single crystal growth and magnetic properties of rrhin5 compounds

Doctoral Thesis Single Crystal Growth and Magnetic Properties of RRhIn5 Compounds ( R: Rare Earths ) Nguyen Van Hieu Department of Physics, Graduate School of Science Osaka University, Japan January, 2007 Abstract A series of ternary compounds RRhIn5 (R: rare earths) was grown in the single crystalline form by means of the flux method Magnetic properties of these compounds were investigated by measuring the lattice parameter, electrical resistivity, specific heat, magnetic susceptibility and magnetization All the compounds crystallize in the tetragonal HoCoGa5 -type structure Most of these compounds order antiferronmagnetically at low tempertures, except for R= Y, La, Pr and Yb The observed temperature dependence of the specific heat and the anisotropic features in the magnetic susceptibility and magnetization were analyzed on the basis of the crystalline electric field (CEF) model It is suggested that the overall splitting energy of RRhIn5 in the CEF scheme decreases as a function of 4f -electron number from 330K in CeRhIn5 to 44K in ErRhIn5 , which might be correlated with the c/a value in the lattice constant The antiferromagnetic easy-axis corresponds to the [001] direction in RRhIn5 (R= Nd, Tb, Dy and Ho), while it is in the (001) plane for R= Ce, Sm, Er and Tm It is noticed that this might be related to the sign of B20 in the CEF parameters For the former compounds, we observed characteristic metamagnetic transitions Below a N´eel temperature TN = 11.6K, the magnetization of NdRhIn5 reveals two metamagnetic transitions at Hm1 = 70 kOe and Hm2 = 93 kOe for the magnetic field along the [001] direction The saturation moment of 2.5 µB /Nd is in good agreement with the staggered Nd moment determined by the neutron diffraction experiment These metamagnetic transitions correspond to the change of the magnetic structure TbRhIn5 , DyRhIn5 and HoRhIn5 are found to be the similar antiferromagnets with TN = 47.3, 28.1 and 15.8 K, respectively The magnetization curves of these compounds are also quite similar to those of NdRhIn5 , revealing two metamagnetic transitions The magnetic structures in magnetic fields are proposed by considering the exchange interactions based on the crystal structure Furthermore, we observed the de Hass-van-Alphen (dHvA) oscillation of PrCoIn5 , PrRhIn5 and PrIrIn5 to clarify the Fermi surface properties The detected topology of the Fermi surface is found to be the same as that of LaRhIn5 , consiting of two kinds of corrugated cylindrial (bands 14 and band 15) Fermi surfaces and a lattice-like Fermi surface We detected an inner orbit named ϵ1 in the band 13-lattice-like hole-Fermi surface of PrIrIn5 , which was not observed previously in LaRhIn5 This is mainly due to the high-quality single crystal sample of PrIrIn5 Contents Introduction Magnetic Properties of Rare Earth Compounds 2.1 Magnetic properties of rare earth ions and metals 2.2 Crystalline electric field (CEF) effect 2.3 Kondo effect and heavy fermions 2.4 Magnetic properties of RIn3 and RRhIn5 compounds Motivation of the Present Study 6 14 24 27 43 Single Crystal Growth and Measurement Methods 4.1 Single crystal growth 4.2 Measurement methods 4.2.1 Electrical resistivity 4.2.2 Specific heat 4.2.3 Magnetic susceptibility and magnetization 4.2.4 High field magnetization 4.2.5 de Haas-van Alphen effect 4.2.6 Neutron scattering Experimental Results and Discussion 5.1 Magnetic properties and CEF scheme in RRhIn5 5.2 Fermi surface and magnetic properties of PrTIn5 (T: Co, Rh and Ir) 5.3 Unique magnetic properties of RRhIn5 (R: Nd, Tb, Dy, Ho) 5.4 Neutron scattering study in RRhIn5 (R: Nd, Dy , Ho) 44 44 51 51 53 55 57 59 66 73 73 98 120 137 Conclusion 155 Acknowledgments 156 References 158 Publication List 165 Introduction The rare earth compounds