The axial magnetic phase diagram of the antiferromagnet Fe0.95Mg0.05Br2 is studied by specific heat, superconducting quantum interference device, and Faraday rotation techniques. The diamagnetic impurities give rise to random-field criticality along the second-order phase line Hc(T) between TN=13.1 K and a multicritical point at Tm≈5 K, and to a spin-flop line between Tm and the critical end-point temperature Te≈3.5 K. The phase line H1(T)c(T) ending at Tm is probably due to symmetric nondiagonal exchange

Binek, Christian

Kato, T.

Katori, H. Aruga

Katsumata, K.

Kleemann, Wolfgang

Petracic, O.

English

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University of Nebraska - Lincoln 
DigitalCommons@University of Nebraska - Lincoln 
Christian Binek Publications Research Papers in Physics and Astronomy 
3-14-2001 
Magnetic phase diagram of the diluted metamagnet 
Fe0.95Mg0.05Br2 
H. Aruga Katori 
RIKEN (The Institute of Physical and Chemical Research), Wako, Saitama, Japan 
K. Katsumata 
RIKEN (The Institute of Physical and Chemical Research), Wako, Saitama 351-0198, Japan 
O. Petracic 
Laboratorium fu¨r Angewandte Physik, Gerhard-Mercator-Universita¨t, Duisburg, Germany 
Wolfgang Kleemann 
Laboratorium fu¨r Angewandte Physik, Gerhard-Mercator-Universita¨t, Duisburg, Germany, 
wolfgang.kleemann@uni-due.de 
T. Kato 
Laboratorium fu¨r Angewandte Physik, Gerhard-Mercator-Universita¨t, Duisburg, Germany 
See next page for additional authors 
Follow this and additional works at: https://digitalcommons.unl.edu/physicsbinek 
 Part of the Physics Commons 
Katori, H. Aruga; Katsumata, K.; Petracic, O.; Kleemann, Wolfgang; Kato, T.; and Binek, Christian, "Magnetic 
phase diagram of the diluted metamagnet Fe0.95Mg0.05Br2" (2001). Christian Binek Publications. 16. 
https://digitalcommons.unl.edu/physicsbinek/16 
This Article is brought to you for free and open access by the Research Papers in Physics and Astronomy at 
DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Christian Binek Publications 
by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. 
Authors 
H. Aruga Katori, K. Katsumata, O. Petracic, Wolfgang Kleemann, T. Kato, and Christian Binek 
This article is available at DigitalCommons@University of Nebraska - Lincoln: https://digitalcommons.unl.edu/
physicsbinek/16 
Magnetic phase diagram of the diluted metamagnet Fe0.95Mg0.05Br2
H. Aruga Katori and K. Katsumata
RIKEN (The Institute of Physical and Chemical Research), Wako, Saitama 351-0198, Japan
O. Petracic, W. Kleemann, T. Kato,* and Ch. Binek
Laboratorium für Angewandte Physik, Gerhard-Mercator-Universita¨t, D-47048 Duisburg, Germany
~Received 7 June 2000; revised manuscript received 13 November 2000; published 14 March 2001!
The axial magnetic phase diagram of the antiferromagnet Fe0.95Mg0.05Br2 is studied by specific heat, super-
conducting quantum interference device, and Faraday rotation techniques. The diamagnetic impurities give rise
to random-field criticality along the second-order phase lineHc(T) betweenTN513.1 K and a multicritical
point atTm'5 K, and to a spin-flop line betweenTm and the critical end-point temperatureTe'3.5 K. The
phase lineH1(T),Hc(T) ending atTm is probably due to symmetric nondiagonal exchange.
DOI: 10.1103/PhysRevB.63.132408 PACS number~s!: 64.60.Kw, 75.25.1z, 75.30.Kz, 75.50.Ee
The magnetic phase diagram of the antiferromagnetic
~AF! insulator FeBr2 has attracted appreciable interest in re-
cent years.1 It is much more complex than that of the related
metamagnet FeCl2.
2,3 In the hexagonal unit cell of FeBr2
@space groupD3d
3 5P3̄m1, Néel temperatureTN514.1 K;
see Fig. 1~a!, inset#, adjacent~001! layers of Fe21 ions are
separated by two layers of Br2 ions. The spin directions at
low temperaturesT!TN and in zero external magnetic field
H are conventionally assumed to point parallel and antipar-
allel to @001#, respectively, from layer to layer, thus giving
rise to a Ne´ l-type ground state with ‘‘up’’ and ‘‘down’’ spin
sublattices as in FeCl2 ~space groupD3d
5 5R3̄m, TN
523.7 K!. However, while FeCl2 reveals a classic tricritical
point on itsH-T phase line,2,3 FeBr2 behaves in a more com-
plicated fashion@Fig. 1~a!#.
Similarly as in FeCl2, the linesHc1 and Hc2 denote the
phase transition of first order from AF long-range order to
the paramagnetic~PM! saturated phase via a mixed phase
(AF1PM). However, above the multicritical-point~MCP!
temperatureTm54.6 K, apart from the critical phase line
Hc(T), regions of strong noncritical fluctuations are encoun-
tered. They peak along lines denoted asH2(T) andH1(T),
respectively.4 In addition, a first-order phase transition line
H1(T) is revealed by specific heat measurements
5 in the vi-
cinity of H2(T). Recently,
1 by using neutron scattering
transverse AF ordering was observed in both phases AFI and
AFII, as depicted schematically in Fig. 1~a! by tilted arrows.
