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Spectral shift and excited state exchange fields in high magnetic fields
Physica B 155 (1989) 383-386 North-Holland. Amsterdam
SPECTRAL SHIFT AND EXCITED IN HIGH MAGNETIC FIELDS Hidenobu
HORI
and Muneyuki
STATE EXCHANGE
FIELDS
DATE
Department of Physics, Faculty of Science,
Osaka University, Toyonaka.
Osaka S60, Japan
The spectral shift in magnetic fields and determination of the excited antiferromagnets. The practical application to YbCrO, is shown and the excited estimated to be 55% of the ground state value.
fields are discussed for field between Cr” spins is
exchange fields and g-values. An application YbCrO, is shown as an example.
1. Introduction When a photon is absorbed in an antiferromagnetic crystal and an ion is excited, the spin on the ion feels an exchange field which differs from the ground state value of H,. It is called the excited state exchange field, which will be given the notation HL in this work. The present paper gives a new method for determining Hf: by using a magneto-optical procedure under high magnetic field. Some attempts to estimate the excited state exchange fields have been reported. One method uses the optical spectra of a pair spin system in nonmagnetic isomorphous crystals [l] and another uses temperature dependent exchange shifts [2, 31. However, spectral line broadening is serious in these methods and a satisfactory method has not been reported. A new method of determining HA by observing the optical spectra in high magnetic fields was proposed in our previous work [4]. The central idea is shown in the following way. A strong magnetic field makes a large spin canting in the antiferromagnetic spin network and a considerable magnitude of the spectral shift, due to the canting, is expected. As the shift should be explained by the change in the ground and excited exchange fields, one can estimate the excited state parameters by considering the shift and magnetization data. The purpose of this work is to show the general treatment of determination of excited state 0921-4526/89/$03.50 0 (North-Holland Physics
state exchange state exchange
Elsevier Science Publishers Publishing Division)
2. Field dependence of the effective simple antiferromagnet
to
fields in a
Consider a simple antiferromagnet which has two sublattices, M, and M,, coupled with the intersublattice exchange field H, and the anisotropy field is assumed to be small. An intrasublattice exchange field of H, is also considered and H, is tentatively assumed to be ferromagnetic. Then the effective field Hcff on M, is given by H,, H, and an external field H,, , which are schematically shown in fig. l(A). When a photon is absorbed by a ground state magnetic ion with spin S on the sublattice M,, the spin changes to S’ with the different exchange fields Hk and H:. Therefore, the resultant field HL,, is modified, as shown in fig. l(B), where the directions of HL and H& are invariant with those of the ground state, because the symmetry of the surrounding ions does not change in the optical transition process. The effective fields on the ground and excited states are assumed to be isotropic and they are given by H,,, = H,, + H, + H, >
(1)
H;,, = H,, + H;: + Hi .
(2)
The B.V
magnetization
in
the
antiferromagnet
384
Fig. 1. Effective
field on the ground
state
(A) and the excited
gives H, = 2H,. The effective field Hefl above H, is different from the field below H,. The exchange fields in both cases are given by [4] l&f1 = H, + (f&(
0 s H,, s 2H,
H, .
= H,, - H, + H, ,
.
H,, > 2 HP .
(3)
+ Hi)’ + H;(l
- H;/H,)
’.
x (1 + H;/HJ’
OS H,,s2H,.
(5)
Above the critical field H, < H,,, the effective fields become simple and the following two cases are given: IH:frl=H,,-H;-+H:,. JH;~~\=-H,,+-
H;:-
A simple expression I-I,, = 2 ’ “H, as lHlfrl = [(HE - H;)”
H,,>H;-Hi. H;,
H,,
aspects of the level shift in the excited state. The cases I-IV shown in fig. 2 correspond to the conditions HL + H: = 0, H; > H,. H; = H,. and H;, < H,,, respectively. The energy difference E between the ground and excited states is written as
where 3, g and g’ are the energy gap of the optical excitation and the ground and excited g-values, respectively, and pB is the Bohr magneton. Eq. (9) gives the spectral shift due to the magnetic held. Experimentally speaking, the energy difference of E given by eq. (9) is measured as a function of H,,. It is assumed that the ground state parameters g, H, and H, are known. Then the excited state parameter g’ is simply determined by the field shift above H,, and H; and Hi are determined
(6) H:. .