indicate a variety of electronic states such as magnetic ordering, quadrupole (multipole) ordering, charge ordering, heavy fermions, Kondo insulators and anisotropic susperconductivity These phenomena are closely related to hybridization of almost localized 4f electrons with the conduction electrons The 4f electrons in the rare earth atom are pushed deeply into the interior of closed 5s and 5p shells This is a reason why the 4f electrons possess an atomic-like character even in the compounds On the other hand, the tail of their wave function spreads to the outside of the closed 5s and 5p shells, which is highly influenced by the potential energy, the relativistic effect and the distance between the lathanide atoms This results in the hybridization of the 4f electrons with the conduction electrons These cause the various phenomena mentioned above Recently, the family of rare earth 115 compounds with the HoCoGa5 -type tetragonal crystal structure1 attracts strongly interests in the field of condensed master physics, after the dicovery of heavy fermion superconductivity in CeTIn5 (T: Co, Rh, Ir)2–4 with the quasi-two dimentional electronic state CeCoIn5 and CeIrIn5 are superconductors at ambient pressure, with the superconducting transition temperature Tsc =2.3 K and 0.4K, respectively On the other hand, CeRhIn5 indicates an antiferromagnetic ordering with the N´eel temperature TN = 3.8K but becomes superconductive above 1.6GPa The uniaxially distorted AuCu3 -type layers of RIn3 and RhIn2 layers in RRhIn5 (R: rare earths) are stacked sequentially along the [001] direction (c-axis) The Fermi surface properties of LaRhIn5 and CeRhIn5 5, were studied via the de Haas-van Alphen(dHvA) experiments The Fermi surface of a non-4f reference compound LaRhIn5 is quasi-two dimensional, reflecting the unique tetragonal structure The topology of the Fermi surface in CeRhIn5 is similar to that of LaRhIn5 , but the cyclotron mass in CeRhIn5 is larger than that of LaRhIn5 These findings motivated us to undertake more investigations of the magnetic properties of RRhIn5 series in the single crystal form Namely, the present study is to clarify the fundermental magnetic properties of localized 4f -electrons, such as the crystalline electric field (CEF) scheme, together with the magnetic exchange interactions between the 4f electrons in rare earth atoms (ions) via the conduction electrons The single crystals of RRhIn5 were grown by the self-flux method using In as flux Structural parameters of RRhIn5 were determined by the single-crystal x-ray diffraction experiments with the Mo-Kα radiation The electrical resistivity was measured by the 4-probe DC method The magnetic susceptibility and magnetization measurements were carried out with a commercial SQUID magnetometer The specific heat was measured by the quasi-adiabatic heat-pulse method and commercial PPMS The high-field magnetization was also measured by the standard pick-up coil method, using a long-pulse magnet We also measured the dHvA oscillation using a so-called 2ω detection of the field modulation method From the results of these measurements, we clarified the magnetic properties of RRhIn5 series The present thesis consists of the following contents In Chap 2, the fundamental 2.1 Magnetic Properties of Rare Earth Compounds Magnetic properties of rare earth ions and metals First we will explain the magnetic properties of rare earth atoms (ions) Rare earth (R) atoms include 15 elements of lanthanide series, scandium (Sc) and yttrium (Y) La, Ce, Pr, Nd,(Pm), Sm and Eu are called the light rare earths We also put the name of heavy rare earths for Gd, Tb, Dy, Ho, Er Tm and Yb The magnetic properties change systematically and regularly because of the 4f -electronic configuration : Xe shell 4f n 5s2 5p6 6s2 The atomic radius of R3+ shrinks monotonically