Macroscopic random magnetic anisotropy constant in crystalline Dy x Y1−x Al2(x=0.3, 0.4)A. del Moral, M. Ciria, J. I. Arnaudas, J. S. Abell, and Y. J. Bi Citation: Journal of Applied Physics 75, 5850 (1994); doi: 10.1063/1.355536 View online: http://dx.doi.org/10.1063/1.355536 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/75/10?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Magnetocaloric effect in as-cast Gd1−xYx alloys with x=0.0, 0.1, 0.2, 0.3, 0.4 J. Appl. Phys. 115, 17A910 (2014); 10.1063/1.4862086 The Volleben effect in magnetic superconductors Dy1– x Y x Rh4B4 (x=0.2, 0.3, 0.4, and 0.6) Low Temp. Phys. 38, 154 (2012); 10.1063/1.3681903 Magnetic properties of cubic R x Y1−x Al2 (R=Dy, Tb) intermetallic random anisotropy magnets (invited) J. Appl. Phys. 76, 6180 (1994); 10.1063/1.358345 Magnetic properties of crystalline random anisotropy Tb x Y1− x Al2 magnets J. Appl. Phys. 69, 5069 (1991); 10.1063/1.348150 Temperaturecompensated Pr1−x−y Sm x R y Co5−δ permanent magnets (R=Er, Dy, Ho, Gd, and Tb;x=0.24; y=0.2, 0.3, and 0.4) J. Appl. Phys. 67, 4662 (1990); 10.1063/1.344846

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Macroscopic random magnetic anisotropy constant in crystalline DyJ, -,A12 (x=0.3, 0.4)

A. del Moral, M. Ciria, and J. I. Arnaudas Laboratorio de Magnetisnla, Dipartimetzto F&u de Materia Condetmada and ICiMA, Universidad de Zaragoza and CSIC, 50009 Zaragoza, Spain

J. S. Abell and Y. JR School of Metalhrrgy and Materials, University of Birmingham, Birtninghatn Bl5 2fl United Kingdom

Cooling in a weak magnetic field the random magnetic anisotropy (RMA) spin glasses Dy&Y, -XAl, (x-0.3,0.4) induces unidirectional and uniaxial anisotropies, on top of the cubic coherent one. The unidirectional anisotropy constant KkMA has been determined at 3.8 K, amounting at zero applied field 127 and 255 J/m3 for x=0.3 and 0.4, respectively. The predicted model ratio between KkM,4 and the uniaxial constant KEMA, i.e., fc&,=2KiM,, has been confirmed. As by-product the relevant RMA parameter D”JJ, where D is the RMA crystal field strength and J, the exchange constaut has been determined, as well as separate estimates of D and J.

I. INTRODUCTION AND EXPERIMENTAL DETAILS

The intermetallics Dy,Y,_,N, crystallize in the cubic Laves phases structure. Extensive magnetic measurements: low field ac susceptibility,‘1” low field FC and ZFC magnetizations,“il Arrott plots,” hysteresis,3*5 ferromagnetic- like critical scaling,3 critical scaling of the nonlinear susceptibility,‘.” law of magnetization approach to saturation,“*” small angle neutron scattering (SANS j.7 obser- vation of Gabay Toulouse transition lines,” and Bragg neu- tron scattering,s point out the existence of a weak random magnetic anisotropy (RMA), induced by the yttrium substi- tution and, in part, of magnetoelastic origin,’ superposed to the cubic coherent one. The magnetic phase diagram,‘939b en- compasses paramagnetic (P), spin glass (SG), correlated spin glass (CSG), random-ferromagnetic (RFM), and ferromag- netic (FM) phases, with a triple point at x,=0.31 and I?,=59 K. The predicted9 low-temperature first-order phase transi- tion from CSG to FM, driven by the cubic coherent anisot- ropy, was observed”2” by the first time. Estimates of the RMA crystal field strength parameter D and of the ferromagnetic exchange constant J yield ratios D/J=0.05.3 A determina- tion of (D/J)“(R,/a)“, where a is the lattice constant and R, the structural correlation length, shows an increase of Ar(D/J)” with decreasing X.

We have now focused on the determination of the mac- roscopic field-cooled-induced anisotropy of RMA origin, with the determination of the corresponding anisotropy con- stant RRMA, the. system exhibiting, at the lower fields of mea- surement (HsO.7 kOe), both unidirectional and uniaxial RMA origin anisotropies. Most anisotropy measurements up to now have been done either in canonical SG, polycrystalline,1° or crystalline uniaxial,l’ and where the an- isotropy is of Dzialoshinsky-Moriya (DM) type, or in rare earth-transition metal amorphous alloys, where the anisot- ropy is of RMA character only.12 In our present DyXYI _,A.l, crystals we have the additional complication of the cubic coherent (CC) anisotropy, three orders of magnitude larger than the induced weak of RMA origin, making the determi- nation of the latter considerably more difficult.

