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Specific character of metamagnetic transitions in Fe2P
Journal of Magnetism and Magnetic Materials 43 (1984) 53-58 North-Holland, Amsterdam
53
SPECIFIC CHARACTER O F M E T A M A G N E T I C T R A N S I T I O N S IN Fe 2P E.A. ZAVADSKII, L.I. MEDVEDEVA and A.E. FILIPPOV Physico-Technical Institute, Academy of Sciences of the Ukrainian SSR, 340114 Donetsk, USSR Received 8 August 1983
Temperature and field dependences of magnetization in the fields directed along the easy axis of magnetization are studied on Fe2P single crystals under pressure. It is shown that the first-order magnetic transition from ferromagnetism to paramagnetism (FM-PM) usually observed in sufficiently strong fields can be resolved into two sequential transitions in weak fields ( H ~<600 Oe): 1) from the PM state to the intermediate metamagnetic phase and 2) transition to the low-temperature magnetic phase. The temperatures of these transitions undergo a specific evolution under pressure. A theoretical model, in which the characteristic features of magnetic behaviour of Fe 2P are associated with the successive additional ordering of magnetic components of its composition, is proposed.
1. Introduction It is known that in the fields a b o u t / a n d higher than 1 kOe, Fe2P demonstrates a first-order transition from the ferromagnetic to the paramagnetic state ( F M - P M ) [1,2]. With the pressure rising to P --- 14 kbar [3-5] and in the presence of 2-3 at% Mn impurity [6], this magnetic transition splits into two transitions with the formation of a metammagnetic (MM) phase between them, the magnetic structure of which is found to be noncollinear and incommensurable with crystalline lattice [6,7]. And the P M - M M transition is of second order while the M M - F M transition appears to be of first order. The studies of this transition at pressures less than those at which the pressure-induced metamagnetic (MM) state is observed, are of special interest for the elucidation of the mechanism of the P M - F M transformation in Fe 2 P and of its evolution with pressure. With that end in view, the temperature and field dependences of magnetization o are studied in the present work on single-crystal Fe2P samples at H II c (c-axis of the hexagonal lattice corresponds to the direction of easy magnetization).
2. Experimental Single crystals were grown by a thermal annealing of ingots at temperatures somewhat lower than the melting point, as described in ref. [8]. The Fe2P samples were oriented using the X-ray method. The specimens prepared for the measurements of magnetization were thin long rods of 0.3 × 0.3 x 1.5 mm 3 with the c-axis directed along the sample length. The study was carried out using the induction methods for the measurements of magnetization [9] within the temperature range from 4.2 to 250 K, in the fields 5 0 e ~
54
E.A. Zavadskii et al. / Metamagnetic transitions in Fe 2P
17,/~'~///////"~j; 20 401
200Oe
,,°t //__
_
_
Fig. 1. Temperature dependences of magnetization for Fe2P in different magnetic fields. Fig. 2. Temperature dependences of magnetization of Fe2P at different pressures.
