PHYSICAL REVIEW VOLU M E 126, NUMBER 5 JUNE 1, 1962

Low-Temperature Magnetic Properties of Dilute Mg-Mn, Al-Mn,Mg-Fe, and Al-Fe Alloys

E. W. CGLLINGs* AND F. T. HEDGcocxtDepartment of Physics, University of Ottava, Ottava, Canada

(Received April 27, 1961; revised manuscript received March 5, 1962)

Magnetic susceptibility measurements are reported on somedilute alloys of Mg-Mn and Al-Mn in the temperature range,rpom temperature —1.3'K. Electron spin resonance (ESR) ab-sorption has been observed in the magnesium alloy containing0.6 at. % manganese and studied as a function of temperature.Room temperature magnetic susceptibility measurements andlow temperature ESR experiments are reported fpr Mg-Fe andAl-Fe alloys. The concentration dependence of the Curie constantat high temperature suggests the presence of four unpaired elec-trons for the manganese atom dissolved in magnesium. Similarinformation concerning manganese dissolved in aluminum suggestsone unpaired electron if a completely localized d state is formed.

The susceptibility of dilute Mg-Mn alloys shows departuresfrom a Curie law, which could be interpreted as an increase in thespin state pf the manganese ion in the region of the resistanceminimum. This excess paramagnetism is discussed in terms of thepossible mechanisms which could produce a resistance minimumand leads to the conclusion that if there is a ferromagnetic couplingbetween randomly distributed manganese pairs, the interactipnmechanism pperates over approximately 10 lattice spacings.

The effective magneton number pf Mn in the more dilute

Mg-Mn alloys also increases with temperature at high tempera-tures. The susceptibility of the concentrated Mg-Mn alloy obeysa Curie law except in the region of the resistance maximum whereboth susceptibility and ESR data indicate an antiferromagnetictransition.

The influence of the lpw-temperature transition, occurring inthe magnesium alloy containing about 0.6 at. % manganese, onthe electron spin resonance linewidth and magnetic field value hasbeen measured as a function of temperature giving g values of2.01+0.01 above 6'K. The shift of the position of resonance fieldbelow 6'K is consistent with antiferrpmagnetic behavior inMg-Mn. The line shift is proportional to T ' in the antiferro-magnetic region which would be consistent with a conductionelectron superexchange mechanism for the antiferromagneticmanganese ipn interaction. The linewidth is broadened in theregion of the resistance minimum and attains a constant value asthe temperature is lowered. This behavior is consistent withlocalized spin interactions, giving rise to larger averaged spinvalues in the resistance minimum region as suggested from themagnetic susceptibility studies of the more dilute alloys.

1. INTRODUCTION

HE application of magnetic methods to the studyof low-temperature resistive anomalies occurring

in Cu-Mn, ' ' Cu-Co, ' and' Cu-Fe has led to some under-standing of the influence of internal magnetic fields andthe state of the paramagnetic ion on the anomalousresistive behavior of these alloys. The particular systemwhich has received most attention has been Cu-Mn withpreliminary reports on the Mg-Mn and Au-Mn systems. 'The magnetic measurements on the Cu-Mn systemindicate a complex magnetic behavior with the followingprinciple features:

(i) At high temperatures the magnetic susceptibilityobeys a Curie-tA'eiss law; the Curie temperature 0 ispositive and depends strongly on the manganese con-centration. For example, Owen et al.' report 0 values of0 K and 100 K. for alloys containing 0.019 and 11.1at. % manganese, respectively.

(ii) As the temperature is lowered, a gradual anti-ferromagnetic transition appears to take place at tem-

*Dr. E. W. Collings wishes to acknowledge the support of theNational Research Council of Canada for the award of a post-doctoral fellowship. Present address: The Franklin InstituteLaboratories, Philadelphia 3, Pennsylvania.

f Present address: The Franklin Institute Laboratories, Phila-delphia 3, Pennsylvania.

' J.Owen, M. E. Browne, V, Arp, and A. F. Kip, J.Phys. Chem.Solids 2, 85 (1957); J. Owen, M. Browne, W. D. Knight, and C.Kittel, Phys. Rev. 102, 1501 (1956).

'R. W. Schmitt and I. S, Jacobs, J. Phys. Chem. Solids 3,324 (1957).'I. S. Jacobs and R. W. Schmitt, Phys. Rev. 113, 459 (1959).

4 F. T. Hedgcock, Phys. Rev. 104, 1564 (1956).

peratures slightly higher than the Curie temperaturedetermined from the susceptibility measurements.

(iii) In the antiferromagnetic region the magneticproperties exhibit a hysteresis and remanent mag-netization which is often referred to as "parasiticferromagnetism. "

Schmitt' made the suggestion that a temperaturedependent resistivity could occur at low temperaturesif the spin degeneracy of the paramagnetic ions wasremoved. Later Hart' and Yosida treated the problemtheoretically by considering the magnetic ordering as ashort-range phenomenon; the coupling mechanism be-tween the paramagnetic ions was considered as an s-dsuperexchange mechanism. Yosida found that belowthe Xeel temperature, the resistivity should decreasewith decreasing temperature, whereas above the Neeltemperature the resistance should be independent oftemperature. Therefore, this mechanism would notproduce a resistance minimum. Brailsford and Over-hauser' have suggested a possible mechanism for theresistance minimum by considering local interactionsbetween randomly distributed pairs of paramagneticions. Both Overhauser and Marshall" have recentlydeveloped models for producing a cooperative magnetic

s R. W. Schmitt, Phys. Rev. 103, 83 (1956).' E. W. Hart, Phys. Rev. 106, 467 (1957).7 K. Yosida, Phys. Rev. 106, 893 (1957); 107, 396 (1957).

