The magnetization and differential magnetic susceptibility of powdered samples of DyH3 have been measured at 4.2 K in applied magnetic fields ranging to 9 Teslas. The differential magnetic susceptibility has also been studied in zero applied field as a function of temperature. The magnetization data are described by an equation of the form M =   aB/(1 + bB  + cB. The ratio a/b is a measure of the saturation magnetization and gives an effective moment of 5.12 Bohr magnetons per ion. The zero field susceptibility exhibits a maximum at T = 3.45 K, and an inflection point near 2.85 K. The susceptibility at 4.2 K has a 1/B squared dependence on the applied magnetic field for B approximately greater than 0.3 Teslas

Flood, D. J.

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(NASA-TM-X-71698) MAGNETIZATION AND N75-213841
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MAGNETIZATION AND MAGNETIC
SUSCEPTIBILITY OF DyH 3
by D. J. Flood7
Lewis Research Center
Cleveland, Ohio 44135 , r
TECHNICAL PAPER presented at /,/
American Physical Society Meeting
Denver, Colorado, March 31-April 3, 1975
https://ntrs.nasa.gov/search.jsp?R=19750013312 2020-03-22T23:35:15+00:00Z
MAGNETIZATION AND MAGNETIC SUSCEPTIBILITY OF DyH3
by D. J. Flood
Lewis Research Center
ABSTRACT
The magnetization and differential magnetic susceptibility of
powdered samples of DyH3 have been measured at 4.2 K in applied
magnetic fields ranging to 9 Teslas. The differential magnetic sus-
ceptibility has also been studied in zero applied field as a function of
temperature. The magnetization data are described by an equation of
the form M = [aB/(1 + bB)] + cB. The ratio a/b is a measure of the
saturation magnetization and gives an effective moment of 5. 12 Bohr
magnetons per ion. The zero field susceptibility exhibits a maximum
at T = 3. 45 K, and an inflection point near 2. 85 K. The susceptibility
at 4. 2 K has a 1/B 2 dependence on the applied magnetic field for
B > 0. 3 Teslas.
2Introduction
The magnetic properties of rare earth materials are extremely
varied and numerous, and have been the subject of many investigations.
(See refs. 1 and 2 for excellent reviews of some of the fundamental
aspects of rare earth magnetism. ) The so-called heavy rare earth ions,
listed in table I, have total angular momenta J produced by a strong
spin-orbit coupling of L and S, the orbital and spin angular momenta,
respectively. J values are large in the "heavy" rare earths because
Hund' s rules call for J = L + S, rather than J = L - S as in the
"light'" RE's. Ground state S and L are determined by applying
Hund's rules to the electrons in the 4f shell. gL is the Laud6
g factor. These materials exhibit a surprising degree of free-ion mag-
netic behavior in the solid state, primarily because the 4f shell remains
highly localized, and is often relatively unaffected by the crystalline en-
vironment. Magnetic dipole interactions in the rare earths, for example,
are very weak, causing ordering effects only for temperatures in the
neighborhood of 1 K. Exchange interactions and crystal fields determine
the magnetic behavior, many times with one or the other dominant, and
many times with competing effects, but almost always with effects that
are important only at low temperatures (10 to 100 K). (The energy dif-
ferences between the various J values in the rare earths correspond
typically to 1000 K or more due to the large spin-orbit coupling. )
The heavy rare earths crystallize in hexagonal close-packed struc-
tures (see fig. 1) with c/a ratios varying between 1. 57 and 1. 59,
slightly below the ideal value of 1. 63. Adding hydrogen to the metal
changes the lattice parameters, resulting in a c/a ratio of 1. 801 for
DyH3 (ref. 3). The increase in c/a ratio occurs primarily because of
distension along the c axis, although both c and a are larger in the
trihydride than the pure metal. The magnetic structure found in Dy
metal in the temperature range 85 to 179 K consists of a net moment of
constant amplitude located in the basal plane perpendicular to the c
axis. The direction of the net moment varies from one crystallographic
3plane to the next with a definite spatial periodicity, producing a mag-
netically ordered state with no net moment. In this range Dy is anti-
ferromagnetic. Below 85 K, the moments all line up in one direction
throughout the crystal, producing a ferromagnetic state. There is not,
in either case, a net moment along the c axis. Kubota and Wallace
(ref. 4) reported the complete disappearance of any magnetic ordering
in DyH2 . 92' DyH2 . 93, and DyH2 . 97 in the range '3 to 300 K. Their
explanation is that hydrogen exists in the lattice as an anion, acquiring
electrons from the conduction band of the metal. Since the primary
exchange interaction producing the original magnetic order is via the
conduction electrons, loss of them leaves only the exchange interaction
involving the 4f electrons, which is very weak. Hence ordering can
occur only at lower temperatures, and will most likely be antiferro-
magnetic.
