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Effect of a magnetic field on the magnetic ordering of BaCo2(AsO4)2
Journal of Magnetism and Magnetic Materials 14 (1979) 194 196 © North-Holland Publishing Company
EFFECT OF A MAGNETIC FIELD ON THE MAGNETIC ORDERING OF BaCo2(AsO4) 2 L.P. REGNAULT and J. ROSSAT-MIGNOD
Centre d'Etudes Nuclbaires de Grenoble, 85 X, 38041 Grenoble Cbdex, France
We report a neutron diffraction mvestigatmn of the effect of an applied magnetic field on the magnetic properties of the quasi 2D-xy hehmagnet BaCo2(AsO4) 2 An intermediate ferrlmagnetic structure has been observed as well as a metastable and trreversible behaviour.
1. Introduction
applied field. A 2.4 A wavelength and a 20' vertical collimation was used in order to minimize the horizontal and the vertical instrumental resolution.
The compound BaCo2(AsO4) 2 crystallizes into a rhombohedral unit cell (R3) [1 ]. Co 2÷ ions are located in a honeycomb lattice with parameter a/x/3 = 2.89 A. The large distance between magnetic planes c/3 = 7.82 A gives a two dimensional character. Magnetic measurements and neutron diffraction experiments on single crystals [ 2 - 4 ] have provided evidence for a planar helical ordering (xy type) below 5.33 K (k = [0.261,0, - g4] ) with an abrupt decrease in the ordering parameter. Specific heat measurements [5] show a T 2 contribution as expected from 2D-spin wave theory. At higher temperatures, Cm shows an exponential behaviour, characteristic of a potential barrier [5], which seems related to the particular magnetic structure. In this paper we report neutron diffraction experiments performed with an applied field, in order to understand the magnetization processes in this quasi 2 D - x y compound.
3. Results
Magnetic phase dzagrams. The phase diagrams determined for an Increasing and a decreasing magnetic field, respectively, are reported In fig. 1. For an increasing magnetic field two phase transitions are Induced. First a continuous transition from the helical
2. Experimental Experiments were performed on a single crystal grown by cooling the melted compound slowly [2]. The neutron experiments were carried out on the two axis spectrometer DN3 operating in the reactor SIloe of the CEN-Grenoble. The crystal, placed inside a c r y o s t a t - e l e c t r o m a g n e t assembly, was oriented with a b-axis vertical, parallel to the dtrection o f the
Fxg 1 Magnetic phase diagram for BaCo2(AsO4) 2 when the magnetic field is (left) increased or (right) decreased The magnetic structure associated wath each phase is given. 194
L.P. Regnault, J. Rossat-Mtgnod /Magnettc properties of BaCo2[As04) 2
structure towards a ferrimagnetic state characterized by a magnetization of ~ the saturated value and wavevectors kl = [~, 0, - ~ ] and ks = 0. The thermal variation of the component kx of kl indicates, that at low temperatures, the magnetic order changes rapidly from the hehcal structure with kx = 0.261 towards a structure with kx = ½ - e and then we obtain progresswely a structure with k x = ½. The second transition corresponds to an abrupt change from the ferrimagnetic state towards the saturated paramagnetlc state. The behaviour m a decreasing field is more complex and is characterized by the existence of irreversible and metastable effects when the magnetic field is switched off. For 2 < T < 5.3 K, this irreversibility is partial, in zero field the magnetic structure is frozen with a kx-value between 0.261 and 1_ 3 depending on the temperature. However below 2 K the ferrimagnetic structure associated with k x = ~ Is frozen in zero field. It must be noted that the net magnetization is zero in zero field.
195
wavevector value is associated with an important broadening of the peak along c*, giving rise to a modulated diffusion hne m reciprocal space. This indicated a weak magnetic moment correlation between planes, whereas the magnetic order is well established in the plane (~llk and ~±k > 500 A). The scattering intensity for an ordering with stacking faults can be calculated from [5]'
(1 -p~) [M(kx, O, l) =10 1 + p2 _ 2p COS 27r(l-- L - kz) '
where 1 - p is the probability for a stacking fault between neighbouring planes. The profile of the superlattice peaks in fig. 2 are well accounted for by a value p =13 for T = 1.7 K a n d H = 4 kOe a n d p = 61-for T = 1.7 K and H = 0 + kOe. The In-plane order consists of a stacking along the a* &rection of ferromagnetic chains. From the experimental results two structures are possible. One is collinear with the moment direction along the magnetic field (Y-direction) and a sequence
++--:
4. Ferrimagnetic structure mn,t = t o o [ 1 + 4 cos(27rXn _ lff + tpt)] )9,
The transitmn to the ferrimagnetic state gives rise to important modifications of the shape of the superlattice magnetic peaks. Results for scans performed along the a* and c* reciprocal directions are given in fig. 2, for H = 0 and H = 4 kOe. The change in the
where Xn are the coordinates of Co 2+ ions along a direction ~ perpen&cular to the magnetic field. The other structure is non-colhnear: mrs, : mo [~ + ~ cos(]gXn + ~p,)])3 + m 0 }X,/3 sin(]zrXn + tpi)~ .
