Phase diagram of antiferromagnetic CrFe in the pressure-temperature plane

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Phase diagram of antiferromagnetic CrFe in the pressure-temperature plane

E. Fawcett, C. Vettier

To cite this version:

E. Fawcett, C. Vettier. Phase diagram of antiferromagnetic CrFe in the pressure-temperature plane.

Journal de Physique, 1982, 43 (9), pp.1365-1369. �10.1051/jphys:019820043090136500�. �jpa-00209516�

Phase diagram ^of antiferromagnetic ^{CrFe in the} pressure-temperature plane

E. Fawcett and C. Vettier (*) University ^of Toronto, ^Canada

(*) ^Institut Laue-Langevin, ¹⁵⁶ X, ³⁸⁰⁴² Grenoble Cedex, ^France (Reçu ^{le 11 mars} 1982, accepté ^{le 25 mai} 1982)

Résumé. 2014 Le diagramme ^de phase ^d’un alliage CrFe ^(2,8 % at) ^a été obtenu par diffraction neutronique jusqu’à

des pressions de 4 kbar. On a mis en évidence une transition du premier ^ordre avec hystéresis ^{vers une} phase ^anti- ferromagnétique commensurable; la transition entre les phases paramagnétique ^et incommensurable est du second ordre. Il n’y ^a pas de point triple ^{et le vecteur de} propagation ^{de la} phase incommensurable varie peu, même ^au

voisinage ^{de la} phase commensurable. Cependant, l’amplitude ^de l’onde de densité de spin ^{diminue de 30 % à la}

transition commensurable-incommensurable.

Abstract.

The phase diagram under pressure up ^to 4 kbar of an alloy containing ^{2.8 at %} Fe in chromium has been determined by ^neutron diffraction. A hysteretic first order transition to a commensurate spin density ^wave phase, together ^{with an} apparently ^second order transition from the disordered paramagnetic phase ^{to an incom-}

mensurate phase, is observed. No triple point could be found and there is little change ^{in the} incommensurability parameter ^{as the} commensurate phase ^is approached. ^The amplitude ^{of the} spin density ^{wave decreases from the}

commensurate to the incommensurate phase by ^{about a third.}

Classification

Physics ^Abstracts

75.25

75.30K - 75.50E

1. Introduction.

The critical behaviour near a

Lifshitz point, ^{where in the case of Cr} alloys ^the

commensurate (C), incommensurate (I) and disor- dered (P) phases ^{should coexist,} is of considerable interest. Theoretical aspects of ^the problem ^were

reviewed by ^Hornreich [1], who also discussed briefly

experimental ^{work on} liquid crystals having ^{a Lifshitz} point ^and speculated ^on possible candidates for study

among magnetic systems. ^Michelson [2] ^has analysed

the crossover behaviour to be expected ⁱⁿ magnetic systems having uniaxial and easy-plane anisotropies.

So far only ^{a few} experimental investigations ^of

critical phenomena ^{near the Lifshitz} point ^{of a} magne- tic system have been done [3]. ^{There are} considerable technical problems ⁱⁿ measuring ^{the crossover beha-}

viour while passing through ^the region ^{of the Lifshitz} point by varying ^the composition ^{of a} binary alloy,

since this requires ^the prepatation ^{of a series of homo-}

geneous samples. ^{A much more} attractive system ^for

experimental study ^{would be one} in which the Lifshitz

point ^is approached by varying continuously ^{an inten-}

sive parameter ^{such as} pressure ^or magnetic ^field [3].

2. CrFe alloy system.

^{As Fe is} alloyed ^into

chromium an incommensurate-commensurate (I-C)

transition of the spin density ^wave develops ^with apparently ^a triple point ^{near the} concentration 2.5 at

% ^{Fe and the} temperature ^{250 K. Suzuki} [4] ^has

summarized the experimental ^{data available for} constructing ^a composition-temperature phase ^dia-

gram. His experimental results for the specific ^{heat of}

a series of alloys ranging ^{from 0.45} at ?I Fe to 7.8 at ?I

Fe show that, while the P-I transition (P for parama-

gnetic i.e., disordered) ^{close to the} triple point appears to be second order, the P-C transition is first order with thermal hysteresis. Discontinuous changes ^of

electrical resistance at the P-C transition were first

reported by Arajs ^and Dunmyre [5] ^{and of} length by

Suzuki [6].