the curve o ( T ) has a splash of the uniform magnetization component %=0, which is increased as 7 approaches T~, according to the scaling law o - IT - Tela with the critical exponent fl -- 0.35. This is usually associated with the second-order phase transition [10]. Against a background of this splash in the fields H = 10 Oe at T K = 177 K a new peak of magnetization appears and rapidly grows with increase of H. A temperature hysteresis of about 2 K observed near this peak allows consideration of its adequate transition as the first-order transition. Our investigation of the magnetic crystallographic anisotropy shows that K 1 decreases monotonously with increase of the temperature and K 2 equals zero within the interval 77 to 200 K. Therefore, the appearance of the peak in the curve o ( T ) at T K cannot be due to anisotropic properties but, most probably, corresponds to the transition between two magnetic states. Since, according to our measurements, the susceptibility (X = A o / A H ) is considerably lower near T K < T < Tc than at T < T K, the intermediate phase existing at T K < T < T~ can be interpreted as a metamagnetic one. Further growth of field results in smoothing the anomalies in the curve o ( T ) due to the existence of the M M phase. This process is illustrated by the figure from which it is seen that the separation into two peaks vanishes at first and then in the field of about 600 Oe the splash near T~ is fully hidden behind the magnetization growth of the low-temperature phase (lower than TK) so that only one transition can be observed, namely the first-order F M - P M transition. This very fact creates an illusion of an only first-order transition of order-disorder type in Fe2P at H > 1 kOe, while in reality it seems to be preceded in general, by the development of the phase transition to the metastable state. Application of external pressure leads to a specific evolution of magnetic phase transitions in Fe 2P. As pressure grows, T¢ is decreased more rapidly than T K (fig. 2) (aTjaP = - 6 . 5 K / k b a r ; ~TK/aP---- --1.5 K / k b a r ) , therefore, in some pressure interval (3 kbar _< P ~< 5 kbar) both peaks practically merge and in the curve o(T) only one maximum is observed. When T is fixed, o drops sharply (by a factor of 1.7) within this pressure range and the susceptibility has a local minimum (Ax/X = 0.8). At P = 5.5 kbar the transition splits again into two ones, at T N and TK, the absolute values of newly formed maxima being considerably lower than those at P = 0. The figure presents the dependence o(T) only at cooling. The run of the curve o(T) at heating is given for one pressure only. The hysteresis observed at T K shows that this is a first-order
E.A. Zavadskii et a L /
7-,/( 2OO ~M,~P~
Metamagnetic transitions in Fe2P
55
tt =lOOe
-
H=IOkOe
5
•
t0
Fig. 3. P - T
p h a s e d i a g r a m s f o r F e 2 P a t H = 10 O e a n d H = 10 k O e .
transition. The transition at TN is not accompanied by a hysteresis. The susceptibility of the metamagnetic phase, stable in the temperature range T~ < T < Try, is less than 2% of that at zero pressure (the phase at
TK
3. Discussion Fe I P has a hexagonal structure with two crystallographic nonequivalent sites of magnetic atoms Fe I and Fe 2 [11]. Changes in the character of phase transitions in Fe2P with field and under pressure can be explained by the difference in the behavior of the exchange-interaction energy between the corresponding nonequivalent atoms Fe: jl1, j22 and j12 =j21. Let us proceed from the Heisenberg Hamiltonian for classical moments in the form
(I)
.,~= - ½ E ~-~(n-:n:,"- E H:n-~, I1"
jl
_0"
where / and l' run over all the crystal cells, and the presence of two nonequivalent types of magnetic atoms, Fe I and Fe2, with moments M1 and M2, respectively, is taken into account by introducing an additional index j = 1.2. Here (nJ) z = 1 and the difference between IM~I and IM21 is accounted by redetermination of the exchange integrals ~J4' and the magnetic field H j = MjH. The partition function can be written in the form of the functional integral
Z - I-[ f dnff Dk/ exp lj"
"
-
~ K / - i ~., xJJ'"J'-J ,tll,,~l,r~ I + -f Y~n]H j "
II'jj"
lj
1 j
56
E . A . Z a o a d s k i i et al. / M e t a m a g n e t i c transitions in F e 2 P
Here, taking into account~ . .that the Hamiltonian (1) is obtained with an accuracy up to an arbitrary constanl and, thus, the values of Jff can be chosen arbitrarily, the matrices must satisfy the condition E )t JJ?tJJ"
.
- -
.
.
.
.
+s:Jy)
~-
"
.
~ .
.
jj"
j
Further, it is convenient to make a formal shift K / = K / + 4~ with the requirement H J / T = 1 E htl'Kl' I'j'
=
- i Y~ ',tr--t )tJJ'~J"
so that after the integration over nix the expression for the partition function is
I'j'
.
I
jj,~j,
sinh - 1E Xn'Kr
z - SDKiexp - ~ T (Ri2 + 2RiA{ +'a{:)+
,
-i~X~,'ki"v' l'j'
1] .
