for any lanthanide compound, more than twice
thevalueofJ= +170(10) cm−^1 determined for
Gd 2 @C 79 N( 9 ). Density matrix renormalization
group CASSCF calculations ( 26 ) on1-Gd(SM
section 8.4) revealed a Heisenberg-like spin lad-
der (table S20) and a value ofJ=+389cm−^1 , in
excellent agreement with the experimental fit
value (fig. S100), along withJ′=−9 cm−^1 (4f–4f
exchange). Further, broken-symmetry DFT cal-
culations show increasing agreement to ex-
perimental values with an increasing fraction
of exact exchange (fig. S100 and table S23).
Hence, both methods suggest that the ex-
change coupling is dominated by the direct
exchange terms between thesand 4f elec-
trons (SM section 8.4); thus, the 4f–sinterac-
tion tends to obey Hund’s rules.
Field-cooled dc susceptibility data collected
for1-Tband1-DyunderHdc= 1000 Oe di-
verge from zero-field cooled data at 70 and
75 K, respectively, indicative of magnetic block-
ing below these temperatures (Fig. 4A), that
is, the pinning of the molecular magnetic mo-
ments due to the presence of an energy bar-
rier to relaxation. From dc and ac magnetic
relaxation data, we extracted 100-s blocking
temperatures ofTb= 65 and 72 K and large
thermal barriers to magnetic relaxation of
Ueff= 1383(45) and 1631(25) cm−^1 for1-Tb
and1-Dy, respectively (Fig. 4B). Similar data
were obtained for dilute solutions of1-Tband
1-Dy, confirming the molecular origin of the
slow magnetic relaxation (tables S13 and S15).
The values for1-Dyare the highest reported
for any single-molecule magnet, surpassing
the previous records ofTb= 65 K andUeff=
1541(11) cm−^1 for [(Cp)Dy(CpiPr5)][B(C 6 F 5 ) 4 ]
(Cp, pentamethylcyclopentadienyl) ( 27 ).
CASSCF calculations were performed on
model systems [(CpiPr5) 2 LnLuI 3 ]+(4fn/4f^14 )
and (CpiPr5) 2 LnLuI 3 (4fn–s–4f^14 )forthecases
where Ln is Dy or Tb to elucidate changes to
the local magnetic anisotropy due to the
presence of thes-bonding electron and quan-
tify the 4fn–scoupling (SM sections 8.5 and
8.6). The calculated crystal field splitting in
[(CpiPr5) 2 DyLuI 3 ]+is similar to that of the iso-
lated DyIIIions in2-Dy(table S33, compare
with table S40), whereas the crystal field split-
ting in (CpiPr5) 2 DyLuI 3 is substantially enhanced
by thes-bonding electron (table S36); the same
is true for (CpiPr5) 2 TbLuI 3 (table S29, compare
with table S26). By generalizing an exchange
coupling model proposed for orbitally degene-
rate ions (SM section 8.5) ( 28 ), we calculated
that the magnetic coupling in (CpiPr5) 2 DyLuI 3
and (CpiPr5) 2 TbLuI 3 is dominated by isotropic
spin-spin Heisenberg exchange, withJ= +524
and +519 cm−^1 , respectively (− 2 Jformalism).
This exchange is stronger than the 4f spin-
orbit coupling, and hence theselectron spin
first couples to the total spin of the 4f shell,
followed by coupling to the orbital angular
momentum. These results are consistent with
those for1-Gd, revealing that the exchange
interactions are dominated by direct exchange,
although substantial anisotropy arises in orbital-
ly dependent exchange terms for (CpiPr5) 2 DyLuI 3
and (CpiPr5) 2 TbLuI 3 that are absent in1-Gd. We
next built a model Hamiltonian to describe
the full exchange spectrum for1-Tb(Fig. 4C);
this analysis is more complicated for1-Dy
owing to the proximity of the first-excited^6 F
term to the ground^6 HtermofDyIII(SM sec-
tion 8.6). The ground Kramers doublet for
1-TbisMJ= ±25/2, arising from the maximal
spin^14 I25/2term (the ground doublet for1-Dy
isMJ= ±31/2 from the^12 N31/2term), although
different spin multiplicities are close in energy.
