Optical phonon part in spin-lattice relaxation of Cr3+ and Fe3+ ions in rutile

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Optical phonon part in spin-lattice relaxation of Cr3+

and Fe3+ ions in rutile

A. Jeleńnski, H. Szymczak, M. Gutowski

To cite this version:

A. Jeleńnski, H. Szymczak, M. Gutowski. Optical phonon part in spin-lattice relaxation of Cr3+ and Fe3+ ions in rutile. Journal de Physique, 1975, 36 (10), pp.1011-1013.

�10.1051/jphys:0197500360100101100�. �jpa-00208331�

1011

OPTICAL PHONON PART IN SPIN-LATTICE RELAXATION OF Cr3+ AND Fe3+ IONS IN RUTILE

A. JELENSKI (*), ^{H. SZYMCZAK} (**) ^{and M. GUTOWSKI} (**) (Reçu ^{le 14 avril} 1975, accepté ^{le 21 mai} 1975)

Résumé.

On décrit des mesures de largeur ^{de raies en} RPE pour des ions Cr3+ et Fe3+ dans du rutile à températures ^élevées (80-450 K). ^{Ces mesures montrent} qu’à ^ces températures, la relaxation

spin-réseau ^ne dépend pas de la concentration d’ions paramagnétiques ^{et on établit} qu’au-dessus ^de

100 K, la relaxation dans le rutile est conditionnée par ^un processus Raman ^avec participation ^de phonons optiques.

Abstract.

The results of measurements of EPR line-width at high temperatures (80-450 K) ^are

described for Cr3+ and Fe3+ ions in rutile. These measurements show that at these temperatures spin- lattice relaxation does not depend ^on the concentration of paramagnetic ions and it is demonstrated that at high temperatures (above ¹⁰⁰ K) relaxation in rutile is determined by ^a Raman process involv-

ing optical phonons.

LE JOURNAL DE PHYSIQUE TOME 36, ^OCTOBRE 1975,

Classification

Physics’Abstracts

8.632

At sufficiently ^low temperatures spin-lattice ^relaxa-

tion is dominated by ^one phonon processes, with the participation of acoustical phonons. ^At higher temperatures several other relaxation _processes need to be taken into account, many-phonon processes

including ^those involving optical phonons.

In this _paper the relaxation of Cr3+ and Fe3+ ions

in rutile is investigated with the aim of determining

the nature of the dominant processes ^at high tempe-

ratures.

Relaxation _processes for Cr3+ and Fe 31 ions in rutile were investigated ^{at low} temperatures [1-3]

and at higher temperatures (Tmax = ¹⁰⁰ K) ^{for Cr3+}

ions [3]. Measurements made by pulse methods and CW saturation methods indicated that the relaxation for both ions ^are equal ^{to 1-20 ms at 4 K and that}

there exists a strong dependence ^on temperature ^and concentration of paramagnetic ^ions. Line-width ^mea-

surements of the EPR spectra ^{indicated a} temperature

dependent ^{line width at} temperatures higher ^than

77 K [4] (1). Since the linewidth was proportional ^to

the reciprocal ^of spin-spin ^and spin-lattice ^relaxation

times the line-width measurements can be utilised to determine the spin-lattice relaxation times at high

temperatures.

In the present work, relaxation processes ^were studied by measurements of the line-width variation

with temperature ^at temperatures ^{from 77 to 450 K.}

Measurements were performed ^{with a standard}

X-band EPR spectrometer. ^Several samples ^with

chromium ion concentrations of 0.016 % ^{and 0.070} %

’

and 0.36 %, and iron ion concentràtions of about

0.04 % ^were investigated. Measurements of the diffe- rential line-widths AHpp ^{were performed} for various orientations of the external magnetic field in the

crystal reference frame. A typical dependence ^of AHpp

versus temperature ^for Fe3+Ti02 ^{for the} 1/2 ^{- -} 1/2 ^transition

and the magnetic ^field along ^{the a} axis of the crystal

is shown in figure ^1.

FIG. 1.

Temperature ^linewidth dependence

for iron doped ^rutile.

Similar results for Cr3+Ti02 (the 1/2 ^{- -} 1/2

transition and the magnetic ^field along ^{the c} axis)

are given ⁱⁿ figure ² for three chromium ion concen-

trations.

(*) Institute of Electron Technology, CEMI, Warsaw, ^Poland.

(**) Institute of Physics, ^Polish Academy ^of Sciences, Warsaw, Poland.

(1) Gerritsen, ^{H. J.} Paramagnetic ^resonance of transition metal ions in rutile Ti02. RCA Lab. Final Rep. (unpublished).

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:0197500360100101100

1012

FIG. 2.