A. D. Brailsford and A. W. Overhauser, J. Phys. Chem.Solids 15, 140 (1960).

9 A. W. Overhauser, Phys. Rev. Letters 3, 414 (1959).rs W. Marshall, Phys. Rev. 118, 1519 (1960).

1654

MAGNETIC PROPERTIES OF Mg —Mn, Al —Mn, Mg —Fe, AND Al —Fe 1655

transition to antiferromagnetism in a dilute alloy whichwould allow the occurrence of a resistance maximum.

The influence of impurities on the resistive propertiesof magnesium and of aluminum have been reported bynumerous authors. " Recently experimental data havebeen reported on the influence of the concentration ofmanganese on the low-temperature electrical propertiesof magnesium"" and aluminum. "No anomalies havebeen observed in Al-Mn system, whereas both a re-sistance minimum and maximum have been observedin Mg-Mn.

If it is assumed that alloys containing a paramagneticion are sufficiently dilute when the atom is put intosolid solution with a weakly diamagnetic or paramag-netic solvent, then it should be possible to consider theparamagnetic ion as in the same state as an isolatedatom with the valence or s electrons joining the commonconduction band of the solvent. On such an assumptionthe magnetic susceptibility should obey a simple Curielaw for noninteracting particles. However, most dilutealloys containing paramagnetic ions show deviationsfrom the simple Curie behavior. Attempts have beenmade to interpret the magnetic properties of dilutealloys containing paramagnetic ions in the followingwas:

(i) A thermal activation of electrons or holes into thed shell of the paramagnetic ion by allowing a d level tolie near the Fermi level of the conduction band. "

(ii) A localized coupling between the paramagneticions, the number of such systems depending on thestatistical distribution of ions in the solvent. "

(iii) A change in the density of states of the conduc-tion electrons in the temperature range of the resistanceanomaly. 4

(iv) An s-s electron interaction between Mott-Friedelbound s states and electrons in the conduction band. '

(v) A mechanism which would require the formationof a d band by the Friedel resonance broadeningmechanism. "

(vi) Owen et a/. ' have assumed a coupling of themanganese ion and the conduction electrons and inter-preted the paramagnetic resonance observed in thedilute Cu-Mn alloys as a result of spin Gipping of theconduction electron which is magnetized by the s-dinteraction. This mechanism requires that the man-ganese ion be in an 5 state.

In the hope that measurements on dilute magneticsystems will further the understanding of resistanceanomalies, it is the purpose of the present paper to

"See F. T. Hedgcock, W. B. Muir, and E. E. Wallingford,Can. J. Phys. 38, 376 (1960) for a review of previous work."G. Gaudet, F.T. Hedgcock, G. Lamarche, and E. E. Walling-ford, Can. J. Phys. 38, 1134 (1960)."E, W. Pugh, B. R. Coles, A. Arrott, and J. E. Goldman,Phys. Rev. 105, 814 (1957).

' A. J. Dekker, Physica 24, 697 (1958).'~ J. Friedel, Suppl. Nuovo cirnento 12, 286 (1958).

present measurements on the magnetic susceptibilityand ESR in dilute magnesium and aluminum alloyscontaining small concentrations of manganese or iron.These results will be discussed in the light of the pre-ceding interpretations of the magnetic behavior of dilutealloys containing paramagnetic impurities.

2. SAMPLE PREPARATION ANDEXPERIMENTAL METHOD

2.1 Sample Preparation

The dilute magnesium and aluminum alloys used inthese investigations were the same as those used in theearlier studies of the electrical properties of thesealloys. ""The high-concentration Al-Mn and Mg-Mnalloys were prepared in this laboratory by melting99.99% pure solvent with the desired additive in high-

purity graphite crucibles and quenching from the melt.The ingots were then given a homogenizing anneal andtested for alloy uniformity by measuring the residualresistances of samples cut from various sections of theingot. Electrical resistance and magnetic susceptibilitymeasurements were made on the low-concentrationMg-Mn samples which were given strain-relievinganneals after fabrication. Only the highest concentrationalloy ( 0.6 at.% Mn) was used in the ESR measure-ments. A small piece of rod for susceptibility measure-ments, a wide rolled strip for ESR and a narrow rolledstrip for resistance were all prepared from the samepiece of nominal 0.6% Mn alloy. The samples werequenched in ice water after being heated together in ahelium atmosphere for 2 hr at 600'C, thus ensuring thatthe specimens used in all three measurements had thesame concentration of Mn in solution.

2.2 Method of Measuring the MagneticSusceptibility

The low-temperature susceptibilities were measuredusing the Curie method employing a servo-balanceespecially designed for measurements on materials oflow resistivity. " The absolute susceptibility of thesamples were determined at room temperature on aBunge microbalance which was fitted into a vacuumcase. All of the susceptibility samples were studied as afunction of field (H, =8500 oe) and, whether theCurie method or Gouy method was used to determinethe susceptibility, ferromagnetic corrections were madefor each sample. When the Curie method was used andferromagnetic impurity corrections made, the magneticfield gradients were determined using zone refined ger-manium as a standard with the value of 0.103)(10 'emu''g for the susceptibility. Magnetic field strengthswere determined using a Rawson rotating-coil Quxmeter.The temperature dependence of the susceptibility wasnormally measured relative to the room temperature

"F.T. Hedgcock and W. B. Muir, Rev. Sci. Instr. 31, 390(1960).

