Journal of Magnetism aM Magnetic Materials 90 & 91 (1990) 1-4North-Holland

Invited paper

Field-induced magnetic phase transitions

M. DateDepartment of Physics, Faculty of Science, Osaka Unicersity, Toyonaka, Osaka 560, Japan

Recent trends in the field-induced magnetic phase transitions are reviewed with a short historical survey of the problems.Two new discoveries in the low-dimensional magnets, the Haldane gap quenching and field-induced frustrations produced bythe J-crossover. are shown first. Applications to the highly correlated systems with conduction electrons are highlights in thisfield and various recent results in the "heavy fermion, valence fluctuation and superconducting states are introduced.Field-induced new states in these systems are investigated.

1. Introduction

The field-induced magnetic phase transition is one ofthe most important phenomena in studying magnetism.More than a half century has passed since the conceptof the spin flop was put forward by Neel [1]. This wasthe first example of the field-induced magnetic phasetransition and the experimental evidence was obtainedafter 15 years in CuCl z' 2H zO by the Dutch group [2).The next step was achieved by the discovery of meta­magnetism in FeCl z (3) as the first discovery of the stepmagnetization. Much work on the spin flop, meta­magnetic, antiferromagnetic(AF)-paramagnetic(P) andAF-ferromagnetic(F) transitions have been done afterthese discoveries. It is noted that the metamagnetictransition appears even in the paramagnetic spin sys­tems associated with the crystalline field effect. Theparamagnetic crossover is the keyword in these phe­nomena. It is also noted that the Dzyaloshinsky-Moriyainteraction induces the spin canting and various typesof the step magnetizations and spin reorientations ap­pear under magnetic field. A noteworthy developmentof the field-induced magnetic transition was found inthe helical spin systems where helix-cone, helix-fanand fan-F transitions, etc., are proposed (4) and havebeen found in various helical spin systems.

Use of the superconducting, Bitler and pulsed mag­nets became popular after around 1965 and the studiesof the field-induced magnetic phase transition havebeen rich in variety since the era. An appreciable dis­covery was the two-step metamagnetism in CoCl z'2H zO [5,6) which extended a new scope of metamagne­tism where the concept of competitive or frustratedexchange interaction takes an important role. It is notedthat the spin-cluster excitation, an elementary excitationwith the localized nature in the Ising spin system, wasdiscovered in this salt (7). An extension of the spin-clus­ter model will be discussed in the next section. Ad­vances in the ferrimagnetism were obtained by thediscovery of the spin-canted state (8) and the successive

cantings due to magnetic anisotropy (9). An unexpectedferrimagnetic phase appeared in C6Eu, a graphite inter­calation compound, was explained by the 4-spin ex­change in the frustrated triangular spin system [10].Since the metamagnetic transition in exchange-en­hanced itinerant electron system has been suggested byWohlfarth [11], much work has been done and a clearresult was found in CoSz-CoSez [12]. Recently, theeffect has beeIi observed in various Laves phase com­pounds [13].

Quantum spin effects have been interesting problemsin high field magnetism. Spin fluctuations in low-di­mensional magnets show nonlinear magnetization dueto suppression of the fluctuation [14]. Weakly ferromag­netic metals and compounds also show a similar effect[15]. The Haldane gap problem [16] arises with animpact to the one-dimensional problem with integerspins. The high field magnetism [17] and ESR [18] givea new kind of elementary excitation as will be shown inthe next section.

Recent trends in high field magnetism are con­centrated to the applications for strongly correlatedelectron systems such as high Tc superconductors, heavyferrnions and valence fluctuations in rare earth anduranium compounds, Typical examples will be shown inthe section 3.