The transverse order parameter, which exhibits a peak at
T15T(H1), does not vanish in zero field and vanishes upon
approaching the critical lineHc(T). In addition, a weak
transverse ferromagnetic~FM! moment, which appears be-
low T1 , is considered as a secondary order parameter of
phase AFI.
Since both the experimental data and the theoretical
description6 of FeBr2 are still far from being complete, ex-
periments in order to clarify the situation are necessary. Be-
ing an anisotropic Heisenberg model system with a tendency
towards transverse spin ordering, it seems interesting to in-
vestigate the influence of diamagnetic impurities replacing
the Fe21 ions in FeBr2. They are suitable to diminish the
anisotropy of the exchange interaction, while the uniaxial
single-ion anisotropy should be less affected by ionic re-
placements. Moreover, they break the translational symmetry
and thus allow nondiagonal exchange interaction to become
an effective source of transverse spin ordering.1
In this paper we present data revealing the effect of Mg21
ions doped at a low levelx50.05. First, theH1 phase line
reappears as in the case of pure FeBr2 ~Ref. 1! and seems to
FIG. 1. H-T phase diagrams of FeBr2 ~a! and Fe0.95Mg0.05Br2 ~b!
presented by interpolated lines and data points~see Ref. 1 and text,
respectively, for details!. Hc1 , HSF1 and H1 are first-order phase
lines with upper boundaries of the corresponding mixed phases,Hc2
andHSF2, respectively.H2 andH1 denote the lines of peak posi-
tions of noncritical fluctuations. Critical points~CEP and MCP!,
transition temperatures (TN), and phases~PM, SF, AFI, and AFII!
are indicated~see text!. Tentative spin structures referring to adja-
cent Fe21 layers@inset in~a! shows the unit cell# are schematically
sketched by arrows.
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be stabilized by the intentional disorder. Second, the
quenched randomness of the magnetic vacancy distribution
gives rise to random-field~RF! effects, a well-known phe-
nomenon in dilute uniaxial AF compounds subjected to uni-
form external axial magnetic fields.7 Third, spin-flop-like
transitions are observed below the multicritical point, where
the phase linesHc andH1 meet. This feature is discussed in
view of the revised spin structure of pure FeBr2,
1 which
involves transverse spin components similarly as a classic
spin-flop phase.
The experiments were carried out on Bridgman-grown
samples with the nominal composition Fe0.95Mg0.05Br2 as-
cleft parallel to planes perpendicular to the hexagonalc xis
with thicknesst'0.2 mm and massm'8 mg. Specific heat
measurements were performed with an automatic microcalo-
rimeter~Oxford Instruments, MagLab! in applied axial fields
up tom0H54 T. Magnetometry was performed by means of
the superconducting quantum interference device~SQUID!
technique ~Quantum Design, MPMS 5S! and locally re-
solved Faraday rotation~FR! in axial magnetic fields up to
m0H55 T.
Figure 2 shows the temperature dependence of the mag-
netic specific heat,cm , for axial magnetic fields 0<m0H
<3.2 T after subtracting the diamagnetic lattice background
measured separately in zero external field on a sample of
MgBr2. At H50 a largel-shaped anomaly due to the AF-
to-PM phase transition is observed atTN513.1060.05 K. At
H.0 it shifts towards lower temperatures along the phase
line Hc(T). While its shape becomes more symmetric at
intermediate fields 1.5<m0H<1.8 T, rounding at m0H
.2.25 T indicates the absence of axial long-range order in
high enough external fields. A secondary peak emerges at
lower temperatures form0H>1.5 T @dashed arrows; see also
Fig. 2~c!#. It sharpens at intermediate fieldsm0H'2.5 T and
disappears atm0H.2.8 T. In analogy to observations
5 made
on FeBr2, we attribute this peak to the AFI-to-AFII phase
transition. Its position designates the phase lineH1(T),
which is plotted together withHc(T) in Fig. 1~b! ~solid
circles!. The previously conjectured5 first-order nature of the
anomaly atH1(T) is confirmed by the observation of hyster-
esis in specific heat data recorded after zero-field cooling
~ZFC! and upon field cooling~FC!, respectively@Fig. 2~b!#.
The phase diagram is complemented by data originating
from isothermscm vs H @Figs. 3 and 1~b!, open circles#. With
decreasingT the intensity of the anomaly atHc becomes
gradually transferred to that atH1 ~curves 1–3!. This indi-
cates that more and more entropy is spent at the AFI-to-AFII
phase transition of the transverse order parameters, while the
contribution due to the decay of axial AF order atHc be-
comes less important. As shown in Fig. 1~b!, the two phase
lines H1(T) and Hc(T) meet atTm'5 K in a multicritical
point ~MCP!.
The single peaks occurring belowTm at T54 and 3.5 K
~curves 4 and 5! denoted asHSF1 vanish at the metamagnetic
spin-flip line below the critical end-point~CEP! temperature
Te'3.5 K ~see below!. The flat background obeys the
Clausius-Clapeyron rule for latent heat, dQ
}(dH/dT)H5Hc, at a magnetic first-order phase transition. It
vanishes at very low temperaturesT,1 K along the nearly
horizontal phase lineH5Hc of the metamagnetic transition.
Tentatively, the lower bound of the corresponding coexist-
ence region of the AF and PM phases,Hc1(T), is located at
the kink point of thecm vs H anomaly~Fig. 3, arrows!. The
FIG. 2. ~a! Magnetic specific heatcm vs T of Fe0.95Mg0.05Br2
measured at magnetic fields 0<m0H<3.2 T. The transition tem-
peraturesTc and T1 are indicated by solid and dashed arrows, re-
spectively ~see text!. The insets~b! and ~c! show hysteresis ob-
served atm0H52.25 T upon zero-field~ZFC! and field cooling
~FC!, and an enlarged detail of~a!.
