Nuclear antiferromagnetism in lithium hydride

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Nuclear antiferromagnetism in lithium hydride

Y. Roinel, V. Bouffard, P. Roubeau

To cite this version:

Y. Roinel, V. Bouffard, P. Roubeau. Nuclear antiferromagnetism in lithium hydride. Journal de

Physique, 1978, 39 (10), pp.1097-1103. �10.1051/jphys:0197800390100109700�. �jpa-00208849�

NUCLEAR ANTIFERROMAGNETISM IN LITHIUM HYDRIDE

Y. ROINEL, ^V. BOUFFARD and P. ROUBEAU CEN Saclay, ^{B.P. N°} 2, ^{91190 Gif sur} Yvette, ^France

(Reçu ^{le 22 mai} 1978, accepté ^{le 20} juin 1978)

Résumé.

L’antiferromagnétisme ^{nucléaire a} été créé dans l’hydrure de lithium (LiH) par la méthode désormais usuelle : 1) Polarisation dynamique nucléaire, ^{dans un} champ ^{de 5,5 T ;} 2) ^Désai-

mantation adiabatique ^{dans le} référentiel ^{tournant. Un} réfrigérateur à dilution d’un type spécial

a été construit, pour obéir aux contraintes particulières ^de l’expérience. L’état ordonné subsiste

plus d’une heure après la désaimantation. On a obtenu par RMN trois types d’évidences expé-

rimentales de la structure ordonnée : 1) Forme de la raie d’absorption dipolaire ^des spins ^nucléaires

de 7Li; 2) Comportement ^{de la} susceptibilité perpendiculaire ^{de ces} spins ^en fonction de l’énergie dipolaire; 3) Dédoublement de la raie d’absorption Zeeman des spins nucléaires de 6Li. A la lumière de ces résultats a été entreprise ^une étude de LiH par diffraction de neutrons, qui ^a porté ^ses premiers

résultats.

Abstract.

A nuclear antiferromagnetic ^{structure has been} produced in lithium hydride (LiH) by the usual method : 1) Dynamic ^nuclear polarization ⁱⁿ high ^field (5.5 T); 2) ^Adiabatic demagne-

tization in the rotating frame. ^{A dilution} refrigerator ^of special design has been built for the particular

features of the experiment. The ordered state persists ^{for more than one} hour after the demagne-

tization. Three types of evidence have been obtained experimentally by ^{NMR on} the ordered struc- tures : 1) Shape ^{of the} dipolar absorption ^{line of the 7Li nuclear} spins; 2) Behaviour of the per-

pendicular susceptibility ^{of these} spins ^{as a} function of dipolar energy; 3) Splitting ^{of the Zeeman} absorption line of the 6Li nuclear spins. Following ^{these results, a neutron} diffraction study ^{of LiH}

has been undertaken and has already yielded ^{some results.}

Classification

Physics ^Abstracts

76.50

75.50E - 75.25

76.70E

1. Introduction.

It has been pointed ^{out a} long

time _ago [1] ] ^{that an} assembly ^{of nuclear} spins ^{in a} crystal ^with dipolar interactions should reach an

ordered state at a sufficiently low field and tempera-

ture. An order of magnitude of the critical field Hé

and temperature Te ^is given by the linewidth of the NMR line of those spins, ^{which is} precisely ^{due to} dipolar interactions. This yields typical ^{values of :}

Such low nuclear spin temperatures ^{can be obtained} in insulators through the well known two-step process

proposed by Abragam ^{in 1962} [2]. ^{The first} step consists in a dynamic polarization ^{of the nuclei in a} high field H, ^and brings ^{the nuclear} temperature ^into the millikelvin range. The second step ^{is an adiabatic}

demagnetization ^which eliminates the magnetic field, and reduces the nuclear spinjjempcrature by ^{a factor :}

possibly ^below Te. ^{The two main} conditions the

samples ^{must fulfil} are, obviously, ^a long ^nuclear spin-lattice relaxation time, ^{and the} possibility ^of obtaining high ^nuclear polarizations by ^{means of the}

solid effect. ^These conditions, along ^{with the necessity}

of having ^a simple crystalline structure, ^{were met} in

CaF2 doped ^{with Tm2+} impurities, and since the first successful experiment ^{in 1969} [3] ^{the ordered structures}

of 19F nuclear spins ^have been studied extensively ⁱⁿ CaF2 [4]. ^{The need for} studying other substances and

particularly ^{LiH arose} from the desire to ascertain the nuclear ordered structure by ^neutron diffraction.