2. Advances in low-dimensional magnets

There has been an increasing interest in the energygap in the linear chain Heisenberg antiferromagnet withspin S = 1 since Haldane conjectured that the chainconsisted of the integer spins has an energy gap abovethe ground state. Recently, a high field magnetizationstudy up to 50 T has been done by Katsumata et aI. [17]and the field-induced quenching of the gap at Hcl isfound in NENP, one of the best materials to show theHaldane state. Electron spin resonance of this materialunder high field is done in our group (18) and the

0304-8853/90/$03.50 If! 1990 - Elsevier Science Publishers B.V. (North-Holland) and Yamada Science Foundation

2 M..Date / Field-induced magnetic phase transitions

3. Highly correlated electron systems

J=3J=2a J=1

MAGNETIC FIELD 1\< T )

Fig. 2. Vector models of J = 1, 2 and 3 states in CsFeC13 (a)and the multistep magnetization along the c-axis (b). Thin lines

show the theoretical magnetization.

agreement between theory and experiment is surpris­ingly excellent 'as is seen in fig. 2(b). The fractionalstates given above come from the mixed states of theground (J = 1) and excited (J = 2) spin chains.

b CsFeCI3 15K Hanc-axis

to­Zw~o~

Much work has been done on the high magnetic fieldstudy of the heavy fermion materials and the meta­magnetic nature is seen in some compounds. URu2Si2is known as a typical material with a clear three-stepmetamagnetism around 30 T (22). The detailed studyhas been done by our group and the observed data arewell explained by the model that the heavy fermionstate in the low field region is destroyed by applying astrong magnetic field and the exchange interactionsbetween the field-induced magnetic moments on theuranium atoms produce the successive metamagnetictransitions [23]. The localized magnetic moment on theuranium atom at zero magnetic field is only 0.031!Breflecting the fact that the I-electrons are not on theuranium site but form the heavy fermion band withconduction electrons. Under a strong magnetic field,however, the Zeeman energy of the I-electron exceedsthe heavy electron coupling energy and the phase transi­tion to the magnetic state occurs. It is noted that thereis a frustrating exchange coupling between the field-in­duced moments and the metamagnetic three-steps withthe moments 1/3, 3/5 and 1 (ferromagnetic) appear attheir corresponding critical fields, respectively. Theheavy fermion energy and three exchange coupling

b~9lf=1----H---f.. .... .... ..... . . u J

<;:=5=1

anisotropy parameters-of the first excited state is in­vestigated . A striking fact is that the sign of the ani­sotropy constant D in the ground state of NiH ispositive while that of the excited state triplet is negative.The result is explained by introducing a model that theexcited state is the two-spin bound state with the re­sultant spin S = 1 moving in the chain like a soliton.The ESR data are analyzed by using the theory ofspin-cluster resonance [7) with a satisfactory agreement.The two-spin bound state is schematically shown in fig.1 where an antiferromagnetically correlated spin groundstate is shown in (a) and an excited two-spin boundstate is illustrated in (b). The result strongly suggeststhat the Haldane state has an RVB nature proposed byAnderson [19].

The second topic in the low-dimensional magnets isthe field-induced frustration and associated multistepmagnetization in the triangular arrangement of antifer­romagnetic linear chains. CsFeCI J is a hexagonal anti­ferromagnet with FeH spins where the ferromagneticchains along the c-axis are connected by a triangularantiferromagnetic interaction. However, no long rangeorder is found at low temperatures because of thesinglet ground state with J, = 0 which is a sublevel ofJ = 1. Under a magnetic field, the first crossover occursaround 10 T in the framework of J = 1 [20] with the netmoment of about 31!B' A new multistep magnetiiation isfound above 32 T along the c-axis and it is explained bythe crossover from J = 1 to a sublevel of J = 2 [21]. Thecentral idea of the transition is simply explained in fig.2. The angular coupling of Land S in the J = 2 stategiven in fig. 2(a) shows the presence of a transversecomponent of the spin which is not found in the J = 1and 3 states. The exchange energy proportional to thetran sverse component should be taken into account forthe J = 2 state and it produces the spin frustration inthe c-plane. The analysis was done by the presentauthor [21) and the result is shown in fig. 2(b). Themultistep magnetization with the moments 1/3, 1/2,2/3, ... , is found as expected from the theory and the

Fig. 1. Model of the two-spin bound state in the Haldene stateof the linear chain with s = 1. (a) is the chain model and the

bound state is given by a dotted square in (b).

