High field antiferro-, ferri-and paramagnetic resonance at millimeter wavelengths

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High field antiferro-, ferri-and paramagnetic resonance at millimeter wavelengths

S. Foner

To cite this version:

S. Foner. High field antiferro-, ferri-and paramagnetic resonance at millimeter wavelengths. J. Phys.

Radium, 1959, 20 (2-3), pp.336-340. �10.1051/jphysrad:01959002002-3033600�. �jpa-00236045�

336

HIGH FIELD ANTIFERRO-, FERRI-AND PARAMAGNETIC RESONANCE AT MILLIMETER WAVELENGTHS (1)

By ^{S. FONER} (2),

Lincoln Laboratory, Massachusetts Institute of Technology, Lexington, ^{U. S. A.}

Résumé. 2014 Les champs magnétiques pulsés ^{ont été} employés pour faire varier le couplage ^à

haute fréquence ^des systèmes antiferro-ferri- et paramagnétiques dans les ondes de longueur ^{de 4}

à 8 millimètres. On montre des exemples d’expériences ^de résonance pour chacun de

^ces

systèmes magnétiques ^et les résultats sont décrits et discutés. Pour compléter ^les

^mesures

précédentes,

^{on a}

mesuré les susceptibilités magnétiques des monocristaux de MnF2 ^et Cr2O3. ^On indique ^ensuite

des applications

^aux

appareils ^{à haute} fréquence.

Abstract.

²⁰¹⁴

Pulsed magnetic ^{fields have been} employed ^{to "} tune " the high frequency magnetic

interactions of antiferro-ferri- and paramagnetic systems ^{to 4}

^mm

^{and 8 mm} wavelengths.

Examples ^of

^resonance

experiments for each of these magnetic systems

^are

^given, the nature of the information obtained is reviewed, ^{and results of these} experiments

^are

summarized. Related magnetic measurements

are

also described ;

^a

^detailed summary of susceptibility measurements for single crystal MnF2, CoF2 ^and Cr2O3 ^is given. Applications ^to high frequency ^devices

^are

indicated.

tE JOURNAL D E PHYSIQUE ^{RADIUM: TOME} 20, FEVRIER-MARS 1949,

Pulsed magnetic ^fields up ^to 750 kilogauss, pro- duced by capacitor discharge tbrough suitably designed ^coils [1], permit ^a variety ^of investiga-

tions [2], [3] which heretofore were not possible.

In particular, magnetic ^resonance phenomena

which involve large effective internal fields often

occur in the high-frequency ranges ^not yet ^attain- ed with present day technology. However, ^the high intensity pulsed ^{fields may be used to}

^"

^{tune "}

the resonance to relatively ^low frequencies (35 ^to

70 kMcps) ^dictated by ^source power, pulse ^detec-

tion sensitivity and space limitations. In this paper, several ^{examples of such} resonances in anti- ferro- ferri- and paramagnetic ^{materials are} briefly

described ⁱⁿ order to demonstrate the _scope and limitations of the technique. ^{Ih order to inter-}

pret ^{the resonance} experiments additional detailed

magnetic ^{data are often} required. ^A summary of thèse magnetic measurements is also presented.

Because present information is most limited for

antiferromagnets, ^{more details of both the reso-}

nance and magnetic measurements are presented

for this class of materials. Finally, ^{some brief}

remarks concerning possible high-frequency appli-

cations of these materials and the pulsed ^field technique ^{are also} presented. ^The details of these various investigations ^{are to be} published ^elsewhere.

1. Antiferromagnetie Résonance.

^-

The reso- nance condition for

^an

uniaxial!antiferromagnetic

(1) The research reported in this document

was

sup-

ported jointly by ^{the U. S.} Army, ^{U. S.} Navy and U. S. Air Force under contract with Massachusetts Institute of

Technology.