1656 E. W. COLLINGS AND I". T. HEDGCOCK

value. After it had been shown that the ferromagneticcorrection was not a function of temperature, the rela-tive susceptibility was reduced to an absolute valueusing the room temperature suscep tibility value.Further details of the experimental method can be foundin an earlier publication. '

2.3 Method of ESR Measurement

80

—75

—70

—65

X2.0—

XW

I.5—OX

KI.O-

U

XX~05— 878 I2

60XC9

55 &50

45 ~X

40OO

35 ~X

30 X—25

—20

—15

—IO

00 20 30

TEMPERATURE ('K)40

050

FIG. 1. Magnetic susceptibility of some dilute alloys of Mg-Mnas a function of temperature. The right-hand scale refers tosample No. 87816.

Electron spin resonance measurements were madewith a conventional double-modulation spectrometerwhich employed a reQection-type cavity, 'magic-T'bridge, and operated at a frequency of 9400 Mc/sec. Amicrowave power of 8 mw was absorbed in the cavityand sample, and the 1-kc/sec magnetic 6eld modulationwas 3 oe peak-to-peak or less when examining theMg-Mn alloy. The cavity, operating in the TE~02 modewith a circular coupling hole of 17/64-in. diameter, wasof silver-plated stainless steel. The Varian X13klystronwas immersed in an oil bath, the reflector supplied fromdry cells, the accelerator from a well-stabilized (1 in 10')280-v power supply, and the filament supplied from a6 v accumulator. Its frequency of operation was lockedto tha, t of the resonant cavity (by circuitry similar tothat of the signal detecting circuit) by frequency-modu-lating the klystron with 0.2 to 0.4 v rms at 25 kc/sec and

re-applying the phase-detected dc to the klystronrepellor.

Samples were glued to the vertical, narrow cavitywalls and were thus normal to the field of the magnet.Mounted in this way, four pieces could be placed in the

cavity without the need for any supporting structurewith its accompanying dielectric loss and occasionalspurious signals. With Mg-Mn it was found that twopieces were sufficient for good signal-to-noise ratio andthese were both mounted in the lower half of the cavity.Temperature was measured with a calibrated carbonresistor attached to the cavity wall. Measurementsbelow 4.2'K were done while pumping on a liquidhelium bath, while temperatures above 4.2'K wereattained using the cold gas from boiling liquid helium. "

The magnetic field was produced by a 4-in. Newportelectromagnet supplied from a separately excited dcgenerator. The current was stabilized to 1 in 4000 bycontrolling the field current with an error voltage de-veloped across a 2-ohm resistor in series with the magnetcoils. A 10-turn helipot incorporated in the stabilizingampli6er, and driven by a 1-rpm motor, enabled themagnetic field to be swept within the range 600 to4500 oe, usually at a rate of about 7 oe/sec

The field was measured with a Rawson rotating-coilQuxmeter, the ~-in. probe of which fitted into an alumi-num socket glued to the center of one of the magnet polefaces. The Quxmeter was calibrated at 100-oe intervalsusing proton resonance, and allowance was made for thesmall difference between the magnetic field at the centerof a pole face and that at the sample site. As a check onexperimental accuracy, when an alloy sample happenedto corrode in the cavity and the familiar hyperfinespectrum of Mn++ in a dielectric crystal appeared, themagnetic 6eld (H) at the center of this spectrum was

compared with the field (H,) calculated from the knownaverage g value of Mn++ (viz. , 2.0018).The result of aset of 16 observations is (H H.) =1 oe&—4 (standarddeviation). The error can be accounted for as uncer-tainty in reading the Quxmeter dial which would beabout &5 oe. Other measurements with carefully posi-tioned substances having lines of known g values (suchas DPPH and an e-type silicon semiconductor) con-firmed the above conclusion as to magnetic field

accuracy.

3. EXPERIMENTAL RESULTS

3.1 Magnetic Susceytibi1ity

Figure 1 shows the magnetic susceptibility of moredilute alloys of Mg-Mn as a function of temperature.The susceptibilities have been calculated at maximummagnetic field and corrected for ferromagnetic impurity(see Table I). The susceptibilities have not been cor-rected for the temperature-independent paramagnetismof the solvent. In these curves an excess paramagnetismat low temperature is apparent. Table I contains a list-ing of the effective magneton numbers E,q~ calculatedfrom the room-temperature susceptibility from therelation

(XBjJoy XMg) DX C/T

and I',~i 3kC/XnP', where k=——Boltzmann's constant,

MAGNETIC PROPERTIES OF Mg —Mn, Al —Mn, Mg —Fe, AND Al —Fe 165/

TAIPEI.E I. Values of the room temperature susceptibility and effective magneton numbers for dilute magnesium and aluminumalloys. Absolute values of susceptibility measured relative to zone-refined germanium (g=0.103X10 '+0.001 emu/g).

Sample Wt. % Mn Wt.% Fe y(27'C) X 10' emu/g (FF,/total force)rr„„ P ff (27'C)

7288781287813878148781587816

727-1727—2

0.0010.0050.0190.0380.0461.34

0.00230.0027

Magnesium alloys0.4980.5170.5340.5640.5642.64

0.5020.502

2 Po

20%15%

~ ~ ~

7 +15.0+0.54.8+0.55.5~0.54.8+0.14.7~0.2

4.7+1.54.7~1.5

GKPGKMGKNGKOGKKGKL

0.0010.0110.0530.092

0.02580.025'

Aluminum alloys0.6030.6040.6120.6240.6050.605

1%

~ ~ ~

1.4~0.11.6+0.11.7&0.11.2+0.41.2~0.5

' The maximum solid solubility of Fe in Al at 600'C is approximately 0.25%. The remaining Fe is presumably in the form of A13Fe and owing to thesmall concentration involved gives a negligible contribution to the susceptibility.