Ishikawa et al. [7] found, ^{in an} alloy having ^{a nominal} composition ^{of 2.3} at?% Fe, ^a continuous length change (but ^a discontinuous change in thermal expansion coefficient) ^{at the P-I} transition, ^{with a} large (~ ^{4 x} 10-4 discontinuous length change ^{at the}

I-C transition about 20 K lower in temperature. Syono

and Ishikawa [8] ^found by ^means of electrical resistivity

measurements on a sample ^{of the same} composition

that the I-C transition was depressed ⁱⁿ temperature by ^{about 50 K} by applying ^a hydrostatic pressure of 2.4 kbar.

This result suggested ^to Edwards and Fritz [9, 10]

that a CrFc alloy sample having a ^{P-C transition}

at ambient pressure might ^under applied pressure

move towards a triple point. They ^{found in a} single

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:019820043090136500

1366

crystal sample containing ^{2.8 at} °o Fe that indeed under _pressure the first order P-C transition develops

into a P-I transition followed at a lower temperature by ^an I-C transition. Their resistance and ultrasonic measurements showed that the P-I transition is

continuous, while the I-C transition is discontinuous, hysteretic ^and clearly first order.

Thus the CrFe ^{system appears to} offer the _pos-

sibility ^of approaching ^the triple point continuously by applying pressure. We have measured ^neutron

scattering ^{of such a CrFe} sample ^under pressure ^{to see} whether in fact the system exhibits ^{a Lifshitz} point,

and if so to measure the crossover behaviour in the critical scattering.

3. Experiment.

^Our sample ^of chromium contai-

ning ^{2.8 at} ?I Fe was one of the CrFe single crystals

used by Edwards and Fritz [9, 10]. ^Its magnetic

transitions under pressure up ^to 3.3 kbar as determined

by resistance-measurements are shown in figure ^{1 of} [9] ^{and as} determined by acoustic transit time in figure ²

of [9], while the resultant phase diagram up ^to about 7 kbar is shown in figure ^{3 of} [10]. ^The composition ^of

this sample ^{had been} determined as 2.8 at % _Fe, with

a homogeneity determined by ^electron microprobe analysis ^{of ± 0.15} at % over a distance of several mm.

Previous neutron scattering ^work by Holden and Fawcett [11] ^{on the same} sample had shown it to be a

good quality single crystal. ^Its dimensions are

15 x 8 x 7mm.

Pressure was applied by ^{means of a} helium gas system ^{with the} CrFe sample mounted in an aluminium

alloy pressure cell as described by Paureau and Vet- tier [12]. ^The pressure ^was measured with a manganin

sensor in the intensifier unit. The temperature ^was controlled by using ^a platinum resistor and monitored with a silicon diode. Neutron scattering measurements were made on the DIO diffiractomer at the Institut Laue Langevin ^{in a} triple-axis configuration. ^{A focu-} sing crystal Cu(200) ^{and flat} PG(008) crystal ^were

used as monochromator and analyser ^at wavelength

A

1.253 A.

4. Results.

The resultant phase diagram ^{is shown}

in figure ^{la. As found} by ^{Edwards and Fritz} [9, 10]

there is marked superheating ^and supercooling ^when leaving ^or entering ^the commensurate (C) phase ^from

either the incommensurate (I) phase ^or the parama-

gnetic (P) phase. ^When the transition was made at a constant temperature ^of 242 K from the C-phase ^to

the I-phase ^and back, the range of hysteresis ^{is some-}

what smaller and is not reproductible. ^{This is} probably

because _pressure change ^is accomplished in small but

abrupt steps, ^whereas temperature change ^{is smooth}

and slow, typically ^{at a rate 2 x 10-’ Ks-’.}

The incommensurability parameter 6, ^{which is} defined by ^the equation

Fig. ^1.

(a) ^The phase diagram ^of CrFc ^{in the p-T plane,}

showing the limits of superheating (0) and supercooling (8)

at the first order transition from paramagnetic (P) ^{to com-}

mensurate (C) ^and incommensurate (I) phases ^{with the} points (X) defining the line of second order P-I transitions.

