Journal of Magnetism aM Magnetic Materials 90 & 91 (1990) 1-4 North-Holland
Field-induced magnetic phase transitions M. Date Department 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 by the J-crossover. are shown first. Applications to the highly correlated systems with conduction electrons are highlights in this field 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 of the most important phenomena in studying magnetism. More than a half century has passed since the concept of the spin flop was put forward by Neel . This was the first example of the field-induced magnetic phase transition and the experimental evidence was obtained after 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 step magnetization. Much work on the spin flop, metamagnetic, antiferromagnetic(AF)-paramagnetic(P) and AF-ferromagnetic(F) transitions have been done after these discoveries. It is noted that the metamagnetic transition appears even in the paramagnetic spin systems associated with the crystalline field effect. The paramagnetic crossover is the keyword in these phenomena. It is also noted that the Dzyaloshinsky-Moriya interaction induces the spin canting and various types of the step magnetizations and spin reorientations appear under magnetic field. A noteworthy development of the field-induced magnetic transition was found in the helical spin systems where helix-cone, helix-fan and fan-F transitions, etc., are proposed (4) and have been found in various helical spin systems. Use of the superconducting, Bitler and pulsed magnets became popular after around 1965 and the studies of the field-induced magnetic phase transition have been 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 frustrated exchange interaction takes an important role. It is noted that the spin-cluster excitation, an elementary excitation with the localized nature in the Ising spin system, was discovered 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 the discovery of the spin-canted state (8) and the successive
cantings due to magnetic anisotropy (9). An unexpected ferrimagnetic phase appeared in C6Eu, a graphite intercalation compound, was explained by the 4-spin exchange in the frustrated triangular spin system . Since the metamagnetic transition in exchange-enhanced itinerant electron system has been suggested by Wohlfarth , much work has been done and a clear result was found in CoSz-CoSez . Recently, the effect has beeIi observed in various Laves phase compounds . Quantum spin effects have been interesting problems in high field magnetism. Spin fluctuations in low-dimensional magnets show nonlinear magnetization due to suppression of the fluctuation . Weakly ferromagnetic metals and compounds also show a similar effect . The Haldane gap problem  arises with an impact to the one-dimensional problem with integer spins. The high field magnetism  and ESR  give a new kind of elementary excitation as will be shown in the next section. Recent trends in high field magnetism are concentrated to the applications for strongly correlated electron systems such as high Tc superconductors, heavy ferrnions and valence fluctuations in rare earth and uranium compounds, Typical examples will be shown in the section 3. 2. Advances in low-dimensional magnets There has been an increasing interest in the energy gap in the linear chain Heisenberg antiferromagnet with spin S = 1 since Haldane conjectured that the chain consisted of the integer spins has an energy gap above the ground state. Recently, a high field magnetization study up to 50 T has been done by Katsumata et aI.  and the field-induced quenching of the gap at H cl is found in NENP, one of the best materials to show the Haldane state. Electron spin resonance of this material under 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
M ..Date / Field-induced magnetic phase transitions
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 is positive while that of the excited state triplet is negative. The result is explained by introducing a model that the excited 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 of spin-cluster resonance [7) with a satisfactory agreement. The two-spin bound state is schematically shown in fig. 1 where an antiferromagnetically correlated spin ground state is shown in (a) and an excited two-spin bound state is illustrated in (b). The result strongly suggests that the Haldane state has an RVB nature proposed by Anderson . The second topic in the low-dimensional magnets is the field-induced frustration and associated multistep magnetization in the triangular arrangement of antiferromagnetic linear chains. CsFeCI J is a hexagonal antiferromagnet with Fe H spins where the ferromagnetic chains along the c-axis are connected by a triangular antiferromagnetic interaction. However, no long range order is found at low temperatures because of the singlet ground state with J, = 0 which is a sublevel of J = 1. Under a magnetic field, the first crossover occurs around 10 T in the framework of J = 1  with the net moment of about 31!B' A new multistep magnetiiation is found above 32 T along the c-axis and it is explained by the crossover from J = 1 to a sublevel of J = 2 . The central idea of the transition is simply explained in fig. 2. The angular coupling of Land S in the J = 2 state given in fig. 2(a) shows the presence of a transverse component of the spin which is not found in the J = 1 and 3 states. The exchange energy proportional to the tran sverse component should be taken into account for the J = 2 state and it produces the spin frustration in the c-plane. The analysis was done by the present author [21) and the result is shown in fig. 2(b). The multistep magnetization with the moments 1/3, 1/2, 2/3, ... , is found as expected from the theory and the
b~9lf=1----H---f .. .... .... ..... . . u J
Fig. 1. Model of the two-spin bound state in the Haldene state of the linear chain with s = 1. (a) is the chain model and the bound state is given by a dotted square in (b).
