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NMR study of prssure-induced magnetic transition in EuSe
Solid State Communications, Vol. 52, No. 4, pp. 4 7 9 - 4 8 4 , 1984. Printed in Great Britain.
0038-1098/84 $3.00 + .00 Pergamon Press Ltd.
NMR STUDY OF PRESSURE-INDUCED MAGNETIC TRANSITION IN EuSe K. Hiraoka,* T. Hihara] K. Kojima t and T. Kino Faculty of Science, Hiroshima University, Hiroshima 730, Japan
(Received 4 June 1984 by J. Kanamori) The zero-field tS3EuNMR in EuSe has been observed as a function of the pressure up to 14kbar in the temperature range between 1.7 and 4.2 K. A sequent magnetic phase transition of NSNS-NNS--NNSS-NNN occurs with pressure at 1.7 K. In the NNSS state (2.0 <~P <~4.8 kbar) the NMR frequency u is insensitive to the pressure. In the ferromagnetic state (P ~>4.8 kbar) u depends remarkably on the pressure, and the exchange interaction between the nearest Eu neighbours J~ is shown to increase rapidly with decreasing the E u - E u distance. The pressure dependences of the Eu hyperfine field suggest that the magnetic moment of a Eu 2÷ ion in the ferromagnetic state under pressure is smaller than the ideal saturation value at 0 K.
1. INTRODUCTION EuSe, HAVING the NaC1 crystal structure, shows various magnetic structures such as NSNS, NNS and NNSS below TN = 4.6 K [1,2]. The mechanism of the phase transition is an interesting problem. The complex magnetic phases of EuSe are considered to be primarily due to J~ = -- J : , where Jl and J2 are the ferromagnetic nearest and antiferromagnetic next nearest neighbour exchange constants, respectively. In the previous work [3] the effect of the variation of the interatomic distance on the magnetic phases of EuSe was investigated by measuring the a.c. susceptibility under pressure. It was found that EuSe shows a magnetic transition from the antiferro- to ferromagnetic state at about 4.8 kbar. This paper presents the results of a NMR investigation on the pressure-induced phase transition in EuSe. 2. EXPERIMENTAL A polycrystalline sample was used, which was prepared by heating a pressed pellet of EuSe powder in an enclosed tantalum crucible at 1700 ° C. NMR measurements were mostly made by continuous wave method with a FM marginal oscillator and were made under pressure up to 14 kbar in the temperature range between 1.7 and 4.2 K. The hydrostatic pressure was generated by the clamp cell method. The pressure cell is almost the same as that described by Fujiwara et al. [4] except for the electrical feedthrough. A pair of conventional cones
soldered on Cu wires were used as r.f. electrical feedthroughs, and their insulation from an electrode plug was achieved with epoxy resin. A sample cavity of teflon bucket, in which a r.f. coil was placed, was filled with a 1 : 1 mixture of n-penthane and isoamyle alcohol as force transmitting medium. With a FM marginal oscillator the cell was successfully used under pressure up to 15 kbar in the frequency range below 400 MHz at liquid helium temperature. The pressure in the sample cavity was measured by using the pressure dependences of the lS3Eu and 59CoNMR frequencies in ferromagnetic EuO and f.c.c. Co, respectively, which were calibrated by the pressure shift of the superconducting transition temperature of Sn. By placing a few ten milligrams of EuO or f.c.c. Co, together with the sample, in the sample coil, the pressure was easily determined with an accuracy of-+ 0.2 kbar. Detailed description of the pressure cell and pressure gauge will be given elsewhere. 3. RESULTS Figure 1 shows the lineshapes of the zero-field lS3Eu NMR in EuSe under various pressures P at 1.7 K. At P = 0 the lSaEu NMR spectrum consists of three lines. A small hump at 117.7 MHz is assigned to the NSNS phase, and the peaks at 118.4 and 129.6 MHz come from the nuclei on the S and N sites of the NNS structure, respectively (denoted by NNS and NNS) [5]. The NMR coming from the NNSS phase occurs at nearly the same frequency as that of the NN_S line. As the pressure is increased, the NSNS line disappears at a low pressure, an two NMR of the NNS phase are observed at 1.5 kbar. In the spectra at 3 and 4kbar only the NMR at 129.6 MHz is observed, which is assigned to the NNSS
* Mailing address: Faculty of Integrated Arts and Sciences, Hiroshima University, Hiroshima 730, Japan. t Faculty of Integrated Arts and Sciences, Hiroshima University, Horishima 730, Japan. 479
480
Vol. 52, No. 4
PRESSURE-INDUCED MAGNETIC TRANSITION IN EuSe 140
EuSe 153EuNMR T=I.TK
NNN
EuSe m3EuNMR
136 132
128 124 ~12(
\ o 4.5 k b o r ]
11
3.6 x 2.2 • 1.4
108
\ ~\
~
J
NNSS
~\
\~,,.
NNS
104 10( ~
~" "
~ 0
:2 '
~
'
6
' e, ' 1'0 ' 1'2 ' lZ, ' 16 T 2(K2)
kbor
110 115 1:20 1½5 1:30 135 140 }) (MHz)
145 150
155
Fig. 2. Temperature dependences of the ~SaEu NMR frequencies at various pressures in the NNSS and NNS states. The broken curve represents the result for the NNS line at P = 0.