from cerium to ytterbium, as shown in Fig 2.1 This is well known as ”lanthanide contraction” The 4f electron in the Ce atom is, for example, pushed deeply into the interior of the closed 5s and 5p shells because of the strong centrifugal potential l (l + 1)/r2 , where l = holds for the f electron This is a reason why the 4f electrons possess an atomic-like character in the crystal (rare earth metal and rare earth compound).7 Figure 2.2 shows the radial wave function of Ce (4f 5d1 6s2 ) with and without the relativistic effect On the other hand, the tail of their wave function spreads to the outside of the closed 5s and 5p shells, which is highly influenced by the potential energy, the relativistic effect and the distance between the lanthanide atoms This results in the hybridization of the 4f electrons with the conduction electrons This causes the various phenomena such as RKKY (RudermanKittel-Kasuya-Yosida interaction)9–11 and Kondo effect 12 Under the Hund rule, the Ionic Radius ( Å ) 1.3 1.2 1.1 1.0 0.9 La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu R3+ Fig 2.1 Ionic radius of R3+ 2.1 MAGNETIC PROPERTIES OF RARE EARTH IONS AND METALS 1.0 4f Ce (4f 15d 6s ) |rR(r)| 0.8 5p 0.6 0.4 5d 6s 0.2 0 r [ a u ] Fig 2.2 Radial wave function of Ce (4f 5d1 6s2 ) with and without the relativistic effect.8 J = 72 fold Ce3+ 14 fold ~3000 K doublet J = 52 fold spin-orbit interaction doublet doublet ∆2 ∆1 CEF Fig 2.3 Level scheme of the 4f electron in Ce3+ CHAPTER MAGNETIC PROPERTIES OF RARE EARTH COMPOUNDS strong spin-orbit coupling of the 4f electrons in rare earth ion leads to a low magnetic moment for the light rare earths with J = |L − S|, while J = L + S for the heavy rare earths Here, J is the total angular momentum, L is the total orbital angular momentum and S is the total spin momentum Namely, the 4f multiplets, which obey the Hund rule in the LS-multiplets, split into the J-multiplets (J = 52 and J = 72 in Ce3+ ) by the spin-orbit interaction, as shown in Fig 2.3 Moreover, the J-multipltes split into the 4f levels based on the crystalline electric field (CEF) effect We also show in Table 2.I and Fig 2.4 the electronic configuration and the fundermental magnetic parameters in the rare earth ions The 4f electrons possess an atomic-like character even in the rare earth metals and the rare earth compounds Next we describe the magnetic properties of the rare earth metals The crystal and magnetic structures are very complex in rare earth metals, as shown in Table 2.II and Fig 2.5 The double hexagonal close packed (dhcp) crystal structure is typical, possessing both the cubic symmetry sites and hexagonal symmetry sites Table 2.I Electronic configuration of 4f shell and general magnetic parameters of rare earth ion: spin moment (S), orbital moment (L), total moment √ J, spectroscopy state, Lande factor g, gJ, effective magnetic moment of free ion µeff =g J(J + 1) and de Gennes factor (g-1)2 J(J + 1) R La3+ Ce3+ Pr3+ Nd3+ Pm3+ Sm3+ Sm2+ Eu3+ Eu2+ Gd3+ Tb3+ Dy3+ Ho3+ Er3+ Tm3+ Tm2+ Yb3+ Yb2+ Lu3+ Z 57 58 59 60 61 62 62 63 63 64 65 66 67 68 69 69 70 70 71 4fn 4f0 4f1 4f2 4f3 4f4 4f5 4f6 4f6 4f7 4f7 4f8 4f9 4f10 4f11 4f12 4f13 4f13 4f14 4f14 S 1/2 3/2 5/2 3 7/2 7/2 5/2 3/2 1/2 1/2 0 L 6 3 0 6 3 0 J = L ±S 5/2 9/2 5/2 0 7/2 7/2 15/2 15/2 7/2 7/2 0 spetroscopy S 5/2 F H 9/2 I I 5/2 H F0 7/2 S F6 15/2 H I 15/2 I H F7/2 S g 6/7 4/5 8/11 3/5 2/7 0 2 3/2 4/3 5/4 6/5 7/6 8/7 8/7 0 gJ 2.14 3.2 3.27 2.40 0.71 0 7.0 9.0 10 10 9.0 7.0 4.0 4.0 0 µeff 2.54 3.58 3.62 2.68 0.85 0 7.96 7.94 9.72 10.65 10.61 9.58 7.56 4.54 4.54 0 (g-1)2 J(J + 1) 0.178 0.80 5.11 3.20 4.46 0 15.75 15.75 10.50 7.08 4.50 2.55 1.17 0.32 0.32 0 2.1 MAGNETIC PROPERTIES OF RARE EARTH IONS AND METALS The helical and cone-like helical structures are also typical in the magnetic structure As show in Fig 2.5, Eu is magnetic, meaning that