Yb3+ in RAlO3 (R = Eu, Gd, Tb, Dy, Ho, Er). A 170 Yb Mössbauer effect study of the hyperfine parameters, magnetic ordering and relaxation

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Yb3+ in RAlO3 (R = Eu, Gd, Tb, Dy, Ho, Er). A 170 Yb Mössbauer effect study of the hyperfine parameters,

magnetic ordering and relaxation

P. Bonville, J.A. Hodges, P. Imbert

To cite this version:

P. Bonville, J.A. Hodges, P. Imbert. Yb3+ in RAlO3 (R = Eu, Gd, Tb, Dy, Ho, Er). A 170 Yb

Mössbauer effect study of the hyperfine parameters, magnetic ordering and relaxation. Journal de

Physique, 1980, 41 (10), pp.1213-1223. �10.1051/jphys:0198000410100121300�. �jpa-00208947�

Yb3+ in RAlO3 (R = Eu, Gd, Tb, Dy, Ho, Er). ^{A 170} Yb Mössbauer effect study

of the hyperfine parameters, magnetic ordering ^{and relaxation}

P. Bonville, J. A. Hodges ^{and P. Imbert}

DPh-G/PSRM, ^C.E.N. Saclay, Boîte Postale N° 2, ^{91190 Gif}

Yvette, ^France.

(Reçu ^{le 23 avril} 1980, accepté ^{le 18} juin 1980)

Résumé. 2014 Nous

effectué des

par effet Mössbauer

170Yb dilué dans RAlO3 (R

Eu, Gd, Tb, Dy, Ho, Er), qui complètent ^notre étude antérieure

R

Tm, Yb et Y (Phys. ^{Rev. B 18} (1978) 2196).

Dans tous les

l’ion Yb3+ présente

doublet fondamental de champ cristallin bien isolé et extrêmement

anisotrope (Ising). ^Pour la matrice

magnétique EuAlO3

donnons la fonction d’onde du niveau fonda- mental (à partir ^des

par effet Mössbauer ^et par RPE) ^et

examinons la relaxation de spin ^due

interactions

les phonons. ^{Les autres réseaux} présentent ^des propriétés magnétiques intrinsèques très diffé- rentes, de sorte que l’ion Yb3+ _y subit des interactions magnétiques ^{de nature variée. A} partir ^d’une analyse ^des

formes de raies obtenues à la fois au-dessus et au-dessous de TN,

examinons les interactions magnétiques

entre l’ion Yb3+ et les ions du réseau (influence de l’ordre magnétique ^et de la relaxation croisée spin-spin). ^La

contribution du couplage dipole-dipole à la relaxation paramagnétique ^croisée

^été calculée pour Yb3+ dans les matrices où R est

ion de Kramers. Pour Yb3+ dans DyAlO3, l’interaction dipolaire donne la contribution dominante à la fréquence de relaxation mesurée (1,0

¹⁰⁹ s-1), alors que les fréquences mesurées pour Yb3+

dans ErAlO3 ^et GdAlO3 (3,0 ^et 4,3

1010 s-1) ^{sont dues} principalement à l’interaction d’échange. ^Nous

observé

dépendance

température ^des fréquences de relaxation croisée due à l’interaction spin-spin pour Yb3+ dans ErAlO3 2014 ^causée probablement par

ordre à courte distance

et dans le composé

^{deux sin-} gulets fondamentaux HoAlO3, à la suite du dépeuplement thermique ^du singulet supérieur.

Abstract. 2014 170Yb Mössbauer measurements have been made

Yb3+ substituted in RAlO3 ^(R

^Eu, Gd,

Tb, Dy, Ho, Er) ^and complement

previous study

^R

Tm, Yb and Y (Phys. ^{Rev. B 18 (1978)} 2196). In

all

the Yb3+ _presents

well isolated crystal ^field ground doublet with Ising-like characteristics. For the

magnetic ^lattice EuAlO3

establish the Yb3+ ground ^state

^function (from ^{Mössbauer and EPR measure-} ments) ^and

also examine phonon driven relaxation. The remaining host lattices have widely differing ^intrinsic magnetic properties

^{that the Yb3+} experiences

^number of different magnetic environments. By studying ^the lineshapes both above and below TN

obtain information concerning ^{the Yb3+-host lattice} magnetic interactions (influence ^of magnetic ordering ^and spin-spin

relaxation). The contributions of dipole-dipole coupling ^to

the paramagnetic cross-relaxation rates

calculated for Yb3+ in the Kramers ion host lattices. For Yb3+

in DyAlO3 ^the dipole-dipole interaction ^accounts for the major part of the measured ^rate (1.0 x ¹⁰⁹ s-1) ^whereas

the measured rates for Yb3+ in EuAlO3 ^and GdAlO3 (3.0 ^{and 4.3}

¹⁰¹⁰ s-1)

chiefly ^{due to the} exchange

interaction. Temperature dependent ^Yb3+ spin-spin cross-relaxation rates

observed both in ErAlO3 2014probably

due to short range ordering

and in the two-singlet ground ^state system HoAlO3 following ^thermal depopulation

of the upper singlet.

Classification Physics ^Abstracts 76.80

71.70C

1. Introduction.

The Rare Earth orthoaluminates

(RAI03) ^{used as} host lattices in this study provide

a range of dif’ering magnetic properties ^{whose cha-}

racteristics are generally ^{well known} [1-6]. ^{In most}

cases data is available concerning ^the crystal ^field

levels of the ground multiplet and in addition for those lattices composed ^of magnetic ^{Rare Earth} ions, ^the ground ^state g-values, ^the magnetic ordering

temperatures ^{and the} magnetic structures are also known.