M. Date / Field-induced magnetic phase transitions 3

11

j10 20

MAGNETIC FIELD ( T )

UPdln 4.2K HoIIc-axis

Pr Co, Si, 1.3K Hollc-axis

Z2o>=<l:N

~1zo~

o

..2:zo>=1<l:N>=WZCl

~o 10 20 30

MAGNETIC FIELD ( T )

Fig. 4. Metamagnetism found in PrCazSi2 and UPdIn. Thinlines show theoretical curves at 0 K drawn by the incom­

mensurate mean field model.

site but we assume that there is a quadrupole couplingenergy between neighboring Dy spins with the form ofH3 cos10ij -l)Qij where Qij is the quadrupole cou­pling constant between i- and j-spins and angle Oijmeans the angle between spins. The total energy iscalculated as the sum of the exchange, quadrupole andZeeman energies and the standard mean field. model isapplied. The experimentally obtained steps are ex­plained by a simple spin flop at the 0-1/2 transitionand the successive three transitions are given by thespin flop with the rearrangement of the quadrupoleorder. Agreement between the theory and experiment issatisfactory as is seen in fig. 3. Three exchange parame­ters and three quadrupole coupling constants have beendetermined by this treatment [26). Thus, DyAg gives atypical example of the quenching of the quadrupoleorder under a high magnetic field.

Much work has been reported on the metamagnetictransitions in metals and intermetalic compounds withrare earth or uranium atoms and a considerable part ofthese data can be explained by the standard mean fieldmodel by introducing few exchange coupling parame­ters. However, some metals and compounds show com­plex metamagnetism with complex fraction of the stepmoments. An example is shown in fig. 4 with PrCo2Si 2

where the appeared moments for the intermediate phasesare 1/14 and 3/14. These values are supported by theneutron diffraction experiment. The standard mean fieldmodel is not adequate for these cases because manyexchange parameters are necessary and the problem

DyAg 4.2 K Holl [111J10

>­o

'":;],zo~ 5N>=UJZ(!)<l:~

20 30 40MAGNETIC FIELD ( T )

Fig. 3. Multistep magnetization in DyAg along the c-axis,

parameters are determined by the standard mean fieldapproximation. It is emphasized that the present treat­ment is applicable when the spin system can be re­garded as the Ising network where the sharp transitionis expected.

Quenching of the electronic band gap by magneticfield is usually difficult even when the fields up to 100 Twere used. An exceptional success was found in YbB12which has a gap of about 100 K above the Fermi level.The origin of the gap is believed to come from thehybridization of the f- and conduction bands. The elec­trical resistivity is measured under the field up to 50 Tand a large negative magnetoresistance is found. Theresistivity is unmeasurably small and the _compound issubstantially metalic around 50 T (24) . The observedresult is well explained by the quenching of the J:1y­bridized band due to magnetic field. The Zeeman en­ergy of the f-electron plays an important role for thisphenomenon. This model is supported by the high fieldmagnetization ex-periment where a clear increase in themagnetic moment appears above 50 T. A similar effectis expected for 5mB6 , a typical semiconductor with theband gap due to the hybridization, but the observedmagnetoresistance is about 1/10 compared to that inYbB12• The difference is due to the magnitude of g-val­ues in both materials.

A multistep magnetization observed in DyAg pre­sents a new concept for the high field magnetism. Anexample of the data is shown in fig. 3 where thestepwise magnetization with the magnitudes of 1/2,2/3. 5/6 and 1 are illustrated. A thick line shows theexperimental result and the theoretical steps are givenby the following model. DyAg is a CsCl-type crystalwith an antiferromagnetic transition at TN = 55 K Spinsare parallel to four (111) directions with the four-sub­lattice model [25). A large quadrupole energy stabilizesthe spin structure. The observed step magnetization isexplained by keeping the quadrupole energy on each Dy

4 M. Date / Field-induced magnetic phase transitions

becomes difficult to solve. The incommensurate meanfield model has been introduced to solve these problems[27]. According to this model, spins are assumed to bein a sinusoidal exchange field with a form of J sin(kr +8) where k is the wave vector and is the phase. Thismodel means that spins are immersed in a long rangeperiodic field produced by the RKKY·interaction. Eachspin is assumed to be along the local field direction withthe coupling energy determined by J, k and o. Theconduction electron energy Ue = V(k - ke)2 with v> 0is also introduced where ke is the characteristic wavevector required from the conduction electron system.The model is applied to PrC~Si2 and UPdln in fig. 4with satisfactory agreements with the data . The detailsare given in other papers [28,29].

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