the valence is not trivalent, but divalent: Eu(4f 5s2 4p6 6s2 ) Yb is also not trivalent, but divalent, indicating the nonmagnetic property The ordering temperture is shown in Fig 2.6 Table 2.II Crystal structure, lattice constant and easy axis at 4.2K in rare earth metals Z 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 21 39 crys.struct dhcp fcc dhcp dhcp dhcp rhomb bcc hcp hcp hcp hcp hcp hcp fcc hcp hcp hcp a(˚ A) 3.7740 5.1610 3.6721 3.6582 3.65 3.629 4.5827 3.6336 3.6055 3.5915 3.5778 3.5592 3.5375 3.4848 3.5052 3.4088 3.6482 c(˚ A) 12.171 11.8326 11.7996 11.65 26.207 5.781 5.6966 5.6501 5.6178 5.5851 5.554 5.5494 5.5268 5.7318 easy axis (4.2K) [100] [010] [100] [110] [010] [100] [010] [001] - L, S and J R La Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Sc Y 3+ R Fig 2.4 L ,S and J of R3+ based on the Hund rule 10 CHAPTER MAGNETIC PROPERTIES OF RARE EARTH COMPOUNDS R (a) (b) (c) (d) Temperature ( K ) Fig 2.5 Magnetic structures in rare earth metals: (a) helical, (b) cone-like helical, (c) modulated along the c-axis and (d) helical structure in Er Rare earth metals Fig 2.6 Magnetic properties of rare earth metals AF: antiferromagnetism, CH: conelike helical structure, CM: modulated structure along the c-axis, F: ferromagnetism, FR: ferrimagnetism, P: paramagnetism and HE: helical structure 2.1 MAGNETIC PROPERTIES OF RARE EARTH IONS AND METALS 11 Here, the magnetic ordering in rare earth metals including the rare earth compounds is mainly based on the RKKY interaction We pay attention on the Hamiltonian of exchange interaction Hex between the total spin S of the 4f electrons and the spin s of conduction electrons: Hex = −2Jcf s · S (2.1) where Jcf is the magnitude of the exchange interaction In the indirect exchange model, the 4f electron spin Si at Ri interacts locally with the spin of the conduction electrons, which then interact in turn with the 4f electron spin Sj at Rj This approach is needed because the 4f wave functions have insufficient overlap to give a direct Heisenberg exchange The exchange interaction between Si and Sj is thus expressed as follows: -J(Rij )Si · Si , where J(Rij ) contains a so-called Friedel oscillation of F (x)= (x cos x - sin x)/x4 , as shown in Fig 2.7 Here, Rij =Rj -Ri = x In other words, the mutual magnetic interaction between the 4f electrons occupying different atomic sites cannot be of a direct type such as 3d metal magnetism, but should be indirect one, which occurs only through the conduction electrons When the number of 4f electrons increases in such a way that the lanthanide element changes from Ce to Gd or reversely from Yb to Gd in the compound, the magnetic moment becomes larger and the RKKY interaction stronger, leading to the magnetic ordering At this point, it may be called that the total angular momentum J is a good quantum number and is better to use the projection of spin on J , as suggested by de Gennes We replace S with J : Si = (g − 1)Ji The following equation can be obtained: -J(Rij )(g − 1)2 Ji Jj The magnetic ordering temperature Tord is thus propotional the√de Gennes factor (g − 1)2 J (J + 1) The effective magnetic moment is closed to µeff =g J (J + 1) [µB ], as shown in Fig 2.8 and the ordered moment is also close to gJ [µB ], as shown in Fig 2.9 148 CHAPTER EXPERIMENTAL RESULTS AND DISCUSSION FM 10 HoRhIn ( 11 ) AF2 H m1 Magnetic moment ( µB/Ho ) 3.5K H m2 AF1 10 13 15 19 0 0 0 Magnetic Field ( T ) Fig 5.65 Field dependence of magnetic moment in the ferromagnetic scattering (110) nuclear peak at different temperatures in HoRhIn5 The solid line is a guide the eye The arrows indicate transition fields 5.4 NEUTRON SCATTERING STUDY IN RRHIN5 (R: ND, DY , HO) 149 respsectively in magnetization study, as shown in Fig 5.67 60 Magnetic Field ( kOe ) FM Magnetization, H//c Neutron, ( 3/2 5/2 ) Neutron, (110) AF2 40 