We present ^{here an account of the} properties ^of Yb3 + diluted into the heavy Rare Earth ortho- aluminates RAI03 (R

^Eu, Gd, Tb, Dy, Ho, Er)

obtained using ^{17°Yb Môssbauer} Spectroscopy.

Results for the two remaining members of the series R

Tm and Yb as well as for Yb3 + in YA103

have been published previously [7, 8]. ^The present results relate to both the one ion properties ^such

as the g-values ^{and the} phonon driven relaxation and also to the magnetic interactions between the

Yb3 + ion and the host lattice ions. These interactions

are examined both through ^{the influence on the Yb 31}

ions of magnetic ordering ^{in the} host lattice and also

through the influence of the cross relaxation between the Yb3 + ions and the host lattice ions.

There are two advantages ^for using ^{the Yb3 + ion}

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0198000410100121300

(4f ", 2F7/2) ^{as a probe in the present case. First the}

lowest Yb3 + crystal field level in all the Rare Earth orthoaluminates is well separated from the excited levels. This means that measurements can be made

over a wide temperature range where however only

the Yb3 + ground doublet is populated. Second, ⁱⁿ all cases the Yb3 + ion has Ising-like characteristics

so that to a good approximation ^{it can be taken to}

have uniaxial properties. ^This assumption then facili- tates the relaxation lineshape analysis.

After briefly recalling ^the crystal ^{structure of the}

orthoaluminates and outlining ^the experimental ^details

in section 2, ^we _present and discuss the various results in section 3.

The spin-spin ^cross relaxation data provides ^a

convenient _way of separating ^the presented ^results

into three _groups depending ^{on the} host lattice.

For the first group (section 3.t) EuAI03 (with TmAI03 ^and Y Al03 [7]), ^{the host lattices are non}

magnetic and there is no spin-spin interaction. Any

relaxation present is then driven only by ^the phonons.

As this phonon driven relaxation is temperature

dependent ^{it is} possible by going ^{to low} enough temperatures, ^to suppress any phonon induced line

broadening. ^{In the case of Yb3 +} in the orthoalu- minates this means going below about 30 K, ^where the phonon induced relaxation rates become too low

( N 5 x 1 O8 s -1 ) to broaden the absorption ^lines.

The second _group (section 3.2) GdA103, ErAI03

(with YbAI03 [7]) comprises ^the three host lattice Kramers ions which give relatively high ^{Yb3 +} spin- spin ^cross relaxation rates at low temperatures.

The third _group (section 3. 3) comprises ^{two Van Vleck}

ion lattices TbAI03 ^and HoAI03 ^{and one Kramers}

ion lattice DyAI03 ^all showing ^{low Yb3 + cross}

relaxation rates at low temperatures.

Section 4 contains a discussion of the Yb3+ spin- spin cross-relaxation rates in the various lattices in terms of the possible processes driving the relaxa- tion. Section 5 comments on the misfits observed in two cases between the experimental ^{data, and the}

relaxation lineshapes.

2. Crystal ^{structure and} experimental ^details.

In the orthoaluminate lattice, space group D§f ^Pbnm,

the trivalent Rare Earth ions _occupy sites with Cs symmetry. ^{For all the Rare} Earth ions considered,

one of the local principal directions of the g-tensor lies along ^the crystal ^{c axis,} the other two lying ⁱⁿ

the ab plane. ^{The exact} directions in this ab plane depend ^{on the} particular ^Rare Earth ion but are

generally ^{in the} neighbourhood ^{of + and - 30°}

relative to the crystal ^{a and b} directions, ^{the two} signs corresponding ^{to the two} differently oriented sites which ^are related by ^a mirror reflection. For yb3 + the local z-axis (Ising ^like axis) ^{lies at directions}

near + and - 300 from a crystal ^a axis. For the other Rare Earth ions the directions of the principal

axes in the ab plane, ^{as obtained from} Magnetic Structure, ^Electron Paramagnetic ^{Resonance or} Opti-

cal Zeeman studies will be given ^{in the} appropriate

sections below. A _summary of these properties ^is given in the table.

The Môssbauer absorption ^{results were obtained}

on polycrystalline samples substituted with enriched 17°Yb at concentration levels Yb/Host ^Rare

Earth - 0.025. Lower levels were not feasible as the

absorption signals ^{became too weak.}

3. Results and discussion.

As mentioned in the introduction, ^{the results are} presented ^{in three} groups

. corresponding ^to the three different families of Yb3 + relaxation rates observed in the temperature range where the dominant interaction is spin-spin coupling.

These _groups in turn correspond ^to where the host lattice ion is non magnetic (section 3. 1), magnetic

with low anisotropy (section 3.2) ^and magnetic

with high anisotropy (section 3.3).

For each of the different hosts in ^turn the various results concerning ^the hyperfine parameters ^{and the} influence of magnetic ordering ^are presented ^and

discussed. The Yb3 + relaxation results are also

presented ⁱⁿ this section however the discussion of the relaxation data is defered to section 4.

Table 1.