(2) Staff member.

single crystal, ^derived by ^Kittel [4], ^{Keffer and}

Kittel [5] ^{and others} [6] ^for Ho (2HEHA)1/2 ^is given by

where

⁶⁾

is the angulâr frequency, y is ge/2mc, ^Hr,

is the exchange fieldi HA. ^{is the} anisotropy field,

ce ⁼

XiliX.L (obtained ^from independent magnetic data), ^and Ho ^{is the} applied ^field parallel ^{to the} easy axis. ^{Estimates show that for most antiferro-} magnetics (Hx HA) ^{is so} large that low field obseri vation requires ^one4o one-tenth millimeter wave-

length radiation. The high ^{field mode can be}

observed ^at much lower wavelengths ^if Ho ^{is sufli-} ciently large [4], [5], ^The present capacitor ^dis- charge system [1], (2 ⁰⁰⁰ uF, ^{3 000} V) ^and coils per- mit measurements at 70 kMcps with fields _up to 600 kilogauss ^{at room} temperature ^and up ^to 350 kilogauss ^{at 4.2 OK when a} suitable Dewar

assembly ^{is inserted into the} pulsed field coil. This range of fields permits ^a survey of many antiferro- magnets. ^{To date} single-crystal MnF2, Cr20a, FeTi03, MnO, oc-Fe2O3, FeF2, CoF2, CoO, ^{and NiO}

have been examined ; the ^{results for the first two}

are summarized below, ^{the next three} appear ^to be ^more complex ^{and are still} being investigated,

and no resonance has yet ,been ^{observed in the}

last four. The important quantity, HA, ^{is obtained}

as a function of temperature ^{from the résonance}

data

^-

it is difficult to estimate

or

measure by

other means. The normalized angular dependence

of this resonance for

ce =

0, ^obtained by ^numerical methods, ^{and shown in} figure 1, ^{indicates that for}

low

(ù

/y ^accurate alignment ^{of the} crystal ^{is neces-}

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphysrad:01959002002-3033600

337

sary ^for this resonance mode to be observed.

A second resonance for Ho > (2HEHA)1/2, just

after " spin-flop ", shoiild be observed when

Ho

⁼

[2HgHA + (Coly)2]1n, ^The angular depen-

dence of this mode, ^{shown in} figure 2, ^indicates

FIG. 1.

^-

Angular dependence ^of antiferromagnetic

^reso-

nance

for

an

uniaxial crystal. Symbols :

k0 - Hol(2H2 HA,)’/2, v = (cùly)1(211]EHA)112,

6 is the angle ^between Ho and the c-axis.

FIG. 2. - Angular dependence ^of second mode. The

curves on

the left of 8

⁼

00 may be observable. Those

on

the right correspond ^to non-equilibrium ^conditions (not observable).

that for ^our parameters ^some good ^{fortune is essen-}

tial in order to observe this résonance. (This ^beha-

vior is borne out by many experiments.)

The results for MnF2 [7], [8], summarized in

figure 3, demonstrated that the molecular field

approximations ^{and the} dipolar ^{source of} Hd pre-

FIG. 3.

^-

Temperature dependence ^of (2HEHA) 1/2

for MnF2. ^Solid

^{curve -}

predicted Brillouin function for S

⁼

5/2, triangles

^-

⁴

^mm

data, circles and squares

-

8

mm

data,

^{crosses -}

high frequency data of Johnson and Nethercot (ref. 24).

dicted by ^Keffer [9] ^{were satisfied in} magnitude

and in temperature dependence. ^{Most recent}

results indicate that (2HrH&)112 ^{is closer to 92 kilo-}

gauss, but well within the experimental ^error.

Since the various interactions in MnF2 ^now appear to be well understood, ^this particular ^antiferro- magnet ^{warrants a detailed} analysis. Line-widths

as

narrow as 250 to 500 gauss at 36 kMcps ^were

observed at 4.2 OK. These measurements, ^corres- ponding to ^small differences measured near 80 kilo- gauss, ^are limited by ^various problems ^inherent

with pulse techniques. ’

Examples ^{of the resonance data obtained for} Cr203, again ^with Ho parallel ^{to the} easy axis, ^are

shown in figure ^{4. A constant value of}

FIG. 4.

^-

Resonance field

versus

temperature

for CrZ03 ^{at two} frequencies.

(2HEHJJl/2

⁼

⁶⁰ kilogauss ^{from 4.2 oKto 200 OK}

is calculated from this data if g

⁼

2. 00 is assumed.

