Magnetic-field effect on the phonon echoes in a rare-earth-doped glass

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Magnetic-field effect on the phonon echoes in a rare-earth-doped glass

F. Lerbet, G. Bellessa

To cite this version:

F. Lerbet, G. Bellessa. Magnetic-field effect on the phonon echoes in a rare-earth-doped glass. Journal

de Physique, 1987, 48 (8), pp.1251-1254. �10.1051/jphys:019870048080125100�. �jpa-00210550�

Magnetic-field ^{effect on the} phonon ^{echoes in a} rare-earth-doped glass

F. Lerbet and G. Bellessa

Laboratoire de Physique ^des Solides*, ^Bâtiment 510, Université Paris-Sud, ⁹¹⁴⁰⁵ Orsay, ^France

(Regu le ^{28 avril 1987, accepti} le 21 mai 1987)

Résumé.- Nous

observé des échos de phonons ^dans

dopé

^de l’holmium, jusqu’à ¹⁰ mK, ^{60 kOe}

et dans le domaine de fréquences ^{450-800 MHz.} L’amplitude ^{des échos} augmente d’un facteur 3 quand ^le champ magnétique ^{croît de 0 à 60 kOe. Le} champ magnétique agit ^aussi

^la décroissance des échos de phonons. ^Une expérience de désaturation est décrite. Le temps de relaxation état tunnel-réseau augmente d’un facteur ⁶ quand ^le champ magnétique ^{croît de 0 à 60} kOe. Nous considérons la relaxation des états tunnel _par les ions de terre

Abstract.- We have observed phonon ^{echoes in}

holmium-doped aluminosilica glass, ^{down to 10} mK, up to 60 kOe, ⁱⁿ

the acoustic frequency range 450-800 MHz. The echo amplitude ^increases by

^{factor 3}

^the magnetic field increases from 0 to 60 kOe. The magnetic ^{field acts also}

^the phonon-echo decays. ^A saturation recovery experiment ^is reported. ^The tunnelling-state-lattice relaxation time increases by

^{factor 6}

^the magnetic field increases from 0 to 60 kOe. Relaxation of the tunnelling ^states by the rare-earth ions is considered.

Classification

Physics ^Abstract

43.35 - 63.20P - 75.50K

Photon echoes in

rare-earth-doped glass ^{have shown}

that the optical dephasing ^{rates are enhanced in com-} parison ^{to rates in} crystalline ^materials [1,2]. ^This

enhancement is due to the effect of the atomic tun-

nelling systems ^{on the} rare-earth ions [3-6]. ^{In this}

letter, ^we report ^{on an effect of the} rare-earth ions on

the relaxation rates of the tunnelling systems, ^also called two-level systems (TLS). ^{Phonon echoes are}

powerful ^{tool to} study ^the relaxation rates of TLS in glasses [7,8]. ^{We have} performed ^{such an} exper- iment in a holmium-doped aluminosilica glass. ^The

holmium glasses ^are attractive for acoustic studies on

account of the large spin-orbit coupling ^{of the Ho ions}

[9]. ^{We have obseived an effect of the} magnetic ^field

on

the echo amplitude ^{and on} the relaxation rates of the TLS. This new effect is different from the above- mentioned _one, eventhough ^it implies ^{the same cou-} pling. Here, ^{we observe directly the TLS and the}

rare-earth ions are perturbed by ^the magnetic field,

whereas the photon echoes arises from optical ^transi-

tions between the ground ^and excited levels. In other respects, it is known that magnetism ^{acts on the cou-} pling parameters between the TLS and the acoustic

waves [10], result which has been confirmed recently

in spin glasses [9,11]. Nevertheless, ^{an external} mag- netic field does not change ^these parameters [9]. ^We

shall

that it seems not possible ^to explain ^our

effects by taking ^{into account} only ^the phonon-TLS coupling. So, ^{it is} tempting ^to consider that the _mag- netic moments relax the TLS in magnetic glasses

the conduction electrons do it in metallic glasses [12].

We have observed phonon ^{echoes in an alumi-}

nosilica glass doped with holmium ions (1.5 ^% at.).