S0l11e characteristics of the orthoaluminate lattices studied. The references ^{to the various data are}

giren ^{in the} appropriate ^.sections of ^{the main text.}

3.1 Yb3 + IN EuA’03 (AND TmA’03, YAl03).

This section concerns results for Yb3 + ions substituted into matrices which are truly diamagnetic (YA103)

or behave as if they ^are diamagnetic (EuA103, TmAI03) ^{at low} temperatures ^{due to the} presence of well isolated singlet ground ^{states. At} sufficiently

low temperatures (below ^{about 30} K) the slow relaxa- tion limit spectrum ^is visible in each of the three

cases. The results concerning YA103 ^and TmAl03

have been presented previously [7] ^{and are recalled} briefly ^{here in order to} relate them to the case of

EuAI03 which forms the main part of this section.

In addition to the Môssbauer measurements, EPR data was obtained for single crystals containing ^0.5

and 3.0 % ^{of Yb} having ^natural isotopic ^abundance.

3.1.1 Parameters at 4.2 K.

The EPR g-values

of the Yb3 + ion were found to be the same, to within

experimental ^{error, for the two} concentrations but could be obtained with better precision ^{in the} 0.5 % sample ^{due to the} lower linewidths. One of the princi- pal g-values ^lies along ^the crystal ^{c-axis, the two}

others lying in the ab plane. The values are

ga z b = 6.45 ^{:t 0.01,} g;b = 0.6 ^{+0.1 and} g’ x = 0.5+0.1.

Any contribution to these values arising ^{from the}

second order coupling between the Yb 31 ion and the Zeeman field induced Van Vleck moment on the EU3 1 ions (exchange g-shift) ^is expected ^to be lower than

Fig. ^1.

^{170Yb Môssbauer} Absorption ^for EuAI03 ^{+ 2.5} % Yb". 83 % of the total absorption ^{is due to isolated ions} giving

a

slow relaxation lineshape (curve A). ^The remaining ¹⁷ % ^is mainly ^{due to} Yb" ions which

spin-spin coupled ^{to other} Yb" ions, giving

lineshape influenced by relaxation (curve B).

The total fit corresponds ^{to the}

^C.

the quoted ^{errors and so can be} disregarded. ^The

dominant value g"’ ^{lies at} angles ⁺ and - 30.50 1: ^0.5 relative to a crystal ^a axis. This angle ^{is to be} compared

with the local anisotropy ^{axes for} pure EuAI03,

where one of the principal ^{axes for the Eu3+ ion}

was found to lie at angles ^{of + and - 38° from the}

a axis in the ab plane [1].

The Môssbauer absorption spectrum ^{at 4.2 K} is shown in figure ^{1. From a} previous study ^{of the}

influence of Yb3 + ion concentration on the Môssbauer

absorption ⁱⁿ the orthoaluminate lattice [7] ^we expect that for a concentration of 2.5 % ^{Yb as used then}

near 90 % ^{of the Yb3 + ions} present ^{will not interact} with other Yb3 + ions and will show the slow relaxation limit spectrum ^{whereas the} remaining ¹⁰ % ^{will be} spin-spin coupled ^{to Yb} neighbours giving ^an absorp-

tion lineshape influenced by relaxation effects. The fits to the data show that 80 to 85 % ^{of the} total absorption ^is associated with isolated Yb3 + ions in

EuAI03. The difference between this value and the value 90 %, ^{can be} associated with impurities containing ^{Yb. An} X-ray analysis shows in fact that the impurity ^{level is in the} neighbourhood ^{of 5} %.

In the ground ^Kramers doublet of the Yb3 + ions in the C, sites the _energy levels of the ’7’oYb I = 2 excited state can be described by ^the Hamiltonian

where the magnetic hyperfine ^{« tensor » A and the}

electric field gradient (EFG) ^{tensor are} supposed ^to

have identical local principal axes, both tensors having

their largest ^values along ^{the local z} axis. This _assump- tion stems from the fact that because of symmetry

reasons (mirror plan ¹ c), ^the two tensors will both have the c axis as a principal axis and that the large principal g-value along Oz in the ab plane implies ^a ground ^doublet chiefly ^made up of ± 7/2 ) ^{which in}

tum induces a large ionic contribution to the EFG

along ^{this same} z-direction.

For the Yb3 + ion, ^{the lowest} multiplet ^J

7/2

is well separated from the excited J

5/2 multiplet

so that J remains a good quantum ^{number. In this}

case the A and _g «tensors» are proportional ^to

within a few percent ^and

so that A (MHz)

²⁶⁶ g.

From the slow relaxation limit spectrum ^of figure ¹ we find that A,,

^{25.4 ±} 0.3 mm/s (1.72 ^{x 103} MHz)

which corresponds ^to gZ

6.50 ± 0.07 ⁱⁿ agreement with the EPR result. From the Môssbauer analysis

alone it was not possible ^{to obtain accurate values for}

the small hyperfine parameters A x ^and Ay ^{but these}

are available from the EPR data.

Using the absolute magnitudes ^{of the 3} principal

g-values and the normalization condition we can

derive the Yb3 + wave functions if we make the

approximation that the local symmetry has the form

C2v ^{as then the wave} function involves only ^four

constants. (For the actual symmetry present ^{the wave} functions would involve eight constants.)