In contrast with the observations in MnF2, ^the

temperature dependence ^of (2HEHg)lJ2 ^{does not}

fit

a

Brillouin function for spin 3/2. ^For Cr2O3, HE is about 2.1 X 10" _gauss, (about four times that of MnF2), TN ^{= 308 oR} (TN = 68 ^{oK for} MnF2), ^and HA ^{at low} températures ^{is 900 gauss} (HA

⁼

⁸ 500 gauss in MnF2). Although ^{the reso-}

nance

data near TN agrees with Dayhoff’s ^re-

sults [10], ^the extrapolated temperature depen-

dence and absolute magnitude ^of (2HEHA)1/2 ^are quite different. The low temperature ^{value of} HA ^{is about} 1/3 ^{that estimated} by Dayhoff ^and 1 100 ^to 1/1000 ^{of earlier estimates} [11]. Appa- rently ^{the lattice} distorsions [12] ^{which extend}

over twice the température range investigated by Dayhoff, ^are important [3]. ^{This is one of several}

reasons which _argue that low-frequency ^{data near} TN ^{are not} sufficient and that either high frequéncy

or

high ^field experiments ^are necessary. These

results,

^as

^well

^as

^{recent detailed} magnetic data,

indicate that Cr2O3 ^{is not as} simple ^as MnF 2. ^This

is not surprising ^because crystalline ^{field inter-}

actions are expected ^{to be} important ^{for the C18+}

ion, ^{whereas for the Mn2+} ion, theory ^and experi-

ments indicate this effect is small.

Angular ^{data taken at 4.2} oR and 77 oR for

v

~ 0.2 qualitatively agree with the results in

figure 1 ; ^an additional high ^{field resonance}

appears for 0 > 5° and tends toward ko = 1, ^and

ail resonances disappear ^{for 0} greater ^{than about}

120. A broad very low field resonance was also observed for large ^{0. This is not} predicted by ^the simple theory, ^{and is} being investigated ^further.

2. Ferrimagnetie Résonance.

^---

For the sim-

plest ^case (gi

⁼

g2), ^the high frequency ^{or " ex-} change " ^{resonance for}

^a

^two sublattice ferri-

magnetic ^is given by [4]

where M1 + M2

⁼

nM1 ^and HE == "’AMI. ^Here again Ho ^{can be used to "} tune " the resonance to

low frequencies, ^{so that HE may} be determined.

In this _case, HA ^{and n are} determined from magne- tic data. Eiren for our pulsed fields, the range of

experiments ^{is limited to materials of relatively}

small HE ^{or small n. When} g1 g2 the usual

resonance is given by

^{w =}

( M 1 + M2) _H

e

e

is given y

^{w =} 0

(MllYl + M2/Yt) H0

and the " exchange " ^{resonance is} correspond- ingly ^more complicated. ^In particular, ^{for large} Ho,

^a

large ^term proportional ^to Ho ^HE (gi - g2)

must also be considered in [ ]1/2 . ^{The rare-earth}

iron garnets ^are ideal for such observations because HA ^is small, compensation points ^occur

near

or

below 300 °K, ^and single-crystals ^{are obtai-}

nable. However, appreciable corrections for the

field dependent magnetization ^{must be made for}

these materials [13]. ^{Both the} high ^{and low field}

resonances have been observed for single-crystal gadolinium ^{and erbium} garnets ^{over a wide} tempe-

rature range and ^were reported ^elsewhere [13].

The usual resonance showed the qualitative ^fea-

tures obtained earlier in polycrystalline ^mate-

rials [14].

3. Paramagnetie Résonance.

^-

The large tuning

range supplied by pulsed ^fields may also be used to

study paramagnetic resonance. The pulsed ^field technique ^is particularly useful when

a

large ^zero-

field splitting ^is present because then the usual

laboratory ^{fields limit} observations to small

changes ^{of the} energy levels. From the resonance

data, ^{the various terms in the} spin-Hamiltonian

can be determined. ,

In collaboration with Dr. Horst Meyer ^{of Har-}

vard University, ^this technique

^was

applied ^to paramagnetic ^resonance experiments ^of 02 ^mole-

cules (isolated from each other by ^{about 8} A)

contained in

a

single crystal ^of g-quinol ^clathrate.