Fig. 1. Line shapes (first derivative) of the zero-field lS3Eu NMR in EuSe under various pressures at 1.7 K. phase. Another NMR appears on the high frequency side of the NNSS line at 4.6 kbar, and only the NMR is observable above about 5 kbar. This NMR is assigned to the ferromagnetic (NNN) phase, because the results of a.c. susceptibility measurements under pressure suggest the ferromagnetic order above 4.8 kbar [3]. These NMR results show that the NSNS-NNS, NNS NNSS and N N S S - N N N phase transitions successively occur with increasing the pressure. The zero-field lS3Eu NMR frequencies ~, at various pressures were measured as a function of the temperature, and the results for the NNSS (NNS) and NNN lines are shown in Figs. 2 and 3, respectively. At 4.8 kbar the NNN line became much weaker below 2.5 K with lowering the temperature owing to the N N N - N N S S phase transition at 2.5 K, which is suggested by the a.c. susceptibility result [3]. The temperature dependences of the NMR frequency u(T) at three pressures in the NNSS state follow the T 2 law and agree among them within the experimental error, u(T) for the NNS line at 1.4 kbar exhibits also a T 2 dependence. The values of u extrapolated to 0 K for the NNSS and NNS lines are equal to each other and are 134.2(1)MHz, which corresponds to an effective magnetic field H i = -289.7(2) kOe at Eu nuclei (~s37/27r = 0.4632 MHz/kOe).
)~
EuSe ~3Eu NMR
15C i
1461 14~
13B 134 "1-
3;130 126 1221-
4.8
118
114 r
,o~
\ \ 5.7\
.
~
.
~.
' 6 T 3~ ( K 3~2)
°o~ 7.3 '
8
'
1'o
Fig. 3. Temperature dependences of the lS3Eu NMR frequency at various pressures in the ferromagnetic state.
Vol. 52, No. 4
155
481
PRESSURE-INDUCED MAGNETIC TRANSITION IN EuSe
0.06
EuSe OEu NMR
330
OK
15C 320
0.05
1.7 K
145
310
,.-,,14C -~135
"~o .04 o~ •
290 -i= I
0.03 131
1.7~ :
280
12
2.5K
2?0 0.03
12 11
3.oK • '
:
260
=:
~ 'Z'
'g'1o I?
25O 14
0
' ½ ' }* ' 6
' 8 ' 1'0 ' 1'2 ' 1'4 ' 16 P (kbor)
Fig. 5. The exchange constant Je = J1 -t- J2 as a function of the pressure. The value at P = 0 ( 4 ) i s taken from [1 ].
P (kbor)
Fig. 4. Pressure dependences o f the lS3Eu NMR frequency at various temperatures.
0.12 0.11 0.1(
In the ferromagnetic state v(T) largely depend on pressure, but they are well described by the T 3/2 dependence. By fitting the data to the spin wave relation of v ( T ) = Po(1 - - CT3/2), the values of Vo and C are determined as a function of the pressure. Figure 4 shows the pressure dependences of p at some typical temperatures, which are deduced from the results shown in Figs. 2 and 3. The frequencies of the NNSS and NNS lines are nearly independent of the pressure; a careful measurement at 1.7 K resulted in (au/aP)T <~ ± 5 X 10 -3 MHz/kbar, corresponding to (aHi/~P)T <~+-0.01 kOe/kbar. In the ferromagnetic state, on the other hand, v increases rather rapidly with increasing the pressure, the rate of the increase being larger at lower pressures. The slope of (av/aP)7,=o at OK is 0.40 and 0.21 MHz/kbar at 5 and 14kbar, respectively, corresponding to (~Hi/aP)7,=o = - 0.86 and -- 0.45 kOe/kbar. These values are nearly equal to (aHi/aP)T=o = -- 0.7~0.4 kOe/kbar at P = 14~27 kbar in the ferromagnetic state o f Euo.99Sno.ol Se, which was obtained by the lSlEu M6ssbauer measurement under pressure [6]. An extrapolation o f the u vs P curve to P = 0, which is shown by the broken curve in Fig. 4, results in Uo = 146.5(3)MHz at 0 K. The corresponding effective field is Hi = -- 316.3(6)kOe, which also agrees with the M6ssbauer value o f - - 315 kOe. The constant C in the Bloch T 3/2 law is related to the exchange constantsJ~ and J2 Using a quadratic spin wave dispersion law for small k values and neglecting the
0.5 0.0~ o.o
O.OE o
0.~
oo o
% %
0.0z 0.0~ EuS 0.0212 0
' ' ' 4•'2 4 ' 4.L28 ' 4.32 4.36 Eu-Eu DISTANCE r (A)
4.40
Fig. 6. The exchange constant Je = Jl + J2 as a function o f the Eu -Eu distance. The value of Je for EuS is taken from [8]. dipolar and other interactions, the exchange constant is given by
Je = J1 + J2 = (k/8rrS)(2.612/4SC) 2/a, where k is the Boltzmann constant, and S (= 7/2) is the electronic spin of Eu 2+ ion. The deduced value Of Je is shown as a function of the pressure in Fig. 5, where the value at P = 0 is taken from [1 ]. Je increases from 0.033 to 0.052 K with increasing the pressure from 5 to 14kbar, the slope of ~Je/aPbeing 2.5 x 10 -a and 1.9 x 10 -3 K/kbar at 5 and 14 kbar, respectively. The Je vs P curve is similar to the Te vs P curve obtained by the a.c.