(2)
Expression (2) is formally exact. Since the magnetization o is small near the point of phase transition it can serve as.a parmeter in the. free-energy F = _-. T In Z expansion. On the other hand, since AJ - H j and, in its turn, o / - 8 F I S H J - K/, the values of K / may be taken as the components of the order parameter, Expanding now eq. (2) in powers of J~/ up to the terms of the order of ~ ( K 4) and proceeding to the Fourier-representation over the variables ! - l' we obtain
F
¥={E
(
J}J'~ -
T
3Jl/%1 + 5- E(I,aDI + 2AJ_q/ ) +
qff" ~
(3)
jq
The terms with AJ can be neglected in the weak uniform field H J ~q.oMJno . And from formula (3) it is seen that the stability of a paramagnetic phase at a temperature decrease is violated for the first time for those modes of KqJ whose form -
j j/,
F° =
--T
{ qg", E ~jj,T -- -q i K J K f 3 ]--q---q
(4)
for the first time changes the sign of F ( T = T~)= 0. There are two independent possibilities to meet this requirement. The first of them is certainly a method of simultaneous ordering of both components j~l and k 2, at which the system chooses some compromise magnetic structure at once, is condensed in it, and then suffers no subsequent transitions. However, there is another method of ordering, at which F0 first changes its sign at nonzero either k ~ or k 2 separately. Physically it corresponds to the initial ordering of only one type of magnetic moments in the presence of chaotic orientation of moments of another type. They form some magnetic structure, o t - K q0i i exp(iqoil ), which, generally speaking, is noncollinear and incommensurate with the lattice (here k I ~ 0, k 2 = 0 for exactness). Its wave vectors q0, corresponds to the positions of the Fourier-image maxima of the exchange integral in the Brilloin zone, which are equivalent with relation to the transformations of the lattice symmetry group. Since in the absence of temperature fluctuations at T = 0 both subsystems of magnetic atoms should be ordered, there must be another critical temperature at which an additional ordering of the components of magnetization occurs. This transition should possess some peculiarities. Firstly, the order-order transition will take place in the first subsystem due to the fact that the system as a whole will choose some compromise magnetic structure at the additional ordering of the second-type moments. Secondly, if both transitions are sufficiently scattered in temperature, the condensed modes k q0i 1 at T = Tc will be macroscopically great and have equilibrium values determined by the equation ( g aq0i g i - - q o i j q0i/"~/2 = Jqo L[(/~q~oi [(1 qoi Jqoi )WE]/T, where L is the Langevin function. Hence, the transition at i
--
E.A. Zavadskii et aL/ Metamagnetictransitions in Fe2P
57
T K should proceed as a first-order transition starting directly from the noninfinitesimal E2. and E~^, ~ 1 ~ 2 ~un whose contribution to free energy for the first time appears to be higher than that at gqo ~~ 0 _v.and Kq -- 0, respectively. Within the lowest approximation the equation for T K is
E
jj, ,
¢~jj'TK
q°nlgJ E j qoi 3 J qo. -qon = T K - T
E1
El
qo, --qoi"
(5)
This should be supplemented with two equations for E~'/On : OF/OEZ = 0. Their joint solution is bulky and , "/On senseless in the absence of complete information on integrals dq)J. Qualitative conclusions, however, can be drawn directly from relation (5). It is mentioned above that the Fe2P sample is comparatively easy magnetized at P = 0 and T K < T < T¢, so that 0/ seems to form a long-wave spiral easily destroyed by the external field and, therefore, the maxima q0i of integral j q l l a r e near q = 0. Further, according to the results of refs. [12,13] the exchange j22 is considerably weaker than two other types of exchange (at P = 0) and the main role in additional ordering K2oo is played by the ferromagnetic exchange F e l - F e 2. Thus, the condition (5) is readily satisfied at qon --- 0 and the formed structure is easily magnetized. However, this structure is not, strictly speaking, purely ferromagnetic, since the sample at T < T K does not possess a homogeneous component of magnetization. We interpret it as quasiferromagnetic (quasi-FM) just in case of its proximity to q = 0 and relative easiness of its magnetization by the external field. From fluctuations of Oq in the vicinity of T¢ the magnetic field singles out a homogeneous component ~'q-0 and intensifies it (%=0 - Hq~o, eq. (3)). Owing to this fact the splash of magnetization associated with the second transition in Fe2P becomes noticeable against a