Meyer, O’Brien, ^and Van Vleck [15] ^{have conclud-}

ed ^from magnetic ^{data that the} 02 ^{molecules are}

influenced by ^the crystalline field, ^{and that}

^a

large zero-field splitting, corresponding ^{to about}

4.15 OK, ^{should be} present. ^{In this} interesting

case both higb ^{fields and} high frequencies ^would

be required ^{in order to observe} paramagnetic ^reso-

nance of the 02 spins. Preliminary experiments

at 4.2 ^{OK with} pulsed ^fields and both 37 kMcps

and 71 kMcps ^{showed this resonance and confirmed}

thé large zero-field splitting.

4. Magnetie Measurements.

^-

Examination ’of the literature

on

antiferromagnetics indicates that the data are too limited to permit accurate tests of numerous existing theories. The difficulties arise from two causes. First, few known anti-

ferromagnetic systems have " simple " ^structures

-

MnO, ^{the classic material chosen for} comparison

with theory, ^is quite complex. Second,

^no

^measu-

rements have been made

on a

simple ^antiferro- magnetic ⁱⁿ sufficient detail and over a sufficiently

wide range of temperatures. ^{The best results so}

far were obtained in uniaxial anhydrous ^fluorides by ^{Stout and} Matarresse [16] ^and by ^{Bizette and}

Tsaï [17]. Bizette and Tsaï also demonstrated that measurements in single-crystal ^antiferro- magnets ^{are essential.}

Evaluation of the antiferro- and ferrimagnetic

resonance data also requires ^accurate magnetic

data over

a

wide temperature range. Detailed

single-crystal susceptibility ^and magnetization

data are easily ^{obtained in}

^a

^uniform magnetic

field with the vibrating-sample magnetometer [18].

Since such data are of general interest, ^{some of the}

results are summarized below.

339

As

an

example, ^the perpendicular susceptibility

of

a

small single crystal ^of MnF2. plotted ^{on an} expanded scale, ^{is shown in} figure ^5. The results

FIG. 5.

^-

Relative perpendicular susceptibility

of MnF2

^versus

temperature.

of such measurements on MnF2 ^{are :} 1) xx varies

by less ^{than 1} % ^{from 4.2 OK to 50} °K ; ^{of the} numerous spin-wave theories, ^Ziman’s [19] predicts

that _xi should be independent ^of temperature ; 2) if the break in _ya or the _XII curve is used as

a

criterion, TN

⁼

⁶⁸ OK, just ^{at the} specific ^heat anomaly ; 3) data from 300 OK to 350 °K lead

to 0

^~

80 OK (here ^{e is the constant in the Curie-}

Weiss law, x

⁼

c/(T + e)), ^and 4) ^{above 20 °K}

x,,

^oc

71.5, ^where

^as

^{below 20} oK, XI,

^oc

T1.8. ^On the other hand, ^similar measurements ^on CoF2 ^indi-

cate U increases with increasing temperature,

XII

^oc

T1.6 above 15 °K, and X

^oc

T3-8 below ¹⁵ oK, ^but

does ^not follow

a

simple power law ^at lowest tempe-

ratures. Furthermore, XII does not approach

^a

^zero

value ^at low temperatures. Finally, ^the suscep-

tibility measurements on Cr20S ^{show that} X, is constant to within 1 % from 4.2 oK to 100 OK,

and then increases with increasing temperature, and that _xjj reaches a small constant value below 20 OK, ^{and does not show}

^a

simple power depen-

dence below 20 OK.

Recently, 19F nuclear resonance data [20] ^of

various antiferromagnetic ^{fluorides have been used}

to examine the temperature dependence ^{of the}

sublattice magnetization, ^M. It should be rea-

lized that susceptibility measurements permit ^eva-

luation of HE, ^{do not} depend

^on

^the presence of

appropriate ^nuclear spins species, and may ^com- pare in accuracy ^{to the resonance} results. The low temperature ^{19F resonance} data indicate that aMoc T3.5 for MnF2, ^{and OlVI oc T5.0 for} CoF2, ^where

AM

⁼

M(0) - M(T). ^{If M varies}

^{as an}

appro-

priate ^Brillouin function, xjj should show

a

tempe-

rature dependence ^one power lower ^than given by

the M data. This is almost the case

^-

the devia- tions and the particular temperature dependence

must be explained by spin-wave theory. Magne-

tic measurements from 1.5 ^to 4.2 °K are being

made to study ^this problem ⁱⁿ greater ^detail.