Single. crystals with Dy concentrations x=0.3, 0.4 were grown by the Czochralski technique, the samples being discs, with their base parallel to the ill0) plane, containing the (100) easy axis, for the CC anisotropy. The RMA origin easy axis was induced by cooling the samples from the PM phase in the presence of the measuring magnetic field (0.3-20 kOe), down to 3.8 K, both compounds being in the SC regime. 1,3*4 The PC direction was (loo), to have the CC and macroscopic RMA easy axes coincident. The magnetic an- isotropy was measured from the perpendicular to the field H, magnetization component M,, inasmuch as the anisotropy torque is Lk=M,H. The sample was rotated within the field and in the (110) plane, and M, recorded versus the angle of rotation ‘iv formed by H with (100) direction. Corrections were made to determine the angle f? formed by the magneti- zation vector M with the (100) initial direction. M, was measured using an induction-extraction magnetometer. The magnetic field was accurately monitored with a calibrated Hall probe.

II. OUTUNE OF MODEL OF MACROSCOPIC RMA

Two models have been proposed which predict the ex- istence of unidirectional and uniaxial anisotropy contribu- tions in RMA and DM spin glasses and ferromagnets with RMA. One is the anisotropy triad model of Saslow,‘3 the other the mode.1 proposed by Henley et aZ.‘14 (HSH). We will adhere to the HSH model: with specific application to our problem of weak RMA crystalline systems. We start with the usual RMA Hamiltonian,

,

H=Jx c SrS;+Dx (p;S;)‘, (1) iJ 0 ia

where tii are the local RMA easy axis (EA) direction. i,j stand for the sites and a$ for the spin components. We assume uncorrelated EAs, i.e., (YiUPf)av=f4jSn,/3~ whe.re (...I, stands for the spatial average. In our situation of weak RMA <,0/J small)? in any metastable state of the SG system in zero applied field, spins will try to remain aligned due to the strong exchange, tilting away from the local EAs. Then, from the situation of perfect alignment of spin and EA

5850 J. Appl. Phys. 75 (lo), 15 May 1994 0021-8979/94/75(10)/5850/3/$6.00 Q 1994 American Institute of Physics

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direction corrpment~sS, exchange energy will increase on av- erage, AE,, = J(SpSf - F;IP$?)~~ = J(SFSSp - ~S~jS~p)avv From the point of vi& of the weak anisotropy, spins will appear perfectly aligned by the strong exchange, so that c;r;$qp = ~SuB, the decrease in anisotropy energy being, for a single-ion i,

&y,= -D&y@-p$f).

In equilibrium U’,,+U?,=O, obtaining (SFSP), ~--(11M)p~~$, which introduced in Eq. (1) yields for the average RMA energy, per spin,

i2) 0 4 8 Applied field &Pe)

16 20

Performing now a uniform or bodily rigid rotation, fi,( 01, of the s@rt system part in Eq. G), i.e., of @~J$),, where R( 8) is the SO3 matrix, the average anisotropy energy cost becom- ing from Eq. (2) is

&T RhM=$-Fi Co:~~)C(~Pi)“(RpijPl-IpiapP,2>. (3)

Introducing a reference frame system fUred to the sample and averaging SK,, over the local EA disorder, one obtains a macroscopic anisotropy energy for the metastable state of the form (except for a constant term),

RAM _ Ea, - --KRf&% cos e- 2Ji;RMA ad 8, (4

where

KRh$.a= & N q, (5)

.N being the ion number per volume unit. The total anisot- ropy energy is E::‘” plus the CC one EiE, the torque acting upon the magnetization vector, I’,,= -[4~E,R,hlA+E~)/dO], becoming

Kl Kl I?,?& O)= -K,,,A(sin 8-t 2 sin 28j- -+- sin 28 i ! 4 64.

(6)

where K1 and KZ are the CC anisotropy constants. Therefore, the uniaxial RMA torque is contaminated by the CC anisot- ropy one, one of the main difficulties for the determination of -hhf,.