AF1 20 TN 0 12 16 20 Temperature ( K ) Fig 5.66 Magnetic phase of antiferromagnetic ( 32 25 ) peak (open squares) and nuclear magnetic (110) (open triangles) peak show two steps at Hm1 and Hm2 , which consist with magnetization data (open circles) 150 CHAPTER EXPERIMENTAL RESULTS AND DISCUSSION Magnetization ( µB/Ho ) 10 9.8µ B HoRhIn5 H // [001] T= K Hm2 4.9µ B Hm1 䎃 0 20 40 60 80 Magnetic Field ( kOe ) Fig 5.67 Magnetic filed dependence of magnetization for H//[001] at 2K.80 5.4 NEUTRON SCATTERING STUDY IN RRHIN5 (R: ND, DY , HO) 151 Intensity ( counts/sec ) 50 40 NdRhIn5 (110) 30 H//[001] T= 3.0 K Hm1 AF2 20 (a) 10 AF1 0 Magnetization ( µΒ/Nd ) Hm2 50 100 Hm2 0 NdRhIn5 H//[001] T= K Hm1 (b) 50 Magnetic Field ( kOe ) 100 Fig 5.68 (a) Field dependence of magnetic intensity in the ferromagnetic scattering (1 0) nuclear peak at 3K and (b) the magnetization curve for H//[001] (b) at K.80 152 CHAPTER EXPERIMENTAL RESULTS AND DISCUSSION In this work, the ground-state magnetic structure of NdRhIn5 was found to be a commensurate antiferromagnetic structure with a magnetic wave vector Q = ( 21 12 ) below TN , as in Chang et al.60 The staggered Nd moment at 1.6 K is 2.5 µB /Nd, aligned along the [001] direction The similar magnetic structure was also clarified in TbRhIn5 63 Moreover, DyRhIn5 and HoRhIn5 also revealed an antiferromagnetic structure Q=( 21 ) in the ground state Therefore, it is suggested that the RRhIn5 (Nd, Dy, Ho) shows the same antiferromagnetic structure with Q=( 12 12 ) This is most likely due to the localized character of 4f electron of rare earth elements Thus, these compounds have very similar electronic structures , namely the similar Fermi surfaces This is in strong contrast the itinerant 5f -electron systems, namely UTGa5 and NpTGa5 Actinide 115 compounds show a huge variety of the magnetic structure with A-type, G-Type, C-type, ferromagnetic and canted structures It has been pointed out that the orbital degree of freedom would play an important role for the variety of the magnetic structures Next, we mention about the magnetic structure in AF2 There are eight rare earth atoms sited at the conner of the tetragonal unit cell In the AF1 phase, these eight atoms form two magnetic sublattices with four of them moment up, and the other four atoms with moment down As the antiferromagnetic modulation amplitude in the AF2 phase is half of AF1 , the two rare earth moments change the direction from down to up with application of the field Therefore, we have two magnetic sublattices of six rare earth atoms with moment up, and two atoms with moment down The net with four moments provides the ferromagnetic moment in the AF2 phase, which is half of the saturation moment, and the remaining four atoms contribute to the antiferromagnetic modulation with Q=( 21 12 ) This is a very important boundary condition for the magnetic structure in the AF2 phase and the mechanism of the metamagnetic transition We could not determine the magnetic structure in the metamagnetic intermediate AF2 phase As mentioned above, it has been revealed that both the ferromagnetic moment and the antiferromagnetic modulation with q = ( 12 21 ) has the amplitude corresponding the half of the saturation moment Thus, we can propose the simplest model structures, with six rare earths moment parallel to the field and remained two anti-parallel to the field in unit cell Three typical examples are shown in Fig 5.69 We can predit the antiferromagnetic reflections, which are characteristic to AF2 phase, e.g, ( 12 00), (0 12 0), ( 12 12 0), (00 12 ), ( 12 12 12 ) However, none of them has been observed in HoRhIn5 on the (h0l),(hhl), and (hk0) scattering plane, and on the (hk0) scattering plane for NdRhIn5 We often observed spurious ( 21 12 0) reflection even in the AF1 phase for HoRhIn5 and DyRhIn5 We confirmed that this