FIG. 3. Semilogarithmic plot of the magnetic specific heatcm vs
H, measured atT510.0 K ~1!, 8.0 K ~2!, 6.0 K ~3!, 4.0 K ~4!, 3.5 K
~5!, 3 K ~6!, and 1.0 K~7!. Phase transition fieldsHc , H1 , HSF1,
Hc1 , andHc2 and anomaliesH1 are indicated by arrows.
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broad anomaly at higher fields referring to the upper
anomaly line,H1(T),
4,5 shifts towards lower fields on cool-
ing and seems to merge intoHc2(T) at the upper bound of
the AF1PM coexistence region.
Figure 4 shows derivatives of isothermal magnetization
curves,dM/dH vs H ~a!, recorded within 2<T<9 K. The
peaks observed atT.5 K @Fig. 4~a!, arrow at curve 1# des-
ignate the critical fieldHc(T) in perfect agreement with the
cm data @Fig. 1~b!, open squares#. At low temperatures
~curves 7 and 8!, the susceptibilitydM/dH maximizes and
behaves plateau like as expected for a first-order metamag-
netic transition between the boundary valuesHc1 andHc2 of
the mixed AF1PM phase@Fig. 1~b!, crosshatched squares#.
The levels of curves 7 and 8 are smaller than expected,
dM/dH'1/N'1.1 ~N5demagnetization factor!, since the
transverse components of the AFI phase reduces the effective
susceptibility. The situation changes forTe'3.5 K,T,Tm
'5 K, where a sharp peak atHSF1 and the upper edge of the
subsequent plateau atHSF2 define the lower and upper
bounds of a new ‘‘spin-flop-like’’~SF! phase@Fig. 1~b!,
crosshatched diamonds#. At T'6 K the horizontal part of the
dM/dH plateau starts to shrink as a consequence of the
bending down of the second-order upper phase boundary to-
wards the MCP, where it meets the two first-order~H1 and
HSF1! and one second-order (Hc) phase boundaries.
The SQUID magnetometric results are confirmed by use
of FR. By probing very small sample volumes via a pinhole
of about 50mm diameter, blurring effects of concentration
gradients are overcome. As a consequence, e.g., a consider-
able increase of theHSF1 peak is encountered atT54.9 K
@Fig. 4~b!, curve 5, solid squares#.
The new ‘‘spin-flop-like’’ phase contrasts with a classic
one, since the magnetization, when extrapolated to zero, does
not hit the field axis atH50. We presume this to be related
to the nearby AFI and AFII phases, which both possess
transverse AF spin components. The different phases meet-
ing at the MCP might be described by the order parameters
La , Lt , Ma , and Mt , whereL, M, a, and t designate AF,
FM, axial, and transverse, respectively. In analogy with
FeBr2,
1 we propose all of the four order parameters to exist
in the ‘‘parent’’ phase AFI, while in the two ‘‘daughter’’
phases with transverse orderingLtÞ0, eitherMt[0 ~AFII !
or both Mt[0 andLa[0 ~SF!. In the PM phase all order
parameters but the induced one,Ma , vanish.
The peaks in the isomagnetic ac susceptibility curves,x8
andx9 vs T in Figs. 5~a! and 5~b!, respectively, reveal values
of Hc(T) ~arrows!, which fit well with the phase diagram for
m0H<2.4 T @Fig. 1~b!, crosses#. HereTc(H50)513.05 K is
in good agreement with the caloric value ofTN513.15 K
~Fig. 2!. Large anomalies~arrows! for m0H<2.4 T are due to
noncritical fluctuations atH2(T), while the flat peak ob-
served atm0H53.8 T refers toH1(T) @Fig. 1~b!, tilted
cross#.
Isothermal ac susceptibility data,x8 vs H @Fig. 6~a!#, con-
firm the static magnetization ones,dM/dH vs H @Fig. 4~a!#.
Owing to the finite frequencyf 520 Hz of the probing field,
however, the peaks atHSF1 are missing at low temperatures
~curves 1 and 2!. A slightly rounded peak emerging at higher
T characterizesHc(T). The increase ofx8 at H.HSF1 in the
SF regime~curves 1 and 2! is tentatively attributed to the
low-f dispersion of multidomain states compatible with the
FIG. 4. Field derivatives of the magnetization,dM/dH vs H ~a!,
and of the Faraday rotation,d(FR)/dH vs H ~b!, recorded at~a!
T59.0 K ~1!, 8.0 K ~2!, 7.0 K ~3!, 6.0 K ~4!, 5.0 K ~5!, 4.4 K ~6!,
3.0 K ~7!, and 2.0 K~8! and~b! 10.0 K ~1!, 6.1 K ~3!, 4.9 K ~5!, and
2.1 K ~7! on field increasing and 8.0 K~2!, 5.7 K ~4!, and 4.3 K~6!
on field decreasing, respectively. The positions ofHc1 , Hc2 , HSF1,
HSF2, andHc are indicated by arrows.
FIG. 5. Susceptibility componentsx8 vs T ~a! andx9 vs T ~b!
recorded atm0H50 T ~1!, 1.0 T ~2!, 1.5 T ~3!, 2.0 T ~4!, 2.2 T ~5!,
2.4 T ~6!, and 3.8 T~7!. Anomaly temperaturesT2 , T1 , TN , and
Tc are indicated by arrows.