111. U(PERIMENTAL RESULTS AND INTERPFiETATtON

The CC anisotropy constants K, and 17~ are (see below) around three orders of magnitude larger than K,,,. Then, high-field measurements where the sample is likely a single domain are useless to determine K,,,. To perform such a determination we need to average out the CC anisotropy. This has been realized by decreasing the measuring field be- low a experimentally determined level where the crystal be- comes decomposed, in the II-‘0 limit, in six systems of magnetic domains, along (lOO> directions, giving an average spontaneous magnetization (I@=O, the only magnetization

0 90 180

&degrees) 270 360

!ZIG. 2. High-field (H=lO kOe) torques at 3.8 K va the angle 0 of the magnetization vector with the [lOO] direction and within the (110) plane, for the x=0.3 (0) and x=0.4 (0) compounds. The curves are Fourier fits including sin H, sin 2t), sin 46’, and sin 60 components. The coefficient of sin 0 is irrelevant.

J. Appl. Phys., Vol. 75, No. IO, 15 May 1994 del Moral et a/. 5851

I.5

0.5

A - 0

- -0.5

3 q

--I 3 ,w

FIG. 1. Field dependence of the cubic anisotropy constants K, and RZ at 3.8 K, for DY,,~Y~.~A~~‘!O,O~ and Dy,,Y,,,J& rA,Aj.

being the induced thermoremanent one (TRM), due to the RMA. At finite but low enough fields, the magnetization vec- tor will be M=xH+M,., where x is the first-order cubic susceptibility (isotropic) and M,, the TRM. We have traced l?,,(Q) torques for decreasing fields, between 220 and ~0.25 kOe. In Fig. 1 we present the field dependences of K, and K2 for both compounds, and we can observe how both constants decrease with decreasing field, the RMA torque dominating at low enough fields. At high fields, torque curves show in fact clearly sin 48 and sin 68 components isee Fig. 2).

In Fig. 3 we present the measured torques at the fields of measurement H= 0.30 and 0.25 kOe for -x=0.3 and 0.4, respectively, together with fits including only sin 8 and sin 28 components. Notice, for x=0.4, the strong unidirectional character of the torque. The 8 dependent torque is superim- posed on a constant one, responsible for the rotational “hys- teresis” observed when performing a 2~ rotation, not con- sidered in Eq. (6). The origin of this torque could be ascribed to a magnetization component rotating in phase with H, cast by spins with short relaxation times.

Xld

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600

_ PO0 “g 2

200

11

-200 L----L-- r I

0 90 180 270 360

fj(dC!grd

FIG. 3. Same as Fig. 2 with applied field N=O.ZS kOe. (0) x=0.3, t,Oj x=0.4. The curves are the fits with the theoretical torque ohtained from Eq. (4’). The constant torque background is I’,,=381 and 357 J/m3, forx=0.3 and x2-0.4, respectively.

In Fig. 4 we show the field dependence of KRMA ob- tained from the sin 13 component of I’,,, not contaminated by the CC torque. The linear variation allows to determine, by extrapolation to H= 0, k’,,, at the zero-field spin-glass metastable state. The values so obtained, at T=3.8 K, were KRMA iH=O)=127 and 255 J/m3 for x=0.3 and x=(1.4, re- spectively. We notice that the Fourier coefficient of sin 29, r2

180 -

lh0 -

140 -

120 -

IIW) -

80 -

60 - T=3.8K

40 I I I t I I

0 0.2 0.4 0.6 0.8 1 Applied field (kOe)

FIG. 4. Field variation of the induced unidirectional anisotropy constant K KM,,, at T-3.8 K, for x 4.3 f.0) and x=0.4 (0). Insert: Field variation of K,/4+K2/64), at 3.8 K, for x=0.3 (0). Difference !rz-2r,) (0) for the low-field coefficients of sin q(rl) and sin 2H(T,) according to the model Eq. f.6).

was not r2=2r1 [I‘, is the coefficient for sin 0) as in Eq. (6j] for the RMA contribution. This should be the effect of the CC anisotropy contamination, as demonstrated in the Fig. 4 insert where we plot (r2-3rI) below ~0.7 kOe (points l ) and [K,/4) +(K,/Wj], determined from the coefficient of the sin 28 torque component for higher fields (points O), for x =0.3. The merging of both lines probes the point. Therefore the model Eq. (4) for the induced macroscopic RMA origin anisotropy has been plainly confirmed.

Our final task is to determine D’i/J, from the model ex- pression (S), using the H=O, KKhM values. We obtain D’/J=O.O07 and 0.01 in K, for x=0.3 and 0.4, respectively. This parameter is quite relevant inasmuch as it determines the magnon gap S in weak RMA systems,” i.e., s=(2/15)(D”iJ)(R./n)-‘. We can also separately estimate the D and .I values. Tt was shown ’ that for x=0.4, D/J= 0.045, assuming R,=lOn. Therefore from the D’/J value we obtain lIH1.23 K/ion and JX.11 K.

ACKNOWLEDGMENT

We acknowledge the financial help of the Spanish DGI- CYT through Grants. No. PBS1014 and No. PB!X-0936.

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