482
PRESSURE-INDUCED MAGNETIC TRANSITION 1N EuSe
susceptibility measurement under pressure [3]. The pressure-induced increase Of Je may be primarily attributed to that of J1, since J2 is insensitive to pressure [7]. For the f.c.c. Heisenberg ferromagnet the Curie temperature is expressed as [8]
Te = 0.790(2/3S(S + 1)12J~)(1 + 0.619J2/J~), and its pressure derivative is approximately given by ~Tc/aP ~. 99.5aJ1/aP. From the experimental values o f aTc/OP = 0.26 and 0.19 K/kbar at 5 and 14kbar, respectively [3], we obtain MI/aP = 2.6 x 10 -a and 1.9 × 10 -a K/kbar at 5 and 14kbar. These are in good agreement with the values of 8Je/OP, confirming that the pressure variation Of Je is attributed to that of J1. The dependence Of Je on the E u - E u distance r is shown in Fig. 6, where the compressibility K = 1.9 x 10 -12 cgs unit [9] is used, and the value Of Je for EuS [8] is also plotted. Je and, therefore, J~ increase rapidly with decreasing r, especially in the vicinity for r = 4.380 A (P = 0). A value of ~Je/b in r = -- 5.1 K estimated from the initial slope at P = 0 nearly agrees with ~Jl/O In r = 4.9 K obtained by the magnetostriction measurement [10], although there is some uncertainty in the values of Jt and J2 at P = 0. -
-
4. DISCUSSION The effective magnetic field at a Eu nucleus H i in Eu chalcogenides consists o f the core polarization field due to the own 4 f spins He, the hyperfine field transferred from neighbouring Eu 2+ spins Ht and the magnetic dipolar field Ha, i.e.,
H i = H e + H t + H a.
(1)
The transferred hyperfine fields Ht in various magnetic states are given by Ht(NNN)
=
12H1
-~- 6H2,
Ht(NNSS) = Ht(NNS) = + 6H1
(2) (3)
and Ht(NSNS) = Ht(NNS) = -- 6H2,
(4)
where HI and HE are the fields transferred from a nearest and a next nearest Eu 2+ neighbour, respectively. In the previous work [5] the value of H2 was estimated as -- 4.1 (3)kOe b y measuring frequency shifts for the satellite lines of the lSaEu NMR in Sr-doped EuSe. Using Hi(NNSS ) = -- 289.7(2)kOe obtained in this work and H/(NSNS) = -- 263.0(2)kOe [11 ], together with the calculated dipolar fields of 4.27 and 3.95 kOe for the NNSS and NSNS states, respectively [12], we estimated HI = -- 0.4(3) kOe and H c = - - 292(2) kOe. The small value o f H1 is consistent with the previous result [ 12]. It is to be noted that, if Hi(NNN ) = -- 316.3 kOe
Vol. 52, No. 4
extrapolated to P = 0 is used, the observed difference of Hi(NNN) - - H / ( N N S S ) is equal to that of Hi(NNSS) -Hi(NSNS ). This indicates that the two parameter description o f H t given by equations ( 2 ) - ( 4 ) is valid at P=0. It is expected that the pressure variation o f H i in EuSe primarily comes from that of i l l , because H e and HE are insensitive to the pressure [7] and the variation of lid with pressure is very small (OHd/OP ~-- 10 -2 kOe/ kbar). No detectable pressure shift of Hi in the NNSS state is due to a small value of 3(6H1)/3P <~ 10 -2 kOe/ kbar, which is related to the small value o f 6H1 = - - 2 . 4 kOe estimated above. In the ferromagnetic state the remarkable dependences o f H i on the pressure at high temperatures are mainly due to changes in the temperature variations of Hi, which are caused by the pressure-induced increase of J1. But the pressure variation o f H i at 0 K cannot be attributed to that of the nearest neighbour contribution o f t2H1, which is expected to be small as in the NNSS state. The values of OHi/~P at 0 K actually are much larger in their magnitude than the M6ssbauer value o f - - 0.18 kOe/kbar at 4.2 K [7], which was obtained at high pressure and high magnetic field and was attributed to ~(12H1)/OP. The variation o f H i with pressure shows a tendency toward the saturation and is similar to that with applied magnetic field [13, 14]. The value o f H i at 5 kbar, for example, is lower by 2.4% than H~ = -- 329kOe in the saturation ferromagnetic state at 0 K [14]. This pressure behaviour o f H i can be explained by supposing that the magnetic moment in the ferromagnetic state under pressure is smaller by a few % than the ideal saturation value even at 0 K and increases toward the saturation with increasing the pressure. The reduction in the ferromagnetic moment at 0 K is also suggested by the experimental fact that Hi(NNN) -- Hi(NNSS ) is equal to HI(NNSS) - Hi(NSNS) at P = 0. This indicates that, if the ferromagnetic state is assumed to be stable at P = 0, the magnetic moment in the ferromagnetic state at P = 0 is nearly equal to the zero point-reduced moments in the NNSS, NNS and NSNS states. A reduction value o f 4% in the ferromagnetic state at P = 0, which is estimated from the values of Hi and H s, is comparable to the value of about 3% in the NNS state obtained by the magnetization measurement [10]. A possible mechanism of the reduction in the ferromagnetic moment at 0 K is the zero point effect of the magnetic dipolar interaction described by H o l s t e i n Primakoff [ 15]; the complete ferromagnetic alignment is not an eigenstate of the Hamiltonian including the magnetic dipolar interactions. The large reduction value may be due to small values of J1 + J2 and a comparatively large dipolar interaction (2S(J1 + J2) = 0.2 K at 5 kbar and 41rpBM = 0.9 K. This suggests that the
Vol. 52, No. 4
PRESSURE-INDUCED MAGNETIC TRANSITION IN EuSe