It has long ^been recognized [5] that this was not

possible ⁱⁿ CaF2 because of _{the very} small spin- dependent amplitude ^{of the} neutron-fluorine scatter-

ing ⁱⁿ contrast to the case of protons [6]. In addition,

it was interesting ^to study ^{a structure} slightly ^more complicated than that of CaF2. ^{LiH contains} prin- cipally ^{two nuclear} species, protons ^and ’Li, ^with spins respectively 1/2 ^and 3/2, having comparable magnetic moments, and forming ^two imbricated f.c.c.

lattices. The theoretical calculations due to Gold-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0197800390100109700

1098

man [4] predict ^{that each} species contributes to the ordered phase, ^{and that both} protons ^{and lithium are} present in each sublattice. Nuclear antiferromagne-

tism studies had been made previously ^{on lithium}

fluoride (LiF) ^{whose structure} is identical ^to that of LiH [7]. ^{We wish to} report ^{here recent} experiments

on nuclear antiferromagnetism ^{in LiH as observed} by ^NMR. During ^the writing ^{of this} article, ^{a nuclear} superstructure line has been observed by ^neutron

diffraction in LiH, ^{and this} preliminary ^{result is} reported ^elsewhere [14]. ^We restrict ourselves in this article to the description ^{of the NMR} observations made on antiferromagnetic ^{LiH in} August ^and Sep-

tember 1977, before the diffraction experiment.

2. Dynamic polarization.

^The principle ^of dyna-

mic nuclear polarization (DNP) consists in saturating

off-centre the ESR line of some paramagnetic impu-

rities present ^{in the} sample. The result obtained

depends very much on the nature and the concentra- tion of the paramagnetic impurities, ^{as well as on}

the experimental conditions such as : magnetic field, lattice temperature, ^{etc. A recent and} complete ^review

of DNP can be found in ref. [8]. ^We simply specify

here the features relative to our samples. ^{The mecha-}

nism of polarization ^{in LiH as in LiF} containing ^a

few 10-4 of F-centres, is well established and consists in a cooling of the nuclei by ^thermal mixing ^{with the}

electronic spin-spin interactions reservoir, itself cooled

by the effect of the microwave irradiation of the ESR line of the F-centres. However, ^some spurious effects,

not well understood _{up to now,} limit the nuclear

polarization ^to values lower that what could be

expected ^from theory [8] ^and dependent upon the

sample preparation. Samples ^of pure LiH, kindly

furnished by ^{Dr. Bédère} (1), ^{in the} shape ^{of thin}

slices of dimensions 5 ^x 5 ^x 0.5 _mm, were irradiated with 1.5 MeV to 3 MeV electrons in order to create the F-centres. Previous studies [9] have shown that the temperature ^{of the} sample during this irradiation

plays ^an important role, ^{and a} special temperature control apparatus has been built [10]; ^however, obtaining ^a good sample ^{is still} subject ^to uncertainties.

The best results have been obtained with sample ^{n° 1}

of ref. [9] which reached after 50 hours of polarization

a nuclear temperature ^{of 3 mK in a field of 5.5} T;

this corresponds ^{to a} proton polarization ^{of 95} % (80 % ^for ’Li). ^{Another of the} samples studied, labelled # 17, reaches smaller polarizations (80 % ^for protons) ^{but in} only ^{15 hours.} The F-centre concen-

tration Ne and relaxation time Tle ^{of this} sample

have been measured by ^the methods described in ref. [9] ^{and are} respectively :

(1) Service de Métallurgie Physique, ^{B III} Bruyères-le-Châtel,

B.P. n° 61, ⁹²¹²⁰ Montrouge, ^France.

Most of the apparatus ^{is the same as in ref.} [10].

However, ^we introduced in July ^{1977 two} important

modifications. The first is the use of a dilution refri- gerator (Fig. 1) ^{of the} type ^new geometry described

by Roubeau in ref. [11] ; the second is a lower part ^of the ’He dewar which is composed ^{of two coaxial} cylindrical ^{Kel-F tails} glued ^to the upper parts by

means of stycast. The Kel-F-metal bounding ^{is found}

to be leak-proof ^{over a} period of several months, ^and

to be quite unsensitive to thermal shocks and to vibrations. The inner tail has an internal diameter of 6 mm and contains only ^the sample and its Kel-F

holder, plus ^{a small 0.7 x 1 mm} teflon tube driving

the concentrated phase ^{down to below the} sample.

