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Magnetic phase transitions and giant magnetoresistance in La1−xSmxMn2Si2 (0≤x≤1)
Journal of Alloys and Compounds 343 (2002) 14–25
L
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Magnetic phase transitions and giant magnetoresistance in La 12x Sm x Mn 2 Si 2 (0#x#1) E.G. Gerasimov*, V.S. Gaviko, V.N. Neverov, A.V. Korolyov Institute of Metal Physics, 18 Kovalevskaya St., 620219 Ekaterinburg, Russia Received 30 November 2001; accepted 18 January 2002
Abstract The magnetic properties of La 12x Sm x Mn 2 Si 2 (0#x#1) quasi-ternary layered intermetallic compounds have been studied by magnetic measurements. Based on the results of magnetic measurements, the x–T magnetic phase diagram of the compounds was defined. The concentration-dependent change in the magnetic state of the Mn sublattice in the compounds correlates with an unusual dependence of the type of interlayer Mn–Mn magnetic ordering on the intralayer Mn–Mn distance in the RMn 2 X 2 -type compounds. The compounds La 12x Sm x Mn 2 Si 2 with x50.25, 0.27 exhibit SmMn 2 Ge 2 -like magnetic behavior and giant magnetoresistance (2DR /R¯27%) at the field-induced antiferro-ferromagnetic metamagnetic phase transitions. The field-induced metamagnetic transitions were described in a model taking into account a strong Mn anisotropy, exchange magnetostriction and a strong dependence of the interlayer Mn–Mn exchange interactions on the Mn–Mn intralayer distance in the compounds. 2002 Elsevier Science B.V. All rights reserved. Keywords: Rare earth compounds; Transition metal compounds; Anisotropy; Phase transition; Magnetoresistance PACS: 71.20. Lp; 75.30. Gw; 75.30 Kz; 71.70 Gm; 75.70. Pa
1. Introduction The ternary intermetallic RM 2 X 2 (R is a rare-earth metal, M is a 3d (4d) metal X5Si or Ge) compounds belong to the class of compounds with a naturally layered structure. The compounds crystallize in the tetragonal ThCr 2 Si 2 -type lattice (space group I4 /mmm). The atoms of each sort lie within equivalent crystal planes (layers) stacked along the c-axis in the following sequence: –M– X–R–X–M–. The compounds exhibit a very wide spectrum of physical phenomena, including superconducting and heavy fermions behavior, crystal field effects, mixed valence of the rare-earth ions and different types of magnetic structures and magnetic phase transitions [1]. An interesting feature of the RM 2 X 2 compounds with different 3d transition metals (M5Mn, Fe, Co, Ni) is that only the M5Mn atoms have nonzero magnetic moments in these compounds. The RMn 2 X 2 compounds exhibit a unique set of magnetic phase transitions and an unusually strong correlation between the intralayer Mn–Mn distance *Corresponding author. E-mail address: [email protected] (E.G. Gerasimov).
and interlayer magnetic arrangement of the Mn magnetic moments. The type of interlayer magnetic ordering of Mn strongly depends on the lattice parameter a (intralayer Mn–Mn distance d Mn – Mn 5a / œ2) and does not depend on the change in lattice parameter c (interlayer Mn–Mn distance). The critical distance d c for intralayered Mn atoms is considered to be equal to approximately 0.285– 0.287 nm at room temperature. As a rule, the Mn layers are ordered along the c-axis ferromagnetically at d Mn – Mn .d c and antiferromagnetically at d Mn – Mn ,d c [1,2]. The critical spacing d c between the Mn atoms at which the type of interlayer magnetic ordering becomes unstable is close to the distance at which a localization–delocalization of Mn 3d electrons is supposed to occur in binary alloys [1,2]. Therefore, an assumption is made that at d Mn – Mn |d c , the electron band structure of the compounds changes considerably. In particular, in Ref. [3], the interlayer Mn–Mn exchange interaction was supposed to depend on the density of electron states at the Fermi level. The density of electron states in the vicinity of the critical Mn–Mn distance was considered to change strongly, which results in a change in the type of interlayer Mn–Mn magnetic ordering. Yet, direct experimental and theoretical
0925-8388 / 02 / $ – see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 02 )00110-X
E.G. Gerasimov et al. / Journal of Alloys and Compounds 343 (2002) 14 – 25
evidence of the reality of the electronic band structure changes in the compounds is absent to date. The value of the Mn magnetic moment varies insignificantly upon changing the type of interlayer Mn–Mn magnetic ordering. Nowadays, as the only evidence for the change in the electronic band structure of the RMn 2 X 2 compounds one can take the strong difference in the temperature-independent contribution of the high-temperature Curie–Weiss dependence of the paramagnetic susceptibility for compounds with d Mn – Mn ,d c and d Mn – Mn .d c [4]. The instability of the type of interlayer Mn–Mn magnetic ordering can also be described in the model of localized magnetic moments, based on the assumption that there exists a strong dependence of the Mn–Mn exchange coupling on the crystal lattice parameters. Such an assumption allows one to qualitatively explain the existence of spontaneous and field-induced antiferromagnetic–ferromagnetic phase transitions in the compounds [5,6]. However, the role of the magnetic anisotropy of the Mn sublattice in the formation of unusual magnetic properties and magnetic structures in the compounds remains unclear. In our previous work, it was shown that the Mn sublattice in the LaMn 2 Si 2 compound possesses a strong uniaxial anisotropy [7]. The goal of the work presented was to investigate the anisotropic magnetic properties of the La 12x Sm x Mn 2 Si 2 solid solutions in which the distance between Mn atoms in layers can be gradually changed from d Mn – Mn .d c (LaMn 2 Si 2 ) to d Mn – Mn ,d c (SmMn 2 Si 2 ).
15
mm) in external magnetic fields up to 120 kOe. Contacts were welded to the sample surface with indium.
3. Results and discussion
3.1. Magnetic properties and x–T magnetic phase diagram of La12 x Sm x Mn2 Si2 (0# x #1) compounds Fig. 1 shows the concentration behavior of the lattice parameters of the La 12x Sm x Mn 2 Si 2 compounds. Replacement of La by Sm, which has a smaller atomic radius, leads to a gradual decrease in the lattice parameters and the unit-cell volume of the compounds. This decrease occurs isotropically, the ratio c /a being practically unchanged. The data on the crystal lattice parameters of the compounds are summarized in Table 1. For the compounds La 12x Sm x Mn 2 Si 2 with x50; 0.2, the magnetization curves and the temperature dependences of the magnetization measured in the magnetic field directed both along (Mi ) and perpendicular to (M' ) the c-axis have a shape similar to those for a uniaxial anisotropic ferromagnet with the easy axis magnetization directed along the c-axis (Fig. 2a,b). The positions of kinks on the Mi (T ); M' (T ) curves correspond to the Curie temperatures T C of the compounds. At temperatures T ,
2. Experimental details The La 12x Sm x Mn 2 Si 2 (x50, 0.2, 0.25, 0.3, 0.35, 0.4, 0.6, 0.8, 1.0) compounds were obtained from pure components by induction melting in an argon atmosphere followed by annealing in vacuum at T5900 8C for 1 week. X-Ray diffraction analysis of the sample was carried out using Cr Ka monochromatized radiation. The compounds crystallize in the ThCr 2 Si 2 -type structure, and the amount of additional phases in the samples does not exceed 3%. The magnetic properties of the compounds have been studied on polycrystalline samples for the antiferromagnets. In the case of ferromagnets, the powder samples were aligned at room temperature in an external magnetic field (H512–15 kOe) along the easy magnetization direction and fixed by an epoxy resin. The direction of alignment of the powder particles was checked by X-ray diffraction to be along the tetragonal c-axis in the ThCr 2 Si 2 -type structure. The magnetic measurements were carried out using a SQUID magnetometer MPMSR5-XL (Quantum Design) in external magnetic fields up to 50 kOe in the temperature range 4,T ,400 K. The electrical resistance and magnetoresistance of the compounds were measured using a standard four-probe method on massive polycrystalline samples (|103535
Fig. 1. Lattice parameters as a function of Sm content for the La 12x Sm x Mn 2 Si 2 compounds at room temperature.
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Table 1 The lattice parameters for La 12x Sm x Mn 2 Si 2 compounds at room temperature x
a (nm)
c (nm)
V 310 3 (nm 3 )
c /a
d Mn – Mn (nm)
0 0.2 0.25 0.27 0.3 0.35 0.4 0.6 0.8 1.0
0.4114 0.4091 0.4084 0.4081 0.4076 0.4067 0.4060 0.4036 0.4004 0.3977
1.0655 1.0645 1.0597 1.0597 1.0610 1.0617 1.0593 1.0575 1.0550 1.0512
180.3 178.2 176.8 176.4 176.3 175.6 174.6 172.3 169.1 166.3
2.6 2.6 2.6 2.6 2.6 2.61 2.61 2.64 2.63 2.64
0.291 0.289 0.289 0.289 0.288 0.288 0.287 0.285 0.283 0.281
T C , there are no anomalies in the Mi (T ) dependences and one can suggest that the easy magnetization direction in the compounds remains unchanged with temperature. In the compound with x50.2, in which the magnetic rare earth Sm ions are present, an increase in the magnetization M' (T ) with decreasing temperature is observed that is related to the ferromagnetic ordering of the magnetic Sm ions in the basal plane at temperatures T ,50 K. For the compounds with Sm content x$0.3, the temperature dependences of the magnetization M(T ) at temperatures T .80 K have a form typical of antiferromagnets with maxima in the vicinity of the Neel temperatures T N (Fig. 3a). X-Ray analysis showed that in the powders of the antiferromagnetic compounds with x$0.3 oriented in a
Fig. 2. Temperature dependences of magnetization for La 12x Sm x Mn 2 Si 2 (x50, 0.2) compounds parallel and perpendicular to the c-axis at H50.5 kOe (a). Magnetization curves for LaMn 2 Si 2 parallel (open circles) and perpendicular (closed circles) to the c-axis at T54.2 K (b).
Fig. 3. Temperature dependences of magnetization for polycrystalline samples of La 12x Sm x Mn 2 Si 2 (x50.3, 0.35, 0.4, 0.6) at H520 kOe (a). Magnetization curves for powders of SmMn 2 Si 2 oriented at room temperature along (circle) and perpendicular to the texture direction (squares) at T54.2 K (open symbols) and at T5285 K (closed symbols) (b).