background of its flucutations near T¢just at a certain minimum field H >_ 10 Oe. On the other hand, as H grows the magnetization at T = T K is increased so rapidly that in the fields H = 0.6 to 1 kOe it covers the fluctuation splash near T¢ completely. And the transition becomes a pure ferromagnetic first-order transition. However, it cannot be asserted for sure that this is a first-order transition of the order-disorder type. In fact, this transition is always preceded by the transition to the metamagnetic (MM~) phase, whose development resembles the second-order phase transition. The fact that this transition does not manifest itself in magnetization curves in the field H < 5 0 e is due to a weak scatter of both transitions in temperature (at P = 0). Nevertheless, its existence is proved by the experiments on the study of spin-wave excitations in FeEP [7] which evidence the presence of one-dimensional "ferromagnetic chains" along the c-axis of easy magnetization, they being present above the ferromagnetic-ordering temperature ( T K) either. And the two-dimensional magnetic order in the perpendicular plane suffers considerably changes at T K (due to which, in particular, the three-dimensional structure above T K is destroyed). Apparently, " a domestic disorder" for the MM 1 phase is observed here, which seems to be "a foreign disorder" for the phase lying below T K in sufficiently strong fields. The effect of pressure (and impurities Mn and Ni, respectively [6,]1,12]) on JJJ" is twofold. Firstly, it changes the distances between the magnetic moments, which in itself distorts J~J" even at unchanged spatial dispersion of Jt~(, and secondly, the lattice distortion under pressure changes this very spatial dispersion of JJJ" itself [14]. Since Tc is determined by jql2 and rapidly drops with the growth of P or impurity quantity (fig. 3), a consistent result of the pressure effect leads, therefore, to a lowering of maxima of jqn. The temperature of the second transition, T K, is decreased slower, so that both transitions practically merge at P = 3 kbar. Essentially, this means that only one transition which consists in simultaneous ordering of both mgnetic components is preserved. This transition is accompanied by a very wide fluctuation region, which results in a considerable anomaly of susceptibility in an intermediate pressure range (PF phase). At P -- 6.5 kbar the Fe~-Fe 1 exchange is so weak that the initial FeE-Fe 2 ordering (at T = TN) turns out to be more advantageous. The transition splits again thus forming an intermediate metamagnetic phase MM 2 (T~ < T < Tr~). The neutron-diffraction experiments on the analogous phase induced in (Fe0.97Mn0.03)EP at T = 77 K evidence the formation of an incommensurate antiferromagnetic spiral extending along the (110)
58
E.A. Zaoadskii et al. / Metamagnetic transitions in Fe2P
direction in the plane .1_ to c with period 79 A [6]. The susceptibility of this structure is much lower along c-axis than that of long-wave "ferromagnetic chains" and is 0.02 of the latter. In conclusion we note that Fe2P does not seem to be the only substance where the reciprocal transitions between magnetic phases are due to a successive "reordering" of different magnetic components of their composition connected with different behaviour in the energies of exchange interaction between nonequivalent magnetic moments.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14]
L. Lundgren, G. Tarmohamed, O. Beckman, B. Carlsson and S. Rundqvist, Phys. Scripta 17 (1978) 39. R. W~ippling, L. H~iggstr6m, T. Ericsson, S. Devanarayanan and E. Karlsson, J. Solid State Chem. 13 (1975) 258. L.I. Medvedeva, Fiz. Tverd. Tela 23 (1981) 3682. L.I. Medvedeva, Fiz. Tverd. Tela 24 (1982) 322. H. Kadomatsu, K. Tohma, H. Fujii, T. Okamoto and H. Fujiawara, Phys. Lett. 84A (1981) 442. H. Fujii, T. Hokabe, K. Eguchi, H. Fujiwara and T. Okamoto, J. Phys. Soc. Japan 51 (1982) 414. S. Komura, K. Tajima, H. Fujii, Y. Yshikawa and T. Okamata, J. Magn. Magn. Mat. 15-18 (1980) 351. H. Fujii, T. Hokabe, T, Kamigachi and T. Okamoto, J. Phys. Soc. Japan 43 (1977) 41. H. Fujiwara, H. Kadomatsu, K. Tohma, H. Fujii and T. Okamoto, J. Magn. Magn. Mat. 21 (1980) 262. S. Ma, Modem Theory of Critical Phenomena (Benjamin, New York, 1976). R. Fruchart, A, Roger and J.P, Senateur, J. Appl. Phys. 40 (1969) 1252. H. Fujii, T. Hokabe, H. Fujiwara and T. Okarnoto, J. Phys. Soc. Japan 44 (1978) 96. H. Fujii and T. Okamoto, J. Phys. Soc. Japan 49 (1980) 419. H. Fujiwara, H. Kadomatsu and K. Tohma, J. Phys. Soc. Japan 51 (1982) 1401.