magnetic dipolar interaction has an appreciable influence on the low temperature spin wave spectrum. But the dipolar interaction is simply neglected in our analysis on v(T), in which the values ofJ~ + J2 and H i are obtained, and no theoretical estimation of the zero point reduction is made. The effect of dipolar interactions is expected to cause also a deviation of v(T) from the T 3/2 law at TITe ~ 1. In the temperature range down to 1.7 K, however, the T ~:2 law is well satisfied at all the pressures except 4.8 kbar, where such a slight deviation of v(T) is found near 1.7 K. Our lowest measuring temperature of 1.7 K is probably not low enough to observe the effect of dipolar interactions. It is hoped to make high-pressure NMR measurements at much lower temperatures and reexamine the data on v(T) by taking into account the dipolar interactions without approximation as done in EuS [ 16]. In our pulsed NMR measurements under pressure an echo signal was observed with a decay time of T~' = 2/~sec in the NNSS state, while no NMR signal was observable in the ferromagnetic state (T~' < 1/lsec). It was found in previous NMR experiments of EuSe [13, 14] that in the coexistence of the NNN and NNS phases at applied magnetic fields the NMR frequency of the NNN line shows a much faster temperature variation than those of other lines. These suggest a faster relaxation of Eu 2÷ electronic spins in the ferromagnetic state than in the NNSS and other states. A magnetic structure of EuSe is regarded as a collection of quasitwo-dimensional (111) plane ferromagnets coupled with J1 + J2 and the magnetic dipolar interaction [17, 18]. The faster spin relaxation is a characteristic in the ferromagnetic state close to the NNSS-NNN phase boundary, where J1 + J2 is small, and may be that of the (111) plane ferromagnets weakly coupled with small J1 -b J2 and the dipolar interaction as suggested for EuSel-x Sx [19]. On the other hand, the NNSS order is rather well stabilized by a magnetoelastic effect [10, 17] in spite of small J~ + J2, resulting in a slower relaxation of Eu 2÷ spins. It is interesting to compare the obtained results in EuSe under pressure with those in the EuSel_xS x system, which is magnetically analogous to EuSe under pressure. A sequent magnetic phase transition and a fast spin relaxation similar to those in EuSe under pressure have been observed in NMR and magnetic works on EuSel_xSx [20]. The magnetic phases of EuSel-xSx are different from those of EuSe under pressure in the NNSS-NNN boundary region o f x = 0.1, where the presence of a spin glass phase was suggested [18, 19]. The values of Jl + J2 deduced from the low temperature specific heats of the ferromagnetic samples with x = 0.15 and 0.20 in EuSel_xS x [18] nearly agree with those in the ferromagnetic state of EuSe under pressure.
483
A recent lSlEu M6ssbauer experiment of EuSel_xS x [19] has shown that in the ferromagnetic states of x = 0.125-0.20 the effective hyperfine field H i at 0 K is lower than expected and increases in its magnitude with increasing x. The lower field was attributed to a short range ferromagnetic order and an imperfect ferromagnetic alignment of the (111) plane ferromagnets. The dependence of Hi on the sulphur concentration in EUSel-xSx is similar to that of Hi on the pressure in EuSe, suggesting that the observed lower field in EuSel_xS x at 0 K is primarily attributed to the zero point reduction in the magnetic moment as in EuSe under pressure. The M6ssbauer experiment [ 19] has also shown a faster spin relaxation in the ferromagnetic samples o f x = 0.125-0.20, being similar to that in the ferromagnetic state of EuSe under pressure.
Acknowledgements - We would like to thank Prof. T. Kamigaichi for his valuable discussion and Mr Y. Kasamatsu for his help in assembling the high pressure apparatus. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.
W. Zinn, J. Magn. Magn. Mater. 3, 23 (1976). R. Griessen, M. Landolt & H.R. Ott, Solid State Commun. 9, 2219 (1971). H. Fujiwara, H. Kadomatsu, T. Hihara, K. Kojima & T. Kamigaichi, Solid State Commun. 42, 509 (1982). H. Fujiwara, H. Kadomatsu & K. Tohma, Rev. Sci. Instrum. 51, 1345 (1980). T. Hihara, S. Nishizawa, K. Kojima & T. Kamigaichi, J. Phys. Soc. Japan 51, 1123 (1982). J. Moser, G. Wortmann, N. Bykovetz & G.M. Kalvius, J. Magn. Magn. Mater. 12, 77 (1979). Ch. Sauer, A.M. Zaker & W. Zinn, J. Magn. Magn. Mater. 38, 225 (1983). L. Passell, O.W. Dietrich & J. Als-Nielsen, Phys. Rev. BI4, 4897 (1976). F. Levy & P. Wachter, Solid State Commun. 8, 183 (1970). T H. Fukuma, . Komatsubara, T. Suzuki, S. Kunii, E. Kaldis & T. Kasuya, J. Magn. Magn. Mater. 3 1 - 3 4 , 431 (1983). T. Hihara, K. Kojima & T. Kamigaichi, J. Phys. Soc. Japan 50, 1499 (1981). N. Bykovetz, Solid State Commun. 18, 143 (1976). T. Komaru, T. Hihara&Y. Koi,J. Phys. Soc. Japan 31, 1391 (1971). M. Kawakami, H. Ltitgemeier, H.G. Bohn & K. Fischer,J. Magn. Magn. Mater. 3 1 - 3 4 , 425 (1983). T. Holstein & H. Primakoff, Phys. Rev. 58, 1098 (1940). S.H. Charap & E.L. Boyd, Phys. Rev. 133, A811 (1964). H. Callen&M.A. deMoura, Phys. Rev. B16,4121 (1977).
484 18. 19.
PRESSURE-INDUCED MAGNETIC TRANSITION IN EuSe K. Westerholt & H. Bach, J. Phys. F: Metal Phys. 12, 1227 (1982). T. Bauermann, M.M. Abd-Elmeguid, J.P. Sanchez, T. Takabatake & H. Micklitz, J. Phys. C16, 6435 (1983).