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field of H510 kOe at T5293 K, the c-axis is aligned perpendicular to the external magnetic field direction (texture direction). The texture direction lies in the abplane in a powder particle. The c-axes of the particles are disordered in a plane that is perpendicular to the texture direction. Since an antiferromagnet is aligned in an external field perpendicular to the magnetic moment direction, the assumption can be made that the uniaxial anisotropy is retained in the compounds with x$0.3 and the magnetic moments of Mn in adjacent layers are ordered antiferromagnetically along the c-axis. At low temperatures T ,80 K, just as in the case of the compound with x50.2, all compounds represent an increase in the magnetization that is related to the ferromagnetic ordering of Sm magnetic moments in the basal plane. In Fig. 3b, the magnetization curves along M' (H ) and perpendicular to the texture direction Mi (H ) are shown for powders of the SmMn 2 Si 2 compound oriented at room temperature and fixed by a epoxy resin. At all temperatures, a strong anisotropy in the magnetization curves is observed and in magnetic fields H #50 kOe, the relationship Mi (H )¯(2 / 3)?M' (H ) holds, i.e. magnetic moments of Mn and Sm ions virtually do not decline from the easy magnetization directions (c-axis for Mn and ab-plane for Sm). For the compounds with x50.25; 0.27, the observed temperature dependences of magnetization are qualitatively similar to those of the SmMn 2 Ge 2 compound for which d Mn – Mn ¯d c [1,8]. As seen from Fig. 4, in the compounds,
three different magnetically ordered states with critical temperatures of magnetic phase transition T C , TAF , and T Sm can be distinguished. At temperatures T ,T C , in the compounds a spontaneous magnetization along the c-axis is revealed (ferromagnetic F state). When lowering temperature below T5TAF , the spontaneous magnetization disappears (antiferromagnetic AF state). On further lowering the temperature to T ,T Sm the spontaneous magnetization appears again in the compounds, which is due to the ferromagnetic ordering of the Sm magnetic moments in the ab-plane (reentrant-ferromagnetic AF9 state). The value of the magnetic moment in the basal plane at T54.2 K for all compounds far exceeds the value for a magnetic Sm 31 ion mSm (x)¯0.7mB ?x (Fig. 5). One can suggest that ferromagnetic ordering of the Sm magnetic moments in the basal plane leads to the appearance of a small ferromagnetic in-plane component of the Mn magnetic moments due to the ferromagnetic Sm–Mn exchange interaction. The large scatter of the magnetic moment values shown in Fig. 5 for the antiferromagnetic compounds with x.0.27 is caused by the fact that the measurements were carried out on polycrystalline samples. Fig. 6 shows the x–T magnetic phase diagram of the compounds constructed using the values of the critical temperatures given in Table 2. Also shown is a schematic picture of the interlayer Mn–Mn magnetic ordering supposed for the compounds in different magnetic states. Substitution of Sm for La in the La 12x Smx Mn 2 Si 2 com-
Fig. 4. Temperature dependences of magnetization for La 12x Sm x Mn 2 Si 2 (x50.25, 0.27) parallel (solid lines) and perpendicular (dashed lines) to the c-axis at H50.5 kOe.
Fig. 5. Maximal magnetic moment of La 12x Sm x Mn 2 Si 2 as a function of Sm content at T54.2 K (symbols and solid line). Dashed line shows the contribution of Sm ions to the total magnetic moment calculated as mSm (x)50.7mB ?x (x is the Sm concentration).
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also showed antiferromagnetic ordering of the Mn magnetic moments in the ab-plane (AF0 state) which is retained up to the Neel temperature T N 5470 K [9]. A specific feature of the AF0 state is that it is detected only by ¨ neutron-diffraction and Mossbauer effect experiments at T .T C for all ternary compounds RMn 2 X 2 with d Mn – Mn . d c [10]. In this paper, we could not determine the boundaries of the region of existence of the AF0 state in the x–T magnetic phase diagram of the La 12x Sm x Mn 2 Si 2 compounds, using only magnetic measurements. The x–T magnetic phase diagram obtained for the La 12x Sm x Mn 2 Si 2 compounds is similar to those constructed for solid solutions of the type R 12x R 9x Mn 2 Si 2 and RMn 2 (Si 12x Ge x ) 2 in which with changing concentration x, the d Mn – Mn distance can be gradually varied from d Mn – Mn .d c to d Mn – Mn ,d c [11,12]. The F→AF magnetic phase transition in the La 12x Sm x Mn 2 Si 2 compounds takes place in the concentration range 0.2,x,0.3 at the value d Mn – Mn 5a / œ2¯0.289 nm (Table 1), which is quite close to the value of d c ¯0.285–0.288 nm observed earlier for other quasiternary compounds of the R 12x R 9x Mn 2 X 2 -type. Thus, the concentration change in the magnetic state in the La 12x Sm x Mn 2 Si 2 compounds confirms again the existence of a correlation between the sign of interlayer Mn–Mn exchange coupling and the distance between Mn atoms inside the layers observed for the RMn 2 X 2 -type compounds. Fig. 6. The x–T magnetic phase diagram of the La 12x Sm x Mn 2 Si 2 compounds and a schematic picture of the interlayer Mn–Mn magnetic ordering proposed for the compounds in different magnetic states.
pounds leads to a change in the type of interlayer Mn–Mn magnetic ordering from ferromagnetic ordering (F state) to antiferromagnetic ordering (AF state). At low temperatures, there occurs ferromagnetic ordering of the Sm magnetic moments in the ab-plane and partial distortion of interlayer antiferromagnetic structure of the Mn magnetic moments caused by the Sm–Mn ferromagnetic exchange interaction (AF9 state). Note that at T .T C in the ternary compound LaMn 2 Si 2 neutron diffraction measurements
Table 2 The critical temperatures La 12x Sm x Mn 2 Si 2 compounds
of
x
T Sm (K)
TAF (K)
T c (K)
T N (K)
0 0.2 0.25 0.27 0.3 0.35 0.4 0.6 0.8 1.0
– 12 11 12 12 14 20 25 25 41
– – 160 190 – – – –
305 280 294 300 – – – –
–
–
470 a – – – 280 305 320 346 400 398
a
The value from Ref. [1].
magnetic
phase
transitions
in
3.2. Spontaneous and field-induced magnetic phase transitions in the La0.75 Sm0.25 Mn2 Si2 compound As shown above, in the compounds La 12x Sm x Mn 2 Si 2 with x50.25; 0.27, a SmMn 2 Ge 2 -like magnetic behavior is observed that is characterized by the existence of a spontaneous AF→F magnetic phase transition (Fig. 4). An increase in the external magnetic field strength results in a decrease in the phase transition temperature and in a reduction of the temperature range of existence of the interlayer antiferromagnetic ordering of the Mn magnetic moments (Fig. 7). Fig. 8 shows typical magnetization curves for the La 0.75 Sm 0.25 Mn 2 Si 2 compound measured along and perpendicular to the c-axis at temperatures corresponding to different magnetic states. In the ferromagnetic F state (TAF ,T ,T C ), the Mi (H ) and M' (H ) curves for this compound are typical of a high-anisotropic uniaxial ferromagnet with the easy magnetization axis directed along the c-axis (Fig. 8c). The temperature dependences of the magnetic anisotropy constants K1 (T ), K2 (T ) determined from the magnetization curves for the compound La 0.75 Sm 0.25 Mn 2 Si 2 at TAF ,T , T C virtually coincide with those obtained earlier [7] for LaMn 2 Si 2 (Fig. 9). Partial replacement of nonmagnetic La ions by magnetic Sm ions does not affect the magnetic anisotropy of the La 0.75 Sm 0.25 Mn 2 Si 2 at high temperatures where the anisotropy is controlled solely by the Mn
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Fig. 7. Temperature dependences of magnetization for polycrystalline sample of La 0.75 Sm 0.25 Mn 2 Si 2 at H50.5 kOe (1); H520 kOe (2); H550 kOe (3).
Fig. 9. Temperature dependences of magnetic anisotropy constants K1 (T ), K2 (T ) for La 0.75 Sm 0.25 Mn 2 Si 2 (closed symbols) and LaMn 2 Si 2 (open symbols).
sublattice. There are no grounds for the assumption that the anisotropy of the Mn sublattice in the La 0.75 Sm 0.25 Mn 2 Si 2 compound will change at the AF→F magnetic phase transition. Therefore, in further consideration we use the temperature dependences K1 (T ), K2 (T ) obtained for the LaMn 2 Si 2 to describe the magnetic anisotropy of the Mn sublattice in La 0.75 Sm 0.25 Mn 2 Si 2 . In the AF and AF9 states (T Sm ,T ,TAF ), the magnetization curves of the La 0.75 Sm 0.25 Mn 2 Si 2 compound exhibit metamagnetic phase transitions of the AF9→F, AF→F type induced by an external magnetic field (Fig. 8a,b). Unlike a uniaxial anisotropic antiferromagnet, in
which the metamagnetic transition takes place only when magnetizing along the easy magnetization axis, in La 0.75 Sm 0.25 Mn 2 Si 2 the metamagnetic transition is observed in magnetic fields directed both parallel and perpendicular to the easy c-axis. The existence of the AF→F magnetic phase transition in magnetic fields oriented both parallel and perpendicular to the easy axis of the compound can serve as an indication of the electron band origin of the magnetic phase transition. The metamagnetic transitions in the compounds are smeared out and as critical fields of the metamagnetic
Fig. 8. Magnetization curves parallel and perpendicular to the c-axis for La 0.75 Sm 0.25 Mn 2 Si 2 at T54.2 K (a); 120 K (b); 250 K (c).