For Yb3+ in EuAI03 ^{we obtain}

which _compares with Yb3 + in Y AI03 [8]

and _compares with Yb3 + in TmAI03 for which the coefficient of 1 ± 7/2 ) ^{is also near 0.935.}

The quadrupole splitting parameter x ^{was obtained} from the Môssbauer data by blocking the A-values

at their EPR values. In fact two slightly ^different

values for x are found depending ^{on the} signs ^assumed

for the A-values. If the product of the three A-values is taken to be positive ^{a - 4.1} mm/s (279 MHz)

whereas if the same product ^{is taken to be} negative

then a - 3.8 mm/s (258 MHz). ^Now our measure- ments in the ordered region ^{of Yb3 + in} GdAI03 unambiguously ^{show that oc is near} 3.85 mm/s (262 MHz) ^{whereas for Yb3 + in} TmAl03 (X ^{is unambi-} guously ^{near 4.05} mm/s (275 MHz). ^As EuAI03

has crystallographic parameters ^{which are much} closer to those of GdAI03 ^{than to those of} TmAI03

it seems that for EuAI03 OC - ^3.85 mm/s (262 MHz)

is a more plausible choice. Also favouring this choice

are the calculated values of the dominant 4f part ^of the quadrupole splitting obtained from the above

wave functions which is 0.4 mm/s higher ^{for both} Yb 31 in YAl03 ^{and Yb3 + in} TmAI03 ^{than for Yb 31}

in EuAl03. ^{In tum these} results show that the product

of the 3 principal ^A (or g) values has a negative sign

in EuAI03.

The parameter 11 ^is expected ^{to be small} following

the highly uniaxial character of the ground ^doublet.

This is confirmed by the fits of the high temperature almost _pure quadrupole spectra. ^{The fits to the slow} relaxation spectra ^{at 4.2 K are in} fact insensitive to

the value ouf 1.

3.1.2 Phonon induced relaxation and crystal field splittings.

Above about 35 K the absorption lineshapes ^{show the influence} of electronic spin

relaxation effects. These spectra ^{have been} fitted to the relaxation lineshape ^{for extreme} anisotropy given by equation (79) of reference [9] ^{which involves} only

one relaxation parameter W -1. ^The lineshape expres- sions used strictly apply ^if only ^the ground ^Kramers

doublet of the Yb3 + ion is populated. ^An experi-

mental verification of this population ^{criterion can}

be obtained by following ^the thermal variation

Fig. ^2.

^The quadrupole splitting parameter

^for Yb’* in

YAI03 (0), TmA103 (e) ^and EuAI03 (D). ^With increasing tempe-

rature

in EuAI03 ^falls

rapidly ^{than in} YA103 ^and TmA103.

of the quadrupole parameter. Namely, ^{if this} para- meter varies as a function of temperature ^{then states} other than the ground ^{doublet are} populated ^{in the}

considered temperature range. However we make here what seems to be a reasonable approximation

that even in the _range where the quadrupole splitting parameter ^varies slightly ^with temperature ^{the same}

lineshape expressions ^{can be used. We} thus obtain both the relaxation rate W and the quadrupole splitting x ^as functions of temperature. ^The quadru- pole splitting ^results together ^{with those for Yb3 +}

in YAl03 ^{and Yb 31 in} TmAI03 ^are given ⁱⁿ figure ²

and the relaxation data in figure ^{3. Both} figures

Fig. ^3.

Electronic relaxation rates for Yb3+ in Y A 10

(0), TmAI03 (8) ^and EuA103 (0)

function of temperature. ^The results for YAI03 ^and TmAI03 ^{have been} decomposed ^{into Raman}

and Orbach contributions

shown by ^{the lines.}

show differences between the results for Yb" in

EuAI03 ^{and those for Yb 31 in} Y Al03 ^{or in} TmAI03.

For YAl03 ^and TmAI03 ^the quadrupole splitting

remains constant up ^to about 70 K whereas for

EuAI03 ^it begins ^to drop ^{at much lower} temperatures.

As the lattice contribution to the electric field gradient

is small and almost temperature independent, ^the

decrease of the quadrupole splitting ^with increasing temperatures ^for EuAI03 ^arises chiefly from the 4f electron contribution. Despite ^the large ^{error bars}

this clearly shows that Yb3 + states other than ground

state are significantly populated ^at temperatures where the phonon ^driven relaxation begins ^to modify

the Môssbauer lineshape.

Thus in EuAI03 the excited Yb3 + levels are at lower energies ^{than in} YAI03 ^and TmAI03. ^This

in tum suggests ^that the fitted values for W in Yb3 +

in EuAI03 ^{towards the} higher temperatures ^examined where the Yb 3 ’ excited levels are appreciably popu- lated are in fact not exact. This interpretation ^is supported by ^the observation that the relaxation data for Yb3 + in EuAI03 ^{cannot be} decomposed

into meaningfull Orbach and Raman contributions

as was done for YAl03 ^and TmAI01.

Yb34- in EuAI03 ^{thus has a} slightly ^less anisotropic ground ^state and lower lying excited levels than Yb3 + in Y AI03 ^or TmAI03.

3.2 Yb 3+ ^IN GdAI03, ErAl03 (AND YbAI03 [7]).

-

This section concerns the results for the ortho- aluminates which show the common property ^{of a} fairly ^fast Yb 3+ -host lattice spin-spin relaxation rate.

The host lattices concerned are all composed ^of

Kramers ions.

3 . 2 .1 Yb3 + in GdAI03. - The host lattice

GdAI03 ^{for which} TN = ^{3.87 K} [2] ^has low intrinsic

anisotropy. ^The crystal ^field anisotropy ^{of the Gd3+}

ions as measured by ^{EPR in} YA!03 [10] ^{defines a}

local _easy axis at roughly ⁺ and - 300 from a crystal

a-axis. This anisotropy ^{is not} sufficient to impose

the magnetic ^structure which well below TN ^{is in}

fact of the colinear antiferromagnetic type, ^the ordering ^direction being along ^the crystal ^a-axis [11].