II. Experimental Techniques
The investigation was made on commercially prepared samples of
DyH3 . X-ray analysis by the supplier showed no traces of other phases
of the hydrides, nor of elemental Dy. Magnetization data were obtained
by sweeping the dc magnetic field and integrating the induced difference
voltage from two search coils, one of which contained the sample. Dif-
ferential susceptibility measurements, using standard field-modulation
techniques, were made to study Xdiff both as a function of field and as
a function of temperature. Temperatures were measured using standard
1/8 watt, 100 ohm carbon resistors calibrated against the vapor pres-
sure of liquid helium. Field modulation measurements were made in a
10.5 Tesla (1 T = 10 k gauss), 2. 5 in. diameter bore (6. 35 cm) supercon-
ductive solenoid, and magnetization measurements were made in a
7.5 Tesla, water-cooled 4 in. diameter (10.2 cm) bore copper solenoid.
4III. Results and Discussion
The dc magnetization at 4. 18 and 3. 97 K is shown as a function
of applied field in figure 2. The solid line is a plot of the function
M aB + cB (1)
1 + bB
using a = 94. 0x10 4 (amp/m)/T, b = 1.85 T - 1 , and c = 11.5x10 3
(amp/m)/T, with B in Teslas. The curve generated using the above
values fits the experimental data to within 1.5 percent over the range
1.0 to 7.4 Tesla. Below 1. 0 Tesla the agreement gets increasingly
worse, reaching as much as 16 percent at 0. 13 Tesla. No one set of
(abc) values provided a fit over the whole range that was within ex-
perimental accuracy at all points, which means that eq. (1) is not an
entirely suitable approximation for all fields. Since it does describe
the moderate to high field behavior very well, however, we shall use
it to calculate the saturation magnetization. From eq. (1)
lim (M(B) - cB) =Msa t = lim aB =a/b (2)
B- sa Boo 1+ bB
From the values given for a and b,
Msa t = 5. 08x10 5 amp/m (3)
However, for wide multiplet splitting compared to kT,
Msa t = N 1B(gJ') (4)
where N is the number of magnetic ions per m3' 1B is the Bohr mag-
neton, gp is the spectroscopic splitting factor appropriate for a powder,
and J' is the effective spin of the ground state. For the sample used,
N = 10.7 ± 0.4 x 102 7 ions/m 3 and
(gpJ') = 5. 12±0. 18 (5)
is the effective saturation magnetic moment per ion. The above result
is considerably below the free ion value of 10, and is an indication of the
effect of the crystal field on the magnetic ground state. From the dis-
cussion on structure in the introduction, it is not unreasonable to expect
that DyH3 will be extremely anisotropic since c/a - 1. 8. Such would
be the case if the ground state were a Kramers doublet with Jz = ±15/2.
In that situation gp = gL(Jz), where gL is the free-ion Lands g-factor,
and J' = 1/2. Hence
(gJ) (15 x 15 (6)
3\2, 2
which agrees, within the indicated uncertainty, with the result in eq. (5).
Figure 3 is a plot of the differential susceptibility (in arbitrary units)
as a function of temperature in zero applied magnetic field. A rather
broad maximum occurs in Xdiff near T = 3.45 K, with xp(0)/xp(TN)
2/3 indicating antiferromagnetic ordering below that temperature.
The local minimum in Xdiff near T = 2. 85 K is unusual and as yet un-
explained. It may possibly indicate the actual Neel temperature TN,
which is always lower than the temperature for which x is a maximum,
although normally only an inflection is observed in X versus T at TN(dx/dT is a maximum at TN). Measurements of the specific heat or
magnetic entropy should help provide an understanding of the anomaly.
(It may have its origin in the presence of a magnetic impurity which
somehow escaped detection when the sample purity was analyzed. All
of the rare earth sesquioxides (R2 0 3 ) order antiferromagnetically below
4.2 K. It is not likely to be DY20 3 , however, since TN = 1.6 K for
that compound.)
