PHYSICAL REVIE% 8 VOLUME 15, N UMBER 9 1 MA Y 1977

Magneto-optical observations of the magnetic domains in the nearly-two-dimensional

Heisenberg ferromagnet (C&H7NH3)~CnBr4

H. van Kempen, F. H. Mischgofsky, ~ and P. %'yder

Physics Laboratory and Research Institute for Materials, University of ¹jimegen, Toernooiveld, Nijmegen, The Netherlands

(Received 20 October 1976)

We studied the magnetic behavior of (C,H~NH, ),CuBr4 crystals by means of the Faraday effect. We observed

that at low temperature the crystals can exist in two crystallographic modifications. One modification shows,

below the magnetic transition temperature, magnetic domains in zero magnetic field. This modification can be

described by the Pb'c'a structure, the spins being in the bc plane with an angle between spins and b axis

of 24'. The other crystallographic modification shows domains in the field range between 215 and 350 Oe.This modification can be described by a Pb'ca' structure at fields ldwer than 215 Oe, a Pb'c'a structure

at fields higher than 350 Oe while in the field range of 215-350 Oe are alternating domains of Pb'c'a andPb'ca' structure. The coexistence of the two magnetic structures in the field range of 215-350 Oe shows

that the field-induced phase transition from the Pb'ca' structure to be Pb'c'a structure is a first-order

phase transition.

INTRODUCTION

The series of compounds (C„H,„„NH,),CuX„where X represents a Cl or Br atom and n variesfrom 1 to 10, have been studied intensively latelybecause these compounds are good examples ofnearly perfect two-dimensional Heisenberg ferro-magnets. ' ' The orthorhombic crystals consistof nearly quadratic layers of CuX, (in the abplane) separated by two layers of nonmagneticC H2 + iNH3X. The detailed crystal structure ofsome of the Cl compounds has been determinedand is found to crystallize in the Wca spacegroup. " However, for nearly all the compoundsthe dimensions of the unit cell have been deter-mined by Kop. ' Recently Daoud' extended the listof known structures and found also the Pbca struc-ture for the Br compounds at room temperature.

The magnetic interaction within the CuX, layeris ferromagnetic and is very strong comparedwith the interaction between the layers. Althoughaccording to the theory of Mermin a.nd Wagner' anideal two-dimensional Heisenberg ferromagnetshould not have long-range order above 0 K, thesecompounds show an anomaly in the susceptibilityat a temperature (T,) of approximately 10 K. Atthis temperature the magnetic system orders in athree-dimensional way as can be concluded fromthe occurrence of magnetic domains in some ofthe compounds below T,." T, is determined main-ly by the strong intralayer exchange interaction.However, which three-dimensional magneticstructure exists below T, is determined by smalldeviations from the ideal such as the interlayerinteractions and the anisotropy energies. VVithinthe series one can find ferromagnetic, antiferro-magnetic, and canted antiferromagnetic stacking

of the ferromagnetic layers.In the present paper we describe observations,

made by means of the Faraday effect, of the weakferromagnetic domains in his (propylammonium)copper(II) tetrabromide, (C,H,NH, ),CuBr, . Weobserved that around or somewhat below liquid-nitrogen temperature often, but not always, acrystallographic phase transition takes place.Two different magnetic structures exist below T,depending on the occurrence of this structuralphase transition.

EXPERlMENT

The observations of the domains were carriedout by means of the Faraday effect. At room tem-perature the (C,H, NH, ),CuBr, crystals are veryopaque in the visible-light range up to about 0.6pm; only in the red the crystals are somewhattransparent. During cooling the crystals becomemore transparent, but still very thin (less than100 pm) crystals were needed to have enough lightfor our microscopic observations. The crystalswere grown in the form of thin platelets, perpen-dicular to the e axis, of 20 to 100 p,m in thicknessand up to 5 mm in diameter. They were made byevaporation of a solution of the compound in wateror in ethyl-alcohol. The samples made from theethyl-alcohol solution shattered less frequentlyduring cooling.

The apparatus is fully described elsewhere. "It consisted of a glass Dewar with optical windowsin the bottom. Under the Dewar a polarizing mi-croscope was placed with objective lenses withlong working distance. The optical resolution was1 pm. Light reached the sample via a rotatablelight guide with a polarizer on its lower end. Bothbroadband and filtered light were used. The filter

4386

MAGNET0-0PTICAL 0BSERVATIONS 0F THE MAGNETIC. . . 4387

was transparent for wavelengths above 0.6 pm.The samples were mounted with the c axis along

the line of sight between two copper grids on whichan Allen-Bradley carbon thermometer was gluedor were placed free on the bottom glass window.