1V=number of Mg atoms/g, n=atom fraction of Mn,and P =Bohr magneton.

In the case of sample No. 87816 the second of thetwo values of E,ff is derived from the slope of the inversesusceptibility curve above room temperature t Fig. 2(c)j.The values of the solvent susceptibilities were measuredto be 0.498)&10 ' emu/g and 0.603&&10 ' emu/g formagnesium and aluminum, respectively, and thesevalues are both lower than those listed elsewhere. '~

Since the ferromagnetic corrections are small in thesepure materials and since the susceptibility temperaturecoefficient produces a change of less than 1% in thesusceptibility at liquid helium temperatures, it isthought the observed values are a result of samples ofhigher purity than those previously measured. I',« forthe alloy was calculated at room temperature assumingthe gneiss constant to be negligible at room temperatureand using the atom fraction n of the transition element,as determined from spectroscopic analysis. The errorin e represents the largest contribution to the error inthe determination of I',ff. It will be noticed that noneof the values for I',ff in Table I correspond to the effec-tive magneton number expected for Mn++ in an S state(i.e., 5.9); the effective magneton number being muchlower in aluminum than in magnesium. A smoothedvalue of I',ff can be obtained for Mn in Mg by plottingA7f vs concentration. This is shown in Fig. 2(a), theslope of the line yielding an average value of 5.2&0.2for I',«. This value is again considerably lower than5.9 expected. for Mn++ in an S state. An eRective mag-neton number for sample 87816 was determined fromthe susceptibility above room temperature as shown inFig. 2(c) and listed in Table I. The effective magneton

"Coastasttes Setectsolnees (Masson and Cie, 1957), Vo1. 7.

ECO

O. IO

O.Oe

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00

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4

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) I.OOO

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300 400 600 800TEMPERATURE (4K)

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0 20 40 60TEMPERATURE ( K)

Fro. 2. Inset (a) is a graph of the paramagnetic susceptibilityof manganese in magnesium as a function of manganese content.(b) Inverse susceptibility of Al+1% Mn alloy as a function oftemperature. (c) Inverse susceptibility of Mg-Mn alloy No. 87816at high temperatures. (d) Inverse susceptibility of Mg-Mn alloyNo. 87816 at low temperatures. The inverse susceptibility has beencorrected for the paramagnetism of the solvent.

number from the high temperature Curie constantagrees quite well with the values determined at roomtemperature. Figure 2(b) shows the inverse suscepti-bility of an Al-Mn alloy as a function of T and it canbe seen that a Curie law is not obeyed. In Fig. 2 (d) theplot of Ax ' vs T for sample No. 87816 shows a levelingoR at the low temperature end. This could be consideredas evidence for antiferromagnetism. From the linear

1658 E. W. COLLINGS AND F. T. HEDGCOCK

portion of this curve a value of 4.1&0.1 is found forP ff, This is lower than the values of 4.8&0.1 calculatedfrom the room temperature susceptibility and 4.7&0.2calculated from the slope of Fig. 2(c).

In Fig. 3 the normalized susceptibility, t1&/t1Xit. T.,for the Mg-Mn alloys is shown as a function of T '.It will be noticed that the Mg-Mn alloys all showdeviations from a Curie law and in fact there is anexcess paramagnetism in the region of the resistanceminimum as has been previously reported in dilutecopper alloys. ' This excess paramagnetism is shown inthe inset of Fig. 3 and it can be seen to vary inverselywith temperature. Excess specific heats in the Cu-Fe,"Cu-Mn, "Cu-Co" systems have also been observed tovary inversely with temperature in the region of theresistive minimum. Calculations of P,qq from the slopesof the two sections of straight lines yield values of 3.6and 4.1 in the temperature region between 50'K and20'K, and 20'K and 7'K, respectively, as comparedwith the average room temperature value of 5.2. Alter-natively one can assume the average room temperaturevalue of 5.2 for P,ff and calculate the percent alignmentof spins from the low-temperature susceptibility results.This calculation yields a 50% alignment between 20'Kand 50'K and a 70% alignment between 7'K and 20'K.This spin alignment deficit (as compared to the Curieprediction) is in qualitative agreement with specific heatmeasurements on the alloys" where it appears thatconsiderable entropy is available if complete orderingis to occur at lower temperatures.

It has been previously reported" that iron in mag-nesium produces a resistance minimum while iron inaluminum does not. Included in Table I are values forP ff of iron in aluminum and magnesium. The errors arelarge since the ferromagnetic correction is quite largeand because of the limited solid solubility of iron inthese materials, there is a large error in the concentra-

0.3

xAlIO-„0.2 — 8

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~~0 878I3X~0io~ ~ 878I4 x

I

0 20 40 60 80 IOO I20 I40TIxl0 ( K j

Fin. 3. The reduced susceptibility Ax/Dxa, T plotted as afunction of reciprocal temperature. The inset in the figure is theexcess paramagnetism 5 plotted as a function of temperature.

tion of iron in solid solution. Because of the uncertaintiesin these samples, no experiments on the temperaturedependence of the magnetic susceptibility wereattempted.

3.2 Electron Spin Resonance

Figure 4 shows a typical resonance curve for mag-nesium sample No. 87816 containing a nominal concen-tration of 0.6 at. %%uoM nmeasure da 1, 4.2'K.

