged measurements it is necessary to collect the points
in the PC’s RAM 共time relaxations can be observed even
after 105 s兲. The LIA used in this work is able to communicate with the PC simultaneously with buffering. With the
time interval of the LIA set to 1.25 ms and the number of
points available for one channel equal to 16 384, the time
window covered with the LIA buffer is 20.48 s. As we have
mentioned, the PC starts to collect the data around 1 s after
FIG. 2. Comparison of the signal-to-noise ratios of the same data collected
with the LIA buffer 共narrow gray line兲 and with the ADC buffer through the
FASTX LIA’s output 共wide black stripe of the stored data; see text兲. Both
buffers collected points with 800 Hz共1 / 1.25 ms兲. The LIA’s input was connected directly to the LIA’s sinusoidal output 共no coils in between兲 with
other parameters in the range of the actual measurement. Left inset: Enlarged curves from the main panel. Noise is digitized because the ADC is in
the dc coupling regime. Right inset: The same noise from the ADC buffer in
the ac coupling regime and with the 5 MHz acquisition rate.
FIG. 3. Time window around the change of the dc field with the
Ru1222EuCe sample in the coils. 共a兲 Profile of the dc current. The inset
shows an expanded view of the transition. t0 is associated with the half of
the maximum dc current. 共b兲 Points from the LIA buffer. During the period
with the dc field on, there is a slight change in the inductivity of the coils,
resulting in a misbalance between the secondary coils.
the change in the dc field. This implies that there will be a
time window of approximately 20 s where the two sets will
overlap, allowing for the adjustment of the PC data with
respect to the exact t = 0 s time. Afterwards, these two sets of
data can be merged together and used for further analysis.
To illustrate the method described above we have used a
polycrystalline sample of rutheno-cuprate RuSr2EuCeCu2O10
共Ru1222EuCe兲 revealing, as it was shown recently,7 a pronounced time relaxation. The measurements were performed
at 80 K. The frequency of the driving field was 10 031 Hz
and the magnitudes of ac and dc fields were 0.1 and 34 Oe
共with 100 mA dc current兲, respectively. The time constant
was set to 160 ␮s.
Figure 3 shows the points from both buffers depicting
the dc field switching off with the sample in the coils. The
values buffered by the ADC reveal the transition width of
around 170 ␮s 关10%–90% window, see the inset in Fig.
3共a兲兴. The points within the transition can be used to define
t = 0 s. We have defined t = 0 s as the point where the current
through the D coil reaches half of its maximum value
共50 mA in our case兲. Noteworthy, different definitions for t
= 0 s would introduce only a very slight change in the behavior of the measured points. For this particular measurement a
new time scale is obtained by shifting the points buffered by
the LIA by t0 = 60.295 ms 共bottom scale兲. The points from
the transformed time scale will be used later on to show the
time relaxation.
The buffered points from the LIA are shown in Fig. 3共b兲.
Unfortunately, the first two points cannot be used due to the
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096101-3
Rev. Sci. Instrum. 76, 096101 共2005兲
Notes
nate between the two sets. That makes the small correction
of the time coordinate of the PC data 共of the order of
100 ms兲 with respect to the buffered points a task that can be
done manually. The PC data should be shifted so that the first
couple of points from the PC fall correctly inside the region
covered with points from the LIA buffer. After that, two sets
of data can be merged and used for further analysis 共Fig. 4兲.
It is obvious that the additional three decades below 1 s
quantitatively and qualitatively change the observed behavior of Ru1222EuCe. A further analysis will be published
elsewhere.
1
FIG. 4. ac susceptibility of Ru1222EuCe as a function of time over seven
decades. Two sets of data are overlapping in time, allowing for a small
adjustment of the PC data with respect to the t0 共see text兲.
unknown disturbance of the LIA buffer 共most likely related
to the specific model8兲. Repeated measurements have shown
no systematic behavior in the y values of the first two points,
implying that the LIA’s internal processing is affected by
canceling out the dc current.
Now we can complete the procedure by merging the
LIA-buffered points with a PC data that cover the time window from 1 to 10 000 s 共actually arbitrarily long in time兲.
Due to the fact that the points are taken with the PC while
the buffering is in process, there is no shift in the y coordi-
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H. Kronmüller, Philos. Mag. B 48, 127 共1983兲.
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D. N. H. Nam, R. Mathieu, P. Nordblad, N. V. Khiem, and N. X. Phuc, J.
Magn. Magn. Mater. 226, 1340 共2001兲.
4
C. Sangregorio, T. Ohm, C. Paulsen, R. Sessoli, and D. Gatteschi, Phys.
Rev. Lett. 78, 4645 共1997兲.
5
M. Muroi, R. Street, J. W. Cochrane, and G. J. Russell, Phys. Rev. B 62,
R9268 共2000兲 and references therein.
6
Instruction manual for model 7265 DSP lock-in amplifier.
7
I. Živković, Y. Hirai, B. H. Frazer, M. Prester, D. Drobac, D. Ariosa, H.
Berger, D. Pavuna, G. Margaritondo, I. Felner, and M. Onellion, Phys.
Rev. B 65, 144420 共2002兲.
8
We have compared three different 7265 LIA units; all of them show the
same type of behavior. We have also encountered some issues with the
synchronization of the LIA buffer with the ADC buffer, which were solved
but the explanation would significantly extend the size of the paper.
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