for eq. (5) is obtained
+ (H,
(H) spms for the M, sublattice
(4)
H, + He > 0 is required from the stability condition of the antiferromagnet. The excited state effective field below H, is given by [4] H:,, = [(H;
state
+ H:,)‘]“’
4
(7)
iXCl7ED
STATE
at
(8) HE * tie
3. Spectral shift and determination magnetic parameters
of the
GROUND CRYSTAL FIFLD
I
The typical field dependence of the energy levels is schematically shown in fig. 2. The conditions for the exchange fields give the various
:; TATE
EXCHANGE-FIELD I I
HEBHE
0
Fkg. 2. Schematic gy laels.
diagram
ZHE
of magnetic
> MAG. FIELD (HL’)
ficld dependent
cncr-
(Pl)
.
6’L
=
’ I“i = ‘HtH
ahHla)H
’ z.z-
‘S9.1 = ‘H/:H
=
7hH13$H
’ SS’O = “Hl:H
se pau!t?lqoa.u2splay apes punol8 Yurpuodsallo3 aql icq pazqwulou splay a%II?qDXa alels pa)!Dxa ayL ."H puno.n? 1daDxa ‘san[elzIeluau+adxa
ql!~ luauraa&?
poo8
Z
u!
s!1lnsaJaqL ‘g ‘By u! aAm pqos aql /cq uhoqs s! IJ!qs aql 30 aAm pmgaIoaq1 aqL .“:H 01 sagdde uoyssnmp .nzl!uIys v ‘i3!qs aqi 01 uognq!liuoD luwodtu! aql sa,@ surds +c~~ aql uaahzlaq play a2heq3xa aql play 2gauku
q%q e u! lnq ‘uo!%al
play MOI aql u! y!qs le.wads aql 01 aAgDa33a s! +,qA woq play aZueq3xa aqi ieqi isa%hs silnsal pwaugadxa aqL “H pue 'H ql!M pa_wdruo3 a%el OS lou a.w ""H pue 3h~ Ieql pa2rlou S' 11 '1 S’9 = ahH pUk? LLL'p= 'hH ‘L6'+i "H ‘LI'f,[='H
‘LLL'6L= "H
SE? Splay a%Ueq3Xa
aqi pau!umiap [s] ‘1~ ia meyoiofl .[ti] L 6.9 ie pun03 play dg-uyds aql s! "H alaqM ‘iC[aA!l -Dadsal “H > "H pue “H < ‘)H saw3 aql 103 pasn s! (~1) .ba u! i 30 - pue + aqL ‘““H - “H = y pue E +y u! uMoqs a@2 Bugue3 aqi s! x) alaqM
‘H - “H) -
’ z;,[Yb’ZU!S
(El)
ahH(DZ SO3 "H - "H)D SOCJZT
L/(DZSOS"H - 'H)DLIU'SZ i sZ/+ sahH +
s! pue (I)
[b] se uall!.m
&DZSOD'H
,@'zU!S "H - 'H)+
‘slxe-o “‘H play paqdde: aqi LII ‘E ‘8~ JO iiasu! aqi u! UMoqs s! [s] x 811 = No Mo[aq ainlmils u!ds 3gwuaq3s aqL ‘[@I “oi3qA u! +ci3 30 uo~~~sueii gz--vti aql s! q3!qM saug-8 aqi 103 paAiasq0 3!lauk_u q%q u! lJ!qs lemads aqL
SBM splay
.yloMauwlJ luasald aqi u!qiiM paie%gsaizu! aq um siau%_uoiia~~iu~ sums put alqeI!me awo3aq my (L oar) aom 1 leau 01 dn play 3gauBem I? ‘lalzahzoq ‘iCllua3 -ax ~s~aukuoiiaj~~ut2 jensn 103 q&q hail am “HZ lnoql? JO splay pmialxa pal!nbal aql asnesaq pawo3Jad uaaq IOU scq cap! luasald aqi qi!M sDgdo-olau8ew aql JO Apnls pwraw!ladxa aqJ
- 'H)]z~~~H
.ba SE poqlaur
ain8y
+cqA pue +c~3 ~013 splay e@om-gsu!qso+a sag!iielqns su!ds uIO.IJ Put Pue +$A awes pue al!soddo aql uo su!ds +E~3 LLIO_IJ splay
(II)
.IT?~!UI!S e iiq ua@
s! ""H
./([aA!lDadsaI ‘sulds
a%I??q3Xa aql alIZqNqM ahH pUE 'H ‘"hH '"H “H 30 splay a8ueqDxa aAy pue "H play paqdde aql sass u!ds +,.I3 f~' 'E '%y u! UMoqs
oml
awes aqt laa3 saD!lwjqns
aqi
uo
‘ :H - :H + ‘HZ-
= fJa,l
Lq ua@Fi am aqi
(01)
u! ,,g
‘
z,,
pue
[,(:H
,g
ie splay
+ ‘H) + ,(:H
=!i~a33a
aqi
pue
- ‘H)] = I’““HI
Se '[Jo]
paAlasq0 SBM "';xIpue ““H 30 a3uaia331paql 01 anp 13!qsIwlsads aql lnq ‘pamasqo IOU s! +E~3 JO aql u! %u!llqds lewads aql pue splay aA!l
awl-8
-3a33aaql JO apnl!uku ~!lau%two1ia3yue
su!ds +&)
aql
SE Uall!.IMale Z '8y U! UMOqS ,,VpUE ,v le splay arlgDa33a qioa .aldur!s hlaA!leieduIo3 am splay asaqi ie si3!qs Biaua aqi asnmaq 3Hz pue 3~,, ,z ale splay ajqeioAe3 aqL “H MoIaq slu!od OH 0~1 le iJ!qs pzlpads aql %!Aiasqo hq
386
H. Herr
and M.
Dare I Spectral shift arrd excited excharlge field