The RF coils and the microwave system ^{are now} rejected ^to the outside of the outer tail (of ^external

diameter 10.5 mm) ^{in the ’He bath at 2.5 K. This}

geometry, ^well adapted ^{to the} perspective ^{of neutron} diffraction, has also the advantage ^of minimizing ^the

losses due to microwave during ^the DNP, ^{and to the} radiofrequency during ^{the adiabatic} demagnetization.

FIG. 1.

The lower part of the dilution refrigerator cryostat.

a) Insulating vacuum ; b) Still ; c) Insulating vacuum ; d ) 06 ^mm guide filled with the sample holder ; e) Spirally wound heat exchan- ger ; f ) ^{Leak flow} impedance; g) Coiled heat exchangers;

h) Pseudo-mixing chamber ; i) Metal-Kel-F stycast glued joints ;

j) ^Kel-F tails ; k) Concentrated phase tubing.

At the optimum polarizing ^microwave power, the temperature ^{of the} sample ^{is about 200 mK whereas}

in ref. [10] ^{in the same} conditions it was 500 mK and the ’ Li polarization ^{could not exceed 35 to 40} %.

The lowering ^{of the} sample temperature ^{seems thus}

to be essential for these experiments, ^{and a new refri-} gerating system taking these features into account has been built for neutron diffraction and is presently being tested. Another particularity ^{of this} refrigerator

is the _presence along its axis of a 6 mm diameter passage for introducing ^the samples ^{at low} temperature (the ^{F-centres are not stable at room} temperature).

It takes about one hour to remove a sample, ^introduce

a new one and cool it from 77 K to 100 mK.

No NMR measurements were made on the protons because of the _presence of a very strong spurious signal ^{due to} protons probably located in the cryostat tails and in the sample ^holder (the Kel-F available to us does contain protons). ^The polarization ^{of the}

’Li nuclei is measured by comparing ^{the area of the} absorption signal ^{of those} spins with that obtained at thermal equilibrium ^{at 4.2 K. The} polarization ^of

the two other nuclear spin species (’ H ^and 6Li) ^is calculated, using the well-verified [15, 16] hypothesis

of equal spin temperature.

3. Adiabatic demagnetization.

^For the second step, ^{we use} the so-called Adiabatic Demagnetization

in the Rotating ^Frame (ADRF). This consists in a

familiar fast passage stopped exactly ^at the nuclear

resonance. More details about this technique ^{can be}

found in ref. [4]. ^The difference with the case of CaF2

lies here in the fact that both ’Li and 1 H must be

demagnetized simultaneously. ^{The NMR} frequencies

chosen in our experiment ^are respectively

and

The amplitudes ^{of the two RF fields are of the}

)rder of 50 mG, ^{and the} sweep ^rate dH/dt ^{is 1} G/s.

B. well-known advantage of the ADRF as compared

:o conventional demagnetization is that the ordered

;tates produced ^can be observed by the usual techni- lues of NMR, ^{since the} high magnetic field is still présent. Furthermore the Hamiltonian responsible ^for

;he ordering ⁱⁿ high ^field being the truncated dipolar Hamiltonian, ^{which is} orientation-dependent, ^{it is} possible ^to produce different kinds of ordering by -hoosing the orientation of the field with respect ^to

;he crystalline ^axes. Positive and negative temperatures

iave been investigated. ^{With a} given initial nuclear

)olarization, ^{this can be done} by simply starting ^the

ADRF from above or below the resonance. In both -ases, with H ç [100], ^{the structure} predicted by ,heory ^is antiferromagnetic ^{and consists in} (110) )lanes in which the spins ^are alternatively parallel ^and mtiparallel ^{to H} (Fig. 2). ^{At T} > 0 the spins ^of protons ind lithium nuclei are parallel ^{in a} given (110) plane,

FIG. 2.

Stable structure expected ^{at low} temperature ^with Ho 1’[100] ^at negative ^and positive temperatures.

whereas they ^are antiparallel ^{at T 0. A} very impor-

tant feature for NMR is the _presence of lithium in both sublattices, ^{as will} appear later.