Môssbauer absorption spectra ^at 0.35, 1.35, 2.14, 2.54, 3.18, ^{3.55 and 4.2 K are shown in} figure ^4.

In the paramagnetic region ^{at 4.2 K where the mea-}

sured relaxation rate is due only ^to spin-spin coupling

the rate observed is 4.3

10’ ° s-’ . This is to be com- pared ^{with the} spin-spin ^{rates for Yb 31 in} ErAI03 (3.0

¹⁰¹⁰ s-’) ^{and in} YbA103 (3.5

¹⁰¹⁰ s - 1).

At the lowest temperature ^studied (0.35 K) ^{a well}

defined limiting effective field lineshape ^{is observed.}

For the fit shown we obtain that the saturating hyperfine ^field experienced by ^{the Yb 3’} nucleus is 3.36 M0e and that it is directed along ^{the local Yb 3+}

Ising axis. This saturating hyperfine ^{field value} H_, corresponds ^{to a value} A.,

^25.3 mm/s (1.72 GHz)

or to a g.-

6.45 and is thus the same value obtained from the paramagnetic slow relaxation spectrum ^for

Fig. ^4.

^{"°Yb MÔssbauer} absorption ^for GdAI03 ^{+ 2.5} % ^{Yb3 +.}

The paramagnetic relaxation lineshape ^fit

^{used at 4.2 K whereas}

for the six temperatures ^below TN

^{3.87 K the data}

^fitted

to

mode] of relaxation between the molecular field split ^levels

of the Yb 31 ground doublet. The results at 0.35 K

be equally

well fitted by

effective field lineshape.

Yb3 + substituted in EuAl03 ^{which is the} adjacent

member of the orthoaluminate series. The value of the quadrupole splitting ^{is 3.85} mm/s (262 MHz).

In the ordered region ^{from 1.35 K to 3.55 K the}

results cannot be fitted by simply introducing ^an

effective field and it is necessary ^to include inter- mediate relaxation ef’ects. The fits shown on figure ⁴

were obtained by considering ^the relaxation between the two levels of the Ising-like ^{Kramers doublet as} split by ^the molecular field. This lineshape theory

follows that previously ^used by Nowik and Wick-

man [12] ^{and involves the} parameters ^{i which is} related to the fluctuation rate between the two elec- tronic levels and d their separation. ^As g. is known d

can alternatively ^be expressed ^{as 9,,} PH_, directly giving Hz ^the component ^{of the} molecular field

experienced by ^{the Yb3 + ion} along its local Ising-

like axis.

T is defined by (WT ⁺ W!)-l ^where WT ^and Wl

are the transition rates between the levels of the doublet. In the limiting ^{case where the} temperature is much higher ^{than Li then} WT = Wl ^and

where W-t ^{is the} relaxation rate which enters in the relaxation lineshape analysis ^{in the} paramagnetic region.

For the data between 1.35 and 3.55 K two fitting hypotheses ^were used. First T was blocked at a value

(2 WjP)-’ ^where Wï is the relaxation rate observed in the paramagnetic region (4.3

¹⁰¹⁰ s-’). ^This

gave ^{a set} of values for 4 which are shown by ^{the full}

circles on figure ^{5. A second set} of values for d, ^as shown by ^the open circles on figure ^{5 were obtained} by simultaneously fitting ^{both r and Lt. d is thus}

defined to within approximate ^limits encompassed by ^{the two sets} of results. When

is also fitted it

progressively ^increases by up ^{to a} factor of four with decreasing temperature.

Fig. ^5.

^The separation (4 ) between the two components ^{of the} Yb 3+ ground doublet in GdAI03

function of temperature.

The full circles

obtained by blocking the relaxation rate at the value found just ^above TN

3.87 K. The open circles where obtained by fitting ^{both A} and the relaxation rate. The two solid lines correspond ^to Brillouin functions for J

7/2 pegged ^at

T

3.87 K and normalized to different arbitrary heights ^at T

0.

It is to be noted that at the lowest temperature studied (0.35 K) ^the absorption lineshape ^obtained

is _very close to that associated with the fully ^saturated

effective field lineshape ⁱⁿ presence of fast relaxation and also with the slow relaxation limiting lineshape

for an Ising like level. In other words at these low temperatures (essentially ^kT L1) relaxation effects have _very little influence on the lineshape. ^{As L1 cannot}

be obtained with any accuracy in the region ^{where the} lineshape ^is independent of the relaxation rate, no

value for L1 at T

0.35 K can be given ^on figure ^5.

The two solid lines on figure ^{5 are} Billouin functions for J

7/2 ^both pegged ^at TN

^{3.87 K but with}

two arbitrary vertical normalizations chosen to rough- ly encompass the experimental ^{results. To within} expérimental accuracy L1 is described by ^Brillouin

function that is, ^the molecular field H,, experienced by ^{the Yb3 + ions} essentially ^{follows the J =} 7/2

host lattice magnetization.

It is not possible ^{to use} measurements on the Yb3 + impurity ^{to examine} any possible rotations of the Gd3 + moments as a function of temperature. ^{This is} for two reasons. First because of the high ^intrinsic anisotropy ^{of the} Yb3 + ion, ^{the field at} the Yb nucleus will remain parallel ^{to the local} easy-axis ^whatever

the direction of the molecular field (Ref. [7], Appendix)

and second the anisotropic ^{Yb3 +-ion} probably locally

distorts the magnetic ^{structure of} neighbouring ^iso- tropic ^{Gd3 + ions.}

3. 2. 2 Yb3+ in ErA103.