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transitions we used the values which were defined as ≠Mi ≠M' Hi 5 ]] , H' 5 ]] . The temperature de≠H max ≠H max pendences of Hi (T ), H' (T ) for the compound are nonmonotonous when lowering the temperature from T5TAF . At first, the critical fields increase with decreasing temperature, and then start to decrease at temperatures at which the Sm magnetic moments begin to order ferromagnetically in the ab-plane. At all temperatures, the values of critical fields of metamagnetic phase transitions are smaller than the anisotropy field of the Mn sublattice HA 5 2(K1 1 2K2 ) ]]]] (Fig. 10). MS Thus, the following peculiarities of metamagnetic AF→F, AF9→F phase transitions in the compounds can be emphasized. First, metamagnetic phase transitions exist in magnetic fields directed both parallel and perpendicular to the easy-magnetization axis. Second, the temperature dependence of the critical field of the metamagnetic transition is nonmonotonous. Third, the values of the critical fields of the metamagnetic transitions in the whole range of temperatures are smaller than the anisotropy field of the compounds. Below, we describe the AF→F, AF9→F magnetic phase transitions in La 0.75 Sm 0.25 Mn 2 Si 2 in a model of a twosublattice uniaxial anisotropic antiferromagnet.
S D
S D
3.3. Model of the field-induced magnetic phase transitions in the La12 x Sm x Mn2 Si2 compounds As was noted in the Introduction, a phenomenological approach to the description of the AF→F phase transition with changing sign of the interlayer Mn–Mn coupling in the compounds of the SmMn 2 Ge 2 -type was suggested in Refs. [5,6], where the constant of interlayer Mn–Mn exchange coupling was supposed to be strongly dependent on the lattice parameter and small temperature changes in the lattice parameters in the compounds with d Mn – Mn ¯d c could initiate a spontaneous phase transition AF→F [5]. Accordingly, the magnetic field-induced phase transition AF→F can be initiated by strong magnetostriction changes in the lattice parameters of the compound [6]. Indeed, as was shown in Ref. [13], relative magnetostriction changes in the lattice parameters of the SmMn 2 Ge 2 at the AF→F phase transition may reach gigantic values |10 23 . However, the authors of Refs. [5,6] neglected the anisotropy of the Mn sublattice. The results obtained in our work (Fig. 10) indicate that the anisotropy of the Mn sublattice is higher or comparable with the molecular field of interlayer Mn–Mn exchange interaction. We investigated the influence of the Mn sublattice anisotropy on the AF→F phase transitions in the compounds of the SmMn 2 Ge 2 -type using as an example the La 0.75 Sm 0.25 Mn 2 Si 2 compound. To describe the field-induced AF→F and AF9→F phase transitions in La 0.75 Sm 0.25 Mn 2 Si 2 we applied the model of a two-sublattice uniaxial anisotropic antiferromagnet in which each sublattice has a magnetization determined by the total magnetic moment of the Mn atoms in a layer, M5MMn1 5MMn2 5MS / 2 (Fig. 11a). The molecular field of the Mn–Mn interlayer interaction was supposed to change with changing orientation of the sublattice magnetizations from antiparallel to parallel as a result of strong magnetoelastic deformations of the crystal lattice. The influence of the magnetic Sm ions was treated as the influence of a molecular field of the Sm sublattice HSm 5 lMn – Sm MSm (where lMn – Sm is the constant of molecular Mn–Sm ferromagnetic exchange interaction; MSm is the spontaneous magnetization of the Sm sublattice) which acts on the Mn sublattices, under the assumption that the molecular field vector HSm is localized in the ab-plane, i.e. the Sm ions possess strong in-plane anisotropy. The case when the Sm sublattice is oriented in a magnetic field along the c-axis was analyzed specially. A general expression for free energy of a two-sublattice antiferromagnet depicted in Fig. 11a can be written in the form: E 5 EH 1 EA 1 Eex
Fig. 10. Temperature dependences of the magnetic anisotropy field HA (square) and critical fields of metamagnetic transitions parallel (circle) and perpendicular (up triangle) to the c-axis for La 0.75 Sm 0.25 Mn 2 Si 2 .
(1)
where EH is the Zeeman energy, EA is the magnetic anisotropy energy, Eex is the Mn–Mn interlayer exchange energy. Eq. (1) in an external magnetic field H directed parallel (E iAF ) and perpendicular (E ' AF ) to the easy-magnetization axis takes the following forms:
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Fig. 11. Model for a two-sublattice uniaxial anisotropic antiferromagnet. Schemes of a magnetic sublattice orientation at small magnetic fields (a) and in magnetic field-induced ferromagnetic states by magnetizing parallel (b) and perpendicular (c) to the c-axis.
E iAF 5 2 MH(cos(u1 ) 2 cos(u2 ))
H 1 HSm sin(u ) 5 ]]] HS
1 2 MHSm (sin(u1 ) 1 sin(u2 )) 1 ]K(sin 2 (u1 ) 2 AF 1 sin 2 (u2 )) 2 H Mn – Mn M cos(u1 1 u2 )
(2)
E' AF 5 2 M(H 1 HSm )(sin(u1 ) 1 sin(u2 )) 1 AF 1 ]K(sin 2 (u1 ) 1 sin 2 (u2 )) 2 H Mn – Mn M cos(u1 1 u2 ) 2 (3) where H is the external magnetic field; M is the Mn sublattice magnetization (M 5 (1 / 2)MS ); K is the magnetic AF anisotropy constant of the Mn sublattice; H Mn – Mn is the molecular field of interlayer Mn–Mn antiferromagnetic exchange interaction for antiparallel orientation of the magnetization vectors of the Mn sublattices; HSm is the molecular field of the Sm sublattice (HSm 5 lMn – Sm MSm ); Q1 , Q2 are the angles between the magnetization vectors of the Mn sublattices and the c-axis (Fig. 11a). Minimizing Eq. (2) with respect to the angles Q1 , Q2 , we find the equilibrium values of the angles Q1 5 Q2 5 Q : HSm sin(u ) 5 ]] HS
(4)
where HS is the saturation field: HS 5 HA 1 2H AF Mn – Mn
(5)
HA 5K /M is the magnetic anisotropy field of the Mn sublattice. Minimizing Eq. (3) with respect to the angles Q1 , Q2 we also find the equilibrium values of the angles Q1 5 Q2 5 Q for the case of magnetizing perpendicular to the c-axis:
(6)
In order to take into account the changes in H AF Mn – Mn , let us assume that upon the external field-induced ferromagnetic ordering in the Mn sublattices, the value H AF Mn – Mn F becomes equal to H Mn – Mn . The expression for the free energy in the ferromagnetic states induced by a magnetic field E Fi , E F' (Fig. 11b,c) takes the following form: E iF 5 2 2MH 1 H FMn – Mn M
(7)
F E' F 5 2 2M(H 1 HSm ) 1 K 1 H Mn – Mn M
(8)
The critical metamagnetic transition fields are found from the equality of the energies E iAF (Hi ) 5 E Fi (Hi ) and ' E AF (H' ) 5 E F' (H' ) when substituting values of the equilibrium angles Q1 , Q2 (Eqs. (4) and (6)) into Eqs. (2) and (3). Without accounting for the molecular field produced by the Sm ions, we obtain the following expressions for the critical fields H 0i , H 0' of the metamagnetic phase transitions: 1 H 0i 5 ](H AF 1 H FMn – Mn ) 2 Mn – Mn ]]]]]] H 0' 5 HS 2œH 2S 2 HS (HA 1 2H 0i )
(9) (10)
In the case when the interlayer Mn–Mn exchange interaction does not change at the antiferromagnetic–ferAF F romagnetic metamagnetic transition (H Mn – Mn 5 H Mn – Mn ), the expressions (9) and (10) take the form characteristic for a uniaxial high-anisotropic antiferromagnet:
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H 0i 5 H AF Mn – Mn
(11)
H 0' 5 HS
(12)
When magnetizing the antiferromagnet along the c-axis, the metamagnetic transition takes place in a magnetic field equal to the field of the interlayer Mn–Mn exchange coupling (Eq. (11)). Magnetizing perpendicular to the c-axis is accompanied by a smooth turning of the magnetization vectors of the sublattices and completes in the saturation magnetic field HS equal to the sum of the anisotropy fields and twice the field of the interlayer Mn–Mn exchange interaction (Eqs. (5) and (12)) (Fig. 12a). In the case of changes in the interlayer Mn–Mn coupling with changes in the mutual orientation of the F sublattice magnetizations (H AF the Mn – Mn ± H Mn – Mn ), metamagnetic transition is also observed in the magnetization curves measured perpendicular to the c-axis (Fig. 12b). In such a case, the values of the critical transition field H 0i , H 0' are determined from expressions (9) and (10) and the shape of the magnetization curves coincides with that of the experimental magnetization curves for the compound La 0.75 Sm 0.25 Mn 2 Si 2 in the temperature range T Sm ,T ,TAF (Fig. 8b). Taking account of the influence of the exchange molecular field produced by the Sm sublattice, the expressions for the critical fields of the metamagnetic transitions Hi , H' have the following form: H 2Sm 1 0 0 Hi ¯ H i 2 ]] H 2 ? Hi 1] 2 A HS
(13)
H' 5 H 0' 2 HSm
(14)
S
D
As seen from Eqs. (13) and (14), the molecular exchange field of the Sm magnetic moments results in lowering of the critical field values, and the magnetization curves acquire the shape shown in Fig. 12c, which qualitatively agrees well with the shape of the experimental magnetization curves for the compound La 0.75 Sm 0.25 Mn 2 Si 2 in the temperature range T ,T Sm (Fig. 8a). Thus, the model suggested describes qualitatively the magnetization curves for the compound quite well. To compare the model and experimental results quantitatively using the experimental dependences M' (H ), we plotted the temperature dependences (HS (T )2HSm (T )), HS (T ) and HSm (T ) (Fig. 13). As is seen from the figure, the magnetic moments of the Sm ions become ferromagnetically ordered and, correspondingly, the Sm molecular field starts exerting an essential effect on the magnetization processes in the compound La 0.75 Sm 0.25 Mn 2 Si 2 at T¯50 K, which, in accordance with Eq. (13) leads to a decrease in the Hi (T ) values with decreasing temperature. To exclude the influence of HSm on the shape of the Hi (T ) dependence and to obtain the H 0i (T ) dependence, we approximated the
Fig. 12. Calculated magnetization curves parallel and perpendicular to the c-axis for two-sublattice uniaxial anisotropic antiferromagnet in cases F AF F of: H AF Mn – Mn 5 H Mn – Mn , HSm 5 0 (a); H Mn – Mn ± H Mn – Mn , HSm 5 0 (b); F H AF ± H , H ± 0 (c). Mn – Mn Mn – Mn Sm
experimental dependence of the critical field Hi (T ) at T ,50 K by a linear one that increases with lowering temperature and then, using Eqs. (10), (13) and (14), calculated the values of H 0' (T ), Hi (T ) and H' (T ) (Fig. 14). As is seen from the figure, there is a good quantitative agreement between the experimental and theoretical temperature dependences of the critical fields for the metamagnetic phase transitions in the compounds. In particular, we analyzed the possibility of turning the
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Sm magnetic moments when magnetizing along the c-axis. In this case, expression (13) takes the following form: H 2Sm 1 0 ]] Hi ¯ H 2 2 ? H i 1 ]HA 2 HSm 2 HS 0 i
Fig. 13. Temperature dependences of saturation field HS (T ) and Sm molecular field HSm (T ) for La 0.75 Sm 0.25 Mn 2 Si 2 .
