Rare Earth Elements, Hydrides and Mutual Alloys

408 Pages·1991·19.65 MB·English

by  H. Drulis

Ref. p. 1831 2.1.1 Rare earth elements: introduction 1
2 Magnetic properties of rare earth elements,
alloys and compounds
2.1 Rare earth elements
2.1.1 Introduction
The main feature of the rare earth metals is the progressive filling of the 4f shell which is physically shielded by
the 5dds conduction band electrons. The structure of the partially filled 4f shell of rare earth metals have been
determined from the X-ray photoemission spectroscopy as shown in Figs. 8 and 9. In view of such highly
localized 4f wave functions which overlap very little with near-neighbor wave functions there is essentially no
direct exchange as in 3d transition metals. Consequently the magnetic interaction mechanism in the rare earth
metals has to come from the indirect exchange in which the conduction electrons sample the 4f spins on one
atom and pass this information on to the neighboring atoms.
Besides giving rise to the exchange coupling between the ionic magnetic moments, the polarization of the
conduction electrons manifests itself by the contribution Ap = (gJ- l)JJ,,N(Ef)pB to the total magnetic moment
per atom of the metal. It produces a shift in the g-value of the magnetic ions which can be determined by ESR
measurements. The polarization also gives rise to a hypertine field which may be measured by NMR and
Mijssbauer techniques.
The paramagnetic susceptibility of the rare earth metals is the same as that of the free ions except for
samarium and europium, where it is necessary to include the Van Vleck term considering the small energy
separation between the ground state and the first excited state.
The magnetic structure of the rare earth metals as revealed by neutron diffraction studies is summarized
schematically in Fig. 2. The corresponding temperature ranges and magnetic moment values are indicated in
Table 2. The magnetic properties of free rare earth ions are given in Table 6.1.1o f subvolume 111/12co f Landolt-
Bornstein, New Series.
The light rare earth metals have a complex double hexagonal crystal structure in which the stacking sequence
of the layers is ABACABAC (seeF ig. 1). Thus in the double structure the atoms in the layers occupy sites with
alternately hexagonal and cubic environments. The spin structures of the light rare earths are less well known
than those of the heavier elements, but a basic picture does exist for all the available metals. The ordering in the
double hexagonal phase of cerium is ferromagnetic within each hexagonal plane but the planes appear to be
stacked alternatively, so that the overall structure is antiferromagnetic. Both praseodymium (see Fig. 49) and
neodymium (Fig. 79) show a preferential ordering of the magnetic moments on the hexagonal sites over those on
cubic sites. In the former element it appears that the magnetic moments on the cubic sites may never order while
those on the hexagonal sites order only after application of a magnetic field. In neodymium ordering on the cubic
sites occurs several degreesb elow the temperature at which the magnetic moments on the hexagonal sites order
(see Fig. 89). Finally europium (seeF ig. 2), which crystallizes in a bee structure, has a helical antiferromagnetic
configuration with the magnetic moments lying in the (100) planes with an angle of about 50” between the
magnetic moments in adjacent planes.
The basic magnetic configuration of the heavy rare earth metals consist of six types:
(1) a helical spin arrangement in which the atomic magnetic moments in any one basal-plane layer are
mutually parallel, with, however, a constant precession (turn angle) from layer to layer as in Tb, Dy, and Ho;
(2) a helix combined with a ferromagnetic c axis component commonly referred to as a conical ferromagnet
as in Er and Ho;
(3) a modulated c axis magnetic moment with no order present in the basal plane as in Er for T> 53 K;
(4) a combination of modulated (sine or square wave) c axis magnetic moment with helical order in the basal
plane as in Er just above 19K;
(5) the Tm 4t-31 ferrimagnetic order for T < 32 K;
(6) a conventional c axis, basal plane, or intermediate angle, ferromagnetism in which the preferred direction
or plane is determined by the axial anisotropy.
Additional details about these magnetic structures and their modifications can be found in Table 1 and in a
review by Koehler [72 K 11.