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 fractional states given above come from the mixed states of the ground (J = 1) and excited (J = 2) spin chains. 3. Highly correlated electron systems Much work has been done on the high magnetic field study of the heavy fermion materials and the metamagnetic nature is seen in some compounds. URu2Si2 is known as a typical material with a clear three-step metamagnetism around 30 T (22). The detailed study has been done by our group and the observed data are well explained by the model that the heavy fermion state in the low field region is destroyed by applying a strong magnetic field and the exchange interactions between the field-induced magnetic moments on the uranium atoms produce the successive metamagnetic transitions . The localized magnetic moment on the uranium atom at zero magnetic field is only 0.031!B reflecting the fact that the I-electrons are not on the uranium site but form the heavy fermion band with conduction electrons. Under a strong magnetic field, however, the Zeeman energy of the I-electron exceeds the heavy electron coupling energy and the ph ase transition to the magnetic state occurs. It is noted that there is a frustrating exchange coupling between the field-induced moments and the metamagnetic three-steps with the moments 1/3, 3/5 and 1 (ferromagnetic) appear at their corresponding critical fields, respectively. The heavy fermion energy and three exchange coupling
M. Date / Field-induced magnetic phase transitions
parameters are determined by the standard mean field approximation. It is emphasized that the present treatment is applicable when the spin system can be regarded as the Ising network where the sharp transition is expected. Quenching of the electronic band gap by magnetic field is usually difficult even when the fields up to 100 T were used. An exceptional success was found in YbB 12 which has a gap of about 100 K above the Fermi level. The origin of the gap is believed to come from the hybridization of the f- and conduction bands. The electrical resistivity is measured under the field up to 50 T and a large negative magnetoresistance is found. The resistivity is unmeasurably small and the _compound is substantially metalic around 50 T (24) . The observed result 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 this phenomenon. This model is supported by the high field magnetization ex-periment where a clear increase in the magnetic moment appears above 50 T. A similar effect is expected for 5mB6 , a typical semiconductor with the band gap due to the hybridization, but the observed magnetoresistance is about 1/10 compared to that in YbB12• 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. An example of the data is shown in fig. 3 where the stepwise magnetization with the magnitudes of 1/2, 2/3. 5/6 and 1 are illustrated. A thick line shows the experimental result and the theoretical steps are given by the following model. DyAg is a CsCl-type crystal with an antiferromagnetic transition at TN = 55 K Spins are parallel to four (111) directions with the four-sublattice model [25). A large quadrupole energy stabilizes the spin structure. The observed step magnetization is explained by keeping the quadrupole energy on each Dy
30 ( T)
Fig. 3. Multistep magnetization in DyAg along the c-axis,
Pr Co, Si,
~1 z o
2: z o
j 10 20 MAGNETIC FIELD ( T ) UPdln
>= W Z
10 20 30 MAGNETIC FIELD ( T )
Fig. 4. Metamagnetism found in PrCazSi 2 and UPdIn. Thin lines show theoretical curves at 0 K drawn by the incommensurate mean field model.