is due to a multiple scattering effect from the neutron energy dependence of the scattering intensity Therefore, the magnetic structure of AF2 phase would not be so simple Moreover, in the neutron measurement of HoRhIn5 on the (hhl) scattering plane with horizontal magnet, we observed the other peaks and the equivalent (0.63 0.63 0), (1.32 1.32 -3) and (1.63 1.63 -3) reflections with E = 14.7 meV, appearing only in AF2 phase 5.4 NEUTRON SCATTERING STUDY IN RRHIN5 (R: ND, DY , HO) 153 However, we concluded that they are spurious peaks, because the (0.63 0.63 0) peak was not reproduced on the (hk0) scattering plane with a vertical magnet On the (hk0) plane, however, we observed (0.52 1.2 0), (0.46 0.2 0) reflections for NdRhIn5 and (0.20 0.53 0) reflection for HoRhIn5 in the AF2 phase We have not checked, if there are suprious or intrinsic The small windows of the high field magnet make difficult to obtain reliable results Thus the magnetic structure in AF2 phase is tillnow unknown, which should be studied further to understand the mechanism for the two metamagnetic transition in RRhIn5 ( R: Nd, Dy, Ho) AF2 (a) Model I (b) Model II (c) Model III Fig 5.69 Three types of proposal magnetic structure in AF2 for RRhIn5 ( R: Nd, Dy, Ho): (a) model I with the magnetic wave vector ( 12 00), (b) model II with (0 12 0) and (c) model III with ( 12 12 0), (00 12 ),( 21 12 12 ) Finally, we conclude the present experimental results of neutron scattering experiments RRhIn5 (R: Nd, Dy, Ho) exhibits antiferromagnetic order with propagation magnetic vetor of q = ( 12 12 ) in the ground state (AF1 phase), where the magnetic moment parallel to the c-axis The identical antiferromangetic structure in these compounds is due to the similar localized 4f electrons The obtained moments size in these 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Matsuda, Yoshinori Haga, Tetsuya ¯ Takeuchi, Masayuki Hagiwara, Koichi Kindo and Yoshichika Onuki : Single crystal growth and magnetic Properties of RRhIn5 (R= Rare Earths) Osaka University-Asia Pacific-Vietnam National University, Hanoi- Forum 2005 :” on Frontiers of Basic Science: Toward New physics-Earth and Space ScienceMathematics” (Sep 2005), edited by Hideaki Takabe, Nguyen Hoang Luong, ¯ Yoshichika Onuki ( Osaka University Press, Japan, 2006), p.283 4) Nguyen Van Hieu, Hiroaki Shishido, Hiroshi Nakashima, Kiyohiro Sugiyama, Rikio Settai, Tetsuya Takeuchi, Tatsuma D Matsuda, Yoshinori Haga, Masayuki Hagi¯ wara, Koichi Kindo and Yoshichika Onuki : Magnetic properties in RRhIn5 ( R= Rare Earths ) J Magnetism and Magnetic materials 310,(2007) 1721 5) Nguyen Van Hieu, Hiroaki Shishido, Tetsuya Takeuchi, Chie Tonohiro, Tsutomu Yamada, Hiroshi Nakshima, Kiyohiro Sugiyama, Rikio Settai, Tatsuma D Matsuda, Yoshinori Haga, Masayuki Hagiwara, Koichi Kindo, Shingo Araki, Yasuo ¯ Nozue and Yoshichika Onuki : Magnetic Properties and Crystalline Electric Field Scheme in RRhIn5 ( R= Rare Earths ) J Phys Soc Jpn (2006) submitted 165 [...]... that of the corresponding La compound The cyclotron mass is also extremely large, reflecting a large γ-value of γ ≃ 104 /TK (mJ/K2 ·mol) The 4f electron in these compounds without magnetic ordering is clarified to be itinerant at low temperature from the dHvA experiments and energy band calculations 2.4 MAGNETIC PROPERTIES OF RIN3 AND RRHIN5 COMPOUNDS 2.4 27 Magnetic properties of RIn3 and RRhIn5 compounds. .. series of RIn3 The magnetic susceptibility of RIn3 compounds were measured between 4.2K and 500K with magnetic field up to 30kOe by Buschow et al.34 AuCu 3 -type cubic structure R In Fig 2.16 AuCu3 -type cubic structure of RIn3 compounds Larger spheres without pattern and small spheres with pattern show the rare earth atoms and indium atoms, respectively 28 CHAPTER 2 MAGNETIC PROPERTIES OF RARE EARTH COMPOUNDS. .. LaIn3 , with the