Fig. 14. Temperature dependences of critical fields of metamagnetic phase transitions parallel and perpendicular to the c-axis for La 0.75 Sm 0.25 Mn 2 Si 2 . The experimental data (symbols) and calculated curves in absent (dashed lines) and present (solid lines) molecular exchange field of Sm sublattice are shown.
S
D
(15)
and the calculated Hi values thus turn out to be lower than the experimental ones. We believe that the Sm moments in the compound have a large in-plane magnetic anisotropy and they remain in the ab-plane in magnetic fields H ,50 kOe. Fig. 15 shows the temperature dependences of the molecular fields of the interlayer Mn–Mn exchange interF action H AF Mn – Mn (T ), H Mn – Mn (T ) that were calculated using Eqs. (5) and (9) for different orientations of the Mn sublattice magnetizations. In the whole temperature range, the interlayer Mn–Mn coupling is less than the anisotropy field of the Mn sublattice. The difference between the F values of H AF Mn – Mn (T ) and H Mn – Mn (T ) decreases with lowering temperature, which may be due to a decrease in the lattice parameters. To analyze the dependences in detail, including the dependence of the interlayer Mn–Mn coupling on the lattice parameters of the compound, additional data on magnetostriction and temperature dependence of the lattice parameters are required. Thus, the existence of metamagnetic transitions in the compound can be explained under the assumption of a strong change in the Mn–Mn interlayer exchange coupling
Fig. 15. Temperature dependences of anisotropy field HA and molecular fields of interlayer Mn–Mn exchange interaction at AF, AF9 states F (H AF Mn – Mn ) and at field-induced F state (H Mn – Mn ) for La 0.75 Sm 0.25 Mn 2 Si 2 .
24
E.G. Gerasimov et al. / Journal of Alloys and Compounds 343 (2002) 14 – 25
scribe the metamagnetic transitions in other SmMn 2 Ge 2 type compounds as well.
3.4. Magnetoresistance in the La0.73 Sm0.27 Mn2 Si2 and La0.75 Sm0.25 Mn2 Si2 compounds
Fig. 16. Temperature dependences La 12x Sm x Mn 2 Si 2 (x50.25, 0.27).
of
electrical
resistance
for
with changing mutual orientation of the layer magnetizations. A peculiarity of the La 0.75 Sm 0.25 Mn 2 Si 2 compound, which determines the character of metamagnetic transitions in it, consists of the fact that the molecular field of the interlayer Mn–Mn exchange coupling is less or comparable in value with the field of the magnetic anisotropy. The model suggested can be applied to de-
The natural layered structure of the compounds RMn 2 X 2 enables us to consider them as a unique object for the verification and development of the theory on magnetoresistance in artificial multilayers. We investigated the magnetoresistance of polycrystals of the compounds La 0.73 Sm 0.27 Mn 2 Si 2 and La 0.75 Sm 0.25 Mn 2 Si 2 in the region of the AF→F magnetic phase transition. The spontaneous AF→F transition in these compounds is accompanied by a change in the electrical resistance (Fig. 16). As in the case of artificial multilayers, the antiferromagnetic Mn–Mn interlayer ordering corresponds to higher values of the electrical resistance in comparison to the case when all the layers are ordered ferromagnetically. The AF→F metamagnetic phase transition induced by a magnetic field is also accompanied by a jump-like change in the electrical resistance (Fig. 17a). The magnetic field strength at which a jump in the magnetoresistance curve is observed coincides with the value at which the metamagnetic phase transition appears in the magnetization curves measured along the c-axis (Fig. 17b). In Fig. 17a, two sets of the magnetoresistance curves are given. The first set which represents the highest values of magnetoresistance 2 DR /R 5 2 (R(H ) 2 R(H 5 0)) /R(H 5 0) ¯ 20–27% corresponds to the first reading. The second set of curves for which the magnetoresistance values 2 DR /R ¯ 6–10%, corresponds to subsequent measurements. In this case, the magnetoresistance values coincide with those of the electrical resistance changes at the spontaneous magnetic phase
Fig. 17. Magnetoresistance for La 0.75 Sm 0.25 Mn 2 Si 2 (open symbols) and La 0.73 Sm 0.27 Mn 2 Si 2 (closed symbols) at T5140 K (a). Two set of magnetoresistance curves coincide with first (1) and following (2) measurements. Magnetization curves parallel (circles) and perpendicular (squares) to the c-axis for La 0.75 Sm 0.25 Mn 2 Si 2 (open symbols) and La 0.73 Sm 0.27 Mn 2 Si 2 (closed symbols) at T5140 K (b).
E.G. Gerasimov et al. / Journal of Alloys and Compounds 343 (2002) 14 – 25
transition in the R(T ) dependence (Fig. 16). A decrease in the magnetoresistance value is likely to be caused by cracking of the massive polycrystalline samples because of the strong magnetoelastic deformations of the crystal lattice that the compounds undergo during the magnetic phase transition. Cracking of the samples leads to an increase in the electrical resistance R and, as consequence, to a decrease in the DR /R value. It may be expected for single crystals and films of the compounds that the values of magnetoresistance can be higher than 20–27%. The reason for the existence of a giant magnetoresistance in the compounds accompanying the phase transition AF→F remains unclear. As in artificial multilayers, it can be traceable to a decrease in the effective scattering of the conduction electrons on the ferromagnetically aligned magnetic moments of the Mn atoms. On the other hand, a decrease in the electrical resistance in the compounds accompanying the phase transition AF→F is likely to be related to the changes in the electronic band structure of the compounds because of strong changes in the lattice parameters that take place at the phase transition.
25
netic transition in magnetic fields directed both parallel and perpendicular to the easy-magnetization axis and the nonmonotonous temperature dependence of the critical fields of the metamagnetic transitions. The field-induced antiferromagnetic–ferromagnetic phase transitions in the compounds are described in the framework of a phenomenological theory taking into account the existence of magnetic anisotropy of the Mn sublattice, strong magnetoelastic deformations of the crystal lattice, and the dependence of the interlayer Mn–Mn exchange coupling on the parameters of the crystal lattice. In the compounds La 12x Sm x Mn 2 Si 2 with x50.25; 0.27, giant values of the magnetoresistance were detected in the region of the antiferromagnetic–ferromagnetic phase transition.
Acknowledgements This work was supported by Grant 72 of the 6th Concurs of the Russian Academy of Sciences (1999).
References 4. Conclusion The studies of the concentration changes in the magnetic properties of the La 12x Sm x Mn 2 Si 2 solid solutions carried out in this work confirm the interrelation, which is general for the RMn 2 X 2 compounds, between the type of magnetic ordering of the Mn magnetic moments located in adjacent layers of the crystal lattice and the distance between the nearest Mn atoms in the layer. The critical spacing at which the transition from ferromagnetic to antiferromagnetic interlayer ordering of Mn atoms in the La 12x Sm x Mn 2 Si 2 compounds takes place corresponds to the value d Mn – Mn ¯0.289 nm at room temperature which is close to the value d c ¯0.285–0288 nm observed earlier for other quasi-ternary intermetallic compounds of the R 12x R 9x Mn 2 X 2 type. In the La 12x Sm x Mn 2 Si 2 compounds with x50.25; 0.27, where d Mn – Mn ¯d c , a spontaneous and a field-induced change in the type of interlayer Mn–Mn magnetic ordering from antiferromagnetic to ferromagnetic is observed. The main features of the field-induced antiferromagnetic–ferromagnetic phase transition are the existence of metamag-
[1] A. Szytula, in: Handbook of Magnetic Materials, Vol. 6, Elsevier, Amsterdam, 1991, p. 85. [2] H. Fujii, T. Okamoto, T. Shigeoka, N. Iwata, Solid State Commun. 53 (8) (1985) 715. [3] H. Fujii, M. Isoda, T. Okamoto, T. Shigeoka, N. Iwata, J. Magn. Magn. Mater. 54–57 (1986) 1345. [4] G. Venturini, J. Alloys Comp. 232 (1996) 133. [5] J.H.V.J. Brabers, A.J. Nolten, F. Kayzel, S.H.J. Lenczowski, K.H.J. Buschow, F.R. de Boer, Phys. Rev. B 50 (1994) 16410. [6] J.H.V.J. Brabers, K.H.J. Buschow, F.R. de Boer, Phys. Rev. B 59 (14) (1999) 9314. [7] E.G. Gerasimov, M.I. Kurkin, A.V. Korolyov, V.S. Gaviko, Physica B, submitted. [8] C.J. Tomka, Cz. Kapusta, C. Ritter, P.C. Riedi, R. Cywinski, K.H.J. Buschow, J. Phys. B 230–232 (1997) 727. [9] M. Hoffmann, S.J. Campbell, S.J. Kennedy, X.L. Zhao, J. Magn. Magn. Mater. 176 (2–3) (1997) 279. [10] I. Nowik, Y. Levi, I. Felner, E.R. Bauminger, J. Magn. Magn. Mater. 147 (3) (1995) 373. [11] A. Szytula, S. Siek, J. Magn. Magn. Mater. 27 (1) (1982) 49. [12] G. Venturini, B. Malaman, E. Ressouche, J. Alloys Comp. 241 (1996) 135. [13] G. Guanghua, R.Z. Levitin, V.V. Snegirev, D.V. Filippov, Phys. Solid State 43 (2001) 496.