53
SPECIFIC CHARACTER O F M E T A M A G N E T I C T R A N S I T I O N S IN Fe 2P E.A. ZAVADSKII, L.I. MEDVEDEVA and A.E. FILIPPOV Physico-Technical Institute, Academy of Sciences of the Ukrainian SSR, 340114 Donetsk, USSR Received 8 August 1983
Temperature and field dependences of magnetization in the fields directed along the easy axis of magnetization are studied on Fe2P single crystals under pressure. It is shown that the first-order magnetic transition from ferromagnetism to paramagnetism (FM-PM) usually observed in sufficiently strong fields can be resolved into two sequential transitions in weak fields ( H ~<600 Oe): 1) from the PM state to the intermediate metamagnetic phase and 2) transition to the low-temperature magnetic phase. The temperatures of these transitions undergo a specific evolution under pressure. A theoretical model, in which the characteristic features of magnetic behaviour of Fe 2P are associated with the successive additional ordering of magnetic components of its composition, is proposed.
1. Introduction It is known that in the fields a b o u t / a n d higher than 1 kOe, Fe2P demonstrates a first-order transition from the ferromagnetic to the paramagnetic state ( F M - P M ) [1,2]. With the pressure rising to P --- 14 kbar [3-5] and in the presence of 2-3 at% Mn impurity [6], this magnetic transition splits into two transitions with the formation of a metammagnetic (MM) phase between them, the magnetic structure of which is found to be noncollinear and incommensurable with crystalline lattice [6,7]. And the P M - M M transition is of second order while the M M - F M transition appears to be of first order. The studies of this transition at pressures less than those at which the pressure-induced metamagnetic (MM) state is observed, are of special interest for the elucidation of the mechanism of the P M - F M transformation in Fe 2 P and of its evolution with pressure. With that end in view, the temperature and field dependences of magnetization o are studied in the present work on single-crystal Fe2P samples at H II c (c-axis of the hexagonal lattice corresponds to the direction of easy magnetization).
2. Experimental Single crystals were grown by a thermal annealing of ingots at temperatures somewhat lower than the melting point, as described in ref. [8]. The Fe2P samples were oriented using the X-ray method. The specimens prepared for the measurements of magnetization were thin long rods of 0.3 × 0.3 x 1.5 mm 3 with the c-axis directed along the sample length. The study was carried out using the induction methods for the measurements of magnetization [9] within the temperature range from 4.2 to 250 K, in the fields 5 0 e ~
54
E.A. Zavadskii et al. / Metamagnetic transitions in Fe 2P
17,/~'~///////"~j; 20 401
200Oe
,,°t //__
_
_
Fig. 1. Temperature dependences of magnetization for Fe2P in different magnetic fields. Fig. 2. Temperature dependences of magnetization of Fe2P at different pressures.