4. Observations on the ordered state.

The NMR

absorption signal of lithium nuclei is recorded with

a voltage Q ^meter, during ^{linear sweeps of the} magnetic

field. The methods of detection, using ^a multichannel

analyzer, ^{and the} general geometry ^{of the} experiment

have already been described elsewhere [10, 7]. ^After

the ADRF, ^the spin temperature is of the order of 1 gK, ^{and then} begins ^{to increase} slowly ^{under the}

effect of the dipolar spin-lattice relaxation, ^{at a rate} depending ^on the lattice temperature ^and varying

somewhat from one sample ^{to another} [9]. Typically,

the lattice temperature ^{is 100} mk during ^this phase

of the experiment, ^{and the} dipolar relaxation time is several hours.

4. 1 SHAPE OF THE ’Li ABSORPTION LINE. - The NMR absorption signal ^{of the ’Li} nuclei is shown on

figure ^{3 at} different times after the ADRF. The first

signals strongly suggest the existence of two species

of ’Li nuclei, ^with opposite polarizations, ^and seeing opposite ^local fields, ⁱⁿ accordance with the Weiss field description ^of antiferromagnetism. ^{As the time} elapses, the disorder of the spins increases, ^{and the}

two components broaden and _merge together. ^The shape of the line evolves smoothly towards the usual, paramagnetic, high temperature dipolar ^line (Fig. 3f),

and it is difficult to detect accurately by this method the antiferro-paramagnetic transition.

4.2 TRANSVERSE SUSCEPTIBILITY OF 7Li NUCLEI.

Another evidence for the existence of an antiferroma-

gnetic ^{state is the near} constancy ^{of the transverse}

susceptibility xl of the spins ^{for the lowest} spin ^tem- peratures ^T. However, ^the temperature ^{in this} highly

non-linear domain is not related in a simple ^manner

to quantities ^measured by ^{NMR. A better} parameter is given ^instead by ^the dipolar energy of the spins,

which is an increasing function, of 1/ T (proportional

1100

FIG. 3. - Negative temperature. Sample ^{n° 1. NMR} absorption signal ^{of ’Li nuclei versus} magnetic ^{field at} various times t after

the ADRF (t ^{= 0 :} beginning ^{of the} ADRF). a) ^{t =} 2’ ; b) ^{t =} 10’;

c) t = 20’ ; d) t = 30’; e) t = 40’ ; f) ^{t = 80’.}

to 1/T ^at high temperature). As shown in ref. [4] ^and [12] ^{the first moment of the NMR} dipolar absorption

line is proportional ^{to the} dipolar energy, when

only ^{one nuclear} spin species ^is present. ^{With two} nuclear species, ^{1 H and} ’Li, ^{the first moment is} pro-

portional ^to

where JC’LiLi ^{is the} part of the truncated dipolar ^Hamil-

tonian relative to interactions between’Li nuclei, ^and

£’LiH ^the part ^{relative to} interactions between ’Li and iH nuclei. The transverse susceptibility xi ^can be extracted from the dipolar absorption signal through

a Kramers-Krônig ^transform [4]. Both xl ^{and the}

first moment, (5) ^{can be} calibrated by comparison

with a Zeeman signal corresponding ^{to a known} polarization [12], ^so that it is possible ^{to have absolute}

values for these quantities, ^for comparison ^with theory.

The computation ^{of the first moment and the} Kramers-Krônig ^{transform are} performed ^{on the}

recorded dipolar signals by ^{means of a HP 9820 elec-}

tronic calculator. The experimental ^{results are shown}

on figure ⁴ (points). ^{We have also} plotted ^{on the same} figure the theoretical curves 1) ^{in the} paramagnetic

FiG. 4.