The magnetic domains could be photographed,but long time exposures were needed due to thelow transparency and because the domains wereonly observable between almost-crossed polar-izers near the extinction position of the birefrac-tive crystals. Moreover, too much light on thesample will heat the sample relative to the carbonthermometer. There was not enough light tophotograph directly the fast crystallographic phasetransition, so in that case we used a video camerawith image intensifier. " A small superconductingmagnet supplied the magnetic field along the direc-tion of the light pa,th, that is the c axis direction.During the period that the liquid-helium level wasbetween the sample and the bottom of the solenoidspace the sample warmed sufficiently slowly toallow measurements up to 12 K.

OBSERVATIONS

During cooling to liquid-helium temperature weobserved the birefractive crystals in the extinctionposition between almost-crossed polarizers. %efound that large crystals showed a sudden changein brightness, caused by a rotation of the extinc-tion axis, at some temperature below 100 K. Thisshows that these crystals underwent a structural

SOv

FIG. 1. Domains in zero applied field in type-Acrystals at T =2 K. The contrast is enhanced by photo-graphic methods.

MMq1-

0,5-

0-

-0,5-

//

//

//

//

//

//

///-1--

-300 -200 -100 0I

100 200 300H, (o~)

FIG. 2. Magnetization M versus applied field H forfour different samples. The magnetization M is plottedrelative to the single domain magnetization M&. Themagnetization is deduced from the dimensions of the do-mains by direct microscopic observation {) or bymeasuring the micrographs (0,G, A). The data pointsin this figure were taken at 2 K, but can be consideredwithin our accuracy to represent the situation at 0 K.

phase transition. However, some minor parts ofthe crystals and some tiny crystallites did notshow the phase transition. Because our apparatuswas not adapted for temperature control in thetemperature range of this phase transition we canonly make a rough estimate of the transition tem-perature: 70+20 K. In the larger crystals it waspossible to observe the nucleation and growth ofthe low-temperature phase. The low-temperaturephase nucleated somewhere in the form of a spikeand expanded over the whole crystal in a few sec-onds with a speed of a few 100 pm/sec. Duringthe transitions the boundaries between the phasesformed almost parallel straight lines. After thetransition often new twins in the & plane werepresent. Parts of the crystals which underwentthe phase transition on one cool-down could stayunchanged during a subsequent cool-down and viceversa. Very small crystallites usually did notexhibit the phase transition. Hereafter we call thecrystalline parts which underwent the phase trans-ition type A. , the other pa, rts, type B. Crystallineparts of type A are generally larger and opticallymore perfect than those of type K Sometimes thecrystals shattered during cooling or warming.However, when they were mounted carefully,strain free and not grown onto a substrate theygenerally survived unimpaired.

Below a transition temperature T, =10.2+0.5 Ktype A showed magnetic domains in zero appliedfield. The domains were straight and parallel(Fig. 1). The width depended on the sample thick-ness and varied from 2.5 to 4 pm for samplesfrom 20 to 100 pm thick. When a magnetic fieldwas applied in the c direction one type of domaingrew at the expense of the other until at about 180Oe the single domain state was reached (Fig. 2).

4388 H. VAN KEMPEN, F. H. MISCHGOFSKY, AND P. RYDER 15

, 25g, -—A ~

~l

'I

FIG. 3. Domains in a type-B crystal in an appliedfield of 280 Oe at T = 2 K.

After the field was removed the domains returned,however, no longer straight but quite twisted.%hen the temperature was raised close to T, thedomains straightened out again.

Type B did not show domains at zero appliedfield. At a field of about 215 Oe domains startedto appear and grew with increasing field. (Sometraces of domains were already visible at 190Oe). At 280 Oe one type of domain covered abouthalf the surface (Fig. 3) while at 350 Oe the singledomain state was reached (Fig. 2). The observedprocess is typical for a field-induced first-orderphase transition in which case the transition isspread out over a certain field range due to thepresence of demagnetizing fields. " The criticaltemperature T, for type & is 10.5 +1 K. The largeuncertainties in the critical temperatures aremainly due to the heating effect of the polarizedlight beam on sample and thermometer which haveonly limited heat contact in the helium gas. In con-trast to the straight and parallel domains of typeA, the domains of type &are very twisted, branchedand often of short length (Fig. 3).