References [I] A.E. Nikitonov and V.I. Cherepanov. Phys. Status Solidi 14 (1966) 3Y1. 12.1 I. Tsujikawa and E. Kanda, J. Phys. Sot. Jpn. 18 (lY63) 1382.
131 M.W. Passow. D.L. Huber and W.M. Yen. Phys. Rev. Lett. 22 (lY6Y) 477 141 H. Hori and M. Date, J. Phys. Sec. Jpn. 57 (1988). to appear. 151 M. Motokawa. H. Hori, N. Nishimura. K. Tsushima and M. Date. .I. Magn. Magn. Mat. 59 (19X6) 243.
SPECTRAL SHIFT AND EXCITED IN HIGH MAGNETIC FIELDS Hidenobu
HORI
and Muneyuki
STATE EXCHANGE
FIELDS
DATE
Department of Physics, Faculty of Science,
Osaka University, Toyonaka.
Osaka S60, Japan
The spectral shift in magnetic fields and determination of the excited antiferromagnets. The practical application to YbCrO, is shown and the excited estimated to be 55% of the ground state value.
fields are discussed for field between Cr” spins is
exchange fields and g-values. An application YbCrO, is shown as an example.
1. Introduction When a photon is absorbed in an antiferromagnetic crystal and an ion is excited, the spin on the ion feels an exchange field which differs from the ground state value of H,. It is called the excited state exchange field, which will be given the notation HL in this work. The present paper gives a new method for determining Hf: by using a magneto-optical procedure under high magnetic field. Some attempts to estimate the excited state exchange fields have been reported. One method uses the optical spectra of a pair spin system in nonmagnetic isomorphous crystals [l] and another uses temperature dependent exchange shifts [2, 31. However, spectral line broadening is serious in these methods and a satisfactory method has not been reported. A new method of determining HA by observing the optical spectra in high magnetic fields was proposed in our previous work [4]. The central idea is shown in the following way. A strong magnetic field makes a large spin canting in the antiferromagnetic spin network and a considerable magnitude of the spectral shift, due to the canting, is expected. As the shift should be explained by the change in the ground and excited exchange fields, one can estimate the excited state parameters by considering the shift and magnetization data. The purpose of this work is to show the general treatment of determination of excited state 0921-4526/89/$03.50 0 (North-Holland Physics
state exchange state exchange
Elsevier Science Publishers Publishing Division)
2. Field dependence of the effective simple antiferromagnet
to
fields in a
Consider a simple antiferromagnet which has two sublattices, M, and M,, coupled with the intersublattice exchange field H, and the anisotropy field is assumed to be small. An intrasublattice exchange field of H, is also considered and H, is tentatively assumed to be ferromagnetic. Then the effective field Hcff on M, is given by H,, H, and an external field H,, , which are schematically shown in fig. l(A). When a photon is absorbed by a ground state magnetic ion with spin S on the sublattice M,, the spin changes to S’ with the different exchange fields Hk and H:. Therefore, the resultant field HL,, is modified, as shown in fig. l(B), where the directions of HL and H& are invariant with those of the ground state, because the symmetry of the surrounding ions does not change in the optical transition process. The effective fields on the ground and excited states are assumed to be isotropic and they are given by H,,, = H,, + H, + H, >
(1)
H;,, = H,, + H;: + Hi .