(b) ^The incommensurability parameter ⁶ along the P-I line.

where Q ^{is the} wavevector of the incommensurate spin density ^{wave, is} determined at the Neel temperature TPI by extrapolating the measured values below

TPI ^{as shown in} figure ^2. The resultant values ^are

plotted ⁱⁿ figure 1 b. The value of 6 at Tp, hardly changes ^as the transition to the commensurate phase

is approached. This shows clearly that the I-C tran- sition is not a Lifshitz transition. This was confirmed

by the absence of change in the character of the criti- cal scattering ⁱⁿ the disordered paramagnetic phase ^a

little above the N6el temperature ^{as the «} triple point»

is approached

It is interesting ^{to note that the} continuous P-I

transition persists ^{into the} hysteresis ^{range of the first}

order P-C transition, ^{similar to the} behaviour at 1 bar of the 2.5 at % Fe in chromium of Edwards and Fritz [10]. ^There appears ^to be an upturn with decrea-

sing ^{pressure so that the two lines of} transitions, ^conti-

nuous P-I followed by first order I-C at cooling, ^run approximately parallel. Edwards and Fritz [9] report that their acoustic data for our sample ^show only ^a single transition at 1 bar, ^{which is} hysteretic ^{and first}

order. Perhaps ^the discrepancy results from our lowest pressure being 0.07 kbar and not 1 bar. The phase diagram ^{shown in} figure ^la clearly ^{has no} triple point

for decreasing temperature. ^{Even with} increasing temperature ^{the three} phases ^can hardly ^{be said to}

be in equilibrium ^{where the P-I and P-C transition}

lines intersect, since the transition from the C-phase ^is

abrupt.

Figure ² shows that as the P-I transition is approa-

Fig. ^2.

Satellites (1, + 6, 0)

^{0 and} (1,

6, 0) ^{.... at}

constant pressure 2.01 kbar ^as the sample passes through

the Neel temperature (a) intensity (b) full-width-half-maxi-

mum (c) incommensurability parameter 6; ^the apparent values differ for the two satellites because of misalignment

of the sample.

ched the satellite intensity ^decreases continuously

towards zero until close to the N6el temperature TN

the satellite broadens and merges with the critical

scattering ^which persists ^about TN. ^{There is no evi-}

dence of hysteresis greater than about 0.05 K, ^whereas Edwards and Fritz [9] ^{state that in our} sample ^all

transitions exhibit a temperature hysteresis, ^{with that}

of the P-I transition being ^{less than 1 K. The discre-}

pancy might result from a faster sweep-rate ^{in. the} work of Edwards and Fritz [9]. ^In figure ^{2 the time}

interval between successive points ^{was 300 s, which} gives ^{a «} sweep-rate » ^{close to} the transition of only

about 2 ^x 10-4 Ks-1.

The absence of hysteresis and its continuous nature indicates that the P-I transition is second order. It is difficult to be sure of this in an alloy sample, since there is likely ^{to be some} inhomogeneity and the transition temperature is sensitive to composition. ^The phase diagram summarized by Mori et al. [13] ^{shows that}

the change of the P-I transition with temperature ^close

to the ^« triple point » ^is about 20 K (at % ) - 1.

However there is some direct evidence from the

critical scattering ^{that the P-I} transition is second order. At a pressure 0.3 kbar and ^a temperature just

above the P-I transition, i.e., ^{at a} point ^{within the} hysteresis loop of the P-C transition achieved by cooling at constant pressure, the total intensity ^{of the}

incommensurate satellites ^is larger by ^a factor 6.5 than the commensurate peak. Furthermore Edwards and Fritz [9] ^{observe a} significant increase in the acoustic transit time as this transition is approached ^from higher temperature, ^which they ^{attribute to critical}

fluctuations associated with the impending ^{P-I tran-}

sition.

As shown in figure ² the incommensurable parame- ter 6 increases with temperature, ^{i.e. the} spin density

wave moves away from commensurability ^{as the Neel} temperature ^is approached, ^unlike pure chromium.

This was also observed by ^{Mori et a1.} [ 13] ^{for a} sample containing ^{2.0 at} % Fe. They measured both the spin density ^wave and the strain wave having ^wavevector (2 rc/a) (1 ^{± 2} 6) and found that the sign ^{of the} tempe-

rature dependence ^{of 6 reverses} between the concentra- tions 1.5 at % and 2.0 at % Fe in chromium. In our

2.8 at ?% sample ^{we find} that, ^as the pressure is reduced and the systems approaches the transition to the C-

phase, ^{3 becomes} essentially independent ^of tempera-

ture,

We also observed the passage through ^{the I-C} phase

transition with decreasing temperature ^{at a} pressure of 4.0 kbar. We found no indication of _any new magnetic phase, ^{as was} suggested by the kink in the line of I-C

phase transitions at about this _pressure observed by

Edwards and Fritz [10].