(a) AmPlitude of the Resonance Derivative

Figure 5 shows the variation of height of the absorp-tion derivative with temperature. The measurementswere made relative to the heights of DPPH signals,to compensate for changes in cavity Q with temperature.The alloy used showed a resistance maximum in theregion 6'K to 7'K, a phenomenon which would beaccompanied by an increase in skin depth and an ex-posure of a larger number of paramagnetic ions to therf field. But the increase in resistance is only 6% between6 K and 30'K, so that the corresponding percentageincrease in skin depth will be about half this amount andtherefore not sufficient to explain the maximum in theresonance derivative curve. The area under the absorp-tion curve is proportional to the magnetization of themanganese ions and hence at constant field to themagnetic susceptibility of these ions. Since the linewidthis constant in the region under consideration (see below)the height of the absorption curve and consequentlythat of its derivative must also be a function of suscepti-bility. Figure 5, therefore, shows that a maximum in thesusceptibility would be expected. However, the meas-ured values of 1/x show only a leveling off in this region(Fig. 3). In either case an antiferromagnetic transitionis indicated in the vicinity of 6'K.

It was found impossible to detect a resonance in anAl-Mn alloy containing 1 at.% manganese in solid solu-tion. To compare the relative intensities of the Mg-MnESR signal with that of one from Al-Mn, the following

' D. L. Martin and J. P. Franck, ProceeCinf;s of the SeventhInternational Conference on Joe Temperatgre Physics, Toronto,1960 (University of Toronto Press, Toronto, 1960), p. 262."J.E. Zimmerman and F. E. Hoare, J. Phys. Chem. Solids17, 52 (&960).

'0 L. T. Crane and J.E.Zimmerman, Phys. Rev. 123, 113 (1961)."D.L. Martin, Can. J. Phys. 39, 1383 (1961).

I I I I I

3K OERSTED

Ho = 3392 OERSTEDI I I I I I I I I II I I I I I I I I I

4K OERSTE'D

FIG. 4. A typical resonance curve observed in the concentratedMg-Mn alloy No. 87816 (~0.6 atomic percent manganese)at 4.2 K.

MAGNETIC PROPERTIES OF M g —M n, A1 —Mn, M g —Fe, AN D A1 —Fe 1659

experiment was performed. Two pieces of 0.6% Mg™were placed in a resonance cavity together with a sampleof DPPH and the relative heights of the resonance signalwere measured. The experiment was repeated with twoAl-Mn samples in the cavity, but no resonance couldbe detected even at 4.2'K. If a barely detectable signalhad been observed from Al-Mn (i.e., with a signal-to-noise ratio 1:1) the relative height of the absorptionderivatives of Mg-Mn and Al-Mn of equivalent con-centrations and skin depth would have been 30:1 pro-vided of course that the linewidths were equal. It seemstherefore that the spectroscopic state of manganese inaluminum is different from that in magnesium.

Xo ESR signal could be detected from the Mg-Fe,Al-Fe alloys.

(b) Linewidth

Table II shows the average linewidth in severaltemperature groupings. Tests for statistically significantdifferences were applied and it was concluded that thelinewidth was independent of temperature below 18'Kand equal to 313&25 oe. This linewidth corresponds toa relaxation time of 2.2)& 10 "sec and is in good agree-ment with the values observed by Owen et a/. ' Thelinewidth in the region above 18'K yields a relaxationtime of 1.2X10 "sec. Between 6'K and 18'K the re-sistance minimum in this alloy occurs and, as can beseen in Fig. 6, the linewidth is in excess of a simple Tproportionality, indicating an additional broadeningmechanism is operative in this region.

(c) Position of the Etectron Spin Resonance Line

The theory of spin resonance of conduction electronsin a metal h,as been worked out by Dyson" and appliedby Feher and Kip" to Ineasurements on alkali and othermetals. The line shape and magnetic field value at thecenter of the absorption derivative depended (for aparticular specimen shape, say, thick compared to theskin depth) on the quotient T~/Ts, where TD is thetime conduction electrons take to diffuse through the

TABLE II. Width of electron spin resonance (ESR) line.

Temperature range ('K)

1.9 —2.42.5 —3.03.03—3.53.56- 4.25.0 —7.08.8 —10.4

14.8 —17.617.9 -19.9

26.025.0 -45

Linewidth (oe)

298&25318~20296~17329~23311~22292+19305&15337&22381+22440&51

microwave skin under the action of the microwave fieldand T2 is the normal electron-spin relaxation time. Forparamagnetic solutes in alloys, the theory of conductionelectron resonance is taken over for the special caseTD = ~ . It is then found that the absorption derivativehas a characteristic asymmetric shape, the amplitudesof the "positive" and "negative" portions being in theratio 2.55/1. As can be seen in the resonance curve inFig. 4 this is borne out by experiment in the Mg-Mnalloy. The line is also shifted in such a way that if H„„is the field required to satisfy the resonance equationfor the paramagnetic ion, and H is the apparent reso-nance field (where the derivative has maximum slope):H„,„=H AH/3, wher—e AH is the usual linewidth.

To check the present apparatus this relation was firstverified for dilute Cu-Mn at 80'K, at which temperatureit was known to be paramagnetic. The relation wasthen applied to determine the behavior of the Mg-Mnresonance line in the temperature range 1.9'K to 64'K.The corrected resonance magnetic field for insertion inthe equation hv=gPH„„, in order to determine the

g value, is H„„=H AH/3 for—paramagnetic ions in ametallic conductor. For Mg-Mn, this equation gives apractically constant g= 2.00 for temperatures down to6.5'K. Below 6.5'K, the resonance line started to moveto a lower magnetic field in a manner characteristic oftransition to an antiferromagnetic state." In this state

800

hJ~IOI-

Kw 8—CIU.Ohl 6—'DI-

4—X

4J0

~ 0K

~~O-y)0

l l 1 t

4 6 8 IO l2 l4TEMPERATURE (oK)

t I I

I6 l8 20

700—

~ 600—I-

5 50O

400—

300 —~V -0

z 200—

~0~ 0

IOO—

I I I I I ~ I I I I I

2 4 6 8 IO 20 50 40 50 60 70TEMPERATURE (oK)

FrG. 5. Amplitude of the derivative of absorption versustemperature for magnesium sample No. 87816.