ErAI03 ^is unique among the Rare Earth orthoaluminates studied in that when ordered (TN - ^0.6 K) ^{the erbium moments}

do not lie in the ab plane ^{but are oriented} parallel

to the crystal c-axis with Cz type ordering [6]. ^This suggests ^that the easy axis of the crystal ^{field esta-}

blished Er3+ ground ^{doublet is the} c-axis. To confirm this point ^{and also to obtain more} quantitative

information concerning ^{the Er3 +} ground ^{state ani-} sotropy ^{we carried out some} measurements by ^EPR.

EPR results.

For these measurements the Er3+

ions were substituted into single crystal EuAI03.

This lattice was chosen as it is the non magnetic

lattice crystallographically ^{closest to} ErAI03.

(TmAI03 ^{could not be} prepared ⁱⁿ single crystal form.) Any contribution to the Er3 + g-values arising

from the second order Eu3 + -Er3 + interaction is

expected ^{to be} negligibly ^small compared ^{to the} crystal ^field g-values ^{and can thus be} neglected.

We find that the Er 3+ g-tensor ^has principal

directions which are along ^{the c} axis and in the ab

plane with g’

^8.71, gab

^{8.49 and} g’

^{2.60. The} principal ^axis gy6 ^{is at} ± 380 relative ^to the b-axis for the two differently oriented sites present.

These results confirm that the Er3 + single ^ion

easy axis lies along ^the crystal ^c-axis. However gz

is not very much bigger ^{than the next} highest ^value gÿb. ^{This contrasts with the} properties ^{of Er3 + in} ErFe03 [12] ^and ErCr03 [13] where gc ^{is close to}

12 in both ^cases and where it dominates the other two g-values.

Using the Molecular Field Approximation, ^and assuming that gz ^{was 12,} TN ^{due to the} dipolar ^inter-

actions was calculated to be 1.7 K [6]. By scaling

to the correct value of gz ^{as found here we find that}

the dipolar TN is ^{in fact near 0.9 K. As the} experi-

mental TN ^{is near 0.6 K this} suggests ^that dipolar coupling plays ^an important ^{role in} ErAI03.

Môssbauer results.

Môssbauer absorption

spectra ^were obtained over a wide _range of tempe-

Fig. 6.

^Môssbauer absorption ^{for 17°Yb3 + in} ErAI03 (TN - ^0.6 K). The solid lines

calculated using

^relaxation lineshape analysis, ^the relaxation rates obtained being given

figure ^{7. The data at 0.15 K could not be fitted} using ^either

effective field lineshape

analysis ^such

that used for GdAI03 : Yb 31 in the ordered region.

ratures down to 0.15 K. Spectra ^{obtained at 4.2,}

0.55 and 0.15 K are given ⁱⁿ figure ^6.

From just below the onset of phonon ^driven

relaxation (’" ³⁵ K) ^{down to 1 K -the relaxation}

rate has a temperature independent ^{value of}

3.0 ^x 1011 s-’. Between 1.0 K and TN (-0.6K)

the Yb 31 Môssbauer absorption lineshape pro-

gressively ^broadens. By describing ^this broadening uniquely ^{in terms of a} decreasing ^{Yb 3 ’ relaxation}

rate we obtain the values given ^on figure ^{7. This}

decrease _may be due to the onset of short _range

ordering.

Below TN ^the outstanding observation is the absence of _any measurable interna] field on the Yb 31

nucleus even at temperatures ^{as low as 0.25} TN.

Attempts ^{to use the} lineshape analysis of relaxation within a Kramers doublet split by ^a magnetic ^inter-

action as successfully ^{used for Yb3 + in} GdAI03

below TN, ^{failed to} give adequate ^{fits to the data}

in the ordered _range.

The non-applicability of this model ^as well as

the absence of internal field both stem from the

same origin. Namely that the molecular field _pro- duced by ^the Er 31 lattice, ^{which is} chiefly ^of dipolar

Fig. ^7.

Variation of the electronic spin relaxation rate W for Yb" in ErAI03 (TN - ^0.6 K).

origin, ^{is directed} along ^{a difficult axis} for all the substituted Yb3+ ions. That is it is directed along ^the

direction of the principal value gx (g’ « g:b) ^{for all}

the Yb3 + ions.

The only noticeable feature which occurs in the

magnetic ordering region ^is curiously ^a progressive resharpening ^{of the} lineshape ^below TN. The misfits obtained below TN ^{are further} briefly discussed in section 5.

3.3 Yb3+ IN DyAI03, TbAI03, HoA103. - ^This

section concerns the results for the orthoaluminates which show the common property ^{of a} fairly ^slow Yb3 +-host lattice spin-spin relaxation rate.

3 . 3 .1 1 Yb 3+ in DyAI03- - TN ^for DyAI03 ^is

3.5 K [4]. ^The D y3+ ground doublet is highly ^aniso- tropic with gz - ¹⁸ (close ^to the maximum possible

value 2 _gj J

20) ^and with g.l very small. The Ising

axis for the Dy3 + ions lie in the ab plane ^{at about}

± 330 from ^a crystal b-axis. This axis is perpendicular

to the Ising ^{axis for a Yb3 + ion at the same site.} By comparing ^{the Môssbauer} lineshapes ^of 161 Dy ⁱⁿ DyAI03 just ^above TN [14] with those obtained in other Dy3+ Ising systems ^{where the} lineshapes ^are

modified by relaxation [15] ^we estimate that the

spin-spin relaxation in DyAI03 ^is quite ^{low and is} probably well below 1 x 109 S - 1 .