Negative temperature. Sample ^{no 1.} Perpendicular susceptibility xi ^{as a} function of the first moment for ’Li nuclei, in the demagnetized ^{state at T 0.} X, is defined as in ref. [12] ^and

is expressed ⁱⁿ G-1 , MLi1 ^is expressed ^{in G.}

high temperature ^limit neglecting the effect of the

impurities ^and 2) in the Weiss-field approximation, according ^to calculations given ^{in ref.} [7]. ^{As a func-}

tion of time, ^the experimental plot ^{is to} be read from the top right ^to the bottom left. The trend to a plateau

is noticeable at low temperature. However, this effect is not as pronounced ^{as in} CaF2 [4]. ^The discrepancy

of 30 % with the Weiss-field plateau, comparable ^to

that observed in CaF2, ^{is far} outside the experimental

error, and can perhaps be attributed to the crude-

ness of the theoretical model. A discrepancy ^also

exists in the high temperature domain : it can be shown that the reciprocal slope ^{of the curve in the} paramagnetic, high temperature ^{limit is} equal ^{to the}

second moment of the Zeeman absorption ^{line. The}

excess by ^a factor of two observed experimentally (Fig. 4) ^with respect ^to the theoretical second moment of the 7Li absorption ^{line is} presumably ^{due to the}

presence of the F-centres, ^whose dipolar fields add a

Lorentzian broadening ^{in the} wings of the NMR line.

The impurities could also be responsible ^{for the dis-}

crepancy observed at low temperature.

4. 3 SHAPE OF THE 6 Li ABSORPTION LINE. - The

most spectacular effect of the antiferromagnetic ^tran-

sition observed by ^{NMR is the} splitting ^{of the 6Li} absorption line. This isotope ^{of lithium, with a} spin ¹

and a NMR frequency ^{of 34.303 MHz} in the field Ho

of the experiment, ^{has in our} samples ^{an abundance}

c ⁼ 3 % (lower ^than its natural value 7 %). ^{It is used}

here as a probe that should not perturb ^{too much the}

ordered state, and gives local details on the structure.

A similar experiment ^has already ^been performed ⁱⁿ CaF2, using ^{the 43Ca} spin ^{as a} probe [4]. However, in antiferromagnetic CaF2 ^the Weiss-field on calcium sites is _zero, and one could observe a splitting ^{of the}

line only ^{in a different} phase ^called ferrosandwich,

obtained when the demagnetization ^is performed ^with

H parallel ^{to a} [111] ] direction. In antiferromagnetic

LiH on the contrary, the Weiss field on lithium sites

HW ^{is non-zero, and one can} expect ^a splitting by

an amount 2 HwL’ ^{of the 6Li Zeeman} absorption ^line

into two components. ^{The two} components ^{are not}

expected ^{to be} identical in general because of the strong tendency ^to dipolar ordering. ^{Let a be the inverse}

Zeeman temperature ^{of the 6Li} nuclei, ^and fi ^their

inverse dipolar temperature, ^{which is common to all} the nuclear species ^{of the} sample, ^as has been shown

experimentally [13]. Under the effect of the Zeeman interactions alone, ^we should observe two lines of the

same intensity proportional ^{to :}

(where B1 is the Brillouin function for spins ¹ and y6

the gyromagnetic ^{ratio of 6Li} nuclei) ^{and whose}

centres are respectively Ho ⁺ HwLi ^and Ho - HWLi .

On the contrary, under the effect of dipolar ^interac-

tions alone, the Weiss-field theory predicts ^{that the}

two lines will be of opposite intensities, namely :

and

The shape ^{of the ’Li} absorption ^{line in} figure ^{3a is} compatible ^{with a} formula of this type.

A straightforward generalization of the Weiss for- mulae where both Zeeman and dipolar interactions

are taken into account yields ^{for the two} intensities :

and

In order to be able to see two distinct lines of com-

parable intensities, ^{it is} very useful to lower the Zeeman temperature ^{so as to make the term} aHo ^dominant

in (8). ^The technique, ^{as in} [17], consists in mixing ⁱⁿ

the rotating frame the Zeeman reservoir of 6Li with the dipolar reservoir, by application ^{of a} strong ^RF field at a distance Li = - y6 Heff ^{from the resonance} frequency ^{of the 6Li. In a frame} rotating ^{at a fre-}

quency - yHo - d, the inverse Zeeman temperature of 6Li :

will then become equal ^to fl, ^and equations (8) ^can

be written :

and

In practice, ^the mixing ^{in the} rotating ^{frame is} expected ^{to become} exceedingly slow if the effective field Heff ^{is too} large. Experimentally ^{in our conditions}

the limiting ^{value of} Heff ^{is 45 G. A} rough estimate,

of the heat capacity Cf of the effective Zeeman reser-

voir of 6Li in the rotating ^{frame and} Cdip ^{of the dipolar}

reservoir yields :

where y6 ^and 77 ^are the gyromagnetic ^{ratios. With} c = 3 X 10-2, Heff = 45 Gand H!} = 10 G, one

has

and the heating ^{of the} dipolar reservoir induced by

this operation ^is very small. In order to minimize this heating, ^we have made the mixing reversible, by sweeping slowly ^the effective field from an initial value

