- Email: [email protected]
Quadrupolar interactions in Ho1-xYxCu and Ho1-xYxAg
512
Journal of Magnetism
QUADRUPOLAR
INTERACTIONS
I. ABU-ALJARAYESH,
and Magnetic
Materials
54.~57
(1986)512-5 14
IN Ho, _ ,u,Cu AND Ho, _ Jr Ag
J.S. KOUVEL
Ph.vsic,s Dept.. C’nio. of Illinois tit Chicago, Chtcago, IL 60680. USA
and T.O. BRUN MST DIV., Argonne National Lab., Argonne. IL 60439, USA
Crystal-field analyses of magnetization data show that the negative quadrupolar coupling strengthens in Ho, stays constant in Ho,_,Y,Ag as .x rises to 0.9, while the bilinear exchange weakens in both. The quadrupolar ascribed to an instability of the CsCl structure, which in Ho, ,Y,Cu transforms at .Y>, 0.9 upon cooling.
The anomalously large quadrupolar interactions in PrAg [1,2] have been found by magnetization studies to become even stronger when the Ag in this CsCl-structured compound is partially replaced by Cu [3,4]. The strengthening of the quadrupolar coupling in pseudobinary PrAg, ,Cu i is accompanied by a gradual weakening of the net bilinear exchange coupling and, hence. cannot be ascribed to higher-order exchange. Instead, it is seen to be associated, via a dynamic JahnTeller process, with a growing instability of the cubic CsCl-type structure, which culminates when s reaches 0.5 in a transformation upon cooling to an orthorhombic FeBtype structure [3]. We have recently been investigating another rareearth pseudobinary system, Ho, ,Y,Cu. for possible evidence of a similar quadrupolar/structural phenomenon. Like PrAg, ,Cu , . Ho, ,Y,Cu is CsCl-structured at sufficiently low x, and it presumably transforms as x approaches unity since YCu reportedly changes upon cooling to a different (but undetermined) structure [5]. Moreover, the crystal-field states of Ho,zsY, 7s Cu have been deduced from inelastic neutron scattering data [6]. which enables us in principle to determine the quadrupolar coupling coefficients for the CsCl-structured compounds of this and nearby compositions by means of magnetic measurements. The results of such measurements on Ho, _,Y.,Cu are reported here and compared to our results for isoelectronic Ho, ,Y,Ag, which is CsCl-structured for all s. The compounds we have studied to date in detail are Ho_,Y,Cu for .Y=0.80, 0.85. 0.90, 0.92, 0.95, and Ho, ,Y, Ag for .Y= 0.80. 0.90. Polycrystalline buttons of each were prepared by arc-melting 99.95% pure metals under argon. Thin rod samples (= 0.3 x 1 x 8 mm’) were cut from the buttons and annealed successively for 2 days at 400 and 300°C. Their magnetizations were measured in a vibrating-sample magnetometer at temperature down to 4.2 K in fields up to 56 kOe. Selected resistivity measurements were made over the
0304-8853/86/$03.50
‘c Elsevier Science Publishers
,Y,c‘u hut result\
are
same temperature range, using a standard four-probe method. For all the compositions studied (i.e.. for ,I- a 0.8). the initial susceptibilities were seen to follow a Curie-Weiss law [~,,a (T- 0)-‘. with 0 very small and negative] down to 4.2 K. indicating the absence of long-range magnetic order at these low Ho concentrations. Moreover, for Ho,_,Y,Cu. x,,(T) changes very little as .Y is raised to 0.95. thus providing no clear evidence of any structural transformation. This i\ in contrast to our resistivity results which. as shown in fig. 1. reveal a profound change between x = 0.90 and .y = 0.92. Whereas the resistivity of Ho (,.,,,Yo~soCu varies normally and reversibly with temperature down to 4.2 K. the resistivity of Ho,,,,,,Y,,,,Cu undergoes an anomalous increase at = 80 K upon cooling, resulting in an irreversibly altered behavior. Such a resistivity anomaly was previously observed in YCu at = 150 K and was identified, by X-ray diffraction study. with a transformation of the CsCl structure [5]. Thus. in Ho, ,Y,Cu for I LIP to 0.90. it appears that the CsCI-type structure. though is becoming increasingly retained at all temperatures. unstable. To probe the magnetic effects of any structural instability in these compounds. we have measured their magnetizations (M) as detailed functions of field (I{) at various temperatures. The isotherms obtained at 4.2 K are displayed in fig. 2a as Arrott plots of M’ vs. H/M. Since all these compounds are paramagnetic at 4.2 K. the M’ vs. H/M isotherms can be usefully compared with the corresponding isotherms of M’ vs. H,,t/M (H,,t being the total effective field) calculated as polycrystalline averages from the crystal-field states these cubic compounds, At any fixed M. the of HoTi 111 subtraction H,,,/M - If/M yields HeKcl,/M ( Hexih being the net interaction or exchange field). Mean-field analysis has shown that Ncrc,,/M = h + h’M’ plus normally negligible higher-order terms, where h is the usual bilinear exchange coefficient and X’ ix an average
B.V
513
I. Abu- Aijarayesh et al. / Quadrupolar rnteractions in Ho, _ x r,(Cu/Ag)
3
Fig. 1: Resistivity (in arbitrary units) of Ho,,,Y,~~C~ Ho, ,aY,,,,,,Cu for decreasing and subsequently increasing perature.