Figure ⁸ shows the Yb3 + Môssbauer results at 4.2 K and 1.35 K. The spin-spin relaxation rate

above TN ^{is near 1 x 109 S-1} and the variation of this rate at higher temperatures ^{into the} phonon region ^{is shown on} figure ^9.

The absorption lineshape ^{at 1.35 K ( - 0.4} TN)

is only slightly different from that obtained in the

paramagnetic region. ^{The onset of} ordering ^within

the Dy3 + ^lattice slightly modifies the widths of the

absorption lines but does not change ^their positions.

In fact, ^{for an} extremely anisotropic ^{doublet the} absorption lineshape ⁱⁿ the slow relaxation limit in the paramagnetic region is identical with the lineshape

in the magnetically ^ordered region ⁱⁿ presence of a

Fig. ^8.

^Môssbauer absorption ^{for Yb3 + in} DyAI03 (TN

^3.5 K).

The fits shown by the solid lines in both the paramagnetic region

and in the ordered region

^made using

relaxation lineshape analysis.

Fig. ^9.

Spin relaxation rates for Yb3 + in HoAI03 (0), DyAI03 (Â) and TbAI03 (Q). ^For HoAI03 ^{in the} range 2.5 to 8 K the relaxation rate follows

exponential ^law W(109 ^s-’)

^4.0 exp(- 2.3/F)L

saturating intemal field directed along ^{the local}

easy axis. Consequently ^an absorption spectrum which is close to the slow relaxation limit in the para-

magnetic region ^{such as Yb 31 in} DyAI03 ^cannot change ^{much when the host} lattice becomes magneti- cally ^ordered.

To obtain adequate ^{fits in the ordered} region (at least down to 1.35 K) ^a relaxation lineshape ^{has to}

be used. The fit shown in figure ^{8 was obtained} using

the same model of relaxation between the levels of

an Ising ^{doublet whose} degeneracy ^{is lifted} by ^the

molecular field as was used for Yb3 + in GdAI03

in section 3.2.1. The relaxation rate was blocked

at the valued obtained at 4.2 K in the paramagnetic region ^{and L1 was fitted} giving ^L1

^{1.3 K. This}

value, which is only approximate ^{as it} depends ^on

the precise ^value assumed for the fluctuation rate in the ordered region, ^{is about one} third of the saturated value of L1 for Yb 31 in GdAI03 ^obtained by ^{the same}

method.

In DyAI03 ^the magnetic ^structure in the ordered

phase ^{is such that the two nearest} Dy3 + neighbours along the c-axis have their moments aligned per-

pendicular ^{to the Yb3 + local} Ising-like ^{axis. The} molecular-dipole ^{field due to these two} neighbours ^is expected ^to have little influence on the probe ^ion

and a larger contribution to the Yb3 + magnetization probably ^comes from the four Dy’+ neighbours ^{in the}

ab plane. ^{This is to be} compared ^{with the case Yb3 +}

in ErAI03 ^{where the Er moments are all} aligned perpendicular ^{to the} Ising-like axis of the Yb3 + ion and produce ^no discemible polarization ^{of the} probe.

3. 3. 2 Yb3 + in TbAI03. - ^The ground ^state

of the Van Vleck Tb3+ ion in TbAI03 ^is composed

of two singlets separated by ^an energy which is smaller than that corresponding ^{to the} magnetic ordering temperature TN

^{3.95 K, the two} singlets being

made _up chiefly of linear combinations of the highest

allowed MJ = 1 ^± 6 ) ^states [3]. ^The magnetic ordering ^is triggered by interactions within the electronic system.

The Tb3 + moments when ordered lie in the ab

plane ^at angles ^{of ± 350 to a} crystal ^a-axis. They ^are

thus colinear with the local _{easy axis} for a Yb’+ ion

at the same site.

Measurements were made both in the paramagnetic

and in the ordered regions. ^{As shown on} figure ⁹

the temperature independent spin-spin ^rate just ^above TN ^{is near 1.0 x} 109 S - 1. This is almost the same

value as for Yb3+ in DyAI03. ^A conventional phonon

induced relaxation branch is visible above about 30 K.

In the ordered region, the results are again very similar to those for Yb 3+ in DyAI03 ^{and below} TN

relaxation again influences the lineshapes. ^{The fits}

show that at 1.35 K, ^the separation ^{A between the}

Yb3 + ground ^{state levels is} higher ⁱⁿ TbAI03 ^{than in} DyAI03. ^{This can} be correlated with the fact that in

TbAI03 (but ^{not in} DyAI03) ^the Ising like axis of

a Yb 3+ ^{ion is} parallel ^{to the} Ising like axis of the two nearest Tb3 + neighbours along the c-axis. This

parallelism enables the exchange ^and dipole ^fields produced by ^{these Tb3 + ions to be} fully ^effective

so giving ^a larger ^{d .}

3. 3. 3 Yb3+ in HoA103. - ^{The two lowest} singlet

levels of the Van Vleck Ho3+ ion in HoAI03 ^are separated by ^L1

^{7.8 K} [16] ^{and are distant} by

about 60 K from the nearest excited levels [17].