20.
Vol. 52, No. 4
T. Hihara, K. Kojima, S. Nishizawa, K. Hiraoka & T. Kamigaichi, J. Magn. Magn. Mater. 31-34, 429 (1983).
0038-1098/84 $3.00 + .00 Pergamon Press Ltd.
NMR STUDY OF PRESSURE-INDUCED MAGNETIC TRANSITION IN EuSe K. Hiraoka,* T. Hihara] K. Kojima t and T. Kino Faculty of Science, Hiroshima University, Hiroshima 730, Japan
(Received 4 June 1984 by J. Kanamori) The zero-field tS3EuNMR in EuSe has been observed as a function of the pressure up to 14kbar in the temperature range between 1.7 and 4.2 K. A sequent magnetic phase transition of NSNS-NNS--NNSS-NNN occurs with pressure at 1.7 K. In the NNSS state (2.0 <~P <~4.8 kbar) the NMR frequency u is insensitive to the pressure. In the ferromagnetic state (P ~>4.8 kbar) u depends remarkably on the pressure, and the exchange interaction between the nearest Eu neighbours J~ is shown to increase rapidly with decreasing the E u - E u distance. The pressure dependences of the Eu hyperfine field suggest that the magnetic moment of a Eu 2÷ ion in the ferromagnetic state under pressure is smaller than the ideal saturation value at 0 K.
1. INTRODUCTION EuSe, HAVING the NaC1 crystal structure, shows various magnetic structures such as NSNS, NNS and NNSS below TN = 4.6 K [1,2]. The mechanism of the phase transition is an interesting problem. The complex magnetic phases of EuSe are considered to be primarily due to J~ = -- J : , where Jl and J2 are the ferromagnetic nearest and antiferromagnetic next nearest neighbour exchange constants, respectively. In the previous work [3] the effect of the variation of the interatomic distance on the magnetic phases of EuSe was investigated by measuring the a.c. susceptibility under pressure. It was found that EuSe shows a magnetic transition from the antiferro- to ferromagnetic state at about 4.8 kbar. This paper presents the results of a NMR investigation on the pressure-induced phase transition in EuSe. 2. EXPERIMENTAL A polycrystalline sample was used, which was prepared by heating a pressed pellet of EuSe powder in an enclosed tantalum crucible at 1700 ° C. NMR measurements were mostly made by continuous wave method with a FM marginal oscillator and were made under pressure up to 14 kbar in the temperature range between 1.7 and 4.2 K. The hydrostatic pressure was generated by the clamp cell method. The pressure cell is almost the same as that described by Fujiwara et al. [4] except for the electrical feedthrough. A pair of conventional cones
soldered on Cu wires were used as r.f. electrical feedthroughs, and their insulation from an electrode plug was achieved with epoxy resin. A sample cavity of teflon bucket, in which a r.f. coil was placed, was filled with a 1 : 1 mixture of n-penthane and isoamyle alcohol as force transmitting medium. With a FM marginal oscillator the cell was successfully used under pressure up to 15 kbar in the frequency range below 400 MHz at liquid helium temperature. The pressure in the sample cavity was measured by using the pressure dependences of the lS3Eu and 59CoNMR frequencies in ferromagnetic EuO and f.c.c. Co, respectively, which were calibrated by the pressure shift of the superconducting transition temperature of Sn. By placing a few ten milligrams of EuO or f.c.c. Co, together with the sample, in the sample coil, the pressure was easily determined with an accuracy of-+ 0.2 kbar. Detailed description of the pressure cell and pressure gauge will be given elsewhere. 3. RESULTS Figure 1 shows the lineshapes of the zero-field lS3Eu NMR in EuSe under various pressures P at 1.7 K. At P = 0 the lSaEu NMR spectrum consists of three lines. A small hump at 117.7 MHz is assigned to the NSNS phase, and the peaks at 118.4 and 129.6 MHz come from the nuclei on the S and N sites of the NNS structure, respectively (denoted by NNS and NNS) [5]. The NMR coming from the NNSS phase occurs at nearly the same frequency as that of the NN_S line. As the pressure is increased, the NSNS line disappears at a low pressure, an two NMR of the NNS phase are observed at 1.5 kbar. In the spectra at 3 and 4kbar only the NMR at 129.6 MHz is observed, which is assigned to the NNSS
* Mailing address: Faculty of Integrated Arts and Sciences, Hiroshima University, Hiroshima 730, Japan. t Faculty of Integrated Arts and Sciences, Hiroshima University, Horishima 730, Japan. 479
480
Vol. 52, No. 4
PRESSURE-INDUCED MAGNETIC TRANSITION IN EuSe 140
EuSe 153EuNMR T=I.TK
NNN
EuSe m3EuNMR
136 132
128 124 ~12(
\ o 4.5 k b o r ]
11
3.6 x 2.2 • 1.4
108
\ ~\
~
J
NNSS
~\
\~,,.
NNS
104 10( ~
~" "
~ 0
:2 '
~
'
6
' e, ' 1'0 ' 1'2 ' lZ, ' 16 T 2(K2)
kbor
110 115 1:20 1½5 1:30 135 140 }) (MHz)
145 150
155
Fig. 2. Temperature dependences of the ~SaEu NMR frequencies at various pressures in the NNSS and NNS states. The broken curve represents the result for the NNS line at P = 0.