L
www.elsevier.com / locate / jallcom
Magnetic phase transitions and giant magnetoresistance in La 12x Sm x Mn 2 Si 2 (0#x#1) E.G. Gerasimov*, V.S. Gaviko, V.N. Neverov, A.V. Korolyov Institute of Metal Physics, 18 Kovalevskaya St., 620219 Ekaterinburg, Russia Received 30 November 2001; accepted 18 January 2002
Abstract The magnetic properties of La 12x Sm x Mn 2 Si 2 (0#x#1) quasi-ternary layered intermetallic compounds have been studied by magnetic measurements. Based on the results of magnetic measurements, the x–T magnetic phase diagram of the compounds was defined. The concentration-dependent change in the magnetic state of the Mn sublattice in the compounds correlates with an unusual dependence of the type of interlayer Mn–Mn magnetic ordering on the intralayer Mn–Mn distance in the RMn 2 X 2 -type compounds. The compounds La 12x Sm x Mn 2 Si 2 with x50.25, 0.27 exhibit SmMn 2 Ge 2 -like magnetic behavior and giant magnetoresistance (2DR /R¯27%) at the field-induced antiferro-ferromagnetic metamagnetic phase transitions. The field-induced metamagnetic transitions were described in a model taking into account a strong Mn anisotropy, exchange magnetostriction and a strong dependence of the interlayer Mn–Mn exchange interactions on the Mn–Mn intralayer distance in the compounds. 2002 Elsevier Science B.V. All rights reserved. Keywords: Rare earth compounds; Transition metal compounds; Anisotropy; Phase transition; Magnetoresistance PACS: 71.20. Lp; 75.30. Gw; 75.30 Kz; 71.70 Gm; 75.70. Pa
1. Introduction The ternary intermetallic RM 2 X 2 (R is a rare-earth metal, M is a 3d (4d) metal X5Si or Ge) compounds belong to the class of compounds with a naturally layered structure. The compounds crystallize in the tetragonal ThCr 2 Si 2 -type lattice (space group I4 /mmm). The atoms of each sort lie within equivalent crystal planes (layers) stacked along the c-axis in the following sequence: –M– X–R–X–M–. The compounds exhibit a very wide spectrum of physical phenomena, including superconducting and heavy fermions behavior, crystal field effects, mixed valence of the rare-earth ions and different types of magnetic structures and magnetic phase transitions [1]. An interesting feature of the RM 2 X 2 compounds with different 3d transition metals (M5Mn, Fe, Co, Ni) is that only the M5Mn atoms have nonzero magnetic moments in these compounds. The RMn 2 X 2 compounds exhibit a unique set of magnetic phase transitions and an unusually strong correlation between the intralayer Mn–Mn distance *Corresponding author. E-mail address: [email protected] (E.G. Gerasimov).
and interlayer magnetic arrangement of the Mn magnetic moments. The type of interlayer magnetic ordering of Mn strongly depends on the lattice parameter a (intralayer Mn–Mn distance d Mn – Mn 5a / œ2) and does not depend on the change in lattice parameter c (interlayer Mn–Mn distance). The critical distance d c for intralayered Mn atoms is considered to be equal to approximately 0.285– 0.287 nm at room temperature. As a rule, the Mn layers are ordered along the c-axis ferromagnetically at d Mn – Mn .d c and antiferromagnetically at d Mn – Mn ,d c [1,2]. The critical spacing d c between the Mn atoms at which the type of interlayer magnetic ordering becomes unstable is close to the distance at which a localization–delocalization of Mn 3d electrons is supposed to occur in binary alloys [1,2]. Therefore, an assumption is made that at d Mn – Mn |d c , the electron band structure of the compounds changes considerably. In particular, in Ref. [3], the interlayer Mn–Mn exchange interaction was supposed to depend on the density of electron states at the Fermi level. The density of electron states in the vicinity of the critical Mn–Mn distance was considered to change strongly, which results in a change in the type of interlayer Mn–Mn magnetic ordering. Yet, direct experimental and theoretical
0925-8388 / 02 / $ – see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S0925-8388( 02 )00110-X
E.G. Gerasimov et al. / Journal of Alloys and Compounds 343 (2002) 14 – 25
evidence of the reality of the electronic band structure changes in the compounds is absent to date. The value of the Mn magnetic moment varies insignificantly upon changing the type of interlayer Mn–Mn magnetic ordering. Nowadays, as the only evidence for the change in the electronic band structure of the RMn 2 X 2 compounds one can take the strong difference in the temperature-independent contribution of the high-temperature Curie–Weiss dependence of the paramagnetic susceptibility for compounds with d Mn – Mn ,d c and d Mn – Mn .d c [4]. The instability of the type of interlayer Mn–Mn magnetic ordering can also be described in the model of localized magnetic moments, based on the assumption that there exists a strong dependence of the Mn–Mn exchange coupling on the crystal lattice parameters. Such an assumption allows one to qualitatively explain the existence of spontaneous and field-induced antiferromagnetic–ferromagnetic phase transitions in the compounds [5,6]. However, the role of the magnetic anisotropy of the Mn sublattice in the formation of unusual magnetic properties and magnetic structures in the compounds remains unclear. In our previous work, it was shown that the Mn sublattice in the LaMn 2 Si 2 compound possesses a strong uniaxial anisotropy [7]. The goal of the work presented was to investigate the anisotropic magnetic properties of the La 12x Sm x Mn 2 Si 2 solid solutions in which the distance between Mn atoms in layers can be gradually changed from d Mn – Mn .d c (LaMn 2 Si 2 ) to d Mn – Mn ,d c (SmMn 2 Si 2 ).
15
mm) in external magnetic fields up to 120 kOe. Contacts were welded to the sample surface with indium.
3. Results and discussion
3.1. Magnetic properties and x–T magnetic phase diagram of La12 x Sm x Mn2 Si2 (0# x #1) compounds Fig. 1 shows the concentration behavior of the lattice parameters of the La 12x Sm x Mn 2 Si 2 compounds. Replacement of La by Sm, which has a smaller atomic radius, leads to a gradual decrease in the lattice parameters and the unit-cell volume of the compounds. This decrease occurs isotropically, the ratio c /a being practically unchanged. The data on the crystal lattice parameters of the compounds are summarized in Table 1. For the compounds La 12x Sm x Mn 2 Si 2 with x50; 0.2, the magnetization curves and the temperature dependences of the magnetization measured in the magnetic field directed both along (Mi ) and perpendicular to (M' ) the c-axis have a shape similar to those for a uniaxial anisotropic ferromagnet with the easy axis magnetization directed along the c-axis (Fig. 2a,b). The positions of kinks on the Mi (T ); M' (T ) curves correspond to the Curie temperatures T C of the compounds. At temperatures T ,
2. Experimental details The La 12x Sm x Mn 2 Si 2 (x50, 0.2, 0.25, 0.3, 0.35, 0.4, 0.6, 0.8, 1.0) compounds were obtained from pure components by induction melting in an argon atmosphere followed by annealing in vacuum at T5900 8C for 1 week. X-Ray diffraction analysis of the sample was carried out using Cr Ka monochromatized radiation. The compounds crystallize in the ThCr 2 Si 2 -type structure, and the amount of additional phases in the samples does not exceed 3%. The magnetic properties of the compounds have been studied on polycrystalline samples for the antiferromagnets. In the case of ferromagnets, the powder samples were aligned at room temperature in an external magnetic field (H512–15 kOe) along the easy magnetization direction and fixed by an epoxy resin. The direction of alignment of the powder particles was checked by X-ray diffraction to be along the tetragonal c-axis in the ThCr 2 Si 2 -type structure. The magnetic measurements were carried out using a SQUID magnetometer MPMSR5-XL (Quantum Design) in external magnetic fields up to 50 kOe in the temperature range 4,T ,400 K. The electrical resistance and magnetoresistance of the compounds were measured using a standard four-probe method on massive polycrystalline samples (|103535
Fig. 1. Lattice parameters as a function of Sm content for the La 12x Sm x Mn 2 Si 2 compounds at room temperature.
E.G. Gerasimov et al. / Journal of Alloys and Compounds 343 (2002) 14 – 25
16
Table 1 The lattice parameters for La 12x Sm x Mn 2 Si 2 compounds at room temperature x
a (nm)
c (nm)
V 310 3 (nm 3 )
c /a
d Mn – Mn (nm)
0 0.2 0.25 0.27 0.3 0.35 0.4 0.6 0.8 1.0
0.4114 0.4091 0.4084 0.4081 0.4076 0.4067 0.4060 0.4036 0.4004 0.3977
1.0655 1.0645 1.0597 1.0597 1.0610 1.0617 1.0593 1.0575 1.0550 1.0512
180.3 178.2 176.8 176.4 176.3 175.6 174.6 172.3 169.1 166.3
2.6 2.6 2.6 2.6 2.6 2.61 2.61 2.64 2.63 2.64
0.291 0.289 0.289 0.289 0.288 0.288 0.287 0.285 0.283 0.281
T C , there are no anomalies in the Mi (T ) dependences and one can suggest that the easy magnetization direction in the compounds remains unchanged with temperature. In the compound with x50.2, in which the magnetic rare earth Sm ions are present, an increase in the magnetization M' (T ) with decreasing temperature is observed that is related to the ferromagnetic ordering of the magnetic Sm ions in the basal plane at temperatures T ,50 K. For the compounds with Sm content x$0.3, the temperature dependences of the magnetization M(T ) at temperatures T .80 K have a form typical of antiferromagnets with maxima in the vicinity of the Neel temperatures T N (Fig. 3a). X-Ray analysis showed that in the powders of the antiferromagnetic compounds with x$0.3 oriented in a
Fig. 2. Temperature dependences of magnetization for La 12x Sm x Mn 2 Si 2 (x50, 0.2) compounds parallel and perpendicular to the c-axis at H50.5 kOe (a). Magnetization curves for LaMn 2 Si 2 parallel (open circles) and perpendicular (closed circles) to the c-axis at T54.2 K (b).
Fig. 3. Temperature dependences of magnetization for polycrystalline samples of La 12x Sm x Mn 2 Si 2 (x50.3, 0.35, 0.4, 0.6) at H520 kOe (a). Magnetization curves for powders of SmMn 2 Si 2 oriented at room temperature along (circle) and perpendicular to the texture direction (squares) at T54.2 K (open symbols) and at T5285 K (closed symbols) (b).