Land&-Bibstein H. Drulis, M. Drulis
New Series III/l9dl
2 2.1 .l Rare earth elements: introduction [Ref. p. 183
The observations could be understood on the basis of a Hamiltonian containing three terms:
The first of these terms, XC,, is a long-range oscillatory exchange interaction of the Ruderman-Kittel-
Kasuya-Yoshida-type between the localized 4f moments through the 5d6s conduction electron system.
When the exchange energy dominates,
c%f=,, - C Si ’
SjJ(Ri - Rj) .
i=j
the magnetic structure that is stable is determined by a maximum in the Fourier-transformed exchange energy
J(q)= vJ(Ri-Rj)exp{iq’(Ri-Rj)}.
If the maximum in J(q) occurs for q=O, a ferromagnetic configuration results, as for gadolinium. If the
maximum occurs at some general point in the Brillouin zone, the exchange favors an oscillatory helical
arrangement whose interlayer angle dependso n the q-value which itself is strongly dependent on the geometry of
the Fermi surface. The explicit form of the exchange interaction J(q) has been provided by inelastic neutron
scattering.
The second term, in eq. (I), XCr, is a single-ion (crystal-field-type) anisotropy energy resulting from the
crystalline electric field affecting the distribution of 4f electrons in a given rare earth ion. The anisotropy energy
can be represented classically as
(2)
where Yz are n-th order Legendre polynomials, and 0 and C#aJr e polar angles for the angular momentum Ji
measured from the c and a axes, respectively. When the crystal field anisotropy is dominant the directions of the
magnetic moments are determined by minima in the expression for E,,. Near the NCel temperature only the
leading term K: is significant. For thulium and erbium K: is negative and the crystal field anisotropy favors an
initial alignment parallel to the c axis. In holmium, dysprosium and terbium K! is positive and the magnetic
moments are constrained to be normal to the c axis. At lower temperatures the higher-order terms can become
important, for example in holmium and erbium the conical structure reflects the influence of those terms. If the
hexagonal anisotropy Kz is sufficiently large it may, in competition with the exchange energy, drive the system
from a spiral to a planar ferromagnetic state.
The third term in eq. (l), the magnetoelastic energy contribution,Xm,,is thought to be at least as important as
the planar anisotropy in controlling the helical$ferromagnetic phase transition. It varies with temperature
according to a high power of the relative magnetization. It is thus relatively unimportant except at low
temperatures where it can be competitive with the exchange energy.
In the light rare earth metals with large 4f electron radius the magnetocrystalline anisotropy energy is
comparable in magnitude to the exchange energy and, therefore, directly influences the type ofmagnetic order, as
for example is the case in Pr. The anisotropy does also have a pronounced effect on the direction of stable
magnetization.
From the magnetization measurementsa long both the c and the a axis it is evident that the easy direction in
the heavy rare earth metals is different for the various metals, and for some metals is dependent on temperature.
In Tm the easyd irection is the c axis while in Er the low-temperature configuration of the magnetization is a cone
with a half-angle of approximately 30”.
In the heavy rare earth metals there exists also a strong coupling between magnetic and elastic energiesw hich
produces magnetostrictive dilatations on rotation of the magnetic moment from the easy to a hard magnetic
direction. The experimental values of the linear strains in the three major axial directions are, for example, shown
for dysprosium and holmium in Figs. 269 and 323 as a function of temperature. The curves are given for
measurementsb oth with and without an applied magnetic field. It has been shown that in dysprosium the sudden
change in specimen dimension at 85 K arises from an orthorhombic distorsion of the hexagonal lattice.
As mentioned above, in the light rare earth metals the observed magnetization is strongly influenced by the
crystalline electric field which causes single-ion energy splittings comparable to the exchange interaction.
Therefore, there is rather little sensein the direct measuremento f the crystal-field splitting ofrare earth ions in the
pure elemental rare earth metals. Fortunately, a good description of the origin of the crystalline electric field in
the concentrated elemental metals is provided by the crystal field found for dilute rare earths in yttrium, lutetium
and lanthanum, as is shown in Table 3.