the curve o ( T ) has a splash of the uniform magnetization component %=0, which is increased as 7 approaches T~, according to the scaling law o - IT - Tela with the critical exponent fl -- 0.35. This is usually associated with the second-order phase transition [10]. Against a background of this splash in the fields H = 10 Oe at T K = 177 K a new peak of magnetization appears and rapidly grows with increase of H. A temperature hysteresis of about 2 K observed near this peak allows consideration of its adequate transition as the first-order transition. Our investigation of the magnetic crystallographic anisotropy shows that K 1 decreases monotonously with increase of the temperature and K 2 equals zero within the interval 77 to 200 K. Therefore, the appearance of the peak in the curve o ( T ) at T K cannot be due to anisotropic properties but, most probably, corresponds to the transition between two magnetic states. Since, according to our measurements, the susceptibility (X = A o / A H ) is considerably lower near T K < T < Tc than at T < T K, the intermediate phase existing at T K < T < T~ can be interpreted as a metamagnetic one. Further growth of field results in smoothing the anomalies in the curve o ( T ) due to the existence of the M M phase. This process is illustrated by the figure from which it is seen that the separation into two peaks vanishes at first and then in the field of about 600 Oe the splash near T~ is fully hidden behind the magnetization growth of the low-temperature phase (lower than TK) so that only one transition can be observed, namely the first-order F M - P M transition. This very fact creates an illusion of an only first-order transition of order-disorder type in Fe2P at H > 1 kOe, while in reality it seems to be preceded in general, by the development of the phase transition to the metastable state. Application of external pressure leads to a specific evolution of magnetic phase transitions in Fe 2P. As pressure grows, T¢ is decreased more rapidly than T K (fig. 2) (aTjaP = - 6 . 5 K / k b a r ; ~TK/aP---- --1.5 K / k b a r ) , therefore, in some pressure interval (3 kbar _< P ~< 5 kbar) both peaks practically merge and in the curve o(T) only one maximum is observed. When T is fixed, o drops sharply (by a factor of 1.7) within this pressure range and the susceptibility has a local minimum (Ax/X = 0.8). At P = 5.5 kbar the transition splits again into two ones, at T N and TK, the absolute values of newly formed maxima being considerably lower than those at P = 0. The figure presents the dependence o(T) only at cooling. The run of the curve o(T) at heating is given for one pressure only. The hysteresis observed at T K shows that this is a first-order
E.A. Zavadskii et a L /
7-,/( 2OO ~M,~P~
Metamagnetic transitions in Fe2P
55
tt =lOOe
-
H=IOkOe
5
•
t0
Fig. 3. P - T
p h a s e d i a g r a m s f o r F e 2 P a t H = 10 O e a n d H = 10 k O e .
transition. The transition at TN is not accompanied by a hysteresis. The susceptibility of the metamagnetic phase, stable in the temperature range T~ < T < Try, is less than 2% of that at zero pressure (the phase at
TK
3. Discussion Fe I P has a hexagonal structure with two crystallographic nonequivalent sites of magnetic atoms Fe I and Fe 2 [11]. Changes in the character of phase transitions in Fe2P with field and under pressure can be explained by the difference in the behavior of the exchange-interaction energy between the corresponding nonequivalent atoms Fe: jl1, j22 and j12 =j21. Let us proceed from the Heisenberg Hamiltonian for classical moments in the form
(I)
.,~= - ½ E ~-~(n-:n:,"- E H:n-~, I1"
jl
_0"
where / and l' run over all the crystal cells, and the presence of two nonequivalent types of magnetic atoms, Fe I and Fe2, with moments M1 and M2, respectively, is taken into account by introducing an additional index j = 1.2. Here (nJ) z = 1 and the difference between IM~I and IM21 is accounted by redetermination of the exchange integrals ~J4' and the magnetic field H j = MjH. The partition function can be written in the form of the functional integral
Z - I-[ f dnff Dk/ exp lj"
"
-
~ K / - i ~., xJJ'"J'-J ,tll,,~l,r~ I + -f Y~n]H j "
II'jj"
lj
1 j
56
E . A . Z a o a d s k i i et al. / M e t a m a g n e t i c transitions in F e 2 P
Here, taking into account~ . .that the Hamiltonian (1) is obtained with an accuracy up to an arbitrary constanl and, thus, the values of Jff can be chosen arbitrarily, the matrices must satisfy the condition E )t JJ?tJJ"
.