The dependence of Xdiff on applied magnetic field is shown in fig-
ure 4 for T = 4.2 K. The solid curve is a plot of the equation
6dM a' +c' (7)
dB (1 + b'B)2
obtained by differentiating eq. (1). The parameters (a'b'c') indicated
in the figure have been chosen to fit eq. (7) to the experimental data
with an error less than 1 percent over the range from 0. 884 to
65.2 Tesla. At 0. 576 Tesla the value given by eq. (7) is 3. 5 percent
too low. It was not possible to get reliable data in the range below
about 0. 5 Tesla, except for the zero field point, with the superconduct-
ing magnet because of its remnant field. The dc measurements indi-
cate, however, that dM/dB is constant up to about 0. 04 Tesla, and
then begins to decrease as B increases. This kind of behavior in the
paramagnetic region is indicative of interactions between the magnetic
moments in the solid. The strong dependence of Xdiff on B at low
fields, and the approach to a constant value at high fields lends support
to the contention that the 16-fold degeneracy of the Dy+ 3 ions has been
removed by crystal fields. The finite value of X at high fields (the c'
term in (7)) results from a van Vleck paramagnetism, which in turn
reflects the presence of unfilled energy levels near the ground state,
causing a perturbation of the ground state wave function.
IV. Conclusion
Results from differential susceptibility measurements on DyH3 in-
dicate that the compound orders antiferromagnetically below 3. 45 K,
and that xdiff varies as 1/B 2 for B 5 0.3 Tesla. A non-zero value
for Xdiff in the high-field region is indicative of van Vleck paramag-
netism. Magnetization measurements yield a saturation magnetic
moment of 5. 12±0. 18 Bohr magnetons per ion, far below the free-ion
value of 10 AB. The results are consistent with the assumption that
the magnetic ground state in DyH3 is a Kramer's doublet with Jz =
±15/2, and that other levels from the original J = 15/2 multiplet, which
has been split by the crystal fields, lie near enough above the ground
state to perturb it slightly.
7References
1. Rhyne, James J.; and McGuire, Thomas R.: Magnetism of Rare-
Earth Elements, Alloys, and Compounds. IEEE Trans. Magnetics,
vol. MAG-8, no. 1, Mar. 1972, pp. 105-130.
2. Cooper, B. R. : Orbital Effects in Rare Earth Magnetism. Critical
Reviews in Solid State Sciences, vol. 3, no. 1, Mar. 1972,
pp. 83-129.
3. Pebler, A.; and Wallace, W. E.: Crystal Structures of Some Lan-
thanide Hydrides. J. Phys. Chem., vol. 66, no. 1, Jan. 1962,
pp. 148-151.
4. Kubota, Yoshio; and Wallace, W. E.: Magnetic Characteristics of
Dysprosium, Erbium, and Thulium Hydrides. J. Chem. Phys.,
vol. 39, no. 5, Sept. 1963, pp. 1285-1288.
8Table I
Metal Config- L S J gL
uration
Gd 3 +  4f 7  0 7/2 7/2 2
Tb 3 +  4f8 3 3 6 3/2
Dy 3 +  4f9  5 5/2 15/2 4/3
Ho 3 +  4f 1 0  6 2 8 5/4
Er 3 +  4f 1 1  6 3/2 15/2 6/5
TM 3 + 4f 1 2 5 1 6 7/6
CFigure 1. - Hexagonal-close-packed (hcp) structure
pertinent to heavy rare earth metals.
600403
500-
940x103 B 11. 5403S400 'M (1 + 1. 85 B)
300-
200 K
O 4.18
100- 0 3.97
0 1 2 3 4 5 6 7 8 9
APPLIED FIELD, T
Figure 2. - Magnetization versus applied magnetic field for DyH3.
100-
DyH3  - 3.45 K
90
80- 2.85 K-,
V 70-
60I I I
2 3 4
TEMPERATURE, OK
Figure 3. - Magnetic susceptibility versus temperature
for DyH3.
90-
0 EXP PTS, 4.2 K
80 -
' 70
< 60
50 dM 75. 6
- 5 +5S Bd 1 + 1. 24 B)2
40-
< 30-
S20-
10-
0 1 2 3 4 5 6 .7
APPLIED FIELD, T
Figure 4. - Magnetic susceptibility versus applied
magnetic field for DyH 3.


Magnetization and magnetic susceptibility of DyH3

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