E.G. Gerasimov et al. / Journal of Alloys and Compounds 343 (2002) 14 – 25
17
field of H510 kOe at T5293 K, the c-axis is aligned perpendicular to the external magnetic field direction (texture direction). The texture direction lies in the abplane in a powder particle. The c-axes of the particles are disordered in a plane that is perpendicular to the texture direction. Since an antiferromagnet is aligned in an external field perpendicular to the magnetic moment direction, the assumption can be made that the uniaxial anisotropy is retained in the compounds with x$0.3 and the magnetic moments of Mn in adjacent layers are ordered antiferromagnetically along the c-axis. At low temperatures T ,80 K, just as in the case of the compound with x50.2, all compounds represent an increase in the magnetization that is related to the ferromagnetic ordering of Sm magnetic moments in the basal plane. In Fig. 3b, the magnetization curves along M' (H ) and perpendicular to the texture direction Mi (H ) are shown for powders of the SmMn 2 Si 2 compound oriented at room temperature and fixed by a epoxy resin. At all temperatures, a strong anisotropy in the magnetization curves is observed and in magnetic fields H #50 kOe, the relationship Mi (H )¯(2 / 3)?M' (H ) holds, i.e. magnetic moments of Mn and Sm ions virtually do not decline from the easy magnetization directions (c-axis for Mn and ab-plane for Sm). For the compounds with x50.25; 0.27, the observed temperature dependences of magnetization are qualitatively similar to those of the SmMn 2 Ge 2 compound for which d Mn – Mn ¯d c [1,8]. As seen from Fig. 4, in the compounds,
three different magnetically ordered states with critical temperatures of magnetic phase transition T C , TAF , and T Sm can be distinguished. At temperatures T ,T C , in the compounds a spontaneous magnetization along the c-axis is revealed (ferromagnetic F state). When lowering temperature below T5TAF , the spontaneous magnetization disappears (antiferromagnetic AF state). On further lowering the temperature to T ,T Sm the spontaneous magnetization appears again in the compounds, which is due to the ferromagnetic ordering of the Sm magnetic moments in the ab-plane (reentrant-ferromagnetic AF9 state). The value of the magnetic moment in the basal plane at T54.2 K for all compounds far exceeds the value for a magnetic Sm 31 ion mSm (x)¯0.7mB ?x (Fig. 5). One can suggest that ferromagnetic ordering of the Sm magnetic moments in the basal plane leads to the appearance of a small ferromagnetic in-plane component of the Mn magnetic moments due to the ferromagnetic Sm–Mn exchange interaction. The large scatter of the magnetic moment values shown in Fig. 5 for the antiferromagnetic compounds with x.0.27 is caused by the fact that the measurements were carried out on polycrystalline samples. Fig. 6 shows the x–T magnetic phase diagram of the compounds constructed using the values of the critical temperatures given in Table 2. Also shown is a schematic picture of the interlayer Mn–Mn magnetic ordering supposed for the compounds in different magnetic states. Substitution of Sm for La in the La 12x Smx Mn 2 Si 2 com-
Fig. 4. Temperature dependences of magnetization for La 12x Sm x Mn 2 Si 2 (x50.25, 0.27) parallel (solid lines) and perpendicular (dashed lines) to the c-axis at H50.5 kOe.
Fig. 5. Maximal magnetic moment of La 12x Sm x Mn 2 Si 2 as a function of Sm content at T54.2 K (symbols and solid line). Dashed line shows the contribution of Sm ions to the total magnetic moment calculated as mSm (x)50.7mB ?x (x is the Sm concentration).
E.G. Gerasimov et al. / Journal of Alloys and Compounds 343 (2002) 14 – 25
18
also showed antiferromagnetic ordering of the Mn magnetic moments in the ab-plane (AF0 state) which is retained up to the Neel temperature T N 5470 K [9]. A specific feature of the AF0 state is that it is detected only by ¨ neutron-diffraction and Mossbauer effect experiments at T .T C for all ternary compounds RMn 2 X 2 with d Mn – Mn . d c [10]. In this paper, we could not determine the boundaries of the region of existence of the AF0 state in the x–T magnetic phase diagram of the La 12x Sm x Mn 2 Si 2 compounds, using only magnetic measurements. The x–T magnetic phase diagram obtained for the La 12x Sm x Mn 2 Si 2 compounds is similar to those constructed for solid solutions of the type R 12x R 9x Mn 2 Si 2 and RMn 2 (Si 12x Ge x ) 2 in which with changing concentration x, the d Mn – Mn distance can be gradually varied from d Mn – Mn .d c to d Mn – Mn ,d c [11,12]. The F→AF magnetic phase transition in the La 12x Sm x Mn 2 Si 2 compounds takes place in the concentration range 0.2,x,0.3 at the value d Mn – Mn 5a / œ2¯0.289 nm (Table 1), which is quite close to the value of d c ¯0.285–0.288 nm observed earlier for other quasiternary compounds of the R 12x R 9x Mn 2 X 2 -type. Thus, the concentration change in the magnetic state in the La 12x Sm x Mn 2 Si 2 compounds confirms again the existence of a correlation between the sign of interlayer Mn–Mn exchange coupling and the distance between Mn atoms inside the layers observed for the RMn 2 X 2 -type compounds. Fig. 6. The x–T magnetic phase diagram of the La 12x Sm x Mn 2 Si 2 compounds and a schematic picture of the interlayer Mn–Mn magnetic ordering proposed for the compounds in different magnetic states.
pounds leads to a change in the type of interlayer Mn–Mn magnetic ordering from ferromagnetic ordering (F state) to antiferromagnetic ordering (AF state). At low temperatures, there occurs ferromagnetic ordering of the Sm magnetic moments in the ab-plane and partial distortion of interlayer antiferromagnetic structure of the Mn magnetic moments caused by the Sm–Mn ferromagnetic exchange interaction (AF9 state). Note that at T .T C in the ternary compound LaMn 2 Si 2 neutron diffraction measurements
Table 2 The critical temperatures La 12x Sm x Mn 2 Si 2 compounds
of
x
T Sm (K)
TAF (K)
T c (K)
T N (K)
0 0.2 0.25 0.27 0.3 0.35 0.4 0.6 0.8 1.0
– 12 11 12 12 14 20 25 25 41
– – 160 190 – – – –
305 280 294 300 – – – –
–
–
470 a – – – 280 305 320 346 400 398
a
The value from Ref. [1].
magnetic
phase
transitions
in
3.2. Spontaneous and field-induced magnetic phase transitions in the La0.75 Sm0.25 Mn2 Si2 compound As shown above, in the compounds La 12x Sm x Mn 2 Si 2 with x50.25; 0.27, a SmMn 2 Ge 2 -like magnetic behavior is observed that is characterized by the existence of a spontaneous AF→F magnetic phase transition (Fig. 4). An increase in the external magnetic field strength results in a decrease in the phase transition temperature and in a reduction of the temperature range of existence of the interlayer antiferromagnetic ordering of the Mn magnetic moments (Fig. 7). Fig. 8 shows typical magnetization curves for the La 0.75 Sm 0.25 Mn 2 Si 2 compound measured along and perpendicular to the c-axis at temperatures corresponding to different magnetic states. In the ferromagnetic F state (TAF ,T ,T C ), the Mi (H ) and M' (H ) curves for this compound are typical of a high-anisotropic uniaxial ferromagnet with the easy magnetization axis directed along the c-axis (Fig. 8c). The temperature dependences of the magnetic anisotropy constants K1 (T ), K2 (T ) determined from the magnetization curves for the compound La 0.75 Sm 0.25 Mn 2 Si 2 at TAF ,T , T C virtually coincide with those obtained earlier [7] for LaMn 2 Si 2 (Fig. 9). Partial replacement of nonmagnetic La ions by magnetic Sm ions does not affect the magnetic anisotropy of the La 0.75 Sm 0.25 Mn 2 Si 2 at high temperatures where the anisotropy is controlled solely by the Mn
E.G. Gerasimov et al. / Journal of Alloys and Compounds 343 (2002) 14 – 25
19
Fig. 7. Temperature dependences of magnetization for polycrystalline sample of La 0.75 Sm 0.25 Mn 2 Si 2 at H50.5 kOe (1); H520 kOe (2); H550 kOe (3).
Fig. 9. Temperature dependences of magnetic anisotropy constants K1 (T ), K2 (T ) for La 0.75 Sm 0.25 Mn 2 Si 2 (closed symbols) and LaMn 2 Si 2 (open symbols).
sublattice. There are no grounds for the assumption that the anisotropy of the Mn sublattice in the La 0.75 Sm 0.25 Mn 2 Si 2 compound will change at the AF→F magnetic phase transition. Therefore, in further consideration we use the temperature dependences K1 (T ), K2 (T ) obtained for the LaMn 2 Si 2 to describe the magnetic anisotropy of the Mn sublattice in La 0.75 Sm 0.25 Mn 2 Si 2 . In the AF and AF9 states (T Sm ,T ,TAF ), the magnetization curves of the La 0.75 Sm 0.25 Mn 2 Si 2 compound exhibit metamagnetic phase transitions of the AF9→F, AF→F type induced by an external magnetic field (Fig. 8a,b). Unlike a uniaxial anisotropic antiferromagnet, in
which the metamagnetic transition takes place only when magnetizing along the easy magnetization axis, in La 0.75 Sm 0.25 Mn 2 Si 2 the metamagnetic transition is observed in magnetic fields directed both parallel and perpendicular to the easy c-axis. The existence of the AF→F magnetic phase transition in magnetic fields oriented both parallel and perpendicular to the easy axis of the compound can serve as an indication of the electron band origin of the magnetic phase transition. The metamagnetic transitions in the compounds are smeared out and as critical fields of the metamagnetic
Fig. 8. Magnetization curves parallel and perpendicular to the c-axis for La 0.75 Sm 0.25 Mn 2 Si 2 at T54.2 K (a); 120 K (b); 250 K (c).