4
5
6
7
8
Q
and tem-
quadrupolar coupling coefficient [l]. Thus, h and X’ are obtainable from a linear plot of M2 vs. H,,,,/M. In following this procedure, we first used the crystal-field parameters, A,(r4) = -68 K (-67 K), A, (r”) = - 15 K ( - 12 K), determined for Ho,,,Y,,,~ Cu (and Ho,,Y,,Ag) by Schmitt et al. [6]. The resulting iz12 vs. H,,,,/M plots for our sample compounds were all found to curve away from an initial linear variation towards larger values of H,,,,/M at high M2. This suggests that for both systems the calculated M2 vs. H,,,/M curves are not rising steeply enough. We therefore adjusted A,(r6) to - 12.4 K (and -9.8 K) and kept the A,(r4) values the same, thereby reducing the splitting beween the ground-state r, level and the lowest excited-state I, level from 48.0 to 36.4 K (and from 35.0 to 24.9 K). The M2 vs. H,,,/M curves calculated with the adjusted parameters for the two systems at 4.2 K are shown in fig. 2a. The resulting M2 vs. H,,,,/M plots, displayed in fig. 2b, are clearly quite linear for all the compounds over most of the range of study. The values of X and h’ taken, respectively, from the abscissa intercepts and the inverse slopes of these lines are listed in table 1. All the values are negative, and the magnitude of X drops rapidly as x increases in both Ho, _ ,Y,Cu and HoiPXYXAg, which is to be expected for the bilinear exchange coupling as the magnetic Ho 31- ions are diluted. However, for the same increases in x. the magnitude of X’ rises considerably in Ho, _,Y,Cu and stays essentially constant in Ho, _,Y,Ag. Hence, in neither case can the quadrupolar coupling be attributed to higher-order exchange. The differences between the X’ and its variations in the two systems are presumably
%xch
‘M (kOe
'+)
M2 vs. H/M curves for Ho, _ ,Y,Cu and Ho,_,Y,Ag of various x, and calculated M2 vs. H,,,/M curves for the two systems. (b) M2 vs. H,,,,/M curves deduced from the curves in (a). All curves are for 4.2 K. A4 is in Bohr magnetons per Ho atom.
Fig. 2. (a) Measured
Table 1 Coefficients pling (h’)
for bilinear
exchange
Sample compound
x We/p
Ho020Yo.du
-
Hoc, I sYo.xs Cu Ho,.wY, s&u Ho, 20YoxoAg Ho, IoYo.,,, Ag
- 1.65
2.44
-0.56 - 2.21 -0.81
a)
(X) and quadrupolar
cou-
h’ We/r;) -
0.0225 0.0258 0.0314 0.0172 0.0172
to the greater structural instability of Ho, _ ,U,Cu, which grows as x rises to 0.9 and eventually culminates, as we have shown, in a structural transformation. ascribable
The work at U.I.C. was supported by the National Science Foundation under Grant no. DMR84-06898 and at A.N.L. by the US Department of Energy.
514
I. Abu -AIJaravesh
et al. / Quadrupolar
[I] T.O. Brun. J.S. Kouvel and G.H. Lander, Phys. Rev. B 13 (1976) 5007. [2] P. Morin and D. Schmitt, Phys. Rev. B 26 (1982) 3891. [3] J.A. Gotaas, J.S. Kouvel, T.O. Brun and J.W. Cable. J. Magn. Magn. Mat. 36 (1983) 208.
inteructions
in Ho,
, Y,(Cu/Ag)
[4] J.A. Gotaas. J.S. Kouvel and T.O. Brun. Phys. Rev. B 32 (1985) 4519. [5] H. Balster, H. Ihrig. A. Kockel and S. Methfessel, Z. Phy\. B 21 (1975) 241. [6] I>. Schmitt. P. Morin and J. Pierre. Phys. Rev. B 15 (1977) 169X.