The temperature dependence ^{of the} amplitude ^of

the commensurate spin density ^{wave is} given ^{as a}

function of _pressure at the fixed temperature ^{of 207 K} in table I. We also give in table I the relative amplitude

at low pressure (0.07 ^{kbar was} the low pressure limit of the apparatus) just below the N6el temperature. ^The first order transition from the commensurate to the

paramagnetic phase ^at the low pressure is very sharp.

At 253 K the amplitude ^{is still} 70% of the 207 K value,

but raising ^the temperature by only ^{0.25 K to enter the} paramagnetic phase reduces the amplitude by ^{a factor}

of at least 200.

Table I. - Relative amplitude of ^the spin density

wave in the commensurate phase.

The relative change ⁱⁿ amplitude ^{of the commen-}

surate and incommensurate spin density ^{waves at the}

I-C transition may be important ⁱⁿ understanding

the mechanism responsible ^{for the} phase change.

Accordingly ^we measured this change ^rather carefully

as follows.

1368

The spin density ^{in the} C-phase ^and I-phase, respectively, may be represented by ^the expressions

where a is the lattice parameter ^{of the bcc structure of} chromium and the wave vector is directed along ^the

x-axis. The ratio mi/m, ^{of the} amplitudes ^{is determined}

from the ratio of the intensity 7c ^{of the} Bragg peak ⁱⁿ

the C-phase ^{to the sum} Ii of the six satellite Bragg peaks corresponding ^{to the three domains of the I-} phase having wavevector along ^{one of the three cubic}

axes. Thus from equation (2) ^{we obtain}

We measured the intensities in the I-phase ^of only

four of the .satellites in the xy-plane ^{for two} Bragg peaks, (1, 0, 0) ^and (0, 1, 0). The results given ^{in table II}

show that the ratio of intensities

fails to distinguish between the helical spin density ^and

the linear spin density ^{wave with} equal ^{amounts of x}

and y-domains. ^However the existence of second- harmonic charge density ^{wave in the} incommensu-

rate phase ^{of a} sample containing ^{2.0 at} % ^Fe [13]

shows that CrFe, ^{like pure chromium, has a linear} spin density ^{wave. Walker} [14] pointed ^{out that a}

helical spin density ^{wave would not be} accompanied by ^a second-harmonic charge density ^wave.

Since the fractions of the sample having ^wavevector along ^{the x-} and y-axes ^are approximately equal (Table II) ^{it is} reasonable to assume that there is a

roughly equal ^fraction having wavevector along ^the

z-axis. Thus the total intensity associated with the incommensurate phase ^is

yielding the values given in the column labelled (4/3)

sum in table II. The ratio IIII,, ^then yields ^{the ratio} mi/m,r according ^to equation (3), which is found to have the value 0.64 + ^0.01.

Thus at the first order incommensurate- commensu- rate transition in CrFe the magnetic ^{moment has a}

strong discontinuity, like the electrical resistance [5]

and the length [6, 7].

Table II.

Intensities of Bragg peaks ^{near the I-C} transition ^at temperature ^{207 K.}

Acknowledgments.

^{We are} grateful ^to

F. A. Schmidt of the Ames Laboratory

ERDA, Iowa State University, ^for preparation ^{of the} sample

and to I. J. Fritz of Sandia Laboratories for lending ^it

to us. We benefited from discussions with S. Redner of

Boston University. ^{One of} the authors (E. F.) ^is indebted to the University of Toronto and to the Natural Sciences and Engineering ^{Research Council}

of Canada for financial support.

References

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5121.

[3] BECERRA, ^C. C., SHAPIRA, Y., OLIVEIRA, ^N. F., CHANG,

T. S., Phys. Rev. Lett. 44 (1980) ^1692.

[4] SUZUKI, T., ^J. Phys. ^Soc. Japan ⁴¹ (1976) ^1187.

[5] ARAJS, ^{S. and} DUNMYRE, ^J. R., ^J. Appl. Phys. ³⁷ (1966)

1017.

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