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sixfold degeneracy ofLt . The values ofHSF1, Hc , andH1
are corroborated by well-resolved peaks ofx9 vs H @Fig.
6~b!, open and solid diamonds in Fig. 1~b!#.
Our investigations show that small amounts of nonmag-
netic impurities have drastic consequences on the magnetic
behavior of the parent compound FeBr2. First of all, when
subjected to axial magnetic fields, Fe0.95Mg0.05Br2 exhibits a
crossover from three-dimensional random exchange to RF
Ising model behavior. This manifests itself in a change of the
critical behavior of the specific heat from an asymmetricl
shape atH50 to a perfectly symmetric semilogarithmic one
cm} log10uT/Tc21u at m0H'1.8 T.
7 Dynamic rounding7 oc-
curs at higher fields until no anomaly is any longer observed
at m0H.2.25 T.
Remarkably, the anomaly atH1(T), being due to trans-
verse spin ordering, is not affected by the longitudinal RF’s.
This explains its sharp appearance in the high-field range
m0H'2.5 T in bothcm vs T ~Fig. 2! andcm vs H ~Fig. 3!.
Obviously, much more entropy is spent at the AFI-to-AFII
than at the AFII-to-PM transition. As conjectured
previously,1 the AFI-to-AFII transition is very probably due
to a strong increase of the transverse AF ordering accompa-
nied by the loss of the weak ferromagnetic transverse mo-
ment. One of the driving mechanisms is assumed to be the
symmetric nondiagonal exchange interaction, which is al-
lowed by symmetry in the trigonal point group of FeBr2.
However, as pointed out by Mukamel8 and verified explicitly
for FeBr2,
1 its contribution to the free energy vanishes in the
case of aq50 Néel-type ground state. Thus the appearance
of the H1(T) phase line in pure FeBr2 is still a puzzle.
1
Tentatively, we propose that unavoidable defects like
stacking faults, which seem to be quite frequent in FeBr2-like
systems,9 break the translation symmetry in real samples of
FeBr2 and thus activate the nondiagonal exchange to a cer-
tain extent. This tendency will be enhanced in a random solid
like Fe0.95Mg0.05Br2. We propose, hence, the strong anoma-
lies atH1(T) to be due to the loss of the threefold rotational
symmetry, which makes nondiagonal exchange effective.
Since this mechanism virtually lowers the anisotropy of the
system, even spin-flop-like transitions become possible in
the low-T range. This is in our opinion the second drastic
effect of the magnetic dilution on the FeBr2 system. Beyond
the transition lineHSF1(T), hence, strong axial susceptibility
is encountered before the system reaches the PM regime at
HSF2(T).
Unusually and not predicted by the mean-field theory of
conventional anisotropic Heisenberg antiferromagnets,10 a
metamagnetic regime evolves from the canted AFI phase at
lowest temperatures. Clearly, more thorough research of this
SF phase and its adjacent critical points~CEP and MCP!
seems highly desirable. In particular, it will be interesting to
confirm these conjectures in future neutron scattering experi-
ments.
Ch.B., W.K., and O.P. gratefully appreciate the hospital-
ity of RIKEN ~Japan! and thank H. Junge for crystal growth
and DFG for financial support. The work done in Japan was
supported by Grants-in-Aid from the Japanese Ministry of
Education, Science, Sports and Culture and from the Hayashi
Memorial Foundation for Female Natural Scientists.
*On leave of absence from the Department of Physics, Tokyo In-
stitute of Technology, Japan.
1Ch. Binek, T. Kato, W. Kleemann, O. Petracic, D. Bertrand, F.
Bourdarot, P. Burlet, H. Aruga Katori, K. Katsumata, K. Prokes,
and S. Welzel, Eur. Phys. J. B15, 35 ~2000!.
2J. M. Kincaid and E. G. D. Cohen, Phys. Rep., Phys. Lett.22C,
57 ~1975!.
3E. Stryjewski and N. Giordano, Adv. Phys.26, 487 ~1977!.
4M. M. P. de Azevedo, Ch. Binek, J. Kushauer, W. Kleemann, and
D. Bertrand, J. Magn. Magn. Mater.140–144, 1557~1995!.
5H. Aruga Katori, K. Katsumata, and M. Katori, Phys. Rev. B54,
R9620~1996!.
6W. Selke, Z. Phys. B101, 145 ~1996!; M. Pleimling and W.
Selke, Phys. Rev. B56, 8855 ~1997!; K. Held, M. Ulmke, N.
Blümer, and D. Vollhardt,ibid. 56, 14 469 ~1997!; M. Pleim-
ling, Eur. Phys. J. B10, 465 ~1999!; M. Acharyya, U. Nowak,
and K. D. Usadel, Phys. Rev. B61, 464 ~2000!.
7For a review, see D. P. Belanger and A. P. Young, J. Magn.
Magn. Mater.100, 272 ~1991!.
8D. Mukamel, Phys. Rev. Lett.46, 845 ~1981!.
9See, e.g., A. Ito and N.-L. Di, J. Phys. Soc. Jpn.68, 1098~1999!;
recentg-ray diffraction data@Ch. Binek, T. Kato, and H. Hu¨n-
nefeld~unpublished!# are in favor of a superstructure along thec
axis in FeBr2.
10I. Vilfan and S. Galam, Phys. Rev. B34, 6428~1986!.
FIG. 6. Susceptibility componentsx8 ~a! and x9 vs m0H ~b!
recorded atT54.4 K ~1!, 5.0 K ~2!, 6.0 K ~3!, 7.0 K ~4!, 8.0 K ~5!,
9.0 K ~6!, 10.0 K ~7!, 11.0 K ~8!, 11.5 K ~9!, 12.0 K ~10!, 13.0 K
~11!, and 14.0 K~12!. Anomaly fieldsHc , HSF1, H2 , andH1 are
indicated.