The magnetic phase transitions in the rare earth metals are accompanied by anomalies in a number of other
properties influenced either directly or indirectly by the magnetic order: the electrical resistivity, for example, is
H. Drulis, M. Drulis Land&-BBmstein
New Series 111/19dl
Ref. p. 1831 2.1.1 Rare earth elements: introduction 3
strongly influenced by two magnetic processes.F irstly, there is the abrupt change at TN of the scattering of
conduction electrons by the thermally disordered 4f spins. This scattering, which is the dominant mechanism,
becomes constant at TN and produces a sharp knee in the basal-plane resistivity curves. Secondly, the c axis
electrical resistivity rises dramatically in the periodically ordered metals below TNd ue to an effective loss in the
area of the Fermi surface normal to the c axis.
Specific heat measurementsh ave been made on all the elements at temperatures below 300 K. The results for
most of the metals show the presenceo f h-type anomalies. The typical temperature variation of the specific heat is
shown in Fig. 259 for dysprosium from which it may be seen that the sharp maxima occur at the magnetic
transition temperatures, 85 K and 179K , respectively. Similar results are observed for the other metals and the
location of the maxima in the anomalies may be expected to provide accurate values for the phase transition
temperatures. The values obtained in this way have been given in Table 1 along with those derived from other
measurements.
Only a brief summary of experimental and theoretical results has been given here. Much more complete
reviews can be found in the books edited by Elliott [72 e 11, Gschneidner and Eyring [79 g 11, or by Coqblin
[77 c 1-J
Land&-Biimstein H. Drulis, M. Drulis
New Series 111/19dl
2.1.2 Tables
Table 1. Survey of magnetic, electrical,spectroscopic, thermal and mechanical properties of rare earth metals.
Crystal Spin 0 T, TN Pdf Q Remarks Ref.
PR
structure order K K K lb P”/R pQ cm
Rare earth metals: general
Fig. 1 6lG2
Fig. 2 wavevector, Fig. 3 65K1,
72Kl
heavy rare earth metals: 72Ll
electrical resistivity
Fig. 6 parallel c axis,
Fig. 7 in basal plane
nonmagnetic rare earth metals: 73Sl
susceptibility, Fig. 4
promotion energy: Fig. 9 74B2
XPS and BIS spectroscopy, 81 Ll
Fig. 8
Fig. 5 Fig. 5 heavy rare earth metals: 83L1
magnetization vs. temperature,
Fig. 5
Cerium (Ce)
a-fee - 50 susceptibility, 300 K < T < 1050 K, 61 Cl
Fig. 17
P-dhcp Fig. 11 12.6 0.64 ordered moment at 4.2 K 61 WI
a-fee, susceptibility vs. temperature, 71 Ml
P-dhcp Fig. 15
a-fee, susceptibility vs. pressure,
y-fee Fig. 16
Table 1 (continued)
Crystal Spin 0 T, TN PR Peff e Remarks Ref.
structure order K K K f.&cm
PB PB/R
Ce
y-fee neutron scattering at T = 293 K, 74Ml
Fig. 19
CEF splitting
(ground state - 1”’ excitated state):
AE = 5.8 meV
cl-fee not ordered heat capacity, Fig. 20 75Kl
y = 12.8m J/mol K2
susceptibility, 1.6 K < T < 150 K, Fig. 14
B-dhcp AF - 38 12.5(l) 2.60 ac susceptibility, Fig. 12 76Bl
susceptibility, Fig. 13
Fig. 26 resistivity, 4 K < T < 300 K
89.2 at 300K
y-fee not ordered - 50 2.52 74.4 at 300K
$-dhcp Fig. 27 magnetic contribution to resistivity 76L2
B-dhcp heat capacity, 12 K < T < 17 K, Fig. 22 76Tl
CEF splitting
(ground state - 1”’ excited state):
AE,,, = 206 K,
AE,,, = 98 K
magnetic heat capacity, Fig. 23:
E,=O.l22meV at OK
y-fee, inelastic neutron scattering vs. pressure, 77Rl
a-fee Fig. 18
CEF splitting
(ground state - 1”’ excited state):
AE =9.1 meV at p= 1 kbar
AE=13.1meV at p=6kbar
continued
Table I (continued)
Crystal Spin 0 T, TN PR Pelf e Remarks Ref.