Journal of Magnetism
QUADRUPOLAR
INTERACTIONS
I. ABU-ALJARAYESH,
and Magnetic
Materials
54.~57
(1986)512-5 14
IN Ho, _ ,u,Cu AND Ho, _ Jr Ag
J.S. KOUVEL
Ph.vsic,s Dept.. C’nio. of Illinois tit Chicago, Chtcago, IL 60680. USA
and T.O. BRUN MST DIV., Argonne National Lab., Argonne. IL 60439, USA
Crystal-field analyses of magnetization data show that the negative quadrupolar coupling strengthens in Ho, stays constant in Ho,_,Y,Ag as .x rises to 0.9, while the bilinear exchange weakens in both. The quadrupolar ascribed to an instability of the CsCl structure, which in Ho, ,Y,Cu transforms at .Y>, 0.9 upon cooling.
The anomalously large quadrupolar interactions in PrAg [1,2] have been found by magnetization studies to become even stronger when the Ag in this CsCl-structured compound is partially replaced by Cu [3,4]. The strengthening of the quadrupolar coupling in pseudobinary PrAg, ,Cu i is accompanied by a gradual weakening of the net bilinear exchange coupling and, hence. cannot be ascribed to higher-order exchange. Instead, it is seen to be associated, via a dynamic JahnTeller process, with a growing instability of the cubic CsCl-type structure, which culminates when s reaches 0.5 in a transformation upon cooling to an orthorhombic FeBtype structure [3]. We have recently been investigating another rareearth pseudobinary system, Ho, ,Y,Cu. for possible evidence of a similar quadrupolar/structural phenomenon. Like PrAg, ,Cu , . Ho, ,Y,Cu is CsCl-structured at sufficiently low x, and it presumably transforms as x approaches unity since YCu reportedly changes upon cooling to a different (but undetermined) structure [5]. Moreover, the crystal-field states of Ho,zsY, 7s Cu have been deduced from inelastic neutron scattering data [6]. which enables us in principle to determine the quadrupolar coupling coefficients for the CsCl-structured compounds of this and nearby compositions by means of magnetic measurements. The results of such measurements on Ho, _,Y.,Cu are reported here and compared to our results for isoelectronic Ho, ,Y,Ag, which is CsCl-structured for all s. The compounds we have studied to date in detail are Ho_,Y,Cu for .Y=0.80, 0.85. 0.90, 0.92, 0.95, and Ho, ,Y, Ag for .Y= 0.80. 0.90. Polycrystalline buttons of each were prepared by arc-melting 99.95% pure metals under argon. Thin rod samples (= 0.3 x 1 x 8 mm’) were cut from the buttons and annealed successively for 2 days at 400 and 300°C. Their magnetizations were measured in a vibrating-sample magnetometer at temperature down to 4.2 K in fields up to 56 kOe. Selected resistivity measurements were made over the
0304-8853/86/$03.50
‘c Elsevier Science Publishers
,Y,c‘u hut result\
are
same temperature range, using a standard four-probe method. For all the compositions studied (i.e.. for ,I- a 0.8). the initial susceptibilities were seen to follow a Curie-Weiss law [~,,a (T- 0)-‘. with 0 very small and negative] down to 4.2 K. indicating the absence of long-range magnetic order at these low Ho concentrations. Moreover, for Ho,_,Y,Cu. x,,(T) changes very little as .Y is raised to 0.95. thus providing no clear evidence of any structural transformation. This i\ in contrast to our resistivity results which. as shown in fig. 1. reveal a profound change between x = 0.90 and .y = 0.92. Whereas the resistivity of Ho (,.,,,Yo~soCu varies normally and reversibly with temperature down to 4.2 K. the resistivity of Ho,,,,,,Y,,,,Cu undergoes an anomalous increase at = 80 K upon cooling, resulting in an irreversibly altered behavior. Such a resistivity anomaly was previously observed in YCu at = 150 K and was identified, by X-ray diffraction study. with a transformation of the CsCl structure [5]. Thus. in Ho, ,Y,Cu for I LIP to 0.90. it appears that the CsCI-type structure. though is becoming increasingly retained at all temperatures. unstable. To probe the magnetic effects of any structural instability in these compounds. we have measured their magnetizations (M) as detailed functions of field (I{) at various temperatures. The isotherms obtained at 4.2 K are displayed in fig. 2a as Arrott plots of M’ vs. H/M. Since all these compounds are paramagnetic at 4.2 K. the M’ vs. H/M isotherms can be usefully compared with the corresponding isotherms of M’ vs. H,,t/M (H,,t being the total effective field) calculated as polycrystalline averages from the crystal-field states these cubic compounds, At any fixed M. the of HoTi 111 subtraction H,,,/M - If/M yields HeKcl,/M ( Hexih being the net interaction or exchange field). Mean-field analysis has shown that Ncrc,,/M = h + h’M’ plus normally negligible higher-order terms, where h is the usual bilinear exchange coefficient and X’ ix an average
B.V
513
I. Abu- Aijarayesh et al. / Quadrupolar rnteractions in Ho, _ x r,(Cu/Ag)
3
Fig. 1: Resistivity (in arbitrary units) of Ho,,,Y,~~C~ Ho, ,aY,,,,,,Cu for decreasing and subsequently increasing perature.