Magnetization measurements of various single- crystal rare-earth iron garnets generally agreed

with earlier polycrystalline ^data [21] ^{in both} magnitude ^and temperature dependence.

5. Applications ^to high; lfrequency ^Devices.

^--

The three magnetic ^{classes discussed above all}

have the géneral feature of very high frequency

response because of large ^{effective internal fields.}

Conversely, ^when millimeter and sub-millimeter

wavelength ^{sources become} available, ^{one would} expect ^that these materials will be useful in practi-

cal devices. Since it is not economically ^feasible

to produce continuous fields of the required magni- tude, magnetic systems ^{with the} appropriate " ^built

in " internal field will be required. Tuning ^could

be accomplished by varying the crystal orientation,

field Ho, ^and /or temperature. ^For example, ^one

could make

an

antiferromagnetic millimeter ^wave modulator. One advantage ^of antiferromagnetic

devices would be that demagnetizing field effects would be negligible.

It was pointed ^our earlier that suitable high ^fre-

quency sources are not yet available. Recently

we have been investigating ^the possibilities ^of generation ^and amplification ^of millimeter ^waves with a pulsed-field ^Maser [22]. ^One proposed

scheme involves

a

three-energy-level paramagnetic system ^{to which a} pulsed ^{field is} applied ^{in order}

to generate

^an

output frequency ^much higher ^than

the pumping frequency. ^{Tests of this device are} being ^made.

The author wishes to thank Dr. H. J. Zeiger ^for

valuable discussions, Dr. H. H. Kolm for his valuable contributions to the developement ^{of the} pulsed ^field system, ^{Mr. B. Feldman} for assistance with the experiments, ^{and the numerous interested}

scientists [23] from various institutions, ^{who so} kindly ^{furnished the} single crystals ^{essential for}

this work.

REFERENCES

[1] ^FONER (S.) ^{and KOLM} (H. H.), ^{Rev. Sc.} Instr., 1956, 27, 547 ; 1957, 28, ^799.

[2] ^FONER (S.) ^{and KOLM} (H. H.), ^Conf.

^on

Magnetism

and Magnetic Materials, ^Oct. 1956, Boston, ^Mass.

(AIEE Proc., Feb. 1957).

[3] ^FONER (S.), Fifth Inter. Conf.

on

Low Temp., Phys.

Chem., 39-4 (Madison, ^Wis., Aug. 1957).

[4] ^KITTEL (C.), Phys. Rev., 1951, 82, ^565.

[5] ^KEFFER (F.) and KITTEL (C.), Phys. Rev., 1952, 85,

329.

[6] NAGAMIYA, YOSIDA and KUBO, Advances in Physics, 1955, 4, 1.

[7] ^FONER (S.), Bull. Amer. Phys. Soc., 1957, ^Ser. II, 2,

128.

[8] ^FONER (S.), Phys. Rev., 1957, 107, ^683.

[9] ^KEFFER (F.), Phys. Rev., 1952, 87, 608.

[10] ^DAYHOFF (E. S.), Phys. Rev., 1957, 107, 84.

[11] ^{MCGUIRE, SCOTT and GRANNIS,} Phys. Rev., 1953, 102, 1000.

[12] ^GREENWALD (S.), Nature, 1956, 177, ^286.

[13] ^FONER (S.), Bull. Amer. Phys. Soc., 1958, ^Ser. II, 3, 42.

[14] ^PAULEVÉ (J.), C. R. Acad. Sc., 1957, 244, 1908 ; 1957, 245, 408.

[15] MEYER, O’BRIEN and VAN VLECK, Proc. Roy. Soc., 1957, 243 A, 414.

[16] ^STOUT (J. W.) ^{and MATARESSE} (L. M.), ^{Rev. Mod.}

Physics, 1953, ^{25, 338.}

[17] ^BIZETTE (H.) ^{and TSAI} (B.), ^{C. R. Acad.} Sc., 1954, 238, 1575.