T:1.7 K
In fig. 3 is reported the thermal variation of the intensity for a scattering vector [0, 0, - 3 ] + [½, 0, _413• A
30
m
.0010 H=O
"3
-4
Fig. 2. Scans performed along the e* and the a* directions. The continuous hne represents the result of the calculation.
Temperature [ K] Fig 3. Thermal variation of a superlattice peak intenslty.
196
L P Regnault, J Rossat-Mlgnod /Magnettc properttes of BaCo2(As04) 2
rapid decrease in intensity is observed at about 4.8 K as in the zero applied field [3].
5, Discussion The two magnetic structures proposed for the ferrlmagnetic state (fig. 1) have the same classical energy. They can be described by a stacking of three kinds of ferromagnetic chains ( t t J , or * t ~ ) . However the coupling between chains belonging to nelghbourlng planes are completely random (p -- ! )3 • Thus the compound BaCo2(AsO4)2 under an apphed field may be a good approximation of the bidimensional x - y system. The unusual behavlour of this compound, with or without magnetic field, seems to be due mainly to the special value o f the wavevectors rather than to the bld~mensional character o f the magnetic interactions. These values give rise to magnetic structures which consist of weakly coupled planes of ferromagnetic chains (fig. 1, structures I and llIa). The similarity between structures I and IIIa and the thermal variation of the associated magnetic superlattice peaks sug-
gests that in b o t h cases the mechanism o f the phase transition is the same. This mechanism may be attributed to the existence of particular excitations, of sohton-type [4]. which are responsible for the destruc tlon of the magnetic order within the planes. This result is very similar to that observed for superfluid helium films [6]. The existence o f the ferromagnetic ctmms allows us to have a better understanding of the irreversible phenomena and of the intermediate value o f k x by the fact that it may exist an ordering of the defects in the stacking sequence of the chains.
References 11 ] S Eymond and A Durif, Mat. Res Bull. 4 (1969) 595 [2] L.P Regnault, P Burlet and J Rossat-Mlgnod, Physlca 86-88B (1977) 660. [3] L.P. Regnault and J. Rossat-M~gnod, to be pubhshed [4] L.P Regnault, J. Rossat-Mlgnod, J Vdlam and A de Combarleu, J. de Phys. 8 (1978) 66-759, [5] A. Guinier, Th6one et techmque de la radlocrlstallographle (Dunod, Paris. 1956). [6] D J Bishop and J.D. Reppy, Phys. Rev Lett 40 (1978) 1727
EFFECT OF A MAGNETIC FIELD ON THE MAGNETIC ORDERING OF BaCo2(AsO4) 2 L.P. REGNAULT and J. ROSSAT-MIGNOD
Centre d'Etudes Nuclbaires de Grenoble, 85 X, 38041 Grenoble Cbdex, France
We report a neutron diffraction mvestigatmn of the effect of an applied magnetic field on the magnetic properties of the quasi 2D-xy hehmagnet BaCo2(AsO4) 2 An intermediate ferrlmagnetic structure has been observed as well as a metastable and trreversible behaviour.
1. Introduction
applied field. A 2.4 A wavelength and a 20' vertical collimation was used in order to minimize the horizontal and the vertical instrumental resolution.
The compound BaCo2(AsO4) 2 crystallizes into a rhombohedral unit cell (R3) [1 ]. Co 2÷ ions are located in a honeycomb lattice with parameter a/x/3 = 2.89 A. The large distance between magnetic planes c/3 = 7.82 A gives a two dimensional character. Magnetic measurements and neutron diffraction experiments on single crystals [ 2 - 4 ] have provided evidence for a planar helical ordering (xy type) below 5.33 K (k = [0.261,0, - g4] ) with an abrupt decrease in the ordering parameter. Specific heat measurements [5] show a T 2 contribution as expected from 2D-spin wave theory. At higher temperatures, Cm shows an exponential behaviour, characteristic of a potential barrier [5], which seems related to the particular magnetic structure. In this paper we report neutron diffraction experiments performed with an applied field, in order to understand the magnetization processes in this quasi 2 D - x y compound.