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Magnetic phase diagram of the diluted metamagnet Fe\u3csub\u3e0.95\u3c/sub\u3eMg\u3csub\u3e0.05\u3c/sub\u3eBr\u3csub\u3e2\u3c/sub\u3e

DigitalCommons@University of Nebraska

University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Christian Binek Publications Research Papers in Physics and Astronomy 3-14-2001 Magnetic phase diagram of the diluted metamagnet Fe0.95Mg0.05Br2 H. Aruga Katori RIKEN (The Institute of Physical and Chemical Research), Wako, Saitama, Japan K. Katsumata RIKEN (The Institute of Physical and Chemical Research), Wako, Saitama 351-0198, Japan O. Petracic Laboratorium fu¨r Angewandte Physik, Gerhard-Mercator-Universita¨t, Duisburg, Germany Wolfgang Kleemann Laboratorium fu¨r Angewandte Physik, Gerhard-Mercator-Universita¨t, Duisburg, Germany, wolfgang.kleemann@uni-due.de T. Kato Laboratorium fu¨r Angewandte Physik, Gerhard-Mercator-Universita¨t, Duisburg, Germany See next page for additional authors Follow this and additional works at: https://digitalcommons.unl.edu/physicsbinek  Part of the Physics Commons Katori, H. Aruga; Katsumata, K.; Petracic, O.; Kleemann, Wolfgang; Kato, T.; and Binek, Christian, "Magnetic phase diagram of the diluted metamagnet Fe0.95Mg0.05Br2" (2001). Christian Binek Publications. 16. https://digitalcommons.unl.edu/physicsbinek/16 This Article is brought to you for free and open access by the Research Papers in Physics and Astronomy at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Christian Binek Publications by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. Authors H. Aruga Katori, K. Katsumata, O. Petracic, Wolfgang Kleemann, T. Kato, and Christian Binek This article is available at DigitalCommons@University of Nebraska - Lincoln: https://digitalcommons.unl.edu/physicsbinek/16 Magnetic phase diagram of the diluted metamagnet Fe0.95Mg0.05Br2H. Aruga Katori and K. KatsumataRIKEN (The Institute of Physical and Chemical Research), Wako, Saitama 351-0198, JapanO. Petracic, W. Kleemann, T. Kato,* and Ch. BinekLaboratorium für Angewandte Physik, Gerhard-Mercator-Universita¨t, D-47048 Duisburg, Germany~Received 7 June 2000; revised manuscript received 13 November 2000; published 14 March 2001!The axial magnetic phase diagram of the antiferromagnet Fe0.95Mg0.05Br2 is studied by specific heat, super-conducting quantum interference device, and Faraday rotation techniques. The diamagnetic impurities give riseto random-field criticality along the second-order phase lineHc(T) betweenTN513.1 K and a multicriticalpoint atTm'5 K, and to a spin-flop line betweenTm and the critical end-point temperatureTe'3.5 K. Thephase lineH1(T),Hc(T) ending atTm is probably due to symmetric nondiagonal exchange.DOI: 10.1103/PhysRevB.63.132408 PACS number~s!: 64.60.Kw, 75.25.1z, 75.30.Kz, 75.50.EeThe magnetic phase diagram of the antiferromagnetic~AF! insulator FeBr2 has attracted appreciable interest in re-cent years.1 It is much more complex than that of the relatedmetamagnet FeCl2.2,3 In the hexagonal unit cell of FeBr2@space groupD3d3 5P3̄m1, Néel temperatureTN514.1 K;see Fig. 1~a!, inset#, adjacent~001! layers of Fe21 ions areseparated by two layers of Br2 ions. The spin directions atlow temperaturesT!TN and in zero external magnetic fieldH are conventionally assumed to point parallel and antipar-allel to @001#, respectively, from layer to layer, thus givingrise to a Ne´ l-type ground state with ‘‘up’’ and ‘‘down’’ spinsublattices as in FeCl2 ~space groupD3d5 5R3̄m, TN523.7 K!. However, while FeCl2 reveals a classic tricriticalpoint on itsH-T phase line,2,3 FeBr2 behaves in a more com-plicated fashion@Fig. 1~a!#.Similarly as in FeCl2, the linesHc1 and Hc2 denote thephase transition of first order from AF long-range order tothe paramagnetic~PM! saturated phase via a mixed phase(AF1PM). However, above the multicritical-point~MCP!temperatureTm54.6 K, apart from the critical phase lineHc(T), regions of strong noncritical fluctuations are encoun-tered. They peak along lines denoted asH2(T) andH1(T),respectively.4 In addition, a first-order phase transition lineH1(T) is revealed by specific heat measurements5 in the vi-cinity of H2(T). Recently,1 by using neutron scatteringtransverse AF ordering was observed in both phases AFI andAFII, as depicted schematically in Fig. 1~a! by tilted arrows.The transverse order parameter, which exhibits a peak atT15T(H1), does not vanish in zero field and vanishes uponapproaching the critical lineHc(T). In addition, a weaktransverse ferromagnetic~FM! moment, which appears be-low T1 , is considered as a secondary order parameter ofphase AFI.Since both the experimental data and the theoreticaldescription6 of FeBr2 are still far from being complete, ex-periments in order to clarify the situation are necessary. Be-ing an anisotropic Heisenberg model system with a tendencytowards transverse spin ordering, it seems interesting to in-vestigate the influence of diamagnetic impurities replacingthe Fe21 ions in FeBr2. They are suitable to diminish theanisotropy of the exchange interaction, while the uniaxialsingle-ion anisotropy should be less affected by ionic re-placements. Moreover, they break the translational symmetryand thus allow nondiagonal exchange interaction to becomean effective source of transverse spin ordering.1In this paper we present data revealing the effect of Mg21ions doped at a low levelx50.05. First, theH1 phase linereappears as in the case of pure FeBr2 ~Ref. 1! and seems toFIG. 