H° f ^{to 45 G} (at positive temperature) ^{or to - 45 G} (at negative temperature). The initial value H ° f ^is

determined in such a way ^{as to} introduce no irreversi-

bility ^{at the} switching ^{on of the RF} power : this means

that the inverse Zeeman temperature a;n of 6Li in the effective field H0eff before the thermal mixing ^{must be} equal ^to the inverse temperature fl ^{of the} dipolar

reservoir : ^-

P ^{is not known but can be} guessed approximately,

and also deduced from the polarization ^{of the 6Li}

nuclei after the mixing ^{as in} [18]. ain is known from the initial ’Li polarization. ^{In our} conditions, ^this polarization, ^{due to the} DNP, ^{is 30} % ^and H.Of f 1 - ^{10 G.}

The results are shown on figure ^5. Figure ^{5a shows}

the signal ^{of 6Li after the DNP} and before the ADRF, and corresponds ^{to a} polarization ^{of 30} %. ^In figure ^5b,

we have saturated the 6Li resonance before the ADRF :

no signal is thus detectable at this time. Figure ^5c

FIG. 5. - Negative temperature. Sample ^{no 1. NMR} absorption signal ^{of 6Li nuclei versus} magnetic field for different polarizations ^P.

a) At the end of the ADRF : ^{P =} 30 % ; b) After saturation of the 6Li : P ⁼ 0 ; c) After the ADRF, when P ⁼ 0 ; d) ^After

the ADRF, ^{when P =} 30 % ; e) After the ADRF + mixing ^with

the dipolar reservoir, ^{when P = 65} % ; f ) Theoretical signal

expected ^{after the ADRF for P = 100} %.

1102

shows the 6Li signal ^{after the ADRF : the Zeeman}

temperature is still infinite (a ⁼ 0) ^{but a} dipolar signal

appears, which _{is very} similar to that of ’Li (Fig. 3).

In another experiment ^{we do} not saturate the ’Li at the end of the DNP, ^{and we} get, after the ADRF of ’Li and 1 H, ^the signal ^of figure 5d, ^{which is a} mixture of a Zeeman plus dipolar signals. ^{It is not} possible ^to distinguish ^two components. ^In figure ^5e

the polarization ^{of 6Li} have been raised _up to 65 % by mixing ^{with the} dipolar reservoir, ^{and one can}

now see two components, ^{but the one on the} right

is smaller than the one on the left. With a 6Li pola-

rization of 100 % ^{one could} expect ^two components of equal intensity, ^{as sketched} by ^the (theoretical) figure 5 f :

The experiments shown above correspond ^{to a} negative dipolar temperature. ^{We can have an esti-}

mate of its value, ^{since a} polarization ^{of 65} % ^{in a}

field of - 45 G corresponds ^{to a} temperature ^of

-

1.4 gK ^{for the 6Li} nuclei. The Weiss field given by

the splitting ^{of the two} components ^of figure ^{5e is} equal ^{to 12 G. In} the Weiss approximation, ^{a ’Li}

local field of 12 G corresponds ^{to a} sublattice pola-

rization of 80 % ^for protons, ⁶³ % ^for ’Li, ^{and to a} spin temperature ^{of - 1.0} gK. ^The discrepancy ^with

the measured temperature ^{is not} surprising ^{with our}

crude model. In addition each ’Li nucleus, if it does not perturb globally ^the ordered state, distorts locally

the structure it is measuring. This should not be the

case with neutron diffraction, where all the protons of the sample ^will participate ^{to the} signal, allowing

to make quantitative comparisons.

As in the case of ’Li, ^{the two} components ^broaden and _merge together during ^the dipolar relaxation.

Figure ^{6 shows the} shape of the line at different times after the ADRF. It is remarkable that although figure ^6e corresponds ^{to a} temperature probably ^well

above the transition, it is still much broader than

figure 6 f, plotted ^{for an infinite} dipolar temperature.

The Zeeman temperature ^{of curves 6b to} 6 f, ^{as indi-}

cated by ^their area, is equal ^{to 1.38} mK, ^{instead of} 3 mK for figure ^6a.