I J. Dyson, Phys. Rev. 98, 349 (1955)."G. Feher and A. F. Kip, Phys. Rev. 98, 337 (1955).

FIG. 6. Line width of manganese resonance in magnesiumalloy No. 87816 as a function of temperature.

4 For a useful review of the effects and full references see F.Keffer, H. Kaplan, and Y. Yafet, Am. J. Phys. 21, 250 (1953).

1660 E. %. COLL I NGS AN D I . T. HEDGCOCK

350 350

300—250—

o40

200—4J I50—

3 I 00—Io 50—X

-50—0 2

I I I I I I I I I

4 6 8 10 20 50 40 50 60 70TEMPERATURE (OK)

300—

00—50—

~Ii

0 8

-500

250—CI4JI- 200—KhlO I50—OO

I

O

I

Q. I

I+0 ~

/0 ~

I I I

0.2 0.3 0.4R EC IPROCAL TEMPERATURE

0.5

FIG. 7. Apparent shift of the resonance field in the concentratedMg-Mn alloy No. 87816 as a function of temperature.

Fzo. 8. Shift of the resonance field in magnesium alloy No. 87816as a function of T '. The position of the electrical resistancemaximum in this alloy is approximately 6'K.

it has not been proved that the resonant field is givencorrectly by II AH/3, so—that Hp H„„may—not bea valid measure of the internal field change (where Hpsatisfies the resonance condition when g= 2.00). Insteadin general, one would be better to plot simply Hp —H toshow the change in line position mith respect to itsposition in the paramagnetic state. In the present case,the linewidth is constant so that no difhculty arises sincethe relative line shift is the same by either method, how-ever, a plot of IIp—H„„ is preferable since it morereadily shows the transition from the paramagneticstate. Figure 7 shows the line shift (Hp —H„„) as afunction of temperature. The shift in position of theresonance line is of particular interest since the re-sistance-temperature plot has a maximum between 6'Kand 7'K. Plotting the line shift against reciprocal tem-perature expands the low temperature region and showsthat below 3.5'K the line shift is inversely proportionalto the temperature. This is shown in Fig. 8.

In determining the resonance field, because of thesometimes large paramagnetic susceptibility of alloyswith paramagnetic solutes, a demagnetizing correctionis sometimes required. If the plane of the sample isparallel to the applied field H, the line is shifted to alow'er field by an amount 2zxB, where x is the volumesusceptibility; while if the plane of the sample is perpen-dicular to H as in these experiments, the line is shiftedto a higher field by amount 4vrxH. For temperaturesbelow 10'K the correction was 2 oe, and above 10'Kwas only 1 oe. Although these corrections were appliedas a matter of course they were actually less than theexperimental error.

(d) Accuracy of 3IIeasuremertt

The accuracy of the quantity H/v is limited only bythe accuracy with which the Quxmeter dial can be readsince the frequency v is known to 1 part in 10'. It isestimated that the field can be measured to &5 oe onthe 4-koe range; and for the Mg-Mn alloy the position

of maximum absorption can be measured almost asaccurately as this, but the corrected position of reso-nance involves the linewidth AH which is the separationof the turning points of the derivative curve. Becauseof the lack of sharpness of these points the g value hasan error of &0.01.The position of the resonance line inrelation to the free-spin value H p (g=2.002) was deter-mined from the calculated value of Hp. A marker suchas DPPH was not used as a reference as it was found tointerfere with the shape of the resonance line and madeaccurate determination of line position difficult.

4. TEST FOR POSSIBLE PERMANENTMAGNETIZATION OF THE SAMPLE

Owen et al. ' observed that Cu-Mn alloys containing1.4 and 5.6 at. %%uomanganes eexhibite d asmal 1 spontane-ous magnetization at 4'K. Measurements of the rema-nence as exhibited by the magnetization of these alloyshave been continued by a number of workers. "Themagnetization measurements can be summarized asfollows:

(i) A soft component of magnetization which resultedwhen the specimen was cooled in zero field. The zero-field magnetization could be reversed by applying anexternal field of 5000 oe.

(ii) A hard component of magnetization which re.suited when the specimen was cooled in a field of 5000 oe-

(iii) The remanent magnetization decreased rapidlyas the temperature was raised and is approximately zeroat the Neel temperature.

(iv) The hard component of magnetization, wheninduced in the sample, shifted the position of the reso-nance line by as much as 250 oe.

Table I includes values of the percentage contributionto the total susceptibility due to the ferromangetic con-tribution. This value was derived at room temperatureby assuming an exponential saturation of the ferrous

MAGNET I C P ROPERTI ES OF M g —Mn, Al —Mn, Mg —Fe, AND A1 —Fe 1661

impurity magnetization. Measurements of the ferro-magnetic correction as a function of temperature showedit to be independent of temperature. Xo detectableremanence was observed in these alloys so that theferrous component can be described as soft.