singlet ground state of CEF scheme in PrIn3 and antiferromagnetic dense Kondo compound in CeIn3 ,(b) the least-squares fits with C = A/T2 +γ T+ DT3 ln (−∆ /T) +βT 3 at low temperatures for NdIn3 and SmIn3 , (c) shows plot of a C/T versus T 1/2 in GdIn3 and (d) indicate the large CN in HoIn3 , TbIn3 2.4 MAGNETIC PROPERTIES OF RIN3 AND RRHIN5 COMPOUNDS 31 The Fermi surfaces of RIn3 are found... exist in most of RIn3 because it is most likely contained in the magnetic Brillounin zone On the other hand, a large spherical fermi surface, denoted a, is modified in the antiferromagnetic state The cyclotron masses of RIn3 are enhanced by twice or three times larger than those of LaIn3 by the electronmagnon interaction 2.4 MAGNETIC PROPERTIES OF RIN3 AND RRHIN5 COMPOUNDS 37 2) RRhIn5 compounds CeTIn5... intermediate -magnetic state, but it is split into the up- and down-spin states in the paramagnetic state, as shown in Fig 2.23 The spin splitting of the dHvA frequency is clearly seen in the second harmonic in Fig 2.22 2.4 MAGNETIC PROPERTIES OF RIN3 AND RRHIN5 COMPOUNDS NdIn3 H // 1 0 dHvA M (µB /Nd) 2 6 8 10 Magnetic Field (T) 12 Fig 2.21 Magnetization curve and dHvA oscillation of NdIn3 a... the angular dependence of the dHvA frequency in the paramagnetic state of NdIn3 is almost the same as that of LaIn3 51 Antiferromagnetic order, however, changes the topology of the Fermi surface because the size of the magnetic Brillouin zone is reduced The magnetic unit cell is tetragonal, as mentioned above Therefore, the volume of the magnetic Brillouin zone becomes half of the chemical Brillouin... kF is half of the caliper dimension of the Fermi surface The metamagnetic transition, which is based on the spin-flip mechanism, is often observed in the antiferromagnets The antiferromagnetic state at zero field is changed into the field-induced ferromagnetic or paramagnetic state at high magnetic fields It is possible to investigate a changes of magnetic properties by increasing the number of 4f electrons... 2.12 (a) and (b) show the temperature dependence of the inverse magnetic susceptibility and magnetization, respectively, for three cases: no CEF, Γ7 ground state and 20 CHAPTER 2 MAGNETIC PROPERTIES OF RARE EARTH COMPOUNDS 400 χ ( mol-Ce/emu ) Ce3+ cubic without CEF 2 300 200 1 without CEF 100 (a) 0 0 200 100 Temperature ( K ) (b) 300 0 0 500 1000 Magnetic Field ( kOe ) Fig 2.12 (a) inverse magnetic. .. 200 24 CHAPTER 2 MAGNETIC PROPERTIES OF RARE EARTH COMPOUNDS 2.3 Kondo effect and heavy fermions The Kondo effect was studied for the first time in a dilute alloy where a ppm range of the 3d transition metal was dissolved in a pure metal of copper Kondo showed the transtion impurity diverges logarithmically with decreasing temperture, and clarified the origin of the long standing problem of the minimum resistivity... magnetic structure are small enough, conduction electrons undergoing cyclotron motion in the presence of magnetic field can tunnel through these gaps and circulate the orbit on the paramagnetic Fermi surface If this magnetic breakthrough (breakdown) effect occurs, the paramagnetic Fermi surface may be observed in the dHvA effect even in the presence of magnetic order For Kondo-lattice compounds with magnetic ... experiments and energy band calculations 2.4 MAGNETIC PROPERTIES OF RIN3 AND RRHIN5 COMPOUNDS 2.4 27 Magnetic properties of RIn3 and RRhIn5 compounds 1) RIn3 compounds Rare earth intermetallic compounds. .. Results and Discussion 5.1 Magnetic properties and CEF scheme in RRhIn5 5.2 Fermi surface and magnetic properties of PrTIn5 (T: Co, Rh and Ir) 5.3 Unique magnetic properties of RRhIn5. .. the magnetic properties of RRhIn5 series The present thesis consists of the following contents In Chap 2, the fundamental 2.1 Magnetic Properties of Rare Earth Compounds Magnetic properties of