site but we assume that there is a quadrupole coupling energy between neighboring Dy spins with the form of H3 cos 10ij -l)Qij where Qij is the quadrupole coupling constant between i- and j-spins and angle Oij means the angle between spins. The total energy is calculated as the sum of the exchange, quadrupole and Zeeman energies and the standard mean field. model is applied. The experimentally obtained steps are explained by a simple spin flop at the 0-1/2 transition and the successive three transitions are given by the spin flop with the rearrangement of the quadrupole order. Agreement between the theory and experiment is satisfactory as is seen in fig. 3. Three exchange parameters and three quadrupole coupling constants have been determined by this treatment [26). Thus, DyAg gives a typical example of the quenching of the quadrupole order under a high magnetic field. Much work has been reported on the metamagnetic transitions in metals and intermetalic compounds with rare earth or uranium atoms and a considerable part of these data can be explained by the standard mean field model by introducing few exchange coupling parameters. However, some metals and compounds show complex metamagnetism with complex fraction of the step moments. An example is shown in fig. 4 with PrCo 2Si 2 where the appeared moments for the intermediate phases are 1/14 and 3/14. These values are supported by the neutron diffraction experiment. The standard mean field model is not adequate for these cases because many exchange parameters are necessary and the problem
M . Dat e / Field-induced magnetic phase transitions
becomes difficult to solve. The incommensurate mean field model has been introduced to solve these problems . According to this model, spins are assumed to be in a sinusoidal exchange field with a form of J sin(kr + 8) where k is the wave vector and is the phase. This model means that spins are immersed in a long range periodic field produced by the RKKY·interaction. Each spin is assumed to be along the local field direction with the coupling energy determined by J, k and o. The conduction electron energy Ue = V(k - k e)2 with v> 0 is also introduced where k e is the characteristic wave vector required from the conduction electron system . The model is applied to PrC~Si2 and UPdln in fig. 4 with satisfactory agreements with the data . The details are given in other papers [28,29]. References [1) L. Ned, Comptes Rendus 203 (1936) 304. (2) N.J. Poulis, J. van den Handel, J. Ubbink , J.A. Poulis and c.r. Gorter, Phys. Rev. 82 (1951) 552. (3) C. Starr, F". Bitter and A.R. Kaufman , Phys. Rev. 58 (1940) 97. (4) T. Nagam iya, K. Nagata and Y. Kitano, J. Phys. Soc. Jpn. 17 suppl. B-1 (1962) 10. [5J H. Kobayashi and T. Haseda, J. Phys. Soc. Jpn . 19 (1964) 765. [6J A. Narath, J. Phys. Soc. Jpn. 19 (1964) 2244. (7) M. Date and M. Motokawa , Phys. Rev. Lett. 16 (1966) 1111. (8) M. Matsuura, Y. Okuda, M. Morotomi, H. Mollymoto and M. Date, J. Phys. Soc. Jpn . 46 (1979) 1031. (9) JJ.M. Fran se, F.R. de Boer, P.H. Frings, R. Gersdorf, A. Menovsky, F.R. Muller, R.J. Radwanski and S. Sinnema, Phys. Rev. B 31 (1985) 4347.
(10) M. Date , T. Sakakibara and K. Sugiyama, High Field Magnet ism (North-Holland, Amsterdam, 1983) p. 41. (11) EP. Wohlfarth and P. Rhodes, Phil. Mag. 7 (1962) 1817.  K. Adach i, M. Matsu i, Y. Ornata, H. Mollymoto, M. Motokawa and M. Date, J. Phys. Soc. Jpn . 47 (1979) 675. (13) T. Sakakibara and T. Goto, private communication. (14) D. Bloch, J. Voiron and L.J. de Jongh , High Field Magnetism (North-Holland, Amsterdam, 1983) p. 19. [15) T. Sakakibara, H. Mollymoto and M. Date, High Field Magnetism (North-Holland, Amsterdam, 1983) p. 167. (16) F.D.M. Haldane, Phys. Rev. Letl. 50 (1983) 1153. (17) K. Katsumata, H. Hori, T. Takeuchi , M. Date, A. Yamagishi and J.P. Renard, Phys. Rev. Lett. 63 (1989) 86. (18) K. Kindo , T. Yosida and M. Date, J. Magn. Magn. Mat. 90 & 91 (1990) 227. (19) P.W. Anderson, Mater. Res. Bull. 8 (1973) 153. [20J T. Haseda , N. Wada, M. Hata and K. Amaya, Physica B 108 (1981) 841. (21) M. Date, High Field Magnetism (North-Holland, Amsterdam, 1989) p. 117. (22) A. de Visser, F.R. de Boer, A.A. Menovsky and J.J.M. Franse, Solid State Commun. 64 (1987) 527. (23) K. Sugiyama and M. Date, J. Magn. Magri . Mat. 90 & 91 (1990) 461. (24) K. Sugiyama, F: Iga, M. Kasaya, T. Kasuya and 1\1. Date, J. Phys. Soc. Jpn . 57 (1988) 3946. (25) D. Morin , J. Rouchy, K. Yonenobu, A. Yamagishi and M. Date, J. Magn . Magri. Mal. 81 (1989) 247. (26) A. Yamagishi , K. Yonenobu, O. Kondo , P. Morin and M. Date, J. Magn. Magn. Mat. 90 & 91 (1990) 51. (27) M. Date , J. Phys , Soc. Jpn. 57 (1988) 3682. (28) T. Shigeoka, H. Fujii, K. Yonenobu, K. Sugiyama and M. : Date, J. Phys. Soc. Jpn. 58 (1989) 394. (29) E Sugiura, K. Sugiyama, H. Kawanaka, T. Takabatake, H. Fujii and M. Date, J. Magn. Magri. Mal. 90 & 91 (1990) 65.