The properties of these echoes have been studied down to 10 mK in

magnetic ^field up ^to 60 kOe, ⁱⁿ

the acoustic frequency range 450-800 MHz. Figure ^la

shows the amplitude variation of the two-pulse ^echo

at 10 mK and 450 MHz as

function of the inci- dent acoustic intensity ^{for 0 and 60 kOe. The} pulse

duration is T=60 ns and the separation between the two excitation pulses ^{is T12}

^{300 ns. It can be seen}

that the maximum of the echo amplitude happens ^at slightly ^different powers by ^{about 2 dB.} (Obviously,

we

have verified that the saturated acoustic attenu- ation in the sample ^{does not} change ^with magnetic

field between 0 and 60 kOe). Figure lb shows the variation of this maximum as a function of magnetic

field. It increases continuously ^{from 0 to 30 kOe and}

then saturates between 30 and 60 kOe.

The phase memory time T2 ^{can be measured} by

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019870048080125100

1252

Fig.l.-a) Variation of the spontaneous-echo amplitude

^func-

tion of relative acoustic _{power, at} 10 mK and 450 MHz.

is for 0 kOe, ^{+ is for 60 kOe.} b) Variation of the maximum- echo amplitude

function of magnetic field, ^{at 10 mK and}

450 MHz.

observing ^the decay ^{of the} phonon ^echo

^function

of the time separation ^rl2 between the two pulses (we

use in this letter the terminology and the notations of Black and Halperin [13] ^and Golding ^{and Graeb-}

ner [7,8]. Figure ^{2a shows the variation of the echo} amplitude ^as

^{function of} 2r12 for different magnetic

fields at 10 mK and 450 MHz. It can be

that, ^for

each magnetic ^field value, ^{there are two different ex-} ponential decays ^with

cross-over time which varies

continuously ^with magnetic field. The characteristic times of the two different decays ^{do not} change ^with magnetic field, except ^{at 0} kOe where it seems that the initial decay ^{is two} times faster than the others.

However, ^{the time} range of this decay ^is very small.

If we choose for T2 the characteristic time of the ini- tial decay (which ^{is very} well defined in high magnetic

field), ^{we obtain} T2

^{3.4. its.} This value is _very short

as compared ^{with the one obtained} by ^{Graebner and} Golding in fused silica [8] ^{and which is} T2

^{20 its}

at 18 mK (thus, leading ^{to the value} T2

^{65 ps at}

10 mK according ^{to the T-2} dependence reported by

these authors). We have also studied the variation of T2

^{as a} function of temperature. T2 ^{varies as T-1}

in the temperature range 10-50 mK [14]. ^{This de-}

pendence ^is different from the T-2 law reported by

Graebner and Golding ^for phonon echoes in fused sil- ica [8] but is the same as the temperature dependence

for the electric dipolar ^{echoes in}

^silica glass doped

with OH- [15].

We have observed three-pulse ^{echoes in our sam-} ple. Figure 2b shows the echo amplitude ^as

^function

of rl3 (the delay between the first and the third pulse)

at 10 mK and 450 MHz for 0 and 60 kOe. The decay

is not exponential. This behaviour is also observed

in fused silica [8] ^and predicted by ^the theory [13].

If, following ^{Black and} Halperin [13], ^{we measure} Ti

(defined ^as the value of T13"- r12 at which the echo falls to e’ 1 ) in figure 2b, ^{we can see that} T, ^{is shorter}

at 0 kOe (15 us) ^{than at 60 kOe} (40 us). ^However,

it must be pointed ^out that these values depend ^cru- cially ^on the initial value. Here again they ^are by

one order of magnitude smaller than those reported

in fused silica [8].

Fig-2--a) Variation of the spontaneous-echo amplitude

^func-

tion of twice the time separation 2Ti2 between the two pulses,

at 10 mK and 450 MHz.

is for 0 kOe, a ^{is for 2} kOe, ^{0 is for}

5 kOe,

^{is for 10} kOe, ^{V is for 20 kOe and + is ’-- 60 kOe.}

The

arbitrary ^shifted along ^the y-axis. b) ^Variation

of the stimulated-echo amplitude

function of the delay r13 between the first and the third pulse, ^{at 10 mK and 450 MHz.}

*

is for 0 to kOe and + is for 60 kOe. The

arbitrary

shifted along ^the y-axis.