Fig. 1. Line shapes (first derivative) of the zero-field lS3Eu NMR in EuSe under various pressures at 1.7 K. phase. Another NMR appears on the high frequency side of the NNSS line at 4.6 kbar, and only the NMR is observable above about 5 kbar. This NMR is assigned to the ferromagnetic (NNN) phase, because the results of a.c. susceptibility measurements under pressure suggest the ferromagnetic order above 4.8 kbar [3]. These NMR results show that the NSNS-NNS, NNS NNSS and N N S S - N N N phase transitions successively occur with increasing the pressure. The zero-field lS3Eu NMR frequencies ~, at various pressures were measured as a function of the temperature, and the results for the NNSS (NNS) and NNN lines are shown in Figs. 2 and 3, respectively. At 4.8 kbar the NNN line became much weaker below 2.5 K with lowering the temperature owing to the N N N - N N S S phase transition at 2.5 K, which is suggested by the a.c. susceptibility result [3]. The temperature dependences of the NMR frequency u(T) at three pressures in the NNSS state follow the T 2 law and agree among them within the experimental error, u(T) for the NNS line at 1.4 kbar exhibits also a T 2 dependence. The values of u extrapolated to 0 K for the NNSS and NNS lines are equal to each other and are 134.2(1)MHz, which corresponds to an effective magnetic field H i = -289.7(2) kOe at Eu nuclei (~s37/27r = 0.4632 MHz/kOe).
)~
EuSe ~3Eu NMR
15C i
1461 14~
13B 134 "1-
3;130 126 1221-
4.8
118
114 r
,o~
\ \ 5.7\
.
~
.
~.
' 6 T 3~ ( K 3~2)
°o~ 7.3 '
8
'
1'o
Fig. 3. Temperature dependences of the lS3Eu NMR frequency at various pressures in the ferromagnetic state.
Vol. 52, No. 4
155
481
PRESSURE-INDUCED MAGNETIC TRANSITION IN EuSe
0.06
EuSe OEu NMR
330
OK
15C 320
0.05
1.7 K
145
310
,.-,,14C -~135
"~o .04 o~ •
290 -i= I
0.03 131
1.7~ :
280
12
2.5K
2?0 0.03
12 11
3.oK • '
:
260
=:
~ 'Z'
'g'1o I?
25O 14
0
' ½ ' }* ' 6
' 8 ' 1'0 ' 1'2 ' 1'4 ' 16 P (kbor)
Fig. 5. The exchange constant Je = J1 -t- J2 as a function of the pressure. The value at P = 0 ( 4 ) i s taken from [1 ].
P (kbor)
Fig. 4. Pressure dependences o f the lS3Eu NMR frequency at various temperatures.
0.12 0.11 0.1(
In the ferromagnetic state v(T) largely depend on pressure, but they are well described by the T 3/2 dependence. By fitting the data to the spin wave relation of v ( T ) = Po(1 - - CT3/2), the values of Vo and C are determined as a function of the pressure. Figure 4 shows the pressure dependences of p at some typical temperatures, which are deduced from the results shown in Figs. 2 and 3. The frequencies of the NNSS and NNS lines are nearly independent of the pressure; a careful measurement at 1.7 K resulted in (au/aP)T <~ ± 5 X 10 -3 MHz/kbar, corresponding to (aHi/~P)T <~+-0.01 kOe/kbar. In the ferromagnetic state, on the other hand, v increases rather rapidly with increasing the pressure, the rate of the increase being larger at lower pressures. The slope of (av/aP)7,=o at OK is 0.40 and 0.21 MHz/kbar at 5 and 14kbar, respectively, corresponding to (~Hi/aP)7,=o = - 0.86 and -- 0.45 kOe/kbar. These values are nearly equal to (aHi/aP)T=o = -- 0.7~0.4 kOe/kbar at P = 14~27 kbar in the ferromagnetic state o f Euo.99Sno.ol Se, which was obtained by the lSlEu M6ssbauer measurement under pressure [6]. An extrapolation o f the u vs P curve to P = 0, which is shown by the broken curve in Fig. 4, results in Uo = 146.5(3)MHz at 0 K. The corresponding effective field is Hi = -- 316.3(6)kOe, which also agrees with the M6ssbauer value o f - - 315 kOe. The constant C in the Bloch T 3/2 law is related to the exchange constantsJ~ and J2 Using a quadratic spin wave dispersion law for small k values and neglecting the
0.5 0.0~ o.o
O.OE o
0.~
oo o
% %
0.0z 0.0~ EuS 0.0212 0
' ' ' 4•'2 4 ' 4.L28 ' 4.32 4.36 Eu-Eu DISTANCE r (A)
4.40
Fig. 6. The exchange constant Je = Jl + J2 as a function o f the Eu -Eu distance. The value of Je for EuS is taken from [8]. dipolar and other interactions, the exchange constant is given by
Je = J1 + J2 = (k/8rrS)(2.612/4SC) 2/a, where k is the Boltzmann constant, and S (= 7/2) is the electronic spin of Eu 2+ ion. The deduced value Of Je is shown as a function of the pressure in Fig. 5, where the value at P = 0 is taken from [1 ]. Je increases from 0.033 to 0.052 K with increasing the pressure from 5 to 14kbar, the slope of ~Je/aPbeing 2.5 x 10 -a and 1.9 x 10 -3 K/kbar at 5 and 14 kbar, respectively. The Je vs P curve is similar to the Te vs P curve obtained by the a.c.