1. H-T phase diagrams of FeBr2 ~a! and Fe0.95Mg0.05Br2 ~b!presented by interpolated lines and data points~see Ref. 1 and text,respectively, for details!. Hc1 , HSF1 and H1 are first-order phaselines with upper boundaries of the corresponding mixed phases,Hc2andHSF2, respectively.H2 andH1 denote the lines of peak posi-tions of noncritical fluctuations. Critical points~CEP and MCP!,transition temperatures (TN), and phases~PM, SF, AFI, and AFII!are indicated~see text!. Tentative spin structures referring to adja-cent Fe21 layers@inset in~a! shows the unit cell# are schematicallysketched by arrows.PHYSICAL REVIEW B, VOLUME 63, 1324080163-1829/2001/63~13!/132408~4!/$20.00 ©2001 The American Physical Society63 132408-1be stabilized by the intentional disorder. Second, thequenched randomness of the magnetic vacancy distributiongives rise to random-field~RF! effects, a well-known phe-nomenon in dilute uniaxial AF compounds subjected to uni-form external axial magnetic fields.7 Third, spin-flop-liketransitions are observed below the multicritical point, wherethe phase linesHc andH1 meet. This feature is discussed inview of the revised spin structure of pure FeBr2,1 whichinvolves transverse spin components similarly as a classicspin-flop phase.The experiments were carried out on Bridgman-grownsamples with the nominal composition Fe0.95Mg0.05Br2 as-cleft parallel to planes perpendicular to the hexagonalc xiswith thicknesst'0.2 mm and massm'8 mg. Specific heatmeasurements were performed with an automatic microcalo-rimeter~Oxford Instruments, MagLab! in applied axial fieldsup tom0H54 T. Magnetometry was performed by means ofthe superconducting quantum interference device~SQUID!technique ~Quantum Design, MPMS 5S! and locally re-solved Faraday rotation~FR! in axial magnetic fields up tom0H55 T.Figure 2 shows the temperature dependence of the mag-netic specific heat,cm , for axial magnetic fields 0<m0H<3.2 T after subtracting the diamagnetic lattice backgroundmeasured separately in zero external field on a sample ofMgBr2. At H50 a largel-shaped anomaly due to the AF-to-PM phase transition is observed atTN513.1060.05 K. AtH.0 it shifts towards lower temperatures along the phaseline Hc(T). While its shape becomes more symmetric atintermediate fields 1.5<m0H<1.8 T, rounding at m0H.2.25 T indicates the absence of axial long-range order inhigh enough external fields. A secondary peak emerges atlower temperatures form0H>1.5 T @dashed arrows; see alsoFig. 2~c!#. It sharpens at intermediate fieldsm0H'2.5 T anddisappears atm0H.2.8 T. In analogy to observations5 madeon FeBr2, we attribute this peak to the AFI-to-AFII phasetransition. Its position designates the phase lineH1(T),which is plotted together withHc(T) in Fig. 1~b! ~solidcircles!. The previously conjectured5 first-order nature of theanomaly atH1(T) is confirmed by the observation of hyster-esis in specific heat data recorded after zero-field cooling~ZFC! and upon field cooling~FC!, respectively@Fig. 2~b!#.The phase diagram is complemented by data originatingfrom isothermscm vs H @Figs. 3 and 1~b!, open circles#. WithdecreasingT the intensity of the anomaly atHc becomesgradually transferred to that atH1 ~curves 1–3!. This indi-cates that more and more entropy is spent at the AFI-to-AFIIphase transition of the transverse order parameters, while thecontribution due to the decay of axial AF order atHc be-comes less important. As shown in Fig. 1~b!, the two phaselines H1(T) and Hc(T) meet atTm'5 K in a multicriticalpoint ~MCP!.The single peaks occurring belowTm at T54 and 3.5 K~curves 4 and 5! denoted asHSF1 vanish at the metamagneticspin-flip line below the critical end-point~CEP! temperatureTe'3.5 K ~see below!. The flat background obeys theClausius-Clapeyron rule for latent heat, dQ}(dH/dT)H5Hc, at a magnetic first-order phase transition. Itvanishes at very low temperaturesT,1 K along the nearlyhorizontal phase lineH5Hc of the metamagnetic transition.Tentatively, the lower bound of the corresponding coexist-ence region of the AF and PM phases,Hc1(T), is located atthe kink point of thecm vs H anomaly~Fig. 3, arrows!. TheFIG. 