DISCUSSION

Structural phase transitions have also beenobserved in crystal having a composition andstructure related to our copper bromine com-pound (CEH, NH, ),CuBr, . For some of the(C„H2„„NH,),MCl, compounds with M = Mn, Cd,or Fe and n =1, a high-temperature tetragonalphase is followed by a room-temperature ortho-rhombic phase and a low-temperature tetragonalphase. "" For the compounds with n=2, 3 and3f =Mn, Cd a transition to a low-temperature Pheon

phase has been observed. ' ' Recently also aseries of structural phase transitions has beenfound in copper bromine compounds with shortalkylamine chains (n& 5), by means of differentialthermal analyses, microscopic observations,transmission spectroscopy, and Quinier powderdiffraction. " The transitions can be explained bychanges in the motions of the alkylamine groups. " 'Far-infrared experiments at our laboratory on thecopper chlorine compounds indicate a change inthe vibrational modes of the metal halogen planesat the transition temperature. ""

Our optical observations show that the structuralphase transitions in (C,E,NH, ),CuBr, do not alwaystake place in the same way. As a result two dif-ferent crystallographic modifications exist at lowtemperatures which have also different magneticproperties. Susceptibility measurements ofde Jongh" on (C,H,NH, ),CuBr, showed that a singlecrystal gives a susceptibility peak at T, = 10.3 Kwhilea powder sample has an additional peak at T, =11..4 K.On repeated heating and cooling of the single crystal,it started to shatter and the susceptibility peak at10.3 K decreased while a peak at 11.4 K developed.This shows that also in his experiment two modi-fications existed; one mainly in large single crys-tals with T, =10.3 K, and one mainly in powderlikecrystallites with T, =11.4 K. It suggests that ourtype A has the same modification as the one withT, = 10.3 K and type B as the one with T, = 11.4 K.

For (C,E,NH, ),CuBr, the lowest structural phasetransition takes place between 90 and 50 K. (Thisresult of our optical experiment is confirmed byother experiments. ") No structural data belowthis temperature are known. However, the pre-sence of twins in the ab plane and the existence of alow-temperature Pbca structure in the Mn and Cdcompounds with n =3,""suggest a low-tempera-ture orthorhombic structure also for our com-pound. Moreover, the low-temperature magneticmeasurements of the Amsterdam group"' showthat both the Cl and Br compounds can very wellbe described by assuming the orthorhombic Pbcasymmetry. So apparently any deviation from thissymmetry is small. Therefore we will discussour observations hereafter assuming our compoundhas the Pbca symmetry.

Bloembergen et al. ' have shown with group-the-oretical methods that assuming two-sublatticeantif erromagnetism with the layers belonging alter-nately to sublattice 1 and 2, four kinds of magne-tic structures are possible for the Plica crystalstructure. Only one of these four structures givesa weak ferromagnetic moment along the c axis,namely the Pb'c'a structure and so correspondsto type A. This structure has the following spincomponents for sublattice 1 and 2 [Fig. 4(a)]:

15 MAGNETO-OPTICAL OBSERVATIONS OF THE MAG N ETIC. . . 4389

z {~) {b)

Y

FIG. 4. Directions of the sublattice magnetization in

the Pb'c'a structure (a) and in the Pb'ca' structure (b).The dashed arrows indicate the directions of the sub-lattice magnetization when a small magnetic field isapplied in the z direction.

1& 2& y ly 2y y gZ 2Z

with the x, y, and z directions along the crystal-lographic a, &, and c axes, respectively. Forthis structure the general expression' for the freeenergy E in the molecular-field approximation at0 K with an applied field H, in the z direction re-duces to

E/Mo = -Hs+Hs(-&', „+&,g)