Temperature ^linewidth dependence

for chromium doped ^rutile.

Dependences ^of AH(T) for other orientations of the

magnetic field and transitions are similar.

These measurements indicate, ^that throughout ^the

temperature range, mentioned above, ^{for all concen-}

trations and orientations EPR lines àre almost

Lorentzian, ^{as observed at lower} temperatures [4, 5].

It implies that ^{the EPR} line-width is proportional ^to

the sum

of ; 1 + ; 2 ^{where T is the spin} lattice rela- T1 T2

xation time and T2 ^the spin-spin relaxation time. The

analysis ^{was carried out} assuming that the linewidth

AHO determined by spin-spin relaxation does not

depend ^on temperature, ^{so that the} temperature dependent part of the line-width is determined

uniquely by spin-lattice relaxation. This part

AH(T) - AHO, also shown in figure 2, is identical for all concentrations, proving that in this tempera-

ture range, the spin-lattice relaxation does not

depend ^on concentration of paramagnetic ^ions.

In the numerical analysis, ^the following spin-lattice

relaxation _processes were considered : 1. One phonon process.

2. Orbach _process.

3. Raman process with acoustical phonons.

4. Raman process with optical phonons.

The analysis ^of experimental data leads to a conclu- sion that they ^are well described by the formula

Only ^the parameter AHO, proportional ^to I/T2 ^is increasing ^with paramagnetic ^ion concentration. The parameters AHo A, ^{C all} depend upon the orientation of the external magnetic ^field except ^{for the} energy

hoeo. ^This energy is very similar for chromium and for iron ions. The mean value of hcoolk ^{for all measu-}

rements is equal ^{to 800 K. The mean values of} para- meters A and C for Cr3+ and Fe" and various orientations of external magnetic ^{field are} given ⁱⁿ

Table I.

TABLE 1

The two last terms in (1) correspond ^to spin-lattice

relaxation _process.

The last term describes a two-phonon ^Raman

process with optical phonons ^{with an} energy of about 800 K. The theory given by Huang [5] anticipates

that for this type of relaxation _process, even parity phonons ^take part. ^These phonons ^can be observed

by ^{means of Raman} Spectroscopy, ^{and their} energy in Ti02 has been determined [6]. It appears that

phonons ^with Alg ^{symmetry have an energy of}

881 K, ^{which is} very close to the value obtained in this _{paper. In} this temperature range, relaxation times measured by ^a saturation method [3] ^{are also inde-} pendent of concentration. On the basis of these results it is possible ^to prove that relaxation in rutile at higher temperatures (above ¹⁰⁰ K) is determined

by ^a Raman process involving optical phonons.

The second term in (1) ^{AT has the same form as} predicted by ^the theory ^of one-phonon processes. The relaxation time Tl corresponding ^{to this} process for measured A values, ^{can be} computed ^{from the} formula .:

The calculation shows that this relaxation time ^at the temperature ^{4 K} is about 10 _ps ànd does not depend

upon concentration. It is contradictory ^{to the} experi-

mental results from [1-3] ^which show that relaxation times Tl ^{for this} temperature depend upon para-

magnetic ^ion concentration, ^{ànd are} of the order of 1-20 _ms, i.e. thousand times longer. ^It implies ^that expression ^{AT in} (1) ^{is not} determined by one-phonon

relaxation process. It ^seems that its _presence in (1)

can be connected with the well known theorem giving

the température dependence ^{the moments of EPR line,}

at low temperature [7].

1013

References

[1] MANENKOV, ^A. A., MILYAEV, ^V. A., PROKCHOROV, ^A. M., Sov.

Phys.-Solid ^{State 4} (1962) ^280.

[2] LAMPE, ^D. R., WAGNER, ^P. E., ^{J. Chem.} Phys. ⁴⁵ (1966) ^1405.

[3] YNGVESSON, ^K. S., ^Res. Rep. ^{No 84} (1968) ^Chalmers University

of Technology, Research Lab. Electronics, ^Sweden.

[4] ANDERSSON, P.O., JELENSKI, A., KOLLBERG, E., On the optical,

EPR and maser properties of heat treated iron and chro-

mium doped rutile, ^Res. Rep. ^{No 107} (1972) ^Chalmers University ^of Technology, ^{Research. Lab.} Electronics Sweden.

[5] HUANG, C. Y., Phys. ^{Rev. 154} (1967) ^215.

[6] SAMARA, G. A., PEERCY, ^P. S., Phys. ^{Rev. B 7} (1973) ^1131.

[7] MCMILLAN, M., OPECHOWSKI, W., ^{Can. J.} Phys. ³⁸ (1960)

1168, 39 (1961) ^1369.