- -
.
.
.
.
+s:Jy)
~-
"
.
~ .
.
jj"
j
Further, it is convenient to make a formal shift K / = K / + 4~ with the requirement H J / T = 1 E htl'Kl' I'j'
=
- i Y~ ',tr--t )tJJ'~J"
so that after the integration over nix the expression for the partition function is
I'j'
.
I
jj,~j,
sinh - 1E Xn'Kr
z - SDKiexp - ~ T (Ri2 + 2RiA{ +'a{:)+
,
-i~X~,'ki"v' l'j'
1] .
(2)
Expression (2) is formally exact. Since the magnetization o is small near the point of phase transition it can serve as.a parmeter in the. free-energy F = _-. T In Z expansion. On the other hand, since AJ - H j and, in its turn, o / - 8 F I S H J - K/, the values of K / may be taken as the components of the order parameter, Expanding now eq. (2) in powers of J~/ up to the terms of the order of ~ ( K 4) and proceeding to the Fourier-representation over the variables ! - l' we obtain
F
¥={E
(
J}J'~ -
T
3Jl/%1 + 5- E(I,aDI + 2AJ_q/ ) +
qff" ~
(3)
jq
The terms with AJ can be neglected in the weak uniform field H J ~q.oMJno . And from formula (3) it is seen that the stability of a paramagnetic phase at a temperature decrease is violated for the first time for those modes of KqJ whose form -
j j/,
F° =
--T
{ qg", E ~jj,T -- -q i K J K f 3 ]--q---q
(4)
for the first time changes the sign of F ( T = T~)= 0. There are two independent possibilities to meet this requirement. The first of them is certainly a method of simultaneous ordering of both components j~l and k 2, at which the system chooses some compromise magnetic structure at once, is condensed in it, and then suffers no subsequent transitions. However, there is another method of ordering, at which F0 first changes its sign at nonzero either k ~ or k 2 separately. Physically it corresponds to the initial ordering of only one type of magnetic moments in the presence of chaotic orientation of moments of another type. They form some magnetic structure, o t - K q0i i exp(iqoil ), which, generally speaking, is noncollinear and incommensurate with the lattice (here k I ~ 0, k 2 = 0 for exactness). Its wave vectors q0, corresponds to the positions of the Fourier-image maxima of the exchange integral in the Brilloin zone, which are equivalent with relation to the transformations of the lattice symmetry group. Since in the absence of temperature fluctuations at T = 0 both subsystems of magnetic atoms should be ordered, there must be another critical temperature at which an additional ordering of the components of magnetization occurs. This transition should possess some peculiarities. Firstly, the order-order transition will take place in the first subsystem due to the fact that the system as a whole will choose some compromise magnetic structure at the additional ordering of the second-type moments. Secondly, if both transitions are sufficiently scattered in temperature, the condensed modes k q0i 1 at T = Tc will be macroscopically great and have equilibrium values determined by the equation ( g aq0i g i - - q o i j q0i/"~/2 = Jqo L[(/~q~oi [(1 qoi Jqoi )WE]/T, where L is the Langevin function. Hence, the transition at i
--
E.A. Zavadskii et aL/ Metamagnetictransitions in Fe2P
57
T K should proceed as a first-order transition starting directly from the noninfinitesimal E2. and E~^, ~ 1 ~ 2 ~un whose contribution to free energy for the first time appears to be higher than that at gqo ~~ 0 _v.and Kq -- 0, respectively. Within the lowest approximation the equation for T K is
E
jj, ,
¢~jj'TK
q°nlgJ E j qoi 3 J qo. -qon = T K - T
E1
El
qo, --qoi"
(5)
This should be supplemented with two equations for E~'/On : OF/OEZ = 0. Their joint solution is bulky and , "/On senseless in the absence of complete information on integrals dq)J. Qualitative conclusions, however, can be drawn directly from relation (5). It is mentioned above that the Fe2P sample is comparatively easy magnetized at P = 0 and T K < T < T¢, so that 0/ seems to form a long-wave spiral easily destroyed by the external field and, therefore, the maxima q0i of integral j q l l a r e near q = 0. Further, according to the results of refs. [12,13] the exchange j22 is considerably weaker than two other types of exchange (at P = 0) and the main role in additional ordering K2oo