Measurements of the _recovery time from satura- tion have been made. In a two-pulse saturation recov-

ery experiment ^{the first} pulse ^{saturates the resonant}

TLS and the attenuation change of the weak second

pulse ^{at a time} 1’12 later, is measured as a function of r12 [16]. ^In principle, ^the recovery time is

direct measurement of T1. Experimentally, ^{there is a distri-}

bution of relaxation times and the decay ^is not expo- nential. Our results

reported ⁱⁿ figure ^{3 for} differ-

ent magnetic field values at 10 mK and 450 MHz. It

appears that the saturation _recovery varies strongly

with the magnetic field. If one chooses for Ti, ^the

characteristic time of the initial decay (which ^corre-

sponds ^to the shortest Ti), ^{one obtains Ti}

^{300 pus}

at 60 kOe and T1

⁵⁰ ps at 0 kOe. The T1 ^variation

between 0 and 60 kOe is _very similar to the curve

in figure ^lb. We have also studied the temperature dependence ^of Ti. We have found a roughly ^{T-1 de-} pendence between 10 and 50 mK [14]. ^Our T1 ^value

at 60 kOe and 50 mK (Ti

⁷⁰ ps) ^{is very near the}

one reported (Ti = ⁶⁰ ps) by Golding and Graebner

Fig.3.- Change in the acoustic attenuation of

weak pulse ^after

a

strong saturating pulse ^{of the}

frequency,

function of the time _-r12 between the two pulses, ^{at 10 mK and 450 MHz.}

*

is for 0 kOe,

^{is for 5} kOe, ^{0 is for 10 kOe and + is for} 60 ^k0e.

in fused silica at the same temperature [16].

The first step, ^before considering the effect of the

magnetic ^{field on the} TLS, ^{is to} try ^to explain ^self- consistently ^{all the} changes ^observed in the frame- work of the phenomenological ^{TLS model} [17]. ^The

echo amplitude increase could be explained ^with

change ^of P,2 (where ^{P is the density of TLS and -1}

the deformation potential). ^{By another way, it is pos-}

sible to measure P,2 through ^the logarithmic depen-

dence of the sound velocity ^{at low} temperature [17].

By measuring ^the velocity variation of acoustic waves

at 70 MHz down to 10 mK, ^{we have} observed that the

slope of ^the logarithmic temperature dependence ^does

not change ^with magnetic field ^{between 0 and 60 kOe}

[14]. Hence, ^{we have obtained} P,2

^{3x log} erg/cm3.

Nevertheless, ^{one could argue that P} and -y change

is such a manner that P,2 ^{remains constant. But}

this is not convincing ^without any physical argument.

Another _{way to} try ^to explain the increase of the echo

amplitude ^with magnetic ^{field is to} point ^{out that in} figure ^la the incident _{power at} which the echo is max-

imum, ^is displaced toward the low values by ^{a factor}

1.5 (2 dB) ^{when the magnetic field is set up. This be-}

haviour can be explained by asserting that the value of the mean elastic dipole 2qfAo/J? ^{is increased by}

factor 1.5 [18]. Since the echo amplitude ^is propor- tional to the dipole, ^{it must also increase} by ^{a factor}

1.5 (experimentally, ^{there is}

^factor 3). ^{But yet,} P,

does not change. ^{So it would mean that} Ao ^increases

with increasing magnetic ^field. Considering ^{the TLS-}

lattice relaxation and assuming

one-phonon ^process,

the relaxation rate is given by ^the expression [17].

where E is the splitting ^{and Ao the} tunnelling ^cou- pling energy. Equation (1) shows that Ti ^{must de-}

crease with increasing Ao, from which one concludes that Ti ^must decrease with increasing magnetic field,

in contradiction with the experiment. Lastly, ^one

may wonder whether the TLS in our sample ^relax

with a rate given by equation (1). ^{We have mea-}

sured T, ^{between 10 and 50 mK and for two different} acoustic frequencies (450 ^{and 720} MHz). ^{We have ob-}

tained a T-1 variation for Tl ^as expected ^from equa- tion (1), ^{but we} have also obtained the same Tl ^at

450 and 720 MHz, ⁱⁿ contradiction with equation (1) [14]. Thus, ^{it seems not} possible ^{to make our} exper- imental results selfconsistent by considering only ^the TLS-phonon coupling.