structure order K K K PEE lb/R @cm
Ce
y-fee, a-fee C, vs. pressure at T=3OOK, Fig. 24 78B2
y-fee dInC,/dp=2.1(1). IOm2k bar-’
a-fee dInC,/dp=-1.3(2).10-2kbar-1
y-fee, a-fee B(P) temperature coefficient vs. pressure, Fig. 25
a-fee, phase diagram, Fig. 10 78KI
P-dhcp, phase transition at p=O:
y-fee, a-t p at 96(6) K
&bcc f3-q at 326(14)K
y-4 at 999(5) K
6-rL at 1071(3)K
a+y at 141 (lO)K
(3-dhcp zub= 12.45 heat capacity, I.5 K < T < 20 K, Fig. 21 78SI
Thel = 13.7
y-fee, a-fee 4f-conduction electron hybridization 83WI
EELS, AE = 25 meV, Fig. 29
XPS, AE=60meV, Fig. 29
a-fee, y-fee paramagnetic enhancement /l vs. 7: Fig. 28 84BI
Praseodymium (pr)
dhcp not ordered magnetic heat capacity. 51 PI
poly., 2 K < T< 100 K, Fig. 61
dhcp 3.56 susceptibility, I .3 K < T < 300 K, Fig. 52 57LI
dhcp, bee susceptibility, 300 K < T< 1500 K, Fig. 53 61A2
dhcp not ordered heat capacity, poly., 3 K < T< 25 K, Fig. 60 67 L I
Table 1 (continued)
Crystal Spin 0 T, TN PR Peff e Remarks Ref.
structure order K K K
PB PBIR clna
Pr
dhcp not ordered 3.56 magnetism, magnetoresistance, Fig. 68 67Nl
cubic sites nearest-neighbour exchange parameters:
JhdkB= 12.8K
Jhc/kB = 2.8 K
J,,/k, = 0.6 K
fee F 8.0 8.7 0.76 at 1.43K and 15 kOe 69B2
fee, dhcp magnetization, Figs. 33, 34
AE(T, - r,) = 69(4)K
dhcp sin. mod. 0.95 ordered moment at 0.02 K 69Hl
nuclear specific heat, Fig. 62
dhcp susceptibility, energy level scheme, Fig. 51 7151,
CEF parameters: 72Rl
AEcu& - r,) = 80 K
A-GA f 1) - IO>)= 25 K
@(cub) = 0
@(hex) = 4.92 K
dhcp magnetic excitations, Fig. 58 71Rl
fee 20 0.65(l) at OK 72Bl
neutron scattering, Figs. 31, 32
crystal field level scheme, Fig. 30
magnetic excitations, Fig. 36,
AE(T, - r,) = 7.2 meV
fee magnetization, Figs. 35, 37 72C2
0.75 x= -0.877 at T=OK
continued
Table 1 (continued)
Crystal Spin 0 T r, PR Pelf e Remarks Ref.