E.G. Gerasimov et al. / Journal of Alloys and Compounds 343 (2002) 14 – 25
20
transitions we used the values which were defined as ≠Mi ≠M' Hi 5 ]] , H' 5 ]] . The temperature de≠H max ≠H max pendences of Hi (T ), H' (T ) for the compound are nonmonotonous when lowering the temperature from T5TAF . At first, the critical fields increase with decreasing temperature, and then start to decrease at temperatures at which the Sm magnetic moments begin to order ferromagnetically in the ab-plane. At all temperatures, the values of critical fields of metamagnetic phase transitions are smaller than the anisotropy field of the Mn sublattice HA 5 2(K1 1 2K2 ) ]]]] (Fig. 10). MS Thus, the following peculiarities of metamagnetic AF→F, AF9→F phase transitions in the compounds can be emphasized. First, metamagnetic phase transitions exist in magnetic fields directed both parallel and perpendicular to the easy-magnetization axis. Second, the temperature dependence of the critical field of the metamagnetic transition is nonmonotonous. Third, the values of the critical fields of the metamagnetic transitions in the whole range of temperatures are smaller than the anisotropy field of the compounds. Below, we describe the AF→F, AF9→F magnetic phase transitions in La 0.75 Sm 0.25 Mn 2 Si 2 in a model of a twosublattice uniaxial anisotropic antiferromagnet.
S D
S D
3.3. Model of the field-induced magnetic phase transitions in the La12 x Sm x Mn2 Si2 compounds As was noted in the Introduction, a phenomenological approach to the description of the AF→F phase transition with changing sign of the interlayer Mn–Mn coupling in the compounds of the SmMn 2 Ge 2 -type was suggested in Refs. [5,6], where the constant of interlayer Mn–Mn exchange coupling was supposed to be strongly dependent on the lattice parameter and small temperature changes in the lattice parameters in the compounds with d Mn – Mn ¯d c could initiate a spontaneous phase transition AF→F [5]. Accordingly, the magnetic field-induced phase transition AF→F can be initiated by strong magnetostriction changes in the lattice parameters of the compound [6]. Indeed, as was shown in Ref. [13], relative magnetostriction changes in the lattice parameters of the SmMn 2 Ge 2 at the AF→F phase transition may reach gigantic values |10 23 . However, the authors of Refs. [5,6] neglected the anisotropy of the Mn sublattice. The results obtained in our work (Fig. 10) indicate that the anisotropy of the Mn sublattice is higher or comparable with the molecular field of interlayer Mn–Mn exchange interaction. We investigated the influence of the Mn sublattice anisotropy on the AF→F phase transitions in the compounds of the SmMn 2 Ge 2 -type using as an example the La 0.75 Sm 0.25 Mn 2 Si 2 compound. To describe the field-induced AF→F and AF9→F phase transitions in La 0.75 Sm 0.25 Mn 2 Si 2 we applied the model of a two-sublattice uniaxial anisotropic antiferromagnet in which each sublattice has a magnetization determined by the total magnetic moment of the Mn atoms in a layer, M5MMn1 5MMn2 5MS / 2 (Fig. 11a). The molecular field of the Mn–Mn interlayer interaction was supposed to change with changing orientation of the sublattice magnetizations from antiparallel to parallel as a result of strong magnetoelastic deformations of the crystal lattice. The influence of the magnetic Sm ions was treated as the influence of a molecular field of the Sm sublattice HSm 5 lMn – Sm MSm (where lMn – Sm is the constant of molecular Mn–Sm ferromagnetic exchange interaction; MSm is the spontaneous magnetization of the Sm sublattice) which acts on the Mn sublattices, under the assumption that the molecular field vector HSm is localized in the ab-plane, i.e. the Sm ions possess strong in-plane anisotropy. The case when the Sm sublattice is oriented in a magnetic field along the c-axis was analyzed specially. A general expression for free energy of a two-sublattice antiferromagnet depicted in Fig. 11a can be written in the form: E 5 EH 1 EA 1 Eex
Fig. 10. Temperature dependences of the magnetic anisotropy field HA (square) and critical fields of metamagnetic transitions parallel (circle) and perpendicular (up triangle) to the c-axis for La 0.75 Sm 0.25 Mn 2 Si 2 .
(1)
where EH is the Zeeman energy, EA is the magnetic anisotropy energy, Eex is the Mn–Mn interlayer exchange energy. Eq. (1) in an external magnetic field H directed parallel (E iAF ) and perpendicular (E ' AF ) to the easy-magnetization axis takes the following forms:
E.G. Gerasimov et al. / Journal of Alloys and Compounds 343 (2002) 14 – 25
21
Fig. 11. Model for a two-sublattice uniaxial anisotropic antiferromagnet. Schemes of a magnetic sublattice orientation at small magnetic fields (a) and in magnetic field-induced ferromagnetic states by magnetizing parallel (b) and perpendicular (c) to the c-axis.
E iAF 5 2 MH(cos(u1 ) 2 cos(u2 ))
H 1 HSm sin(u ) 5 ]]] HS
1 2 MHSm (sin(u1 ) 1 sin(u2 )) 1 ]K(sin 2 (u1 ) 2 AF 1 sin 2 (u2 )) 2 H Mn – Mn M cos(u1 1 u2 )
(2)
E' AF 5 2 M(H 1 HSm )(sin(u1 ) 1 sin(u2 )) 1 AF 1 ]K(sin 2 (u1 ) 1 sin 2 (u2 )) 2 H Mn – Mn M cos(u1 1 u2 ) 2 (3) where H is the external magnetic field; M is the Mn sublattice magnetization (M 5 (1 / 2)MS ); K is the magnetic AF anisotropy constant of the Mn sublattice; H Mn – Mn is the molecular field of interlayer Mn–Mn antiferromagnetic exchange interaction for antiparallel orientation of the magnetization vectors of the Mn sublattices; HSm is the molecular field of the Sm sublattice (HSm 5 lMn – Sm MSm ); Q1 , Q2 are the angles between the magnetization vectors of the Mn sublattices and the c-axis (Fig. 11a). Minimizing Eq. (2) with respect to the angles Q1 , Q2 , we find the equilibrium values of the angles Q1 5 Q2 5 Q : HSm sin(u ) 5 ]] HS
(4)
where HS is the saturation field: HS 5 HA 1 2H AF Mn – Mn
(5)
HA 5K /M is the magnetic anisotropy field of the Mn sublattice. Minimizing Eq. (3) with respect to the angles Q1 , Q2 we also find the equilibrium values of the angles Q1 5 Q2 5 Q for the case of magnetizing perpendicular to the c-axis:
(6)
In order to take into account the changes in H AF Mn – Mn , let us assume that upon the external field-induced ferromagnetic ordering in the Mn sublattices, the value H AF Mn – Mn F becomes equal to H Mn – Mn . The expression for the free energy in the ferromagnetic states induced by a magnetic field E Fi , E F' (Fig. 11b,c) takes the following form: E iF 5 2 2MH 1 H FMn – Mn M
(7)
F E' F 5 2 2M(H 1 HSm ) 1 K 1 H Mn – Mn M
(8)
The critical metamagnetic transition fields are found from the equality of the energies E iAF (Hi ) 5 E Fi (Hi ) and ' E AF (H' ) 5 E F' (H' ) when substituting values of the equilibrium angles Q1 , Q2 (Eqs. (4) and (6)) into Eqs. (2) and (3). Without accounting for the molecular field produced by the Sm ions, we obtain the following expressions for the critical fields H 0i , H 0' of the metamagnetic phase transitions: 1 H 0i 5 ](H AF 1 H FMn – Mn ) 2 Mn – Mn ]]]]]] H 0' 5 HS 2œH 2S 2 HS (HA 1 2H 0i )
(9) (10)
In the case when the interlayer Mn–Mn exchange interaction does not change at the antiferromagnetic–ferAF F romagnetic metamagnetic transition (H Mn – Mn 5 H Mn – Mn ), the expressions (9) and (10) take the form characteristic for a uniaxial high-anisotropic antiferromagnet:
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22
H 0i 5 H AF Mn – Mn
(11)
H 0' 5 HS
(12)
When magnetizing the antiferromagnet along the c-axis, the metamagnetic transition takes place in a magnetic field equal to the field of the interlayer Mn–Mn exchange coupling (Eq. (11)). Magnetizing perpendicular to the c-axis is accompanied by a smooth turning of the magnetization vectors of the sublattices and completes in the saturation magnetic field HS equal to the sum of the anisotropy fields and twice the field of the interlayer Mn–Mn exchange interaction (Eqs. (5) and (12)) (Fig. 12a). In the case of changes in the interlayer Mn–Mn coupling with changes in the mutual orientation of the F sublattice magnetizations (H AF the Mn – Mn ± H Mn – Mn ), metamagnetic transition is also observed in the magnetization curves measured perpendicular to the c-axis (Fig. 12b). In such a case, the values of the critical transition field H 0i , H 0' are determined from expressions (9) and (10) and the shape of the magnetization curves coincides with that of the experimental magnetization curves for the compound La 0.75 Sm 0.25 Mn 2 Si 2 in the temperature range T Sm ,T ,TAF (Fig. 8b). Taking account of the influence of the exchange molecular field produced by the Sm sublattice, the expressions for the critical fields of the metamagnetic transitions Hi , H' have the following form: H 2Sm 1 0 0 Hi ¯ H i 2 ]] H 2 ? Hi 1] 2 A HS
(13)
H' 5 H 0' 2 HSm
(14)
S
D
As seen from Eqs. (13) and (14), the molecular exchange field of the Sm magnetic moments results in lowering of the critical field values, and the magnetization curves acquire the shape shown in Fig. 12c, which qualitatively agrees well with the shape of the experimental magnetization curves for the compound La 0.75 Sm 0.25 Mn 2 Si 2 in the temperature range T ,T Sm (Fig. 8a). Thus, the model suggested describes qualitatively the magnetization curves for the compound quite well. To compare the model and experimental results quantitatively using the experimental dependences M' (H ), we plotted the temperature dependences (HS (T )2HSm (T )), HS (T ) and HSm (T ) (Fig. 13). As is seen from the figure, the magnetic moments of the Sm ions become ferromagnetically ordered and, correspondingly, the Sm molecular field starts exerting an essential effect on the magnetization processes in the compound La 0.75 Sm 0.25 Mn 2 Si 2 at T¯50 K, which, in accordance with Eq. (13) leads to a decrease in the Hi (T ) values with decreasing temperature. To exclude the influence of HSm on the shape of the Hi (T ) dependence and to obtain the H 0i (T ) dependence, we approximated the
Fig. 12. Calculated magnetization curves parallel and perpendicular to the c-axis for two-sublattice uniaxial anisotropic antiferromagnet in cases F AF F of: H AF Mn – Mn 5 H Mn – Mn , HSm 5 0 (a); H Mn – Mn ± H Mn – Mn , HSm 5 0 (b); F H AF ± H , H ± 0 (c). Mn – Mn Mn – Mn Sm
experimental dependence of the critical field Hi (T ) at T ,50 K by a linear one that increases with lowering temperature and then, using Eqs. (10), (13) and (14), calculated the values of H 0' (T ), Hi (T ) and H' (T ) (Fig. 14). As is seen from the figure, there is a good quantitative agreement between the experimental and theoretical temperature dependences of the critical fields for the metamagnetic phase transitions in the compounds. In particular, we analyzed the possibility of turning the
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23
Sm magnetic moments when magnetizing along the c-axis. In this case, expression (13) takes the following form: H 2Sm 1 0 ]] Hi ¯ H 2 2 ? H i 1 ]HA 2 HSm 2 HS 0 i
Fig. 13. Temperature dependences of saturation field HS (T ) and Sm molecular field HSm (T ) for La 0.75 Sm 0.25 Mn 2 Si 2 .