The following ESR experiment was performed tocheck if the soft component of magnetization wouldinhuence the position of the resonance field. The samplewas cooled to 4.2'K in zero field and the field was sweptto 4 koe several times. The sample was then cooled to2.6 K in a field of 3 koe and a series of resonance runswas made with the field sweep, in opposite directions inalternate runs. There was no detectable line shift towithin &1 oe. Hence both the susceptibility and ESRdata indicate that the observed soft magnetization is dueto the presence of very small quantities of ferromagneticimpurities and not associated with the manganese

magnetization.

S. DISCUSSION OF RESULTS

5.1 Excess Paramagnetism in the TemperatureRegion of the Resistance Minimum

Brailsford and Overhauser' have postulated a rnecha-nism for the appearance of resistive anomalies in para-magnetic alloys on the assumption that statisticallydistributed nearest-neighbor pairs of paramagnetic ionsare coupled ferromagneti, cally. Dekker, " Sato et al. ,"and Smart" have discussed the inQuence of the sta-tistical nature of the distribution of paramagnetic ionson the magnetic properties of dilute systems. The generalresult is that ferromagnetic interactions will give rise toan excess paramagnetism with too high a value of E',ff

derived from the low-temperature data. The suscepti-bility of a system containing isolated spin systems (x,)and ferromagnetically coupled pairs (X~) can bewritten as

x= x,+x~= (c/T) f1+ (Ac/c)],

where c=X,I',HAPP'/3k, X,=number of isolated spinsystems, Ac=the excess paramagnetic Curie constantdue to ferromagnetically coupled spins of number S~,and the other symbols have the same meaning as pre-viously. Using a spin value of 2 for the manganese ionat high temperatures and a maximum spin value of 4 percoupled pair yields a value of d,c equal to 3.33 iV~/1V, .To account for the observed excess paramagnetism insample No. 87814 (say, at 7'K) would require 1.8X 10'rferromagnetically coupled pairs per gram. Assuming arandom distribution of manganese ions the statisticalprobability of finding this number of pairs would be lessthan 0.002. If then, a ferromagnetic coupling mechanismis used to interpret the magnetic susceptibility results,

"H. Sato, A. Arrott, and R. Kikuchi, J. Phys. Chem. Solids10, 19 (~959)."J.S. Smart, J. Phys, Chem. Soiids 16, 169 (1960).

the range of the ferromagnetic interaction would haveto be of the order of 10 interatomic distances.

Further experimental evidence that there is someinteraction occurring between the paramagnetic ions canbe seen from the ESR data previously presented inFig. 6, where an excess line broadening is observed be-tween 6'K and 18'K. This could be taken as evidencefor spin interactions resulting in an additional linebroadening as the temperature is lowered. Since bothferromagnetic and antiferromagnetic interactions leadto line broadening, it is impossible to decide which typeof interaction is responsible for the additional linewidthobserved. The fact that the Ax values for all of thealloys lie on the same normalized curve indicates thatthe excess paramagnetism varies linearly with concen-tration. The "size" of the resistance anomaly has alsobeen observed to vary linearly with concentration inthe low concentration region. "Both these observationsand the conclusion from the previous calculation in thissection would lead one to believe that it is unlikely thatpair or higher order coupling between spin systemswould produce these low temperature anomalies. It israther interesting to note that h (the excess paramag-netism, Fig. 3) va, ries linearly with T moreover, withinthe accuracy of the measurement the temperature atwhich 5 appears is independent of paramagnetic ionconcentration.

5.2 Antiferromagnetism

Both the ESR results and the magnetic susceptibilityindicate an antiferromagnetic transition occurring in thehigh concentration Mg-Mn alloy No. 87816 at approxi-mately 6'K. No obvious excess paramagnetism isexhibited in the magnetic susceptibility in the regionof the resistance minimum (approximately 12'K). How-ever, this is probably due to the opposing inhuence ofthe excess paramagnetism discussed in Sec. 5.1 and theantiferrornagnetic transition, the effects acting tolinearize the Curie plot. It should perhaps be pointedout that the value of the Curie temperature is zerowithin the accuracy of the measurement indicating noaverage internal field for the most concentrated alloy.

If it is assumed that the antiferromagnetic structurecan be considered as two interpenetrating sublatticeswith ferromagnetic interactions in each sublattice, thetemperature dependence of the resonance Geld

(Hp —H,.„)can be discussed following the treatment ofOwen et al.' The resonance condition for such a struc-ture is given by

pi= pe'+2H~Hg]&,

where II is the applied static magnetic field perpen-dicular to the preferred axis, H~ is the molecular fieldfor each sublattice and will be proportional to the mag-netization (3E,) of each sublattice, Hz is the anisotropyfield, and y= ge/2 mc. For resonance in the paramag-

1662 E. W. COLLINGS AND F. T. HEDGCOCK

netic region we can write

so that near the transition temperature

2H~IIg ——Hp' —H„„',

and for small line shift

(H p H--) =—HzH~/H p.

If we write H~=XM„where A. is an s-d interactionconstant relating the conduction electron and para-magnetic ion magnetization, then

(Hp —H,.„)= (XHg/Hp) iV, .

Further, if the anisotropy field Hz is temperature inde-pendent and the magnetization of the paramagneticions M, obeys a Curie law, then (Hp —H„„) should beproportional to T '. As can be seen in Fig. 8 this be-havior is observed at temperatures well into the transi-tion region, i.e., less than 5.5'K. It seems reasonable,therefore, to suggest that the exchange mechanism re-sponsible for the antiferromagnetic transition is sometype of s-d superexchange mechanism; with the premise,of course, that the spin system can be considered as twointerpenetrating sublattices with a normal antiferro-magnetic exchange and anisotropy field.