structure order K K K PR PB/R @cm
Pr
dhcp CEF parameters: 72Rl
ALEcu& - I-,) = 90 K
A&,,,(1 + I) - IO>)= 30 K
B;(cub)=O
B!$hex)=42.10-‘meV
Bi(cub)=Bi(hex)=2. 10m4meV
Bg(cub)= Bz(hex)=0.8. 10m4meV
dhcp stiffness constants, Fig. 74 73G2
dhcp inelastic neutron scattering, Fig. 59 75Hl
dhcp magnetostriction, s(T), s.c., Figs. 54, 65 7501
dhcp AF magnetization, Fig. 48 76Cl
pher = 2.71 along [llzO] at u0H=40T and T=4.2K
phcl = 2.08 along [OOOl] at u,H=31.8T and T=4.2K
dhcp AF Thcx= 25 magnetization at 4.2 K, Fig. 46 7682
initial susceptibility, Fig. 47
dhcp AF Fig. 69 magnetoresistance, poly. 7752
dhcp Fig. 66 magnetoresistance, poly. 77M3
Fig. 67 resistivity, magnetic scattering
dhcp AF Thex= 7.5(5) elastic neutron scattering, s.c., 78 M 1
p = 800 bar, Fig. 41
inelastic scattering: excitations vs. pressure,
Fig. 55
along b axis at 2 K
Phcx = o.5
magnetoelastic coupling constant:
B,,(hex) = 20.14 meV
Table 1 (continued)
Crystal Spin 0 T, TN PR Peff e Remarks Ref.
structure order K K K
PB IlB/R @cm
&p
elastic constant, ce6, Figs. 72, 73 78Pl
CEF parameters (hex):
Bg=O.l9meV
Bz= -5.7.10-4meV
B~=1.0.10-4meV
dhcp magnetization, s.c., Fig. 45 79Hl
AE,,,(F, - F,) = 90 K
AJUt IL 1) - IO>)= 30 K
magnetostriction, s.c., Fig. 64
magnetostriction coefficients,
cubic sites (Hll~):
n&=2.8(1). 10-4
3=2.9(4). 10-4
hexagonal sites (H/u):
a& = 1.1(2). 10-4
P=3.0(2).10-4
cubic sites (HI(b):
1”,,=2.0(1)~10-4
1Y=3.6(8).10-4
hexagonal sites (Hjlb):
&=1.9(2).10-4
P=2.3(3). 1O-4
dhcp AF dispersion relation, Fig. 57 79H2
dhcp magnetic form factor, s.c., Fig. 44 79L2
at 4.2K and ~,H=l.STl~a
Pher = o.g
dhcp not ordered heat capacity, s.c., 1 K < T< 6 K, Fig. 63 81Fl
y: magnetic field-dependent
continued
Table 1 (continued)
Crystal Spin 0 7-C TN PR Pelf e Remarks Ref.
structure order K K K PB vn/R @cm
Pr
dhcp AF 40.10-3 0.36 ordered moment at 40mK from satellite 82MI
peak intensity
neutron diffraction, s.c., T < 6 K, H = 0,
Figs. 38, 39
A&,,,([ k 1) -IO))= 3.5 meV
Pr(Nd)2.5% AF 3.5 0.25 ordered moment from central peak intensity
effective moments, Fig. 40, H = 0
dhcp AF dispersion relation, Fig. 57 82M2
dhcp magnetoresistance, s.c., Figs. 70, 71 82YI
dhcp AF Tbcr=23 2.80 susceptibility, poly., 4 K < T < 50 K, 83Al
Figs. 49, 50
Jr+-,+ = - 0.5 meV for nearest neighbours
J,,=0.3eV
dhcp AF Fig. 43 neutron scattering under pressure 8751
Fig. 42 pc = 0.7 kbar, Fig. 42
CEF splitting, Fig. 56
A,?&,,(1+ 1) - IO)) = 3.5 meV at p = 0
Neodymium (Nd)
a-dhcp o,=o 3.45 magnetization, s.c., at 4.2 K, 57BI
0,=5 O<uoH<2.0T, Fig. 83
dhcp susceptibility, 0 < T < 1200 “C, Fig. 91 60A2
dhcp crystal and magnetic structure, Fig. 75 64Ml
19.2 hexagonal sites ordering:
PB= --PC= Phel = 2.3
pd, ~0sQ hexR phcxll(lOiO)b, direction,
Q,,,,=O.l3r,,, at 19.2K
p* = -PA’= 7.5 Pcub= 1.8 cubic sites ordering:
ped, cos Qcd pcUhjl(ll~O)b, direction, Qcuh=0.15t1,,,, at 1.5 K