is played by the ferromagnetic exchange F e l - F e 2. Thus, the condition (5) is readily satisfied at qon --- 0 and the formed structure is easily magnetized. However, this structure is not, strictly speaking, purely ferromagnetic, since the sample at T < T K does not possess a homogeneous component of magnetization. We interpret it as quasiferromagnetic (quasi-FM) just in case of its proximity to q = 0 and relative easiness of its magnetization by the external field. From fluctuations of Oq in the vicinity of T¢ the magnetic field singles out a homogeneous component ~'q-0 and intensifies it (%=0 - Hq~o, eq. (3)). Owing to this fact the splash of magnetization associated with the second transition in Fe2P becomes noticeable against a background of its flucutations near T¢just at a certain minimum field H >_ 10 Oe. On the other hand, as H grows the magnetization at T = T K is increased so rapidly that in the fields H = 0.6 to 1 kOe it covers the fluctuation splash near T¢ completely. And the transition becomes a pure ferromagnetic first-order transition. However, it cannot be asserted for sure that this is a first-order transition of the order-disorder type. In fact, this transition is always preceded by the transition to the metamagnetic (MM~) phase, whose development resembles the second-order phase transition. The fact that this transition does not manifest itself in magnetization curves in the field H < 5 0 e is due to a weak scatter of both transitions in temperature (at P = 0). Nevertheless, its existence is proved by the experiments on the study of spin-wave excitations in FeEP [7] which evidence the presence of one-dimensional "ferromagnetic chains" along the c-axis of easy magnetization, they being present above the ferromagnetic-ordering temperature ( T K) either. And the two-dimensional magnetic order in the perpendicular plane suffers considerably changes at T K (due to which, in particular, the three-dimensional structure above T K is destroyed). Apparently, " a domestic disorder" for the MM 1 phase is observed here, which seems to be "a foreign disorder" for the phase lying below T K in sufficiently strong fields. The effect of pressure (and impurities Mn and Ni, respectively [6,]1,12]) on JJJ" is twofold. Firstly, it changes the distances between the magnetic moments, which in itself distorts J~J" even at unchanged spatial dispersion of Jt~(, and secondly, the lattice distortion under pressure changes this very spatial dispersion of JJJ" itself [14]. Since Tc is determined by jql2 and rapidly drops with the growth of P or impurity quantity (fig. 3), a consistent result of the pressure effect leads, therefore, to a lowering of maxima of jqn. The temperature of the second transition, T K, is decreased slower, so that both transitions practically merge at P = 3 kbar. Essentially, this means that only one transition which consists in simultaneous ordering of both mgnetic components is preserved. This transition is accompanied by a very wide fluctuation region, which results in a considerable anomaly of susceptibility in an intermediate pressure range (PF phase). At P -- 6.5 kbar the Fe~-Fe 1 exchange is so weak that the initial FeE-Fe 2 ordering (at T = TN) turns out to be more advantageous. The transition splits again thus forming an intermediate metamagnetic phase MM 2 (T~ < T < Tr~). The neutron-diffraction experiments on the analogous phase induced in (Fe0.97Mn0.03)EP at T = 77 K evidence the formation of an incommensurate antiferromagnetic spiral extending along the (110)
58
E.A. Zaoadskii et al. / Metamagnetic transitions in Fe2P
direction in the plane .1_ to c with period 79 A [6]. The susceptibility of this structure is much lower along c-axis than that of long-wave "ferromagnetic chains" and is 0.02 of the latter. In conclusion we note that Fe2P does not seem to be the only substance where the reciprocal transitions between magnetic phases are due to a successive "reordering" of different magnetic components of their composition connected with different behaviour in the energies of exchange interaction between nonequivalent magnetic moments.
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