+ Hg2cyz —2HPyyoyz- ScHz Jyz

where H&, H&, H», and H& are the intralayer andinterlayer interaction parameters, the intralayeranisotropy parameter in the y-z plane, and theantisymmetric anisotropy parameter, respective-ly; o isthe reduced spin 8/Sandy, =2g„/g„=1.956.(We use for the g-tensor components g„andg„the values measured by Vega and Maarschall. )In accordance with the definition in Ref. 5 we usefor M, the sublattice saturation magnetization perunit volume: Mo =2Sg„ps/aPoco, where gs is theBohr magneton and a„b„andc, are the dimen-sions of the unit cell. As discussed in Ref. 5 wecan neglect the interlayer antisyrnmetric para-meter because it is expected to be relativelysmall. The part of the interlayer anisotropy orig-inating from the exchange interaction will be verysmall; the part originating from dipole-dipole in-teraction is of the order of 100 Oe" and will beneglected. If e is the angle between the magneticmoments of sublattice 1 and the y axis and of themoments of sublattice 2 and the negative y axis[Fig. 4(a)] we can write expression (1) as

E/Mo Hs + &Hg2 (Hg + zH») cos2Q-Hz slnÃo. - g H sina.

The angle o. can be derived from the measuredmagnetization M versus applied field curve (Fig.2). The samples are flat platelets, hence the de-magnetization factor equals 4m. From the slopeof the M vs H curve it follows that 4', =130+15Oe, where M, is the magnetization of the domainsper unit volume. (In fact the M, so obtained is

still a function of temperature and has been ex-trapolated to T =0 K.) This should be comparedwith the saturation magnetization, 320 Oe, which

can be calculated from the dimensions of the unit

cell. This gives a =24 +3'. Magnetic torsion bal-ance measurements of Bloembergen et al. '6 on

(C,E,NH, ),CuBr, give an estimated Hs =2.5 kOeand H„,=1.2 kOe. Using these values of H~ and

H» and o.' = 24' we find by minimizing (2) H, =3.4kOe.

From the other three allowed magnetic struc-tures only the W'ca' structure has a free energycomparable with the free energy of the Pb'c'astructure [Fig. 4(b)]. The spin components forthe P5'ca' structure are

E2 = ~ H~ 2- [(Hs —2 H») + H g] (3)

If we compare E, with the analogous quantity forthe Pb'c'a structure, E„using the above givenvalues of H», H~, and H~, we find E, =-4.0kOeand E, = -3.3 kOe. This shows that a relativelysmall change in one or more of the interactionparameters can make the P&'ca' structure themost favorable structure.

To discuss the type 8 crystals we have to con-sider the possible structures in the presence of amagnetic field along the c axis. Group-theoreticalarguments" show that also in the case of an ap-plied field along the c axis four different magneticstructures are possible. In the limit of zero fieldthese structures should correspond to the fourzero field structures. In this way we find that thein-field structure S,„=S2„=0&Sly S2yy and Sxz =Smz

corresponds to the P&'c'& structure while S„=S„=0 and arbitrary values of Spy S2yy Sy and S„,corresponds to the P&'ca' structure (Fig. 4). Wecan explain the observed behavior of the type Bcrystals if we assume that the interaction para-meters of type B are such that the Pb'ca' structurehas a slightly lower free energy in zero field thanthe P&'c'a structure. A magnetic field along the zdirection will in first order not change the freeenergy of the Pb'co' structure while for the W'c'+structure the field-dependent part of the free ener-gy changes approximately proportional with field.

Syr =S2x —0j Spy -S2yy Sgz —-S2z

The expression for the free energy at 0 K and zeroapplied field becomes

E/Mo = -Hs + Hs(o', „—&2g) + H»(P g—2H~o„o,g'

1 p 1Hs+ 2HA +(Hs —,H») cos2—P—H~ sin2P,

where P is the angle between the spin moments andthe y axis. The free energy has a minimum fortan2p = H~/(HE --~H»); for this angle of p we findthat E, = E/Mo+Hs —(for 45' ail ~90'):

4890 H. VAN KEMPEN, F. H. MISCHGOFSKY, AND P. %YDER

For a =22' and H, = 215 Oe this becomes

H~ = 0.9'l(Hs + ~H~ 2) —2'l0. (5)

Substituting the above expression (4) for H~ in theexpression for E, (2} and E2 (2) and using E, =E2at H, =H„one can express H» in terms of H~

—,'H~,'(1+sin'a+2 sin'a) -2g,H,H ssinag~, sina+2Hs cos2a

For a = 22' and H, = 215 Qe this becomes

166- H~109 +H~

(6)

As stated above we can not determine H~„H&,and H~, however, if the H~ for type B is of thesame order of magnitude as for type A then itfollows from (5) and (6) that approximately H»=-200 Oe and H~ =0.97H~ -400 Oe. Because ofthe approximations involved we have to considerthe obtained numerical values more as estimatesthan as precise results.