3. Results
Magnetic phase dzagrams. The phase diagrams determined for an Increasing and a decreasing magnetic field, respectively, are reported In fig. 1. For an increasing magnetic field two phase transitions are Induced. First a continuous transition from the helical
2. Experimental Experiments were performed on a single crystal grown by cooling the melted compound slowly [2]. The neutron experiments were carried out on the two axis spectrometer DN3 operating in the reactor SIloe of the CEN-Grenoble. The crystal, placed inside a c r y o s t a t - e l e c t r o m a g n e t assembly, was oriented with a b-axis vertical, parallel to the dtrection o f the
Fxg 1 Magnetic phase diagram for BaCo2(AsO4) 2 when the magnetic field is (left) increased or (right) decreased The magnetic structure associated wath each phase is given. 194
L.P. Regnault, J. Rossat-Mtgnod /Magnettc properties of BaCo2[As04) 2
structure towards a ferrimagnetic state characterized by a magnetization of ~ the saturated value and wavevectors kl = [~, 0, - ~ ] and ks = 0. The thermal variation of the component kx of kl indicates, that at low temperatures, the magnetic order changes rapidly from the hehcal structure with kx = 0.261 towards a structure with kx = ½ - e and then we obtain progresswely a structure with k x = ½. The second transition corresponds to an abrupt change from the ferrimagnetic state towards the saturated paramagnetlc state. The behaviour m a decreasing field is more complex and is characterized by the existence of irreversible and metastable effects when the magnetic field is switched off. For 2 < T < 5.3 K, this irreversibility is partial, in zero field the magnetic structure is frozen with a kx-value between 0.261 and 1_ 3 depending on the temperature. However below 2 K the ferrimagnetic structure associated with k x = ~ Is frozen in zero field. It must be noted that the net magnetization is zero in zero field.
195
wavevector value is associated with an important broadening of the peak along c*, giving rise to a modulated diffusion hne m reciprocal space. This indicated a weak magnetic moment correlation between planes, whereas the magnetic order is well established in the plane (~llk and ~±k > 500 A). The scattering intensity for an ordering with stacking faults can be calculated from [5]'
(1 -p~) [M(kx, O, l) =10 1 + p2 _ 2p COS 27r(l-- L - kz) '
where 1 - p is the probability for a stacking fault between neighbouring planes. The profile of the superlattice peaks in fig. 2 are well accounted for by a value p =13 for T = 1.7 K a n d H = 4 kOe a n d p = 61-for T = 1.7 K and H = 0 + kOe. The In-plane order consists of a stacking along the a* &rection of ferromagnetic chains. From the experimental results two structures are possible. One is collinear with the moment direction along the magnetic field (Y-direction) and a sequence
++--:
4. Ferrimagnetic structure mn,t = t o o [ 1 + 4 cos(27rXn _ lff + tpt)] )9,
The transitmn to the ferrimagnetic state gives rise to important modifications of the shape of the superlattice magnetic peaks. Results for scans performed along the a* and c* reciprocal directions are given in fig. 2, for H = 0 and H = 4 kOe. The change in the
where Xn are the coordinates of Co 2+ ions along a direction ~ perpen&cular to the magnetic field. The other structure is non-colhnear: mrs, : mo [~ + ~ cos(]gXn + ~p,)])3 + m 0 }X,/3 sin(]zrXn + tpi)~ .
T:1.7 K
In fig. 3 is reported the thermal variation of the intensity for a scattering vector [0, 0, - 3 ] + [½, 0, _413• A
30
m
.0010 H=O
"3
-4
Fig. 2. Scans performed along the e* and the a* directions. The continuous hne represents the result of the calculation.
Temperature [ K] Fig 3. Thermal variation of a superlattice peak intenslty.
196
L P Regnault, J Rossat-Mlgnod /Magnettc properttes of BaCo2(As04) 2
rapid decrease in intensity is observed at about 4.8 K as in the zero applied field [3].
5, Discussion The two magnetic structures proposed for the ferrlmagnetic state (fig. 1) have the same classical energy. They can be described by a stacking of three kinds of ferromagnetic chains ( t t J , or * t ~ ) . However the coupling between chains belonging to nelghbourlng planes are completely random (p -- ! )3 • Thus the compound BaCo2(AsO4)2 under an apphed field may be a good approximation of the bidimensional x - y system. The unusual behavlour of this compound, with or without magnetic field, seems to be due mainly to the special value o f the wavevectors rather than to the bld~mensional character o f the magnetic interactions. These values give rise to magnetic structures which consist of weakly coupled planes of ferromagnetic chains (fig. 1, structures I and llIa). The similarity between structures I and IIIa and the thermal variation of the associated magnetic superlattice peaks sug-
gests that in b o t h cases the mechanism o f the phase transition is the same. This mechanism may be attributed to the existence of particular excitations, of sohton-type [4]. which are responsible for the destruc tlon of the magnetic order within the planes. This result is very similar to that observed for superfluid helium films [6]. The existence o f the ferromagnetic ctmms allows us to have a better understanding of the irreversible phenomena and of the intermediate value o f k x by the fact that it may exist an ordering of the defects in the stacking sequence of the chains.
References 11 ] S Eymond and A Durif, Mat. Res Bull. 4 (1969) 595 [2] L.P Regnault, P Burlet and J Rossat-Mlgnod, Physlca 86-88B (1977) 660. [3] L.P. Regnault and J. Rossat-M~gnod, to be pubhshed [4] L.P Regnault, J. Rossat-Mlgnod, J Vdlam and A de Combarleu, J. de Phys. 8 (1978) 66-759, [5] A. Guinier, Th6one et techmque de la radlocrlstallographle (Dunod, Paris. 1956). [6] D J Bishop and J.D. Reppy, Phys. Rev Lett 40 (1978) 1727