2. ~a! Magnetic specific heatcm vs T of Fe0.95Mg0.05Br2measured at magnetic fields 0<m0H<3.2 T. The transition tem-peraturesTc and T1 are indicated by solid and dashed arrows, re-spectively ~see text!. The insets~b! and ~c! show hysteresis ob-served atm0H52.25 T upon zero-field~ZFC! and field cooling~FC!, and an enlarged detail of~a!.FIG. 3. Semilogarithmic plot of the magnetic specific heatcm vsH, measured atT510.0 K ~1!, 8.0 K ~2!, 6.0 K ~3!, 4.0 K ~4!, 3.5 K~5!, 3 K ~6!, and 1.0 K~7!. Phase transition fieldsHc , H1 , HSF1,Hc1 , andHc2 and anomaliesH1 are indicated by arrows.BRIEF REPORTS PHYSICAL REVIEW B 63 132408132408-2broad anomaly at higher fields referring to the upperanomaly line,H1(T),4,5 shifts towards lower fields on cool-ing and seems to merge intoHc2(T) at the upper bound ofthe AF1PM coexistence region.Figure 4 shows derivatives of isothermal magnetizationcurves,dM/dH vs H ~a!, recorded within 2<T<9 K. Thepeaks observed atT.5 K @Fig. 4~a!, arrow at curve 1# des-ignate the critical fieldHc(T) in perfect agreement with thecm data @Fig. 1~b!, open squares#. At low temperatures~curves 7 and 8!, the susceptibilitydM/dH maximizes andbehaves plateau like as expected for a first-order metamag-netic transition between the boundary valuesHc1 andHc2 ofthe mixed AF1PM phase@Fig. 1~b!, crosshatched squares#.The levels of curves 7 and 8 are smaller than expected,dM/dH'1/N'1.1 ~N5demagnetization factor!, since thetransverse components of the AFI phase reduces the effectivesusceptibility. The situation changes forTe'3.5 K,T,Tm'5 K, where a sharp peak atHSF1 and the upper edge of thesubsequent plateau atHSF2 define the lower and upperbounds of a new ‘‘spin-flop-like’’~SF! phase@Fig. 1~b!,crosshatched diamonds#. At T'6 K the horizontal part of thedM/dH plateau starts to shrink as a consequence of thebending down of the second-order upper phase boundary to-wards the MCP, where it meets the two first-order~H1 andHSF1! and one second-order (Hc) phase boundaries.The SQUID magnetometric results are confirmed by useof FR. By probing very small sample volumes via a pinholeof about 50mm diameter, blurring effects of concentrationgradients are overcome. As a consequence, e.g., a consider-able increase of theHSF1 peak is encountered atT54.9 K@Fig. 4~b!, curve 5, solid squares#.The new ‘‘spin-flop-like’’ phase contrasts with a classicone, since the magnetization, when extrapolated to zero, doesnot hit the field axis atH50. We presume this to be relatedto the nearby AFI and AFII phases, which both possesstransverse AF spin components. The different phases meet-ing at the MCP might be described by the order parametersLa , Lt , Ma , and Mt , whereL, M, a, and t designate AF,FM, axial, and transverse, respectively. In analogy withFeBr2,1 we propose all of the four order parameters to existin the ‘‘parent’’ phase AFI, while in the two ‘‘daughter’’phases with transverse orderingLtÞ0, eitherMt[0 ~AFII !or both Mt[0 andLa[0 ~SF!. In the PM phase all orderparameters but the induced one,Ma , vanish.The peaks in the isomagnetic ac susceptibility curves,x8andx9 vs T in Figs. 5~a! and 5~b!, respectively, reveal valuesof Hc(T) ~arrows!, which fit well with the phase diagram form0H<2.4 T @Fig. 1~b!, crosses#. HereTc(H50)513.05 K isin good agreement with the caloric value ofTN513.15 K~Fig. 2!. Large anomalies~arrows! for m0H<2.4 T are due tononcritical fluctuations atH2(T), while the flat peak ob-served atm0H53.8 T refers toH1(T) @Fig. 1~b!, tiltedcross#.Isothermal ac susceptibility data,x8 vs H @Fig. 6~a!#, con-firm the static magnetization ones,dM/dH vs H @Fig. 4~a!#.Owing to the finite frequencyf 520 Hz of the probing field,however, the peaks atHSF1 are missing at low temperatures~curves 1 and 2!. A slightly rounded peak emerging at higherT characterizesHc(T). The increase ofx8 at H.HSF1 in theSF regime~curves 1 and 2! is tentatively attributed to thelow-f dispersion of multidomain states compatible with theFIG. 4. Field derivatives of the magnetization,dM/dH vs H ~a!,and of the Faraday rotation,d(FR)/dH vs H ~b!, recorded at~a!T59.0 K ~1!, 8.0 K ~2!, 7.0 K ~3!, 6.0 K ~4!, 5.0 K ~5!, 4.4 K ~6!,3.0 K ~7!, and 2.0 K~8! and~b! 10.0 K ~1!, 6.1 K ~3!, 4.9 K ~5!, and2.1 K ~7! on field increasing and 8.0 K~2!, 5.7 K ~4!, and 4.3 K~6!on field decreasing, respectively. The positions ofHc1 , Hc2 , HSF1,HSF2, andHc are indicated by arrows.FIG. 5. Susceptibility componentsx8 vs T ~a! andx9 vs T ~b!recorded atm0H50 T ~1!, 1.0 T ~2!, 1.5 T ~3!, 2.0 T ~4!, 2.2 T ~5!,2.4 T ~6!, and 3.8 T~7!. Anomaly temperaturesT2 , T1 , TN , andTc are indicated by arrows.BRIEF REPORTS PHYSICAL REVIEW B 63 132408132408-3sixfold degeneracy ofLt . The values ofHSF1, Hc , andH1are corroborated by well-resolved peaks ofx9 vs H @Fig.6~b!, open and solid diamonds in Fig. 1~b!