It is not uncommon for substances with two-di-Qensional magnetic interactions to exhibit differentpxagnetic structures. Gurewitz et al."found differ-ent structures in Rb,MnC14 depending on the prep-aration method of the samples. Birgeneau et al."observed two structures in samples of RbMnF, .It is not surprising that the two-dimensional mag-netic compounds are likely candidates for thismagnetic polytypy. As mentioned in Refs. 29 and31 the three-dimensional ordered structure is de-termined by the combined influence of a number ofinteraction and anisotropy fields which all are very

This means that a critical field H, exists at which

a field induced first-order phase transition fromthe W'c&' to the P&'e'a structure begins to occurlocally. Demagnetizing fields prevent the spread-ing of the Pb'c'a structure over the whole sample.There is a field interval (coexistence region) aboveH, where domains of W'c'a structure and W'ca'structure alternate while the internal field is keptat 215 Oe due to the demagnetizing fields. In thecoexistence region we have a relation between Hand M analogous to the relation for a simple (weak)ferromagnet: rhH =4mb, M. From the measurements(Fig. 2} it follows that for the weak ferromagneticmoment of the Pb'c'a domains: 4mM~=120+10 Oe.This gives n =22' in an internal field of 215 Oe.In the case of the type-B crystals the informationfrom the experiment (H, = 215 Oe, a = 22') is notsufficient to solve the three unknown parametersH~, Hg„and Hg. However, we can deduce somerelations between the parameters.

Minimization of (2) gives

H~ =(Hs+-,"H„,) tan2a- gH(co as/2 cos2a). (4)

small compared with the interlayer interaction butcan be mutually of comparable magnitude. In sucha situation a small change in the properties of thematerial caused for example by a different prep-aration method (HbMnCl, ), different amount ofimpurities and dislocations, stress, or differentcrystal structure, can easily change the balance ofinteraction and anisotropy fields in such a way thata different magnetic structure becomes the mostfavorable.

CONCLUSION

At liquid-helium temperatures there exist twomagnetic modifications (type A and type H) in

(C,H, NH, ),CuBr, crystals. Crystals (or parts ofcrystals) exhibiting type-A behavior have gonethrough a structural phase transition below 90 K,while the crystals showing type-B behavior havenot. Cooling speed, crystal perfection, stress andcrystal size are decisive factors in inducing thepossible structural phase transition. Especially,both the experiments of de Jongh" as well as ourown observations, indicate that the size of thecrystals plays an important role.

The magnetic properties of type-A crystals be-low the magnetic transition temperature can bedescribed by the weak ferromagnetic Pb'c'a struc-ture consisting of antiferromagnetic coupled ferro-magnetic copper bromine layers with an angle abetween the spins and the xy plane equal to 24 +3',leading to a net ferromagnetic moment. Combin-ing our experimental data with the torsion balancemeasurements of Bloembergen' we find for theantisymmetric anisotropy parameter H~ =3.4 kQe.

The type-B crystals show domains for fields be-tween 215 Qe and 350 Oe. This can be explainedby assuming a magnetic P&'ca' structure in zerofield. At an applied field of 215 Qe or larger theE4'c'a structure becomes energetically more fa-vorable and a first-order phase transition to thisstructure sets in. Between 215 and 350 Qe therecoexist alternating domains of the Pb'c'a andP&'ca' structure. At 350 Qe the single domainstate is reached. A comparable situation has beenobserved in MnF, .""Therein is a small fieldrange (92.4 to 92.9 kOe) above the spin-flop field,where domains of spin-flopped and nonspin-floppedstructure coexist.

ACKNOWLEDGMENTS

%e would like to thank Professor A. R. Miedemafor the suggestion of this problem. %e are indebt-ed to Dr. P. Bloembergen and Dr. L. J. de Jonghfor making available results prior to publicationand for many enlightening discussions, to Dr.

MAGNETO-OPTICAL OBSERVATIONS OF THE MAGNETIC. ~ .

Th. W. J. Janssen for solving a group-theoret-ical problem, and to Dr. P. Bennema for his stim-ulating interest.

This work was performed as part of the research

program of the Stichting voor Fundamenteel On-derzoek der Materie (FOM) with financial supportfrom the Nederlandse Organisatie voor ZuiverWetenschappelijk Onderzoek (ZWO).

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