The magnetic ordering temperature ^{is low} (TN - ^0.02 A) ^{and the} ordering ^is triggered ^{in this}

case by ^the hyperfine interaction [5]. ^In the ordered

region ^{the Ho3 + moments lie in the ab} plane ^at angles + 310 ^{to a} crystal b-axis. This direction is almost perpendicular ^{to the} Ising like axis for a Yb’ ’ ion at the same site. For Yb’+ in HoA’03 (in ^contrast

to Yb3 + in TbA)03) paramagnetic relaxation mea- surements can be made at temperatures ^{much lower} than that corresponding ^{to the} separation ^between

the two lowest singlet ^levels of the host lattice ion.

Figure ^{9 shows a} conventional high temperature

phonon induced relaxation branch above about 40 K and a conventional temperature independent spin-spin ^branch from about 20 K to 40 K where the Yb3 + cross relaxation rate is quite ^low

but higher ^{than for Yb" in} DyAI03 ^and TbAI03.

Below about 10 K the Yb 3’ relaxation rate shows

an unusual spin-spin behaviour in that it decreases with lowering temperature. Identical results were

obtained with samples ^with Yb/Ho concentration ratios of 0.02 and 0.05.

The temperature variation of the Yb3+ relaxation

rate in the _{range 2.5} to 8 K, ^{follows an} exponential

law (see Fig. 9)

4. Discussion of the relaxation results.

In this section we consider the relaxation results with a

view to examining ^the importance of the various

possible contributions to the Yb3 +-host lattice cross

relaxation in the different cases.

4.1 1 KRAMERS IONS HosTS.

We have previously developed ^{a method based on} the Fermi Golden Rule which enables quantitative ^{cross relaxation}

rates to be obtained from the exchange/dipole ^Hamil-

tonian describing the interaction between a substituted ion and the host lattice ions [7]. ^{As in all the Rare}

Earth orthoaluminates the Yb3+ ion has Ising-like characteristics, ^{a natural} quantization axis exists

even in the absence of an externally applied ^field.

The Hamiltonian ^can thus be factorized into two

parts respectively involving ^{terms which are} diagonal

and off-diagonal ^{to the} spin ^{of the Yb3 + ion. The} off-diagonal ^terms provide ^the strengths ^{of the matrix}

elements involving ^{the Yb3 +} electronic spin flips

and the diagonal ^elements provide ^the density ^of

states of the spin ^bath.

This approach ^was previously applied ^to YbAI03

where the substituted ion is the same as the host lattice ion. Here we apply this method to cases where the host lattice ion is different from the substituted ion. Knowing ^the -values ^{for the} different host lattice ions and knowing ^{that the} g-values ^{for Yb3 + are}

essentially ^{constant across} the series we can exactly

calculate the cross relaxation rate due to the dipole- dipole interaction. For DyA103, GdAI03 ^and ErA103

the calculated dipole-dipole ^cross relaxation rates are 0.6, ^{2.5 and 0.9}

^{109 s-’} respectively. ^These

are to be compared ^{with the} experimental ^results 1.0,

43 and 32

109 s -1

respectively.

For Yb3 + in both GdA103 ^and ErAI03 (and ^for YbAI03 [7]) ^the calculated dipole-dipole ^relaxation

rate falls well short of the experimental values. This

clearly ^{shows that the cross} relaxation in both these

cases is chiefly ^driven by ^the Yb3 + -host lattice

exchange interaction. Only ^{for Yb 31 in} DyAI03

does the dipole-dipole interaction account for the greater part of the measured relaxation rate.

The dominant mechanism associated with this

dipole-dipole interaction is the flip (Yb)-diagonal (Dy)

term whose matrix element is proportional ^to (g"y gy’)’. Although the matrix element associated with this flip-diagonal ^{term is} large ^{due to the} high

value of gDy ^(so favouring high relaxation rates),

the density ^{of states of the} spin bath is in turn low

(so favouring low relaxation rates). ^{And in fact}

because changing ^{the value of} ezy ^has opposite

influences on the matrix elements and on the density

of states the calculated flip-diagonal relaxation rate is not particularly ^{sensitive to the} precise ^{value of} 9Dy ^used.

It has previously ^been experimentally ^observed [18]

that for a number of matrices where the Yb" is present in concentrated form (that is the impurity

ion and the host lattice ion are both Yb3 +) ^the spin- spin relaxation rate is low when the Yb3 + g-values

are highly anisotropic (high ^{gz, low} g.1) and that it is

high ^{when the Yb3 +} g-value ^is isotropic. ^{Here we}

see that this tendency also exists for an Yb3 + ion with given g-values interacting with different hosts.

That is, ^the experimental ^{Yb 31 cross relaxation}

rate is low for DyAI03 where the host lattice ion is

highly anisotropic ^and relatively high ⁱⁿ ErAI03 ^and GdAI03 where the host ions are more isotropic.

In the present case we see that these different experi-

mental rates are not due to the influence of the aniso- tropy ^{on the} dipole-dipole interaction but are due rather to differences in the importance of the various Yb3 +-host lattice exchange interactions involved.

4.2 VAN VLECK IONS HOSTS.

The two Van Vleck ion host lattices where magnetic ^{cross relaxation}

occurs are HoAI03 ^and TbAI03. Both host ions ^are characterized by ^{a two} singlet ground ^{state. Such}

two singlet systems ^can be described using ^{the for-}

malism of pseudo spins ^S’

1/2 coupled by exchange [19]

Li is the energy gap between the ^two lowest crystal

field singlets ^and p the angular ^{momentum matrix}