#.Our investigations show that small amounts of nonmag-netic impurities have drastic consequences on the magneticbehavior of the parent compound FeBr2. First of all, whensubjected to axial magnetic fields, Fe0.95Mg0.05Br2 exhibits acrossover from three-dimensional random exchange to RFIsing model behavior. This manifests itself in a change of thecritical behavior of the specific heat from an asymmetriclshape atH50 to a perfectly symmetric semilogarithmic onecm} log10uT/Tc21u at m0H'1.8 T.7 Dynamic rounding7 oc-curs at higher fields until no anomaly is any longer observedat m0H.2.25 T.Remarkably, the anomaly atH1(T), being due to trans-verse spin ordering, is not affected by the longitudinal RF’s.This explains its sharp appearance in the high-field rangem0H'2.5 T in bothcm vs T ~Fig. 2! andcm vs H ~Fig. 3!.Obviously, much more entropy is spent at the AFI-to-AFIIthan at the AFII-to-PM transition. As conjecturedpreviously,1 the AFI-to-AFII transition is very probably dueto a strong increase of the transverse AF ordering accompa-nied by the loss of the weak ferromagnetic transverse mo-ment. One of the driving mechanisms is assumed to be thesymmetric nondiagonal exchange interaction, which is al-lowed by symmetry in the trigonal point group of FeBr2.However, as pointed out by Mukamel8 and verified explicitlyfor FeBr2,1 its contribution to the free energy vanishes in thecase of aq50 Néel-type ground state. Thus the appearanceof the H1(T) phase line in pure FeBr2 is still a puzzle.1Tentatively, we propose that unavoidable defects likestacking faults, which seem to be quite frequent in FeBr2-likesystems,9 break the translation symmetry in real samples ofFeBr2 and thus activate the nondiagonal exchange to a cer-tain extent. This tendency will be enhanced in a random solidlike Fe0.95Mg0.05Br2. We propose, hence, the strong anoma-lies atH1(T) to be due to the loss of the threefold rotationalsymmetry, which makes nondiagonal exchange effective.Since this mechanism virtually lowers the anisotropy of thesystem, even spin-flop-like transitions become possible inthe low-T range. This is in our opinion the second drasticeffect of the magnetic dilution on the FeBr2 system. Beyondthe transition lineHSF1(T), hence, strong axial susceptibilityis encountered before the system reaches the PM regime atHSF2(T).Unusually and not predicted by the mean-field theory ofconventional anisotropic Heisenberg antiferromagnets,10 ametamagnetic regime evolves from the canted AFI phase atlowest temperatures. Clearly, more thorough research of thisSF phase and its adjacent critical points~CEP and MCP!seems highly desirable. In particular, it will be interesting toconfirm these conjectures in future neutron scattering experi-ments.Ch.B., W.K., and O.P. gratefully appreciate the hospital-ity of RIKEN ~Japan! and thank H. Junge for crystal growthand DFG for financial support. The work done in Japan wassupported by Grants-in-Aid from the Japanese Ministry ofEducation, Science, Sports and Culture and from the HayashiMemorial Foundation for Female Natural Scientists.*On leave of absence from the Department of Physics, Tokyo In-stitute of Technology, Japan.1Ch. Binek, T. Kato, W. Kleemann, O. Petracic, D. Bertrand, F.Bourdarot, P. Burlet, H. Aruga Katori, K. Katsumata, K. Prokes,and S. Welzel, Eur. Phys. J. B15, 35 ~2000!.2J. M. Kincaid and E. G. D. Cohen, Phys. Rep., Phys. Lett.22C,57 ~1975!.3E. Stryjewski and N. Giordano, Adv. Phys.26, 487 ~1977!.4M. M. P. de Azevedo, Ch. Binek, J. Kushauer, W. Kleemann, andD. Bertrand, J. Magn. Magn. Mater.140–144, 1557~1995!.5H. Aruga Katori, K. Katsumata, and M. Katori, Phys. Rev. B54,R9620~1996!.6W. Selke, Z. Phys. B101, 145 ~1996!; M. Pleimling and W.Selke, Phys. Rev. B56, 8855 ~1997!; K. Held, M. Ulmke, N.Blümer, and D. Vollhardt,ibid. 56, 14 469 ~1997!; M. Pleim-ling, Eur. Phys. J. B10, 465 ~1999!; M. Acharyya, U. Nowak,and K. D. Usadel, Phys. Rev. B61, 464 ~2000!.7For a review, see D. P. Belanger and A. P. Young, J. Magn.Magn. Mater.100, 272 ~1991!.8D. Mukamel, Phys. Rev. Lett.46, 845 ~1981!.9See, e.g., A. Ito and N.-L. Di, J. Phys. Soc. Jpn.68, 1098~1999!;recentg-ray diffraction data@Ch. Binek, T. Kato, and H. Hu¨n-nefeld~unpublished!# are in favor of a superstructure along thecaxis in FeBr2.10I. Vilfan and S. Galam, Phys. Rev. B34, 6428~1986!.FIG. 6. Susceptibility componentsx8 ~a! and x9 vs m0H ~b!recorded atT54.4 K ~1!, 5.0 K ~2!, 6.0 K ~3!, 7.0 K ~4!, 8.0 K ~5!,9.0 K ~6!, 10.0 K ~7!, 11.0 K ~8!, 11.5 K ~9!, 12.0 K ~10!, 13.0 K~11!, and 14.0 K~12!. Anomaly fieldsHc , HSF1, H2 , andH1 areindicated.BRIEF REPORTS PHYSICAL REVIEW B 63 132408132408-4

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Magnetic phase diagram of the diluted metamagnet Fe\u3csub\u3e0.95\u3c/sub\u3eMg\u3csub\u3e0.05\u3c/sub\u3eBr\u3csub\u3e2\u3c/sub\u3e

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