Thus, the barrier to magnetic relaxation in
1-Tb(and, by extension,1-Dy) originates from
very strong Heisenberg spin-spin coupling be-
tween the 4f andselectrons and large mag-
netic anisotropy at the lanthanide ion (tables
S31 and S39). The largerUeffvalue for1-Dy
versus1-Tbarises from a combination of aslightly stronger crystal field as well as con-
siderably stronger orbitally dependent exchange
interactions (table S35, compare with table S28).
Variable-field magnetization data obtained
between ±14 T for1-Dyand1-Tbrevealed
wide magnetic hysteresis loops that remain
open to 80 and 64 K, respectively, among the
highest temperatures reported for any single-
molecule magnet (figs. S92 and S94). For both
compounds, the coercive field (Hc) increases
dramatically as the temperature is lowered,
and it was not possible to saturate the magnet-
ization below 68 K for1-Dyor 62 K for1-Tb
using a conventional magnetometer (Hdc,max=
14 T). As such, we can only determine a lower
bound ofHc≥14 T below 60 K for1-Dy
(Fig. 4D) and below 50 K for1-Tb. This
value far surpasses the previous record of
7.9 T at 10 K for the single-molecule magnet
[(CpMe4H 2 Tb) 2 (m−N 2 • )]−( 25 ) and coercivities of
commercial magnets SmCo 5 (4.3 T at 4.2 K)
( 29 ) and Nd 2 Fe 14 B(5.0Tat80K)( 30 ). Indeed,
this lower boundHcfor1-Dyand1-Tbis
the largest yet reported for any molecule or
molecule-based material. We can also charac-
terize the magnetic energy density, (BH)max, of
1-Dyand1-Tb(SM section 7.7), and these
values are more than an order of magnitude
greater than those determined for other single-
molecule magnets at comparable temperatures
and even begin to approach those reported for
SmCo 5 and Nd 2 Fe 14 B (table S17). Further in-
vestigation of the magnetic properties of1-Tb
and1-Dyat higher magnetic fields (Hdc>14T)
is ongoing, and preliminary data indicate that
the values ofHcand (BH)maxfor these com-
pounds are substantially underestimated by
measurements between ±14 T. Indeed, field-
cooled demagnetization data collected for1-Tb
between ±35 T reveal a lower-bound estimate
for the coercive magnetic field of 25 T at 50 K
(fig. S93), and even a field of +35 T is unable
to fully saturate the magnetization of1-Tbat
this temperature.
Notably,1-Dyand1-TbdisplayHc≥14 T
at relatively high temperatures, conditions under
which the vast majority of single-molecule mag-
nets display closed hysteresis loops. For com-
parison, only five other molecules—all of the
form [CpR 2 Dy]+—show open hysteresis loops
at 60 K, and the next highestHcvalue at this
temperature is 2.1 T for [(Cp*)Dy(CpiPr5)]+( 27 ).
The largerHcvalues for1-Tband1-Dyrelative
to [CpR 2 Dy]+complexes can be attributed to
the mitigation of Raman and quantum tun-
neling processes, which are the predominant
pathways for magnetic relaxation in mono-
nuclear single-molecule magnets below the
blocking temperature. Indeed,1-Dyexhibits a
magnetic relaxation time (t) ~ 1000 s at 67 K,
whereas [(Cp*)Dy(CpiPr5)]+does not display
t~ 1000 s untilT≤31 K. Previous studies of
dinuclear lanthanide compounds have dem-
onstrated that strong magnetic coupling can200 14 JANUARY 2022•VOL 375 ISSUE 6577 science.orgSCIENCE
A B
Fig. 3. Characterization of valence delocalization.(A) Experimental and simulated EPR data for1-Y.
(B) UV-Vis-NIR and diffuse reflectance spectra for1-Ln. The bandwidth of the IVCT transition (nmax≈
15,000 cm−^1 ) in1-Y,1-Gd,1-Tb, and1-Dysupports valence delocalization.F(R) is the Kubelka-Munk
transformation of the raw diffuse reflectance spectrum.
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