Fig. 14. Temperature dependences of critical fields of metamagnetic phase transitions parallel and perpendicular to the c-axis for La 0.75 Sm 0.25 Mn 2 Si 2 . The experimental data (symbols) and calculated curves in absent (dashed lines) and present (solid lines) molecular exchange field of Sm sublattice are shown.
S
D
(15)
and the calculated Hi values thus turn out to be lower than the experimental ones. We believe that the Sm moments in the compound have a large in-plane magnetic anisotropy and they remain in the ab-plane in magnetic fields H ,50 kOe. Fig. 15 shows the temperature dependences of the molecular fields of the interlayer Mn–Mn exchange interF action H AF Mn – Mn (T ), H Mn – Mn (T ) that were calculated using Eqs. (5) and (9) for different orientations of the Mn sublattice magnetizations. In the whole temperature range, the interlayer Mn–Mn coupling is less than the anisotropy field of the Mn sublattice. The difference between the F values of H AF Mn – Mn (T ) and H Mn – Mn (T ) decreases with lowering temperature, which may be due to a decrease in the lattice parameters. To analyze the dependences in detail, including the dependence of the interlayer Mn–Mn coupling on the lattice parameters of the compound, additional data on magnetostriction and temperature dependence of the lattice parameters are required. Thus, the existence of metamagnetic transitions in the compound can be explained under the assumption of a strong change in the Mn–Mn interlayer exchange coupling
Fig. 15. Temperature dependences of anisotropy field HA and molecular fields of interlayer Mn–Mn exchange interaction at AF, AF9 states F (H AF Mn – Mn ) and at field-induced F state (H Mn – Mn ) for La 0.75 Sm 0.25 Mn 2 Si 2 .
24
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scribe the metamagnetic transitions in other SmMn 2 Ge 2 type compounds as well.
3.4. Magnetoresistance in the La0.73 Sm0.27 Mn2 Si2 and La0.75 Sm0.25 Mn2 Si2 compounds
Fig. 16. Temperature dependences La 12x Sm x Mn 2 Si 2 (x50.25, 0.27).
of
electrical
resistance
for
with changing mutual orientation of the layer magnetizations. A peculiarity of the La 0.75 Sm 0.25 Mn 2 Si 2 compound, which determines the character of metamagnetic transitions in it, consists of the fact that the molecular field of the interlayer Mn–Mn exchange coupling is less or comparable in value with the field of the magnetic anisotropy. The model suggested can be applied to de-
The natural layered structure of the compounds RMn 2 X 2 enables us to consider them as a unique object for the verification and development of the theory on magnetoresistance in artificial multilayers. We investigated the magnetoresistance of polycrystals of the compounds La 0.73 Sm 0.27 Mn 2 Si 2 and La 0.75 Sm 0.25 Mn 2 Si 2 in the region of the AF→F magnetic phase transition. The spontaneous AF→F transition in these compounds is accompanied by a change in the electrical resistance (Fig. 16). As in the case of artificial multilayers, the antiferromagnetic Mn–Mn interlayer ordering corresponds to higher values of the electrical resistance in comparison to the case when all the layers are ordered ferromagnetically. The AF→F metamagnetic phase transition induced by a magnetic field is also accompanied by a jump-like change in the electrical resistance (Fig. 17a). The magnetic field strength at which a jump in the magnetoresistance curve is observed coincides with the value at which the metamagnetic phase transition appears in the magnetization curves measured along the c-axis (Fig. 17b). In Fig. 17a, two sets of the magnetoresistance curves are given. The first set which represents the highest values of magnetoresistance 2 DR /R 5 2 (R(H ) 2 R(H 5 0)) /R(H 5 0) ¯ 20–27% corresponds to the first reading. The second set of curves for which the magnetoresistance values 2 DR /R ¯ 6–10%, corresponds to subsequent measurements. In this case, the magnetoresistance values coincide with those of the electrical resistance changes at the spontaneous magnetic phase
Fig. 17. Magnetoresistance for La 0.75 Sm 0.25 Mn 2 Si 2 (open symbols) and La 0.73 Sm 0.27 Mn 2 Si 2 (closed symbols) at T5140 K (a). Two set of magnetoresistance curves coincide with first (1) and following (2) measurements. Magnetization curves parallel (circles) and perpendicular (squares) to the c-axis for La 0.75 Sm 0.25 Mn 2 Si 2 (open symbols) and La 0.73 Sm 0.27 Mn 2 Si 2 (closed symbols) at T5140 K (b).
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transition in the R(T ) dependence (Fig. 16). A decrease in the magnetoresistance value is likely to be caused by cracking of the massive polycrystalline samples because of the strong magnetoelastic deformations of the crystal lattice that the compounds undergo during the magnetic phase transition. Cracking of the samples leads to an increase in the electrical resistance R and, as consequence, to a decrease in the DR /R value. It may be expected for single crystals and films of the compounds that the values of magnetoresistance can be higher than 20–27%. The reason for the existence of a giant magnetoresistance in the compounds accompanying the phase transition AF→F remains unclear. As in artificial multilayers, it can be traceable to a decrease in the effective scattering of the conduction electrons on the ferromagnetically aligned magnetic moments of the Mn atoms. On the other hand, a decrease in the electrical resistance in the compounds accompanying the phase transition AF→F is likely to be related to the changes in the electronic band structure of the compounds because of strong changes in the lattice parameters that take place at the phase transition.
25
netic transition in magnetic fields directed both parallel and perpendicular to the easy-magnetization axis and the nonmonotonous temperature dependence of the critical fields of the metamagnetic transitions. The field-induced antiferromagnetic–ferromagnetic phase transitions in the compounds are described in the framework of a phenomenological theory taking into account the existence of magnetic anisotropy of the Mn sublattice, strong magnetoelastic deformations of the crystal lattice, and the dependence of the interlayer Mn–Mn exchange coupling on the parameters of the crystal lattice. In the compounds La 12x Sm x Mn 2 Si 2 with x50.25; 0.27, giant values of the magnetoresistance were detected in the region of the antiferromagnetic–ferromagnetic phase transition.
Acknowledgements This work was supported by Grant 72 of the 6th Concurs of the Russian Academy of Sciences (1999).
References 4. Conclusion The studies of the concentration changes in the magnetic properties of the La 12x Sm x Mn 2 Si 2 solid solutions carried out in this work confirm the interrelation, which is general for the RMn 2 X 2 compounds, between the type of magnetic ordering of the Mn magnetic moments located in adjacent layers of the crystal lattice and the distance between the nearest Mn atoms in the layer. The critical spacing at which the transition from ferromagnetic to antiferromagnetic interlayer ordering of Mn atoms in the La 12x Sm x Mn 2 Si 2 compounds takes place corresponds to the value d Mn – Mn ¯0.289 nm at room temperature which is close to the value d c ¯0.285–0288 nm observed earlier for other quasi-ternary intermetallic compounds of the R 12x R 9x Mn 2 X 2 type. In the La 12x Sm x Mn 2 Si 2 compounds with x50.25; 0.27, where d Mn – Mn ¯d c , a spontaneous and a field-induced change in the type of interlayer Mn–Mn magnetic ordering from antiferromagnetic to ferromagnetic is observed. The main features of the field-induced antiferromagnetic–ferromagnetic phase transition are the existence of metamag-
[1] A. Szytula, in: Handbook of Magnetic Materials, Vol. 6, Elsevier, Amsterdam, 1991, p. 85. [2] H. Fujii, T. Okamoto, T. Shigeoka, N. Iwata, Solid State Commun. 53 (8) (1985) 715. [3] H. Fujii, M. Isoda, T. Okamoto, T. Shigeoka, N. Iwata, J. Magn. Magn. Mater. 54–57 (1986) 1345. [4] G. Venturini, J. Alloys Comp. 232 (1996) 133. [5] J.H.V.J. Brabers, A.J. Nolten, F. Kayzel, S.H.J. Lenczowski, K.H.J. Buschow, F.R. de Boer, Phys. Rev. B 50 (1994) 16410. [6] J.H.V.J. Brabers, K.H.J. Buschow, F.R. de Boer, Phys. Rev. B 59 (14) (1999) 9314. [7] E.G. Gerasimov, M.I. Kurkin, A.V. Korolyov, V.S. Gaviko, Physica B, submitted. [8] C.J. Tomka, Cz. Kapusta, C. Ritter, P.C. Riedi, R. Cywinski, K.H.J. Buschow, J. Phys. B 230–232 (1997) 727. [9] M. Hoffmann, S.J. Campbell, S.J. Kennedy, X.L. Zhao, J. Magn. Magn. Mater. 176 (2–3) (1997) 279. [10] I. Nowik, Y. Levi, I. Felner, E.R. Bauminger, J. Magn. Magn. Mater. 147 (3) (1995) 373. [11] A. Szytula, S. Siek, J. Magn. Magn. Mater. 27 (1) (1982) 49. [12] G. Venturini, B. Malaman, E. Ressouche, J. Alloys Comp. 241 (1996) 135. [13] G. Guanghua, R.Z. Levitin, V.V. Snegirev, D.V. Filippov, Phys. Solid State 43 (2001) 496.