4
5
6
7
8
Q
and tem-
quadrupolar coupling coefficient [l]. Thus, h and X’ are obtainable from a linear plot of M2 vs. H,,,,/M. In following this procedure, we first used the crystal-field parameters, A,(r4) = -68 K (-67 K), A, (r”) = - 15 K ( - 12 K), determined for Ho,,,Y,,,~ Cu (and Ho,,Y,,Ag) by Schmitt et al. [6]. The resulting iz12 vs. H,,,,/M plots for our sample compounds were all found to curve away from an initial linear variation towards larger values of H,,,,/M at high M2. This suggests that for both systems the calculated M2 vs. H,,,/M curves are not rising steeply enough. We therefore adjusted A,(r6) to - 12.4 K (and -9.8 K) and kept the A,(r4) values the same, thereby reducing the splitting beween the ground-state r, level and the lowest excited-state I, level from 48.0 to 36.4 K (and from 35.0 to 24.9 K). The M2 vs. H,,,/M curves calculated with the adjusted parameters for the two systems at 4.2 K are shown in fig. 2a. The resulting M2 vs. H,,,,/M plots, displayed in fig. 2b, are clearly quite linear for all the compounds over most of the range of study. The values of X and h’ taken, respectively, from the abscissa intercepts and the inverse slopes of these lines are listed in table 1. All the values are negative, and the magnitude of X drops rapidly as x increases in both Ho, _ ,Y,Cu and HoiPXYXAg, which is to be expected for the bilinear exchange coupling as the magnetic Ho 31- ions are diluted. However, for the same increases in x. the magnitude of X’ rises considerably in Ho, _,Y,Cu and stays essentially constant in Ho, _,Y,Ag. Hence, in neither case can the quadrupolar coupling be attributed to higher-order exchange. The differences between the X’ and its variations in the two systems are presumably
%xch
‘M (kOe
'+)
M2 vs. H/M curves for Ho, _ ,Y,Cu and Ho,_,Y,Ag of various x, and calculated M2 vs. H,,,/M curves for the two systems. (b) M2 vs. H,,,,/M curves deduced from the curves in (a). All curves are for 4.2 K. A4 is in Bohr magnetons per Ho atom.
Fig. 2. (a) Measured
Table 1 Coefficients pling (h’)
for bilinear
exchange
Sample compound
x We/p
Ho020Yo.du
-
Hoc, I sYo.xs Cu Ho,.wY, s&u Ho, 20YoxoAg Ho, IoYo.,,, Ag
- 1.65
2.44
-0.56 - 2.21 -0.81
a)
(X) and quadrupolar
cou-
h’ We/r;) -
0.0225 0.0258 0.0314 0.0172 0.0172
to the greater structural instability of Ho, _ ,U,Cu, which grows as x rises to 0.9 and eventually culminates, as we have shown, in a structural transformation. ascribable
The work at U.I.C. was supported by the National Science Foundation under Grant no. DMR84-06898 and at A.N.L. by the US Department of Energy.
514
I. Abu -AIJaravesh
et al. / Quadrupolar
[I] T.O. Brun. J.S. Kouvel and G.H. Lander, Phys. Rev. B 13 (1976) 5007. [2] P. Morin and D. Schmitt, Phys. Rev. B 26 (1982) 3891. [3] J.A. Gotaas, J.S. Kouvel, T.O. Brun and J.W. Cable. J. Magn. Magn. Mat. 36 (1983) 208.
inteructions
in Ho,
, Y,(Cu/Ag)
[4] J.A. Gotaas. J.S. Kouvel and T.O. Brun. Phys. Rev. B 32 (1985) 4519. [5] H. Balster, H. Ihrig. A. Kockel and S. Methfessel, Z. Phy\. B 21 (1975) 241. [6] I>. Schmitt. P. Morin and J. Pierre. Phys. Rev. B 15 (1977) 169X.