482
PRESSURE-INDUCED MAGNETIC TRANSITION 1N EuSe
susceptibility measurement under pressure [3]. The pressure-induced increase Of Je may be primarily attributed to that of J1, since J2 is insensitive to pressure [7]. For the f.c.c. Heisenberg ferromagnet the Curie temperature is expressed as [8]
Te = 0.790(2/3S(S + 1)12J~)(1 + 0.619J2/J~), and its pressure derivative is approximately given by ~Tc/aP ~. 99.5aJ1/aP. From the experimental values o f aTc/OP = 0.26 and 0.19 K/kbar at 5 and 14kbar, respectively [3], we obtain MI/aP = 2.6 x 10 -a and 1.9 × 10 -a K/kbar at 5 and 14kbar. These are in good agreement with the values of 8Je/OP, confirming that the pressure variation Of Je is attributed to that of J1. The dependence Of Je on the E u - E u distance r is shown in Fig. 6, where the compressibility K = 1.9 x 10 -12 cgs unit [9] is used, and the value Of Je for EuS [8] is also plotted. Je and, therefore, J~ increase rapidly with decreasing r, especially in the vicinity for r = 4.380 A (P = 0). A value of ~Je/b in r = -- 5.1 K estimated from the initial slope at P = 0 nearly agrees with ~Jl/O In r = 4.9 K obtained by the magnetostriction measurement [10], although there is some uncertainty in the values of Jt and J2 at P = 0. -
-
4. DISCUSSION The effective magnetic field at a Eu nucleus H i in Eu chalcogenides consists o f the core polarization field due to the own 4 f spins He, the hyperfine field transferred from neighbouring Eu 2+ spins Ht and the magnetic dipolar field Ha, i.e.,
H i = H e + H t + H a.
(1)
The transferred hyperfine fields Ht in various magnetic states are given by Ht(NNN)
=
12H1
-~- 6H2,
Ht(NNSS) = Ht(NNS) = + 6H1
(2) (3)
and Ht(NSNS) = Ht(NNS) = -- 6H2,
(4)
where HI and HE are the fields transferred from a nearest and a next nearest Eu 2+ neighbour, respectively. In the previous work [5] the value of H2 was estimated as -- 4.1 (3)kOe b y measuring frequency shifts for the satellite lines of the lSaEu NMR in Sr-doped EuSe. Using Hi(NNSS ) = -- 289.7(2)kOe obtained in this work and H/(NSNS) = -- 263.0(2)kOe [11 ], together with the calculated dipolar fields of 4.27 and 3.95 kOe for the NNSS and NSNS states, respectively [12], we estimated HI = -- 0.4(3) kOe and H c = - - 292(2) kOe. The small value o f H1 is consistent with the previous result [ 12]. It is to be noted that, if Hi(NNN ) = -- 316.3 kOe
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extrapolated to P = 0 is used, the observed difference of Hi(NNN) - - H / ( N N S S ) is equal to that of Hi(NNSS) -Hi(NSNS ). This indicates that the two parameter description o f H t given by equations ( 2 ) - ( 4 ) is valid at P=0. It is expected that the pressure variation o f H i in EuSe primarily comes from that of i l l , because H e and HE are insensitive to the pressure [7] and the variation of lid with pressure is very small (OHd/OP ~-- 10 -2 kOe/ kbar). No detectable pressure shift of Hi in the NNSS state is due to a small value of 3(6H1)/3P <~ 10 -2 kOe/ kbar, which is related to the small value o f 6H1 = - - 2 . 4 kOe estimated above. In the ferromagnetic state the remarkable dependences o f H i on the pressure at high temperatures are mainly due to changes in the temperature variations of Hi, which are caused by the pressure-induced increase of J1. But the pressure variation o f H i at 0 K cannot be attributed to that of the nearest neighbour contribution o f t2H1, which is expected to be small as in the NNSS state. The values of OHi/~P at 0 K actually are much larger in their magnitude than the M6ssbauer value o f - - 0.18 kOe/kbar at 4.2 K [7], which was obtained at high pressure and high magnetic field and was attributed to ~(12H1)/OP. The variation o f H i with pressure shows a tendency toward the saturation and is similar to that with applied magnetic field [13, 14]. The value o f H i at 5 kbar, for example, is lower by 2.4% than H~ = -- 329kOe in the saturation ferromagnetic state at 0 K [14]. This pressure behaviour o f H i can be explained by supposing that the magnetic moment in the ferromagnetic state under pressure is smaller by a few % than the ideal saturation value even at 0 K and increases toward the saturation with increasing the pressure. The reduction in the ferromagnetic moment at 0 K is also suggested by the experimental fact that Hi(NNN) -- Hi(NNSS ) is equal to HI(NNSS) - Hi(NSNS) at P = 0. This indicates that, if the ferromagnetic state is assumed to be stable at P = 0, the magnetic moment in the ferromagnetic state at P = 0 is nearly equal to the zero point-reduced moments in the NNSS, NNS and NSNS states. A reduction value o f 4% in the ferromagnetic state at P = 0, which is estimated from the values of Hi and H s, is comparable to the value of about 3% in the NNS state obtained by the magnetization measurement [10]. A possible mechanism of the reduction in the ferromagnetic moment at 0 K is the zero point effect of the magnetic dipolar interaction described by H o l s t e i n Primakoff [ 15]; the complete ferromagnetic alignment is not an eigenstate of the Hamiltonian including the magnetic dipolar interactions. The large reduction value may be due to small values of J1 + J2 and a comparatively large dipolar interaction (2S(J1 + J2) = 0.2 K at 5 kbar and 41rpBM = 0.9 K. This suggests that the