(2)
The B.V
magnetization
in
the
antiferromagnet
384
Fig. 1. Effective
field on the ground
state
(A) and the excited
gives H, = 2H,. The effective field Hefl above H, is different from the field below H,. The exchange fields in both cases are given by [4] l&f1 = H, + (f&(
0 s H,, s 2H,
H, .
= H,, - H, + H, ,
.
H,, > 2 HP .
(3)
+ Hi)’ + H;(l
- H;/H,)
’.
x (1 + H;/HJ’
OS H,,s2H,.
(5)
Above the critical field H, < H,,, the effective fields become simple and the following two cases are given: IH:frl=H,,-H;-+H:,. JH;~~\=-H,,+-
H;:-
A simple expression I-I,, = 2 ’ “H, as lHlfrl = [(HE - H;)”
H,,>H;-Hi. H;,
H,,
aspects of the level shift in the excited state. The cases I-IV shown in fig. 2 correspond to the conditions HL + H: = 0, H; > H,. H; = H,. and H;, < H,,, respectively. The energy difference E between the ground and excited states is written as
where 3, g and g’ are the energy gap of the optical excitation and the ground and excited g-values, respectively, and pB is the Bohr magneton. Eq. (9) gives the spectral shift due to the magnetic held. Experimentally speaking, the energy difference of E given by eq. (9) is measured as a function of H,,. It is assumed that the ground state parameters g, H, and H, are known. Then the excited state parameter g’ is simply determined by the field shift above H,, and H; and Hi are determined
(6) H:. .
for eq. (5) is obtained
+ (H,
(H) spms for the M, sublattice
(4)
H, + He > 0 is required from the stability condition of the antiferromagnet. The excited state effective field below H, is given by [4] H:,, = [(H;
state
+ H:,)‘]“’
4
(7)
iXCl7ED
STATE
at
(8) HE * tie
3. Spectral shift and determination magnetic parameters
of the
GROUND CRYSTAL FIFLD
I
The typical field dependence of the energy levels is schematically shown in fig. 2. The conditions for the exchange fields give the various
:; TATE
EXCHANGE-FIELD I I
HEBHE
0
Fkg. 2. Schematic gy laels.
diagram
ZHE
of magnetic
> MAG. FIELD (HL’)
ficld dependent
cncr-
(Pl)
.
6’L
=
’ I“i = ‘HtH
ahHla)H
’ z.z-
‘S9.1 = ‘H/:H
=
7hH13$H
’ SS’O = “Hl:H
se pau!t?lqoa.u2splay apes punol8 Yurpuodsallo3 aql icq pazqwulou splay a%II?qDXa alels pa)!Dxa ayL ."H puno.n? 1daDxa ‘san[elzIeluau+adxa
ql!~ luauraa&?
poo8
Z
u!