At present ^{we have} performed only ^{a few} experi-

ments at positive temperatures, because the transition is expected ^{to be more difficult to observe} [4]. Using

the same technique ^{as for} negative temperatures, ^we have obtained for the 6Li absorption ^{line a} splitting

. into three components (Fig. 7) suggesting ^{that for}

some reason, parts ^{of the} sample have remained

paramagnetic (the central line is attributed to para-

magnetic regions). ^{The two} side-lines yield ^{a Weiss}

field of 6 G, i.e. twice as small as at negative tempera- ture, ^{for the same} entropy : this result is in agreement with the Weiss calculation. As for the existence of

paramagnetic regions ^{in the} crystal, ^one explanation

would be that the demagnetization ^{has not been} stopped exactly ^at Ho. A calculation outlined in ref. [4] indicates that the most stable structure in non- zero effective field can be in some cases a mixed

FIG. 6. - Negative temperature. Sample ^{n° 1. NMR} absorption signal ^{of 6Li nuclei versus} magnetic field, ^{as a} function of time t after the ADRF and the mixing ^{with the} dipolar reservoir. a) ^Before the ADRF ; b) ^{t =} 6’ ; c) ^{t =} 22’ ; d) ^{t =} 50’ ; e) ^{t =} 90’ ; f) ^{t = oo}

(dipolar reservoir warmed using microwaves).

FIG. 7.

Positive temperature. Sample ^{n° 17. NMR} absorption signal ^{of 6Li nuclei versus} magnetic ^{field as a} function of time t after

the ADRF and the mixing ^{with the} dipolar ^reservoir.

First experiment ^Second experiment a) Before the ADRF a’) Before the ADRF

b) ^t=4’ b’) ^t=4’

c) ^{t = 44’}

d) ^{t = oo} d’) ^{t = oc.}

phase, composed ^of flat domains perpendicular ^{to the} magnetic field and alternatively antiferromagnetic

and paramagnetic. ^{The two} experiments presented ^on

figure ^{7 exhibit a} similar behaviour. Further studies should give ^more information on this phenomenon.

5. Conclusion.

We have been able to produce ^a

nuclear antiferromagnetic ^{state in LiH} doped ^with F-centres, ^{and to} maintain this state for more than

one hour. With the few observations made by NMR, there is unambiguous evidence of its existence. How- ever, in order to get ^more direct and quantitative informations, ^{we have to resort now to neutron dif-}

fraction. In the scattering ^{of a neutron} by ^a nucleus,

there is a strong spin-dependent ^term arising ^from

nuclear interactions. From the point of view of the

neutron scattering, ^a proton ^{behaves as a} giant magne- tic moment whose value p* (the pseudo-magnetic moment) ^is equal ^{to + 5.4 Bohr} magnetons [6]. ^If

one considers a nuclear antiferromagnet, ^the perio- dicity ^{of the} crystal ^{as seen} by ^{the neutrons is twice}

as large ^{as for the} normal lattice, therefore there will appear ^new diffraction line (the superstructure lines).

For example ^{the structure factor F of the} (110) Bragg

line is equal ^{to zero in the} paramagnetic state, and

proportional ^{to 1.46} PH-o.17 PLi in ^the antiferroma-

gnetic state, where PH ^and PLi ^are respectively ^the pro- tons and ’Li sublattice polarizations.

A neutron diffraction experiment ^on antiferroma-

gnetic ^{LiH is} presently ⁱⁿ operation ^{at the EL3 reactor}

of Saclay. ^{As mentioned earlier, a} superstructure signal ^has already ^been observed and this preliminary

result is reported ^{in ref.} [14].

New perspectives ^are opened by ^this experiment,

and undoubtedly, ^{one of the first} tasks will be to measure the sublattice polarization ^{as a} function of the spin temperature. ^{It is} hoped ^{also that the} signal ,

to noise ratio will be good enough ^to study ^the system in the vicinity of the transition.

Acknowledgments.

^{We wish to thank Pr. A. Abra-}

gam and Dr. M. Goldman whose names are intimately

associated with nuclear magnetic ordering ; ^{both have} suggested many of the experiments reported, ^and

have contributed to their interpretation. ^{We thank}

also Cl. Pasquette ^{and M.} Belamy ^{for technical} support

during ^the experiment.

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