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PRESSURE-INDUCED MAGNETIC TRANSITION IN EuSe
magnetic dipolar interaction has an appreciable influence on the low temperature spin wave spectrum. But the dipolar interaction is simply neglected in our analysis on v(T), in which the values ofJ~ + J2 and H i are obtained, and no theoretical estimation of the zero point reduction is made. The effect of dipolar interactions is expected to cause also a deviation of v(T) from the T 3/2 law at TITe ~ 1. In the temperature range down to 1.7 K, however, the T ~:2 law is well satisfied at all the pressures except 4.8 kbar, where such a slight deviation of v(T) is found near 1.7 K. Our lowest measuring temperature of 1.7 K is probably not low enough to observe the effect of dipolar interactions. It is hoped to make high-pressure NMR measurements at much lower temperatures and reexamine the data on v(T) by taking into account the dipolar interactions without approximation as done in EuS [ 16]. In our pulsed NMR measurements under pressure an echo signal was observed with a decay time of T~' = 2/~sec in the NNSS state, while no NMR signal was observable in the ferromagnetic state (T~' < 1/lsec). It was found in previous NMR experiments of EuSe [13, 14] that in the coexistence of the NNN and NNS phases at applied magnetic fields the NMR frequency of the NNN line shows a much faster temperature variation than those of other lines. These suggest a faster relaxation of Eu 2÷ electronic spins in the ferromagnetic state than in the NNSS and other states. A magnetic structure of EuSe is regarded as a collection of quasitwo-dimensional (111) plane ferromagnets coupled with J1 + J2 and the magnetic dipolar interaction [17, 18]. The faster spin relaxation is a characteristic in the ferromagnetic state close to the NNSS-NNN phase boundary, where J1 + J2 is small, and may be that of the (111) plane ferromagnets weakly coupled with small J1 -b J2 and the dipolar interaction as suggested for EuSel-x Sx [19]. On the other hand, the NNSS order is rather well stabilized by a magnetoelastic effect [10, 17] in spite of small J~ + J2, resulting in a slower relaxation of Eu 2÷ spins. It is interesting to compare the obtained results in EuSe under pressure with those in the EuSel_xS x system, which is magnetically analogous to EuSe under pressure. A sequent magnetic phase transition and a fast spin relaxation similar to those in EuSe under pressure have been observed in NMR and magnetic works on EuSel_xSx [20]. The magnetic phases of EuSel-xSx are different from those of EuSe under pressure in the NNSS-NNN boundary region o f x = 0.1, where the presence of a spin glass phase was suggested [18, 19]. The values of Jl + J2 deduced from the low temperature specific heats of the ferromagnetic samples with x = 0.15 and 0.20 in EuSel_xS x [18] nearly agree with those in the ferromagnetic state of EuSe under pressure.
483
A recent lSlEu M6ssbauer experiment of EuSel_xS x [19] has shown that in the ferromagnetic states of x = 0.125-0.20 the effective hyperfine field H i at 0 K is lower than expected and increases in its magnitude with increasing x. The lower field was attributed to a short range ferromagnetic order and an imperfect ferromagnetic alignment of the (111) plane ferromagnets. The dependence of Hi on the sulphur concentration in EUSel-xSx is similar to that of Hi on the pressure in EuSe, suggesting that the observed lower field in EuSel_xS x at 0 K is primarily attributed to the zero point reduction in the magnetic moment as in EuSe under pressure. The M6ssbauer experiment [ 19] has also shown a faster spin relaxation in the ferromagnetic samples o f x = 0.125-0.20, being similar to that in the ferromagnetic state of EuSe under pressure.
Acknowledgements - We would like to thank Prof. T. Kamigaichi for his valuable discussion and Mr Y. Kasamatsu for his help in assembling the high pressure apparatus. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.
W. Zinn, J. Magn. Magn. Mater. 3, 23 (1976). R. Griessen, M. Landolt & H.R. Ott, Solid State Commun. 9, 2219 (1971). H. Fujiwara, H. Kadomatsu, T. Hihara, K. Kojima & T. Kamigaichi, Solid State Commun. 42, 509 (1982). H. Fujiwara, H. Kadomatsu & K. Tohma, Rev. Sci. Instrum. 51, 1345 (1980). T. Hihara, S. Nishizawa, K. Kojima & T. Kamigaichi, J. Phys. Soc. Japan 51, 1123 (1982). J. Moser, G. Wortmann, N. Bykovetz & G.M. Kalvius, J. Magn. Magn. Mater. 12, 77 (1979). Ch. Sauer, A.M. Zaker & W. Zinn, J. Magn. Magn. Mater. 38, 225 (1983). L. Passell, O.W. Dietrich & J. Als-Nielsen, Phys. Rev. BI4, 4897 (1976). F. Levy & P. Wachter, Solid State Commun. 8, 183 (1970). T H. Fukuma, . Komatsubara, T. Suzuki, S. Kunii, E. Kaldis & T. Kasuya, J. Magn. Magn. Mater. 3 1 - 3 4 , 431 (1983). T. Hihara, K. Kojima & T. Kamigaichi, J. Phys. Soc. Japan 50, 1499 (1981). N. Bykovetz, Solid State Commun. 18, 143 (1976). T. Komaru, T. Hihara&Y. Koi,J. Phys. Soc. Japan 31, 1391 (1971). M. Kawakami, H. Ltitgemeier, H.G. Bohn & K. Fischer,J. Magn. Magn. Mater. 3 1 - 3 4 , 425 (1983). T. Holstein & H. Primakoff, Phys. Rev. 58, 1098 (1940). S.H. Charap & E.L. Boyd, Phys. Rev. 133, A811 (1964). H. Callen&M.A. deMoura, Phys. Rev. B16,4121 (1977).
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T. Hihara, K. Kojima, S. Nishizawa, K. Hiraoka & T. Kamigaichi, J. Magn. Magn. Mater. 31-34, 429 (1983).