s!1lnsaJaqL ‘g ‘By u! aAm pqos aql /cq uhoqs s! IJ!qs aql 30 aAm pmgaIoaq1 aqL .“:H 01 sagdde uoyssnmp .nzl!uIys v ‘i3!qs aqi 01 uognq!liuoD luwodtu! aql sa,@ surds +c~~ aql uaahzlaq play a2heq3xa aql play 2gauku
q%q e u! lnq ‘uo!%al
play MOI aql u! y!qs le.wads aql 01 aAgDa33a s! +,qA woq play aZueq3xa aqi ieqi isa%hs silnsal pwaugadxa aqL “H pue 'H ql!M pa_wdruo3 a%el OS lou a.w ""H pue 3h~ Ieql pa2rlou S' 11 '1 S’9 = ahH pUk? LLL'p= 'hH ‘L6'+i "H ‘LI'f,[='H
‘LLL'6L= "H
SE? Splay a%Ueq3Xa
aqi pau!umiap [s] ‘1~ ia meyoiofl .[ti] L 6.9 ie pun03 play dg-uyds aql s! "H alaqM ‘iC[aA!l -Dadsal “H > "H pue “H < ‘)H saw3 aql 103 pasn s! (~1) .ba u! i 30 - pue + aqL ‘““H - “H = y pue E +y u! uMoqs a@2 Bugue3 aqi s! x) alaqM
‘H - “H) -
’ z;,[Yb’ZU!S
(El)
ahH(DZ SO3 "H - "H)D SOCJZT
L/(DZSOS"H - 'H)DLIU'SZ i sZ/+ sahH +
s! pue (I)
[b] se uall!.m
&DZSOD'H
,@'zU!S "H - 'H)+
‘slxe-o “‘H play paqdde: aqi LII ‘E ‘8~ JO iiasu! aqi u! UMoqs s! [s] x 811 = No Mo[aq ainlmils u!ds 3gwuaq3s aqL ‘[@I “oi3qA u! +ci3 30 uo~~~sueii gz--vti aql s! q3!qM saug-8 aqi 103 paAiasq0 3!lauk_u q%q u! lJ!qs lemads aqL
SBM splay
.yloMauwlJ luasald aqi u!qiiM paie%gsaizu! aq um siau%_uoiia~~iu~ sums put alqeI!me awo3aq my (L oar) aom 1 leau 01 dn play 3gauBem I? ‘lalzahzoq ‘iCllua3 -ax ~s~aukuoiiaj~~ut2 jensn 103 q&q hail am “HZ lnoql? JO splay pmialxa pal!nbal aql asnesaq pawo3Jad uaaq IOU scq cap! luasald aqi qi!M sDgdo-olau8ew aql JO Apnls pwraw!ladxa aqJ
- 'H)]z~~~H
.ba SE poqlaur
ain8y
+cqA pue +c~3 ~013 splay e@om-gsu!qso+a sag!iielqns su!ds uIO.IJ Put Pue +$A awes pue al!soddo aql uo su!ds +E~3 LLIO_IJ splay
(II)
.IT?~!UI!S e iiq ua@
s! ""H
./([aA!lDadsaI ‘sulds
a%I??q3Xa aql alIZqNqM ahH pUE 'H ‘"hH '"H “H 30 splay a8ueqDxa aAy pue "H play paqdde aql sass u!ds +,.I3 f~' 'E '%y u! UMoqs
oml
awes aqt laa3 saD!lwjqns
aqi
uo
‘ :H - :H + ‘HZ-
= fJa,l
Lq ua@Fi am aqi
(01)
u! ,,g
‘
z,,
pue
[,(:H
,g
ie splay
+ ‘H) + ,(:H
=!i~a33a
aqi
pue
- ‘H)] = I’““HI
Se '[Jo]
paAlasq0 SBM "';xIpue ““H 30 a3uaia331paql 01 anp 13!qsIwlsads aql lnq ‘pamasqo IOU s! +E~3 JO aql u! %u!llqds lewads aql pue splay aA!l
awl-8
-3a33aaql JO apnl!uku ~!lau%two1ia3yue
su!ds +&)
aql
SE Uall!.IMale Z '8y U! UMOqS ,,VpUE ,v le splay arlgDa33a qioa .aldur!s hlaA!leieduIo3 am splay asaqi ie si3!qs Biaua aqi asnmaq 3Hz pue 3~,, ,z ale splay ajqeioAe3 aqL “H MoIaq slu!od OH 0~1 le iJ!qs pzlpads aql %!Aiasqo hq
386
H. Herr
and M.
Dare I Spectral shift arrd excited excharlge field
References [I] A.E. Nikitonov and V.I. Cherepanov. Phys. Status Solidi 14 (1966) 3Y1. 12.1 I. Tsujikawa and E. Kanda, J. Phys. Sot. Jpn. 18 (lY63) 1382.
131 M.W. Passow. D.L. Huber and W.M. Yen. Phys. Rev. Lett. 22 (lY6Y) 477 141 H. Hori and M. Date, J. Phys. Sec. Jpn. 57 (1988). to appear. 151 M. Motokawa. H. Hori, N. Nishimura. K. Tsushima and M. Date. .I. Magn. Magn. Mat. 59 (19X6) 243.