A change in line position which varies inversely withtemperature could be interpreted as a kind of electronicKnight shift. This situation has been considered byOwen et al. who show that such a shift, if it is occurring,should be observable in the paramagnetic region. Sinceno such movement in position occurs for Mg-Mn in thisregion, it is concluded that the sudden change at 6'Kis indeed due to a magnetic transition.

5.3 Spectroscopic State of theParamagnetic Ion

If manganese and iron contribute 2 electrons per atomto the conduction band of magnesium and aluminum,respectively, then the ions Mn++ and Fe++ should result.Mn++ should be in a (3d)' configuration correspondingto a PS4 ground state. The Fe++ ion should be in a (3d)'configuration with a ground state of 'D2. Using thespin-only equation an effective magneton number of 5.9would be expected for Mn++ and 4.9 for Fe++. As canbe seen in Table I the observed effective magnetonnumbers correspond to 5.2+0.2 for Mn in Mg and4.7&1.5 for Fe in Mg. It can be seen that the error inE ff for Mn in Mg permits one to say that the manganeseion is not in a 'S; state. This has also been observed inthe Cu-Mn system" and would lead one to suggestan S=2 state for Mn in both solvents. The temperaturedependence of the susceptibility for Al-Mn does notobey a Curie law. This effect has been discussed byFriedeP' as evidence of d-band formation in this system.

Presumably similar arguments could be given for theAl-Fe system in order to explain the low effective mag-neton number observed.

As has already been discussed in Sec. 3.1 the effectivemagneton number for Mn in Mg varies with tempera-ture. Perhaps the simplest suggestion to interpret this,and the fact that the effective magneton number doesnot correspond to the one expected, is to assume thatall of the manganese ions are not in an S state. Thesplitting of a d state by a cubic field in a metal has beendiscussed by Callaway and Edwards" and results in alowering of the triply degenerate d state with respectto the doubly degenerate state. If the upper states liesufficiently close to the conduction-band Fermi levelof the solvent, a population of the upper levels wouldresult from electrons in the conduction band. Thescheme suggested would result in a mixture of Mn ionsin Mg existing in (3d)' and (3d)' states. Occupied lowerlevels would give rise to a g value of approximately 2.00and the mixture of the two states would result in aneffective magneton number of approximately 5.2.

If we say that the ionizing energy for a 3d electron istoo great to allow the above process to take place, thenthere is the possibility of the formation of ions in a(3d)' state. Assuming that the exchange energy" couldplace the ground level of a (3d)' state near the Fermilevel, the number of ions in (3d)' and (3d)' electronconfigurations would vary with the position of the Fermilevel. This could produce a lowering of I',ff as theFermi level is raised. Also the attractive possibilityexists that with the Mn ion in a (3d)' state, there is thepossibility that by the action of a crystalline fieldtogether with spin orbit interaction, the ground statedegeneracy of the ion is removed providing levels"which might permit an inelastic scattering to take placeat low temperatures and hence result in the ElliotSchmitt resistivity mechanism. However, it is intendedto determine the susceptibility tensor of single crystalsof Mg-Mn and also the anisotropy in the g factor asdetermined by ESR. It is hoped that the combinationof these two measurements will give some indication asto the order of magnitude of the splitting of the d stateof Mn in Mg.

6. CONCLUSIONS

(1) There is an apparent excess paramagnetisrn inthe dilute magnesium-manganese alloys which could beinterpreted as a ferromagnetic coupling of the man-ganese ions. However, the range of the interaction founddoes not allow the effects to be interpreted as nearestneighbor interactions. The ESR results also indicate an

"J.Callaway and D. M. Edwards, Phys. Rev. 118, 923 (1960).'s In recent theoretical work P. W. Anderson [Phys. Rev. 124,

41 (1961)j and P. A. Wolff [ibid 124, 1030 (.1961)g considermechanisms for the formation of magnetic levels in metals. In theAnderson picture the magnetic states are split by so-called ex-change self-energy rather than the true exchange energy men-tioned above.

MAGNETIC PROPERTIES OF Mg —Mn, Al —Mn, Mg —Fe, AND Al —Fe 1663

additional line broadening in the region of the resistanceminimum which is presumably due to an interactionsimilar to that observed in the susceptibility results.

(2) The ESR and magnetic susceptibility results indi-cate an antiferromagnetic transition is taking place inthe most concentrated Mg-Mn alloy in the region of theresistance maximum. All of the Mg-Mn alloys have azero Curie temperature and there is no evidence of"parasitic ferromagnetism" as shown in the Cu-Mnalloys. '

(3) The susceptibility data indicate that the man-ganese ion in magnesium has an effective magnetonnumber of 5.2&0.2 at high temperatures and 3.6&0.2at low temperatures. The iron ion in aluminum has aneffective magneton number of 4.7~1.5 in magnesiumand 1.2&0.4 in aluminum.

(4) The effective magneton number for Mn in Mg

depends on temperature; the fact that it does not corre-spond to an 5 state suggests that the d state of the ionsis split by the crystalline Geld of the metal. A mixtureof ionic states could lead to the observed results andalso yield a g value of 2.00 for ESR. The most useful ionformed by the activation process would be one in a(3d) ' configuration.

ACKNOWLEDGMENTS

The authors would like to acknowledge the interestand aid of Dr. J. S. Dugdale and Dr. M. Bailyn in thiswork. We would also like to thank Miss M. Treuil forthe determination of the room temperature suscepti-bility of the alloys and G. Mark for his technical assist-ance while carrying out the experiments. The NationalResearch Council of Canada supported this workthrough a grant in aid.