Let

consider now the possible effects of the

magnetic ^{field on} the TLS. It is known that _mag- netism acts on the parameters ^of the elastic TLS.

This property has been established in ferromagnetic glasses [10] and confirmed recently ⁱⁿ insulating mag- netic glasses [9,11]. Thus, P,.,2

^{3 x 108} erg/CM 3

in our aluminosilica glass containing ^{1.5 % of Ho}

ions [14] ^and P-12

^{0.7 x 108} erg/CM 3 ^{in a same}

glass except for the Ho content which is 10 % [9].

Since the magnetic ^{ions are} coupled ^{to the} lattice,

it can be understood that these parameters change

due to the magnetic interactions between the ions.

However, ^{at the low} temperatures ^{where we are work-} ing, ^the expected effect of the magnetic field is rather static. In the framework of the random anisotropy

model of the rare-earth alloys, ^each rare-earth ion is

subject ^{to a local} anisotropy ^{field of} random orien- tation [19,20]. ^The application ^of

magnetic ^field changes the direction of the magnetic ^moments ("it

closes the umbrella" [21]). ^{Hence the rare earth ions}

in a static magnetic field induce static strains on the TLS due to the magneto-elastic coupling. An increase of Ho content between 1.5 % ^and 10 % ^{leads to}

^de-

crease of P,2 but the effect of the magnetic ^{field on}

the dynamics ^{of the} TLS is the same : T’a ^{and Ti are}

roughly ^{the same in all our} samples of different Ho contents between 1.5 % and 10 % [14]. ^{This is not} surprising, ^{since there are} always many magnetic ^ions

between 2 TLS of a given splitting, ^{in our concentra-}

tion _range. Moreover, ^the sample containing ^{10 %}

Ho exhibits

spin glass transition around 400 mK

[22], ^{but this seems not to} change anything

^the

effects reported ^here [14]. ^{We have never considered}

the activation _processes which have been observed in these glasses because their characteristic parameters

are

such that they ^{must be} quenched at very low tem-

perature [9]. ^{If it is easy to see that the magnetic field}

can induce static strains

the TLS, it is difficult to understand how _any static strain

change ^the dy-

namics of the TLS, since there is always ⁱⁿ glasses

large distribution of splitting ^{with a constant} density

of states.

1254

It has not been possible ^to explain the effects

reported ^here by considering only ^the TLS-phonon coupling ^{and the} magneto ^elastic coupling ^{of the rare-}

earth ions. So, ^{it seems that there must be some} magnetic excitations _{at very} low temperature. ^Con- tinentino has considered

coupling between TLS and magnons [23]. ^These excitations give ^{rise to}

^ad-

ditional relaxation mechanism. In our samples, ^the magnetic-ion concentration is low and these excita- tions do not exist. Nevertheless, ^if

suppose that

some rare earth ions can flip ^{on their} anisotropy ^axis

at very low temperature, ^{then it is} possible ^to

plain ^the effect of the magnetic ^field

T1. ^{As the} magnetic ^{field is} set up, the rare earth ions which can

flip, ^{are those} perpendicular ^{to the field} (the ^others

are quenched ^{due to the} magnetic energy). ^These

spins ^can relax the TLS. As the field increases "the

umbrella" progressively ^closes [21], ^{thus removing the}

relaxing spins ^and increasing correlatively Tl. ^Obvi- ously ^this possibility ^is hypothetical. Magnetization

measurements at very low temperature ^{would be} very useful to know more about the rare-earth ion motions.

In _{any case,} they will be insufficient to explain ^conclu- sively ^{our effects as} long ^{as the} theory describing ^the dynamics of the TLS in the _presence of dilute _mag- netic moments will be lacking. ^The present experi-

ments show that there are some interesting physical

effects and we hope ^that they will stimulate theoret- ical works in this field.

The authors are indebted to J. Godard who _pre-

pared ^the samples. One of the authors (F.L.) ^has

been financially supported by

^{contract CIFRE-}

Saint Gobain.

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