[18] ^FONER (S.), ^{Rev. Sc. Instr., 1956,} 27, 548 ; ^Bull.

Amer. Phys. Soc., 1957, ^Ser. II, 2, 237. ^{A detailed} account is to be published.

[19] ^ZIMAN (J. M.), ^Proc. Phys. Soc., London, 1952, ^A 65, 540, 548.

[20] JACCARINO, SHULMAN and DAVIS, ^{Bull. Amer.} Phys.

Soc., 1958, ^Ser. II, 3, ^41.

[21] ^BERTAUT (F.) and PAUTHENET (R.), ^{Part B.} Suppl.

n° 5 IEE Convention

on

Ferrites, 1956, p. ^261.

[22] ^FONER (S.), ^{M. I. T. Lincoln} Laboratory, Quarterly Progress Report, ^{1 Feb. 1958.}

[23] CZERLINSKI (E.), ^JONES (R. V.), ^MEYER (H.), ^NAGA-

MIYA

(T.), ^RODRIGUE (G. P.), ^SCOTT (E. J.), Jr.,

STOUT (J. W.), ^WOLF (W. P.), and many others.

[24] ^JOHNSON (F. M.) and NETHERCOT (A. H.), Jr., Phys.

Rev., 1956, 104, ^847.

DISCUSSION

Mr. Wolf.

^-

^{1 was} priviledged ^{to see} Dr. Foner’s results ^for Cr2O3 a ^few days ^{ago and I have made}

^a

rough estimate of the contribution of the crystal

field effect ^to the anisotropy, using ^{the measured D}

values for ruby. ^{It seems that one would} expect quite ^a large contribution from this _cause, of the order of 1 300 oersteds at T

⁼

0, and 1 think that this can explain qualitatively, ^{and may be even} quantitatively why ^{his curve of} k/2HxHa ^{was so}

different from

a

Brillouin function.

Mr. Kittel.

^--

It would be interesting ^{to see the}

details of this explanation.

Mr. Clogston.

^-

Bythe ^use of nuclear resonance, Jaccarino has observed that the sub-lattice _magne- tization in various antiferromagnetic ^materials departs widely ^as

^a

^{function of} temperature ^from the standard Brillouin ^curve.

Mr. Foner.

^-

If this is the _case, the appropriate

corrections must be made for the temperature dependence ^{of the} sublattice magnetization ^before HA

^can

be evaluated

as a

function of temperature,

but K versus T does not depend directly ^{on 3f.}

Mr. Nagamiya (Remark).

^-

^The _quantity (2HEHA) 1/2 ^for Cr2O3 ^{deduced from Foner’s curve}

for 36 GHz ⁱⁿ figure 4 appears ^as shown in the

accompanying figure. In deducing this, ^the

measured _XII and _xx due to McGuire et al. (Phys.

Rev., (1956), 102, 1000); ^{were used. Since} (2HEHA)1/2 ^is equal ^to (2AK)1/2, ^{where A is the}

molecular field constant and is equal ^to 1 /xl ^and

K is the anisotropy constant, ^{one can deduce the} value of K at absolute zero with the use of the

same X.L and Foner’s value of (2HEHA)1/2 ^{at abso-}

lute zero : K = 4.45.104 erg/gram. ^The dipolar anisotropy ^constant Kàip calculated by ^Tachiki

and Nagamiya (Phy,,. ^Soc. Japan, (1958), 13, 452,

is 9. 28.104 erg/gram,

^so

^one may take the crystal-

line field anisotropy ^{constant to be} Kcryst. = - 4 . 83 .104 erg/gram,

which is one tenth of the value deduced from opti-

cal measurements in ruby ^and opposite ⁱⁿ sign.

Assuming ^these values of Kdip. ^and KCryat.1 ^the temperature dependence ^{of the} quantity (2HcH& )112

was calculated and is shown also in the accompa-

nying"figure. ^The discrepancy ^{between ’these8two}

curves above 130 OK might ^{be due to the} inap- propriate assumption of the molecular field in the the calculated _{curve ;} short range order and crystal-

line deformation accompanying ^the growth ^{of the} antiferromagnetic ordering might play ^an impor-

tant role here.